thesis for the degree of doctor of philosophy

Component and system

design of a mild hybrid
48 V powertrain for
a light vehicle

Stefan Skoog

Department of Electrical Engineering

Chalmers University of Technology
Gothenburg, Sweden, 2020
Component and system
design of a mild hybrid
48 V powertrain for
a light vehicle

Stefan Skoog

Copyright © 2020 Stefan Skoog

All rights reserved.

Technical Report No. 4790

ISSN 978-91-7905-323-9
This thesis has been prepared using LATEX.

Department of Electrical Engineering

Chalmers University of Technology
SE-412 96 Gothenburg, Sweden
Phone: +46 (0)31 772 1000
www.chalmers.se

Printed by Chalmers Reproservice

Gothenburg, Sweden, May 2020
 This thesis is dedicated to the
giants in science and engineering upon
whose shoulders I have the privilege to stand.
Abstract
This thesis presents contributions in three areas relevant for the development
of 48 V mild hybrid electric powertrains for cars. The first part comprises
methodologies and extensive testing of lithium-ion battery cells in order to es-
tablish the electric and thermal performance by using equivalent circuit mod-
els. Empirical, lumped-parameter models are used to ensure fast simulation
execution using only linear circuit elements. Both electrochemical impedance
spectroscopy and high-current pulse discharge testing is used to extract model
parameters. Plenty of parameter results are published for various cells, tem-
peratures and SOC levels. Further on, the model accuracy in voltage response
is also evaluated. It is found that an R+2RC equivalent circuit offers the low-
est error, 11 mV RMSE in a 1.5 h drive cycle, which is among the lowest
numbers found in the literature for similar models.
In the second part, electric machines with tooth-coil windings are explored
as a viable candidate for mild hybrids. First, a method of analytically calcu-
lating the high-level electro-magnetic properties for all possible combinations
of three-phase, dual layer tooth-coil winding machines is established and pre-
sented in a graphically appealing manner. Then, a pair of pseudo-6-phase
50 kW PMSMs are designed, constructed and validated in a custom designed
calorimetric dynamo test stand. These machines feature a in-stator and in-slot
forced oil cooling, enabling very high current densities of 25 A/mm2 continu-
ous and 35 A/mm2 peak. A high net power density (19 kW/l) and a large area
of high peak efficiency (95%) is shown numerically and validated by calori-
metric measurements.
Finally, low-level design, construction and evaluation of 48 V inverter hard-
ware is explored. By using high-performance, extra-low-voltage silicon-based
MOSFETs with custom designed metal substrate printed circuit boards, cus-
tom made gate drivers, and water cooling, 3x220 A RMS is reached experi-
mentally on a 154 cm2 area and an efficiency of 95.6%.

Keywords: Hybrid Electric Vehicle, 48 V, Extra low voltage, Permanent

Magnet Synchronous Machine, Efficiency, Oil cooling, Power density, Calori-
metric, Li-ion battery, Power Electronics, Inverter, PWM, MOSFET, Multi-
phase

i
ii
Acknowledgments
I would like to express my gratitude to the following individuals who helped
me to make this work possible:
Thank you Torbjörn Thiringer and Stefan Lundberg, my examiner and my
supervisors at Chalmers, for excellent support, insightful feedback and valu-
able mentorship throughout my time at Chalmers.

At Volvo Cars, I truly appreciate the collaboration with Torbjörn Larsson,

Alexander Robertsson, Patrik Stridh, Daniel Midholm, and Jonas Forsell.

At Chalmers, special thanks to Alessandro Acquaviva for the fruitful cooper-

ation around electric machine development and testing. And to many of my
colleagues at Chalmers with who I have collaborated or shared office space
with: Andreas Andersson, Christian Dubar, Zeyang Geng, Emma Grunditz,
Elisabeth Jansson, Douglas Jutsell, Felix Mannerhagen, Daniel Pehrman.

Pontus Fyhr at Lund University, for broad and deep discussions on design
and production of vehicle electrification systems.

Jens Groot at AB Volvo, thanks for guidance and interesting discussions re-
garding battery performance testing.

Special thanks to Master’s students contributing to this research project:

Sandeep David[1], [2], for extensive battery measurements leading to the re-
sults in Paper 4.
Biju Jude[3], Akshay Santosh[3], Carl Tisell[4], Usman Tariq[4] for excellent
collaboration in measurements for inverter prototypes and in assisting with
hardware design and test setups.
Thanks to all the other Master’s students whom I had the pleasure to collabo-
rate with and supervise within this research project: Mohanapriya Anandaguru[5],
Andreas Eriksson[5], Akik Biswas[6], Xuming Yao[6], Sebastian Larqvist[7],
Hannes Östergren[7], Linas Brusokas[8], Naveen Raja[8].

Lastly, the financial support from the Swedish Governmental Agency for In-
novation Systems (VINNOVA) is gratefully appreciated.

iii
Acronyms
BEMF: Back-ElectroMotive Force
CFD: Computational Fluid Dynamics
CHT: Conjugate Heat Transfer
CPE: Constant Phase Element
CPE: Constant-Phase Element
DE: Drive end (of electrical machine)
DFT: Discrete Fourier Transform
ECM: Equivalent Circuit Model
ECU: Electronic Control Unit
EIS: Electrochemical Impedance Spectroscopy
EM: Electric Machine
ESS: Electrical Energy Storage System
ESS: Electrical Storage System
EV: Electric Vehicle
FEA: Finite Element Analysis
FEM: Finite Element Method
FFT: Fast Fourier Transform
FSCW: Fractional Slot (pitch) (non-overlapping) Concentrated Winding
G: Graphite (LIB anode material)
HEV: Hybrid Electric Vehicle
HLF: Harmonic Leakage Factor
HTC: Heat Transfer Coefficients
ICE: Internal Combustion Engine
IPM: Internal-Permanent magnet (synchronous) Machine
ISO: International Organization for Standardization
KPI: Key Performance Index
LCO: Lithium-Cobalt Oxide (LIB cathode material)

iv
LFP: Lithium-FerroPhosphate (LIB cathode material)
LIB: Lithium-Ion Battery, referes here to li-ion cell
LMO: Lithium-Manganese Oxide (LIB cathode material)
LPN: Lumped-Parameter Network (model)
LTO: Lithium-Titanium Oxide (LIB anode material)
MBD: Model-Based Development
mHEV: mild Hybrid Electric Vehicle
MMF: Magneto-Motive Force
MTPA: Maximum Torque Per Ampere
NDE: Non-Drive End (of electrical machine)
NMC: (Lithium-)Nickel-Manganese-Cobalt oxide (LIB cathode material)
OCV: Open Circuit Voltage
PHEV: Plug-in Hybrid Electric Vehicle
PM: Permanent Magnet
PMSM: Permanent Magnet Synchronous Machine
RMSE: Root-Mean-Square Error
RMSE: Root-Mean-Squared Error
SOC: State Of Charge
TCWM: Tooth-Coil Wound Machine
VDA: Verband der Automobilindustrie (organization)
WLTP: Worldwide harmonised Light vehicle Test Procedure
VSI: Voltage Source Inverter

v
 Contents

Abstract i

Acknowledgements iii

Acronyms iv

I Overview 1

1 Introduction 3
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Review of previous work . . . . . . . . . . . . . . . . . . . . . . 7
System Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Electric Machines . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Power Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Drive Systems: EM and PE . . . . . . . . . . . . . . . . . . . . 10
Battery modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Purpose of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Thesis outline and methodology . . . . . . . . . . . . . . . . . . 12
1.5 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . 14

vii
2 History and theoretical framework 15
2.1 Short history of electrification . . . . . . . . . . . . . . . . . . . 15
2.2 Levels of electrification . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Hybrid topologies . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Why 48 V? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Battery modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Equivalent Circuit Models . . . . . . . . . . . . . . . . . . . . . 20
2.6 Electric machine . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Winding layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Equivalent circuit for electric machine . . . . . . . . . . . . . . 23

3 Case Setup 27
3.1 System assumptions . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Battery testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Test equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Inverter test setups . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Electric machine setup . . . . . . . . . . . . . . . . . . . . . . . 36
Winding layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Electric machine test setup . . . . . . . . . . . . . . . . . . . . 36

4 Results 43
4.1 Battery modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Parameter results . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Voltage headroom . . . . . . . . . . . . . . . . . . . . . . . . . 44
Model verification . . . . . . . . . . . . . . . . . . . . . . . . . 45
High-level comparison . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Inverter results . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3 Electric machine results . . . . . . . . . . . . . . . . . . . . . . 53
Winding layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Machine construction and results . . . . . . . . . . . . . . . . . 53

5 Conclusions 57
5.1 Main conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A Linear equivalent circuit model 63

State space model . . . . . . . . . . . . . . . . . . . . . . . . . 66

viii
References 69

II Included Papers 77

ix
 Part I

Overview

1
 CHAPTER 1

Introduction

1.1 Background
The fleet of personal vehicles in the world is known to be a considerable
source of emissions by the burning of fossil fuels through internal combustion
engines. In the EU, cars account for 18.2% of the total CO2 emissions[1]. The
transportation sector is the only sector not showing a clear trend in decrease
in total pollution year by year[1]; the total car distance traveled is increasing
much faster than the fleet average propulsion efficiency.
One part of the emission problem is that combustion engines are operated
on hydrocarbons that have been stored for millions of years, which when com-
busted releases green house gasses into the atmosphere, disrupting the the
natural carbon cycle. The other part of the problem is that cars, with their
combustion engines, are releasing most green house gasses in densely popu-
lated areas and thus compromising the air quality where the human population
density is the highest.
Authorities around the world, especially in the EU, have declared goals
and targets for a more environmental friendly car fleet. The standard policy
for fossil fuel based combustion engine vehicles is to put a cap on the fleet

3
Chapter 1 Introduction

average emission level measured in CO2 equivalents. The goal is set to 95 g

CO2 per travelled kilometer on average in a WLTP drive cycle, for 95% of
the car fleet in year 2020. By 2021, all new vehicles must comply to the same
CO2 figure[2]. These figures correspond to 4.1 l/100 km and 3.6 l/100 km
fuel consumption for gasoline and diesel engines, respectively. This can be
compared with the most fuel efficient series produced car, a Volkswagen Lupo
3L, with a real-world driving diesel consumption of 2.78 l/100 km[3]. The EU
established a penalty system that requires each major OEM to pay 95 € for
each car and for each g CO2 /km above the set fleet limit[4], which forms a
clear incentive for the Original Equipment Manufacturers (OEMs) of personal
vehicles to take action.
OEMs are responsible for offering their customers a range of cars that, when
sold, will reach the target fleet average. OEMs now also have an interest
to convince their customers to buy the lower-emitting vehicles they offer.
Reducing a vehicle’s average emission without changing the chassis type and
functionality significantly, typically requires less powerful engines which limits
the ability of active dynamical driving.
Many solutions to lower the average CO2 emissions exist. All requires either
massive change of transportation behavior, and/or massive investment in tech-
nology and infrastructure. Increasing the efficiency of the internal combustion
engine is one feasible engineering leap to pursue, this can be done by en-
gine downsizing, overcharging, cylinder deactivation, usage of more advanced
materials to lower friction[5], exhaust gas recirculation (EGR) for gasoline
vehicles[6] to mention some examples.
However, the goals are still set very challenging and to meet them only
with improvements in combustion technology would imply forcing OEMs to
front-load combustion engine R&D more than ever, which requires resources
hard to allocate. This investment is so ambitious that many other alterna-
tives seem more attractive. Honda and Toyota were the first major OEMs
to introduce mild hybrid electric vehicles (mHEVs) in late 1990’s for produc-
tion cars, proving the viability of such systems. However, the technology was
too expensive to apply on the majority of the car fleet and hybridisation was
limited as a niche product.
The cost of implementing a mild hybridisation with a 48 V system can be
25% less compared to a corresponding class B voltage system according to
Mahle[7]. This cost advantage allows mild hybridisation to be implemented

4
 1.1 Background

Figure 1.1: EU measured real emission levels and legislative targets. Data from[4].

on the majority of car models. Industry sources report a reduction in fuel con-
sumption by 10%(PSA)[8], 13%(Continental)[9], 15%(Johnson Controls)[10]
and (Kia)[11], 17% (Schaeffler and Continental)[12] through the implementa-
tion of a 48 V mild hybrid system. CO2 emissions are generally proportional
to fuel consumption when disregarding transient operating points[13]. Fig-
ures ranging from 7 g/km to 15 g/km (PSA)[8] and (Hella)[14] up to 30 g/km
(ALACD and CPT)[15] in emission reduction are reported. All of those num-
bers are estimates and, unfortunately, the reference drive case are not declared
properly in the sources mentioned.
Increasing the voltage level in light vehicles was suggested before in the
mid 1990’s to cope with the ever increasing electrical loads from convenience
functions and drive support electronics. An enhanced voltage bus at 42 V was
announced[16], but it never gained momentum in the car industry. The 48 V
voltage level was proclaimed by the German automotive organization Verband
der Automobilindustrie (VDA) in 2011[17], and in the first few car models
from Audi and Daimler rolled out equipped with 48 V mild hybridisation in
late 2018.

5
Chapter 1 Introduction

A complete 48 V hybrid system is a complex mechatronic system containing

several new components, or new versions of previously familiar components,
for the automotive market. Time-to-market is critical, and model based de-
velopment (MBD) is used to replace intermediate verification steps involving
hardware design and testing of subsystems. However, MBD requires virtual
models with fair and known accuracy. Also important, the models need to be
straight-forward to plug into and execute efficiently in existing large virtual
vehicle models. The virtual models can be used both to estimate the electri-
cal and thermal performance before any hardware systems are built, and the
same models can also later be used to estimate sub-system performance while
running on-line in the vehicle ECUs.
The first generation of 48 V hybrids typically replace the classical 12 V
belt-driven generator with a higher-power density machine at 48 V designed
for ca 10 kW peak power (P0 or P1 position, see Chapter 2), together with a
small 0.2-0.5 kWh 48 V Lithium-Ion Battery (LIB) and a DC/DC converter.
Such a system will be very limited in the amount of support it can provide in
pure EV traction. The mentioned energy and power levels are confirmed by
a study made by Hella[14].
The next generation of 48 V systems will likely use a purpose-developed,
high-power-density, high-efficiency electric machine positioned inside or ad-
jacent to the gearbox (P2, P2.5, P3), enabling it to offer enhanced brake
re-generation and even some amount of pure EV driving capability. Even rear
axle electric drives are relevant (P4 position). Peak power levels of 20-50 kW
are needed to offer sufficient hybrid functionality. The electric machine, or
machines, used here will likely have more in common with what is today
used as traction machines for EVs, rather than a 12 V generator which serves
as the reference in generation one. Very few car models on the market are
equipped with a P2 or more advanced 48 V solution at the time of writing
this thesis. With 20-50 kW and a LIB of 0.5-1.5 kWh, the performance num-
bers are matching mainstream non-plug-in hybrids such as Toyota Prius and
the same gains in fuel efficiency can be achieved. The market penetration of
48 V mHEVs in cars is expected to be larger than for all other electrification
topologies (PHEV, HEV, EV) combined for the upcoming two decades.

6
 1.2 Review of previous work

1.2 Review of previous work

As the 48 V voltage bus is a new design in the light vehicle sector, there is
not a long history of previous work within this topic, where components and
systems are specifically designed for high-power density and high efficiency.
Some amount of publications are available on prototypes for 42 V systems
from the 1990’s.
The following sections present a review of work done with heavy emphasis on
clear experimental results for electric machines, power electronics and battery
testing.

System Studies
The engineering firm Ricardo[18] establish benefits of mHEV based on the
contribution from each mHEV specific support function. All relevant mHEV
topologies are presented together with power histograms, and challenges and
opportunities with each topology. However, no experimental verification is
performed. The same company presents a full-vehicle demonstrator with an
advanced mHEVsystem called HyBoost[19], claiming an experimentally ver-
ified 40% reduction in emissions; down to 99.7 g CO2 /km for a Ford Focus
sized car. This is done by ICE downsizing, start-stop, re-gen, EGR and e-
supercharger. Although impressive results, the mHEV components are not
based on 48 V technology and the implications of using different drive cycles
are not presented.

Electric Machines
A range of custom-designed electric machines can be found in literature. Be-
low is a selection of machines designed for automotive usage, with a power
range of 5-150 kW, with either high power density, high efficiency, or a novel
cooling layout as a design goal. The net power density of the machines will
be highlighted, meaning peak mechanical output (ca 10 s) divided by volume
of the smallest cylinder that encloses the active iron of the machine.
An automotive e-Assist ISG 115 VDC hairpin stator winding induction ma-
chine is designed and tested by representatives of General Motors in [20].
15 kW peak power is reported at an stack volume of 1.14 l, yielding a net
power density of 13 kW/l. A peak efficiency of 88% is observed through mea-

7
Chapter 1 Introduction

surements.
The design and testing of a 6-phase, 48 V, 9 kW induction machine with
hairpin windings is presented in[21], [22]. It features water jacket cooling
designed for 5 l/min. Maximum mechanical output power is 9.0 kW at
3400 RPM, however, the only reported efficiency point is 85.3% at 2860 RPM,
21 Nm (5.8 kW mechanical). The net and bulk power density at 9 kW is
2.84 kW/l and 9.28 kW/l respectively.
Engineers from Ricardo presents the design and construction of two versions
of 15 kW, 150 V PMSMs for mHEV [23]; one surface-mount PM (SPM) and
one interior-PM (IPM) machine. Peak system motoring efficiency, including
inverter, of 86% and 88% is reported, and the experimentally verified net
power density is 2.54 kW/l and 3.63 kW/l for SPM and IPM respectively.
A high-speed, hybrid excitation machine is designed, built and tested by
ORNL[24], measuring about the same gross volume as the Toyota THS2 main
traction machine[25]. The machine is tested showing a peak efficiency of 95%,
and powers up to 42 kW, yielding a net and bulk power density of 15.4 kW/l
and 3.89 kW/l respectively. The large difference in net and bulk power density
could be explained by the extra volume needed for the wireless rotor excitation
circuit.
Engineers from Mercedes-Benz[26] report on a automotive-grade, high-speed,
oil cooled three-phase PMSM developed for 48 V mild hybrids in P2.5 or P3
position. It is specified at 28 kW peak for 30 s. The measured peak efficiency
is 90.5% and the gross power density is 3.94 kW/l. Unfortunately, no geometry
for the active stack length are available to calculate net power density.
Automotive, mass-produced electric machines are extensively tested by Oak
Ridge National Laboratory (ORNL) in the US. One interesting reference ex-
ample is the 2012 Nissan Leaf traction machine reported in[27], with an net
volume of 4.66 l and a rated maximum power of 80 kW with 97% peak effi-
ciency. Net power density is 17.2 kW/l. This machine serves as a reference
for high efficiency and high net power density. However, no electromagnetic
or thermal design features are discussed.
Another interesting reference machine is the 2004 Toyota THS2 main trac-
tion machine, also tested by ORNL[28], [29] and reported by Toyota[25]. The
rated peak power is 50 kW and the net/gross volume is 4.76 l and 11.2 l re-
spectively. This results in a net and gross power density of 10.5 kW/l and
4.46 kW/l, respectively. Peak efficiencies of 94% are measured.

8
 1.2 Review of previous work

The 2010 Toyota HSD-G3 main traction system is extensively tested in[29],
at 60 kW maximum power, peak efficiency of 96%, resulting in net and bulk
power density of 21.6 kW/l and 5.17 kW/l.
Benchmarking of the BMW i3 traction machine is reported in[30], [31],
showing peak efficiency of 94%, power output of 125 kW, net and bulk power
density of 20 kW/l and 9.2 kW/l respectively.
To sum up, what is rare or even missing in the literature is a report on
the design of a electric traction machine with high efficiency (>90%) and high
power density (>15 kW/l net, >5 kW/l bulk) proven simultaneously by exper-
iments in the power range of 30-50 kW. Even more rare is extra-low-voltage
(<100 VDC ) designs. Several automotive high-power traction machines in
production (BMW, Toyota, Nissan) do indeed fulfill these requirements, but
the performance are reported from third-party benchmarking, leaving out all
comments on the design procedures from the engineering teams.

Power Electronics
In [32], a direct-water-cooled, high-current three-phase 48 V inverter board
using aluminum substrate PCB and six paralleled high-current 100 V MOS-
FETs is experimentally evaluated. While dimensioned for 300 ARM S , the
maximum current achieved in tests was 150 ARM S due to thermal limitations
in the DC capacitor bank, and voltage spikes during switching. The measures
of active components are 150x115x15 mm.
A custom made 48 V inverter with direct-oil cooling is presented in[33],
and tests with phase currents up to 431 ARM S at 17 l/min oil flow. The total
volume for the automotive encapsulated inverter including controller is 13.4 l.
No efficiency numbers are reported.
A compact, three-phase, two-level, water-cooled 48 V inverter in[34] is
tested for peak performance at 55 VDC , achieving 93.9% efficiency at a three-
phase output of 210 ARM S , 10.3 kW, cos(φ)=0.75.
US ORNL presents a modular (6-leg) converter topology in[35], and evalu-
ates the losses for three different SiC MOSFET models operating at 30 kHz
water cooled at 10 l/min. The system is aimed to power a 360 VDC BMW i3
electric machine at 125 kW peak. The modular 6-leg setup uses carrier wave
phase shift to minimize the DC capacitor current ripple. The ripple min-
imisation effect is not quantified, and the resulting inverter efficiency is not
explicitly declared.

9
Chapter 1 Introduction

In[30], it is claimed that the next-generation of automotive inverters for

HEVs are likely to use multi-level inverters, or segmented inverters, meaning
several sets of three-phase VSI powering one electric machine equipped with
open-ended windings. This topology would be an effective method of reducing
the maximum current per phase leg, and minimizing the ripple voltage at the
DC bus, reducing the size of the DC capacitor.
What is lacking in the literature is design and successful testing of compact,
high-power-density (i.e. liquid cooled) extra-low-voltage (<100 VDC ) motor
converters for multiphase electric machines in the power range (>10 kW).

Drive Systems: EM and PE

In[36], Engineers from Mahle present a 48 V rear-axle drive unit (P4 position)
with a 30 kW peak, high-performance EM and integrated power electronics.
A peak EM efficiency of 97% is reported (calculated). The highly integrated,
water cooled MOSFET inverter is designed for 600 ARM S continuous. The
importance of effective cooling is highlighted for both PE and EM, but no
quantification is provided. However, no further design results, e.g. power
density, or efficiency measurements are reported.
In[34], [37], [38], a water-cooled 48 V, 10 kW (peak 30 s) Electrically-Excited
Synchronous Machine (EESM) machine and inverter system is designed, build
and experimentally verified. While the inverter tested up to 371 ARM S , the
machine achieves 34 Nm at 750 RPM, yielding 2.7 kW. The prototype ma-
chine efficiency is limited to 47% at 2.7 kW, and peak 62% at 0.3 kW output
according to measurements in[37]. The net power density for the electric ma-
chine, using active stack length and diameter, excluding the excitation system,
equals to 11.0 kW/l (30 s design target) and 3.0 kW/l verified.
The very-low-voltage asynchronous traction machine ISCAD is presented
in[39]. The design target for both machine and integrated inverter is <60 VDC ,
240 kW[40]. However, no experimental figures for output power or efficiency
are provided. Further ISCAD experiments are presented in [41], but without
any experimental results to indicate power density or efficiency.
An Integrated Modular Motor Drive (IMMD) is presented in[42], where a
five-phase tooth-coil wound machine with key winding factor one (one adjacent
coil per phase) is offering the possibility of controlling each individual coil with
one small inverter board. A prototype is built and powered, and a hypothetical
net power density for the machine of 1.71 kW/l at 2.7 kW is reported. A GaN

10
 1.2 Review of previous work

IMMD is also built for 2x100 V operation[43], but only one open-loop test at
ca 500 W is reported. More concepts and prototypes are built of the IMMD,
but no further high-power operating points can be found in the literature.
A version of the IMMD, from another research team, for an axial-flux 48 V
PMSM is presented in[44]. The effects of using carrier wave interleaving to
minimize DC current ripple i mainly evaluated. The tests are performed up to
4 kW, which means net power density of 2.58 kW/l with size numbers reported
from[45].
Continental are presenting production-ready water-cooled Belt-ISG compo-
nents for 48 V mHEV applications[46], with a 5 s peak gross power density of
3.18 kW/l including power electronics and motor control.
The EU project ECOCHAMPS has reported by Ricardo UK on the design
and testing of components for 48 V hybrids. One examples is a pseudo 6-phase,
oil spray cooled electric machine[33], [47] with hairpin windings, designed for
25 kW and tested up to 15.5 kW output power. An oil flow of 2 l/min is
preferred by design. The net power density is 17.0 kW/l by design target, and
10.5 kW/l validated experimentally. No efficiency numbers are reported.

Battery modeling
A short overview of empirical modeling is presented in Paper 1 , and a more
comprehensive overview in Paper 4. At the start of the thesis work, a lack of
examples was identified in the literature on how various testing methods for
LIB leads to extraction of parameters for linear circuit models which then are
evaluated in load cycles relevant for vehicle use. Further on, most reports on
battery modeling only apply a proposed model to one specific make, model,
size and chemistry of LIB.

11
Chapter 1 Introduction

1.3 Purpose of thesis

System design, component modeling, and component interactions in a high-
performance 48 V mild hybrid electric powertrain is the main focus in this
thesis. Electrical, thermal and electromagnetic properties are to be stud-
ied for the main propulsion components: LIB and EM. Accurate electrical
and thermal models are crucial to maximise the utilisation of LIBs. Novel
design features for high efficiency, high power density EMs are also to be
explored. Relevant test procedures available within the project was electro-
chemical Impedance Spectroscopy (EIS) and high-current pulse charge and
discharge.
Two main research questions have been followed throughout the work pre-
sented in this thesis:
• How can model based design be used to represent high-performance LIBs
of various sizes, performances and chemistries?
– What model accuracy can be established using EIS and pulse dis-
charge when characterizing the electrical and thermal performance
of LIBs?
– What accuracy can be achieved using simple Thevenin models to
represent the electrical behavior in LIBs over a wide operating
range in SOC, temperature and current range?
• Design and construction of an electric machine concept that is promising
for mHEVs, featuring a power output of at least 20 kW, high efficiency
and high power density.
• Demonstration of compact and efficient power electronics hardware to
to allow for tight integration on the electric machine concept.

1.4 Thesis outline and methodology

This thesis consists of a summary of eight papers, of which six are peer-
reviewed and accepted at the time of print on this thesis. To give a context
and understanding of the work, additional theory and history is outlined in
Chapter 2, and the setup in Chapter 3. Highlighted results from papers, as
well as previously unpublished results from the thesis work, are presented in
Chapter 4.

12
 1.5 Contributions

1.5 Contributions
The following list of contributions are claimed:

• Development, and extensive applications, of a high-current, portable,

robust, easy-to-use, and very-high-accuracy test methodology for LIBs
that works across many cell sizes, cell types and various test equipment.

• Applying and quantifying the difference in accuracy between high-current

pulse discharge measurements with low-current electro-chemical impedance
spectroscopy as methods to extract equivalent circuit parameters for
LIBs.

• Development, verification, of accuracy for a high-accuracy empirical

electrical model for LIBs, including publication of the parameter re-
sults. The model is optimized for use in model-based vehicle drive cycle
simulations, using only a limited number of linear electrical standard
circuit elements. Very low average voltage error is shown compared to
literature.

• Development and verification of a lumped-parameter electro-thermal

model for LIBs including reversible entropy heat, and development of
a test method to parameterize the entropy coefficient. This 1D LPN
significantly increases the temperature accuracy in LIB models.

• Experimental measurements of fuel consumption with a prototype car

equipped with a 48 V mild hybrid system, and validation of a simulation
model to emulate the mild hybrid powertrain behavior.

• Categorization, classification and visual presentation of the most impor-

tant electromagnetic properties of double-layer, three-phase tooth-coil
wound machines in a comprehensive way not previously found.

• Design, deployment and calibration of a customized calorimetric test

system for low-viscosity oils as the main coolant, and water as the sec-
ondary coolant medium.

13
Chapter 1 Introduction

1.6 List of Publications

This thesis is based upon the following papers:

I Parameterization of Equivalent Circuit Models for High Power Lithium-

Ion Batteries in HEV Applications
Conference paper presented 2016-09-06 at
EPE2016, Karsruhe, Germany

II Electro-Thermal Modeling of High-Performance Lithium-ion Energy Stor-

age Systems Including Reversible Entropy Heat
Conference paper presented 2017-03-27 at
APEC2017, Tampa, Florida, USA

III Experimental and model based evaluation of mild hybrid fuel consumption
gains and electric machine utilization for personal vehicle application
Conference paper presented 2017-08-08 at
ITEC-AP2017, Harbin, China

IV Parametrization of Linear Equivalent Circuit Models over Wide Temper-

ature and SOC spans for Automotive Lithium-Ion Cells using Electro-
chemical Impedance Spectroscopy
Published 2017-09-22 in Elsevier Journal of Energy Storage

V Pole-Slot Selection Considerations for Double Layer Three-phase Tooth-

Coil Wound Electrical Machines
Conference paper presented 2018-09-03 at
ICEM2018, Alexandroupoli, Greece

VI Design and Verification of In-slot Oil-Cooled Tooth Coil Winding PM

Machine for Traction Application
Published 2020-04-07 in IEEE Journal of Industrial Electronics

VII Electromagnetic and Calorimetric Validation of Direct Oil Cooled Tooth

Coil Winding PM Machine for Traction Application
Submitted 2020-05-17 to MDPI Energies

VIII Manufacturing of in-slot cooled tooth coil winding PM machines

Conference paper submitted to ICEM2020
(2020-08-23, Gothenburg, Sweden)

14
 CHAPTER 2

History and theoretical framework

2.1 Short history of electrification

In the end of the 1800’s, the vehicle fleet consisted of a mix between horse
carriages, steam engines, electric vehicles and internal combustion engines
(ICE). The competition between the different propulsion technologies was
even, but within two decades in the start of the 1900’s, the availability of
gasoline and the advancements in the ICE made both horses and electric
vehicles obsolete. Hybrid electric vehicles (HEVs), a powertrain where one or
several electric machines cooperate with a combustion engine, also existed to
a small degree, more history on this can be read in [48]. The start of mass-
produced hybrid electric powertrains was probably when Ford introduced the
option of an electric starter motor, battery and generator to the Model T
in 1919. The starter motor did only support with power to start up the
combustion engine, to alleviate the driver from the burdensome task of hand-
cranking. Unfortunately, the level of electric hybridisation remained on a
very low level for the next 80 years until late 1990s, when Honda introduced
Integrated Motor Assist and Toyota introduced the Hybrid Synergy Drive on
several car models. The first series produced 48 V mild hybrid electric vehicles

15
Chapter 2 History and theoretical framework

(mHEVs) were sold in 2018, and they quickly gained popularity. It is predicted
that 48 V hybrids will dominate by quantity in the light vehicle market over
HEV and EVs for the next two decades[17].

2.2 Levels of electrification

One way of categorizing the level och electrification in the vehicle powertrain
is to look at the quota between installed electric peak power (PEM ), and
total peak power from both electric machine and ICE (PICE ) and call it the
electrification factor, expressed as

PEM
ef = . (2.1)
PEM + PICE

If this factor is 1, the car is purely electric. In the lowest range of ef for mod-
ern cars we find an example of ef =0.01; a 1 kW starter motor and a 99 kW
ICE. Mild hybrids as a concept has the opportunity to fill a gap of electrifica-
tion factor between 0.05-0.5. Fig. 2.1 shows the connection between vehicle
traction voltage, electrification factor and expected electrification features.

2.3 Hybrid topologies

The electro-mechanical part of a 48 V mild hybrid powertrain can be formed
in many ways. For cost and size reasons, the most common solutions will be
restricted to one eclectic machine situated within a classical mechanical pow-
ertrain where it provides the most beneficial effects. The automotive industry
has united around a vocabulary of how the electric machine installation can
be done, as illustrated in Fig. 2.2. The hybrid topologies are further pre-
sented in[17] and [18]. In this thesis, P0 and P2 are compared in Paper 3.
The electric machine presented in Paper 6-8 is powerful enough to cover all
positions (P0. . .P4).

2.4 Why 48 V?
The International Organization for Standardization (ISO) defines safety levels
for automotive applications in ISO6469-1[49], which is legally binding for light

16
 2.4 Why 48 V?

Conven-
Micro Mild Full PHEV EV
tional
400 V
250 V

150 V
Traction voltage level →

60 V
48 V

12 V
Increasing electrification factor →

0% 10% 50% 100%

Re-gen
Hybridisation features →

E-crank Re-gen Re-gen

Auto- Re-gen
Auto- Re-gen
crank Some
crank in
e-drive
speed
Torque- Pure
fill/boost e-drive
Creep e-
Pure
drive
e-drive
Coasting
New e-
features

Figure 2.1: Features, voltage levels and electrification levels.

road vehicles by UN ECE R100[50]. The limit is fixed at 60 VDC or 30 VAC

and components and subsystems operating above this limit are labeled class B
voltage systems. Class B systems explicitly require proper galvanic isolation
from driver, passengers and service personnel, which must be realized through
a list of mandatory safety features. Below the limit, e.g. <60 VDC , is labels
Class A and implies none or few mandatory safety measures in order to protect
humans from electric shock. However, regardless of voltage level, the hazard
of current induced phenomena such as arc and burning still prevails which
motivates at least a basic protection layer with regards to electrical safety. The
exact range of voltage to be used for automotive 48 V systems are standardized
through VDA320[51] (published in 2014), formerly known as L148, as well as

17
Chapter 2 History and theoretical framework

Figure 2.2: The five viable electric machine topologies for mHEVs (P0..P4).
Courtesy of[33].

through ISO21780[52] (standard under development). An example of allowed

voltage range is illustrated in Fig. 2.3.
For stationary applications, slightly different voltage limits and naming are
defined compared to automotive applications. According to IEC60364[53],
extra low voltage is all systems <120 VDC , and according to EU Low Voltage
Directive[54] <75 VDC means extra low voltage.
Up until the standardization of 48 V in the last few years, all successful
hybrid electric vehicles on the market have utilized a class B voltage sys-
tem, usually utilizing a traction voltage in the range of 150-400 VDC . The
class B system requires substantial protective measures which adds complex-
ity, weight, volume and hence cost to all solutions associated with the class B
voltage bus. By limiting the system voltage to 48 V, cost, size and weight can
be kept at competitive levels.

2.5 Battery modeling

Electrical and electro-thermal models for LIBs are usually either physics-based
or black-box empirical based models. Very related to black-box approach is
a hybrid model called ”gray box“, often represented by en electric equivalent

18
 2.5 Battery modeling

60 V
Overvoltage
54 V Maximum voltage,
52 V
functional degradation
48 V
Normal operation,
full functionality

36 V
Miimum voltage,
functional degradation
24 V
Undervoltage
20 V

Figure 2.3: Allowed voltage levels for a 48 V system according to VDA320[51].

circuit model. The circuit elements and parameters are selected to match the
observed voltage response from experimentation.
The most basic equivalent circuit model (ECM) for a LIB consist of a basic
Thevenin equivalent: An internal voltage source with an internal resistance
in series, see Fig. 2.6a. However, this model does not capture the time
dynamics of most LIBs, even with parameters varying with temperature and
SOC. If this basic circuit is to be used, it is important to specify at what
charge or discharge time the resistance value is sampled. Common values are
1,2,5,10,30 s for automotive usage.
Regarding time dynamics to study, the scope is limited to what makes
most sense to minimize the error within a single drive cycle. LIBs exhibit
interesting effects in the frequency domain from 10 kHz and spanning down
to period times of years (i.e. ageing). A typical drive cycle, such as WLTP, is
30 minutes long and is sampled in 1 s increments. If an FFT is performed on
the drive cycle,
h most of the data i intensity will be focused within a frequency
−1
window of 0.5 (30 · 60) · · · 1 Hz. This is visualized in Fig. 2.4. With this
said, advanced ageing phenomena that arises despite obeying manufacturers’
voltage and temperature limits, are not within the scope of this work.

19
Chapter 2 History and theoretical framework

FFT

Figure 2.4: Means of selecting the most relevant time dynamics for equivalent cir-
cuits to be used in a drive cycle.

Equivalent Circuit Models

The fundamentals of electrical cell modeling usually presupposes a basic Thevenin
equivalent circuit comprising only of an ideal voltage source and a resistance
symbolizing the internal losses, see Fig. 2.6a. The circuit parameters should
be mapped to operating points, such as temperature and charge level (SOC),
to accurately represent the electrical behavior. The most obvious influence
of charge level is the Open Circuit Voltage (OCV). The SOC is an inter-
nal battery state which cannot be directly measured. However, it can fairly
accurately be estimated by a combination of integration of the current and
estimating the OCV on-line and then map the OCV to the SOC. Examples
of how the OCV depends on SOC can be seen in Fig. 4.3.
In the scope of this work, OCV is modeled with look-up tables as a func-
tion of SOC. The dependence of temperature in the OCV is very small and
not critical for electrical performance modeling as long as the SOC value is
normalized for temperature[55] . However, for thermal modeling, the entropy
effect is defined by the change of OCV over temperature, as discussed in Paper
II.
The second current dependent dynamics to capture in ECMs, is a signifi-
cant reactance displayed by LIBs when they are exposed for large changes of
charge, for example a regenerative braking event in a mHEV. The phenomena

20
 2.5 Battery modeling

is referred to as charge diffusion[56], [57] or mass transport. Diffusion typi-

cally increases the reactance in the negative direction proportionally to the
decrease in frequency of current excitation; the battery behaves as a pseudo-
capacitor for low frequencies. The behavior can be accurately modeled by
the non-linear Constant Phase Element (CPE)[58] parallel connected with a
linear resistor. The CPE represent an impedance of

ZCP E = Q−1 (jω)−n , (2.2)

where Q is a pseudo-capacitance (F), j the imaginary operator, ω angular

frequency (rad/s), and n is a unitless real scalar in the range of [0 < n < 1].
When the CPE is parallel connected with a resistor (R), it forms a Zarc
element with the impedance

R  −1
−1 n
ZZarc = = R + Q(jω) . (2.3)
1 + RQ(jω)n

A special case of the Zarc element is defined at n=0.5; the Warburg element,
which is often used to model diffusion[56], [57]. The behavior described by
(2.2) and (2.3) are crucial to the scope of Paper 3. A challenge with Zarcs is
that they cannot be realized in the time domain, they have no direct inverse
frequency transform. The most effective way to use them in a time-domain
simulation (such as a car drive cycle simulation), is to approximate them
with several series connected RC links. In[59], it is suggested that 5 series
connected RC links are used to represent a Zarc element. An EIS measurement
of a automotive LIB is shown in Fig. 2.5 where six RC elements are used to
capture the capacitive behavior. An even more simplified ECM suggested in
this thesis is to further limit the number of RC groups to two, as seen in Fig.
2.6b. This can be done without sacrificing much of the model accuracy in
the frequency range 10 mHz to 10 Hz. An important condition to fulfill is
that the value of the two time constants (τ = R · C) are clearly separated.
A thorough explanation of how the RC links are mathematically modeled is
found in Appendix A.

21
Chapter 2 History and theoretical framework

Figure 2.5: Example of reproduction of impedance from EIS measurements using

only linear ECMs. Results from cell H from Table 3.1 at 25◦ C.

R0
i
+ v0 − +
+ vOCV v
−
−
(a) Simple R0 Thevenin ECM.
R1 i R2 i
R1 R2
R0
i
C1 C2
+ v0 − +
iC1 iC2
+ vOCV +v − +v − v
− 1 2

−
(b) Extended R+2RC Thevenin ECM.

Figure 2.6: Reference ECMs for LIBs.

22
 2.6 Electric machine

2.6 Electric machine

Winding layout
TCWMs can be designed in many high-performance configurations. Paper 5
lays out the theory of key performance indices (KPIs) for three-phase balanced
windings, which is briefly summarized in Table 2.1.

Table 2.1: Summary of TCWM key performance indices

Symbol Name Explanation
Q Slot number Number of total slots in stator
p Pole number Total number of rotor poles (2 · pole pairs)
Slots per pole
q
per phase
Number of symmetric or anti-
t Periodicity symmetric repetitions of the stator winding
layout in one mechanical revolution
Number of consecutive
W Key winding factor teeth coils connected in series to form the
smallest coil group
Multiplication of cogging torque
Mf Cogging multiplier frequency versus electrical frequency
due to stator layout
Linking factor between coil
kw Winding factor
group current and stator induced MMF
Harmonic air gap Excessive stator inductance due to
δσ leakage factor magnetisation of MMF sub- and super-
harmonics over the air gap

Equivalent circuit for electric machine

A standard way of modeling a three-phase electric machine is to transform all
variables to the dq reference frame. The output torque of the machine can be
expressed as[60]  
T = nph np Ψd iq − Ψq id , (2.4)

23
Chapter 2 History and theoretical framework

where Ψ (Wb) is RMS flux linkage, i (A) is RMS stator current, nph number
of phases, and np pole pair number. The flux linkages for a permanent magnet
rotor including saliency are expressed as

Ψd = Ld id + ΨP M (2.5a)
Ψq = Lq iq , (2.5b)

where Ld and Ld (H) are the equivalent stator inductance in d and q direction
respectively. ΨP M (Wb) is the RMS linked flux between rotor permanent
magnet and stator coils of one phase. Linked flux can be established either by
the use of FEA or experimentally for a prototype machine. A reformulation of
(2.4) can now be done using (2.5), highlighting reluctance torque production
through the term (Ld − Lq ):
 
T = nph np ΨP M iq + (Ld − Lq )id iq . (2.6)

The ECM for RMS phase voltages u (V) can be defined as in Fig. 2.7, where
stator phase resistance Rs (Ω) and rotor electrical speed ωe (rad/s) compiles
to
did
ud = Ld + Rs id − ωe Lq iq (2.7a)
dt
diq  
uq = Lq + Rs iq + ωe Ld id + ΨP M . (2.7b)
dt
The mechanical speed ωm scales with the electrical speed with the number
of pole pairs:
ωe = np ωm . (2.8)
di
For steady-state operation, the terms containing L dt can be neglected. For
a special case of no-load (id = iq = 0), steady-state (di/dt = 0, dω/dt = 0)
rotation, the relation between total stator output voltage, electrical speed and
linked permanent magnet flux can be derived from (2.7b) as:

us = ωe ΨP M . (2.9)

This relation is very useful during experimental establishment of permanent

magnet linked flux under no-load conditions.

24
 2.6 Electric machine

id Ld iq Lq
+ + +
− − ωe Ld id
ud + ωe Lq iq uq
+
− ω e ΨP M
− −

Rs Rs
(a) Direct voltage ECM (b) Quadrature voltage ECM

Figure 2.7: Equivalent Circuit Models for electric machine in dq frame.

25
 CHAPTER 3

Case Setup

In this chapter, the boundary conditions and hardware used for LIB, power
electronics, and EM testing is discussed.

3.1 System assumptions

Even though a Electrical Energy Storage System (EESS) consists of many

electrical components, focus in this work has been on modeling the individual
LIB cells, since they are the most influential components on the ESS perfor-
mance. The assumption is that a single-cell electro-thermal model can easily
be scaled to system level by a combination of series and parallel connection of
many cells. With this said, it is assumed that the parameter spread between
cells, for example from production, is negligible. It is also assumed that the
EESS is free from thermal gradients that will induce a spread in parameters
between cells and the EESS. For each cell model, tests are performed on one or
a few specimen with the assumption that the parameter spread is negligible.

27
Chapter 3 Case Setup

3.2 Battery testing

Parameters for a R+2RC equivalent circuit presented in Chapter 2 are ex-
tracted for numerous different LIB models. Most tests are done in room
temperature (20-24◦ C), while some cells are tested more extensively over a
temperature span from -10◦ C to +60◦ C with the help of a temperature cham-
ber. The first batch of cells (C through G) is acquired from the open market
in 2015. About the same time, the first cells for a Formula Student project
at Chalmers became available for measurements; cell A & B. Also, the Au-
tomotive cell H was borrowed from a adjacent research project in the same
lab. In 2017, a batch of new automotive, high-performance, very high power
density cells from leading cell manufacturers was made available for measure-
ments (M,N,S,T). Many different cell types, in various formats, and various
chemistries are evaluated using the same test and characterisation strategy
with the goal of evaluating if the same strategy an electrical model can suc-
cessfully be used generally. Table 3.1 summarizes the main properties of tested
cells and Fig. 3.2 shows pictures of some of the cells. The cell chemistry is a
qualified guess in most cases, as it is rarely disclosed in or outside datasheets.
The energy density Um and specific energy em are derived by measuring the
available energy at room temperature during 1 C charging. Weight and volume
are also measured by own means. The test current is normally 5 C discharge
current as the target application requires 5-30 C in peak discharge and charge.
Please note that the naming of the cells in Table 3.1 is not consistent with
the naming in Paper I and Paper IV. However, all cells tested in all papers
are listed in Table 3.1.

Test equipment
For the first few years of pulse testing, a Digatron BTS-600 battery tester is
used. In the latter part of this project, a PEC ACT 0550 was available in the
lab. The test procedure and post-processing are adapted to work with this
equipment. All EIS measurements are made with a Gamry Reference 3000.
The test procedures are illustrated in Fig. 3.1. For iso-temperature tests, the
thermal chamber ILW53 from Pol-Eko is used.

28
 Table 3.1: Overview of tested LIBs and their basic parameters.
Test Brand Form Chemistry Qnom Vmax Vmin Itest Um em
object Factor (Ah) (V) (V) (A) (Wh/dm3 ) (Wh/kg)
A Melasta Pouch LCO/G 10 4.20 3.00 50 447.5 180.6
B EP Pouch LCO/G 10 4.20 2.75 50 444.5 182.7
C Tinkang Pouch LMO/LTO 20 2.75 1.60 100 - -
D Tinkang Pouch LMO/LTO 15 2.75 1.60 75 128.9 64.6
E Tinkang Pouch LMO/LTO 26 2.75 1.60 130 151.8 67.2
F Tinkang Pouch NMO/LTO 26 3.30 2.00 130 151.7 -
G Tinkang Pouch NMO/LTO 28 3.30 2.00 140 171.7 78.3
H - Pouch (NMC+LMO)/G 26 4.15 2.80 130 345.7 169.6
I A123 Pouch LFP/G 19.6 3.60 2.00 98 - -
M - Prismatic (NMC+LMO)/G 5.0 4.20 2.80 25 230.8 106.6
N - Pouch NMC/LTO 11 2.70 1.50 55 161.5 67.4
J Melasta Pouch LCO/G 7.5 4.20 3.00 37.5 505.7 193.8
S SKC Pouch (NMC+LMO)/G 10 4.30 2.50 50 178.0 101.1
T Toshiba Prismatic NMC/LTO 20 2.70 1.50 100 177.0 90.0

29
3.2 Battery testing
Chapter 3 Case Setup

Pulse discharge testing

Electrochemical Impedance Spectroscopy

LIB ECM
parameters

Figure 3.1: Visualisation of the two utilized test test methods and used equipment
for high-power LIB testing.

Figure 3.2: Pictures and CAD models of a selection of cells, with labels matching
Table 3.1.

30
 3.3 Inverter test setups

3.3 Inverter test setups

Two high-current inverter prototypes are built within the project. Both are
three-leg, two-level topologies with silicon MOSFETs and high-capacity multi-
layer ceramic capacitors. Inverter 1 is depicted in Fig. 3.4, and Fig. 3.5. More
details on the design and testing of inverter 1 can be found in [61]. Inverter
2 can be seen in Fig. 3.7, and more details are presented in [62]. A brief of
the design and the achieved results is summarized in Table 3.2. The common
design features for both inverters are to use high-performance, 100 V, low-
Rds,on MOSFETs with low switching losses to enable 100 kHz PWM switching
frequency (fsw ), as opposed to normal fsw for automotive traction machines
of 5-20 kHz. With the increased fsw , a smaller capacitor bank can be used due
to the small time duration energy need to be stored between switching events.
The switching losses are still a fraction of the conduction losses for these
types of MOSFETs. Water cooling is used to limit the temperature rise of the
MOSFETs, which is necessary to operate close to the rated datasheet current.
To enable high fsw , a robust, well-integrated gate drive is needed. During
the design of inverter prototype 2, a miniaturized, modular phase leg gate
drive card was designed, see Fig. 3.6, based on Texas Instruments UCC27201
gate drive chip and other lessons learned from previous inverter designs. All
inverter prototypes are controlled open-loop with the 32-bit microcontroller
TMS320F28379D from Texas Instruments, and programmed through Matlab
Simulink.

31
Chapter 3 Case Setup

Table 3.2: Design features and test results for prototype inverter
Prototype 1 Prototype 2
Design
Topology 3-leg, 2-level 3-leg, 2-level
Target power 16 kVA 25 kVA
Cooling Water Water
Gate drive Gen1 off-board Gen2 miniature
PCB type Dual layer Single-layer 105 µ copper
PCB substrate FR4 Aluminum
Target (fsw ) 100 kHz 100 kHz
Transistor make Infineon Infineon
Transistor model IPP045N10N3GXKSA1 IAUT300N10S5N015
Transistor package TO220 HSOF-8-1
Transistor config. 1(2)p 2p
Transistor rating 100 V, 137 A, 4.5 mΩ 100 V, 300 A, 1.5 mΩ
Capacitor make TDK TDK
Capacitor model C5750X7S2A156M250KB C5750X7S2A226M280KB
Capacitor rating 100 V, 15 µF 100 V, 22 µF
Capacitor count 60 45
Test Setup
Load type 3-phase coils 3-phase step-up
reactive load transformer plus
400 V resistive loads

32
 3.3 Inverter test setups

Figure 3.3: Test setup for inverter tests. The electric machine is represented by a
high-current RL load or transformer. Courtesy of[61].

33
Chapter 3 Case Setup

Figure 3.4: Picture of inverter 1 prototype, featuring water cooling and external
gate drive board. The power board measures 120x90 mm.

Figure 3.5: Bottom side of inverter prototype 1 board, where half of the dual par-
allel MOSFETs in TO-220 package are mounted. The water cooling
covered by a silicon thermal pad is seen to the right, where footprints
of both ceramic capacitors and MOSFETs can clearly be distinguished,
telling good thermal contact.

34
 3.3 Inverter test setups

Figure 3.6: Picture of miniature, modular gate driver cards for one phase leg, mea-
suring 8x39 mm.

Figure 3.7: Picture of inverter 2 prototype, featuring aluminum substrate which

allows for very effective water cooling. The diameter is 140 mm.

35
Chapter 3 Case Setup

3.4 Electric machine setup

A TCWM is selected because of interesting properties of modularity, flexible
manufacturing, possibility of in-slot cooling, high torque density, and high effi-
ciency. A tooth-coil stator, when combined with a PM rotor, should preferably
feature embedded magnets, in order to reduce the eddy current losses in the
magnets caused by significant sub- and super-harmonics in the airgap mag-
netic wave. In this work, the selected rotor is a single-layer V-insert NdFeB
magnet layout with the intention to offer a large saliency.

Winding layout
With the analysis from Paper 5, and the preference of using six or more open-
ended windings, the most appealing slot (Q) - pole (p) combinations for this
applications is Q12p10 and Q12p8. A comparison of iron losses in Paper 7
favors the Q12p10 layout. To acquire the optimal winding layout for this
slot-pole combination, Cros’ method is implemented as a Matlab script as
described in [63]–[65] and then imported directly to Ansys simulation suite.
Results can be seen in Fig. 3.8 and Fig. 4.9.

Electric machine test setup

A 6-phase, TCWM is designed with the intention to serve either as a traction
machine for a small EV, or as an assist machine in a mHEV. The design
specifications are presented in Table 3.3. CAD pictures of the general setup
is shown in Fig. 3.10. The resulting design for the prototype ready machine
is presented in Table 3.4. More on the design and assembly is found in
Paper 8 and Fig. 3.11. The machine is tested in a dynamo setup reported in
Paper 6-7. The winding layout is presented in Fig. 3.8, showing how twelve
individual tooth coils are series connected in pairs, resulting in six open-ended
phases available on the NDE. The six phases consist of two symmetrical three
phase windings, making it possible to both series and parallel connect two
coil groups for three phase operation. With the open-ended windings, phase
windings can be formed externally by using either Y, Delta or individually
powered coil groups. Three examples are shown in Fig. 3.9.
Efforts are made to identify the signal parameters in the ECM presented
in (2.4) through (2.7). Each coil is measured individually for voltage and

36
 3.4 Electric machine setup

resistance. For inductance, individual coils are measured and the rotor angle
is varied slowly to scan for max and min values. The stator resistance is
measured for each individual phase group consisting of two internally series
connected tooth coils. An excitation current of 10.0 A DC is used while the
voltage drop is measured at the machine terminals with a bench multimeter,
see Fig. 3.12. The phase voltage at no-load is measured with an oscilloscope
while driving the machine with an external dynamo at 1027 RPM, as shown
in Fig. 3.12. The oscilloscope is set up to calculate the true RMS values.
The power electronics and motor controller available for this motor setup is
limited to 110 A RMS per phase, whereas the expected 10 s peak current
for the machine is 600 A RMS. Torque output is measured up to the the
maximum system current in 10 A increments and with a current angle of 90 ◦
advancement, i.e. iq only.

Figure 3.8: Geometry and winding overview of the designed machine.

37
Chapter 3 Case Setup

Table 3.3: Electrical machine design specifications

Quantity Value Unit
Peak torque 140 Nm
Peak power 50 kW
Base speed 3 600 rpm
Max speed 11 000 rpm
◦
Coolant max temperature 60 C
◦
Max winding temperature 180 C
DC bus voltage 48 V

Table 3.4: Geometric parameters for electric machine in 3-phase connection

Quantity Value Unit
Outer Stator diameter 180 mm
Inner Stator diameter 111.4 mm
Airgap radius 0.7 mm
Active length 100 mm
Tooth width 17 mm
Stator Yoke width 13 mm
Magnet thickness 3.5 mm
Conductor diameter 1.5 mm
Parallel conductors per turn 9 -
Turns per coil 3 -
Number of phases 6 -
Max. phase RMS current 600 A
Max. peak current density 35 A/mm2
Hard iron remanent flux 1.31 T
Hard iron type Vacodym 745DHR -
Soft iron type M235-35 -

38
 3.4 Electric machine setup

x6

+ + UB -
UDC
-
Uleg

(a) Six phase single coil groups connection

+ UA
UDC
-
Uleg

(b) Three phase, parallel coil groups Delta connection

+ UA
UDC
-
Uleg

(c) Three phase, parallel coil groups Y connection

Figure 3.9: Examples of electrical configurations of machine and two-level inverter.

39
Chapter 3 Case Setup

(a) Cut-away view (b) Full housing

Figure 3.10: CAD pictures with cut-away of the prototype EM. Length:
100|223 mm stack|total. Diameter: 180|206 mm stack|outer.

Figure 3.11: 48 V machine during manufacturing, stator without housing and be-
fore assembly of phase connection terminals. Each coil has 3 turns of
9 parallel strands 1.5 mm enameled copper wire.

40
 3.4 Electric machine setup

Figure 3.12: 48 V machine during phase resistance measurements with 10 A DC.

Figure 3.13: 48 V machine during low-current (<100 A) testing in dynamo in

calorimetric setup.

41
 CHAPTER 4

Results

4.1 Battery modeling

Parameter results
All parameters for OCV, R0,1,2 and C1,2 are extracted using semi-automated
Matlab scripts that operate on the raw data from the test equipment. The
details of the procedure is more described in Paper I. Results from room-
temperature tests and 5 C discharge pulses for the maximum achievable SOC
window are presented in Fig. 4.3 for OCV, Fig. 4.4 for R0 , and Fig. 4.5
for R0,1,2 and C1,2 . Since all batteries differ in size and charge capacity, the
passive parameters have been scaled with charge capacity to make them fit in
the same plots.
A selection of the LIBs are more thoroughly parameterized over a wide
temperature span. In this case, all R’s and C’s are a function of both SOC
and temperature and thus become 3D look-up tables in the equivalent circuit
model. A simplification of these results, by establishing the R10 resistance, is
shown in Fig. 4.7. More extensive results can be found in [66], in where the
naming of the cells are preserved.

43
Chapter 4 Results

Voltage headroom
When the R+2RC ECM parameters are established, they can be used to pre-
dict power availability instantaneously, as well as fairly accurately for a future
time that is less than the slowest time constant of the RC networks. Project-
ing allowed charge and discharge power is extremely useful in advanced LIB
applications such as automotive systems. The maximum sustainable power
output, i.e. a power level that can be repeatedly used without significantly
damaging och accelerating the aging of the cell, is limited by three things:

• Maximum allowed current magnitude

• Maximum temperature

• Minimum (discharge) or maximum (charging) terminal voltage.

High LIB temperatures are often a result from self-heating due to high cur-
rents and Joule losses (i2 R), in combination with entropy heating as discussed
in Paper 2. Static current limits can be established to limit self-heating, or
due to other bottlenecks in current carriers or due to chemical reaction speed
in LIBs. Terminal voltage limits are usually given as hard limits by the cell
manufacturer. The maximum achievable current can be limited also by the
allowed voltage headroom between the internal voltage (OCV) and the ter-
minal voltage. The difference between the two voltages is the internal voltage
drop. The maximum power theorem cannot be achieved due to the small
voltage drop allowed by static voltage limits. With diffusion and mass trans-
port represented by the two slow RC links, the internal voltage drop increases
over time for a constant current, which means the allowed voltage headroom
shrinks as a function of the duration of charge or discharge current. The first
step in establishing the real-time maximum power capability is to calculate
the projected voltage drop, then solve for the resulting maximum current. Fig.
4.1 shows examples for four cells of how the projected voltage response looks
for a charge and discharge pulse at the maximum allowed peak rate according
to the LIB manufacturer (median value is 10 C). The magnitude of the pro-
jected voltage drop according to ECM parameters vary significantly between
the parameterized LIB cells at the allowed maximum current. This voltage
variation is very important information to include when evaluating the elec-
trical system performance of the adjacent component connected to the same
voltage bus.

44
 4.1 Battery modeling

The resulting power limits, restricted by either static current or voltage

headroom, are illustrated in Fig. 4.2. Please note that the absolute power
limits are hard to compare because of the large variation in size and capacity
for the cells.
Voltage and power in Fig. 4.1 and Fig. 4.2 are evaluated for room temper-
ature. The temperature effect can be incorporated by including temperature
dependence in the ECM parameters.

Cell H
Cell A

Cell N
Cell M

Figure 4.1: The resulting cell voltage at the terminals at the maximum specified
current. The legends represent for how long time the current is present,
to visualize the effect of diffusion. Dotted lines represent the cell volt-
age if it was not limited by the minimum and maximum cut-off voltages.

Model verification
Two steps of verification of the ECM are performed. The first level encom-
passes the simulation of the voltage response with the ECM, feeding in the

45
Chapter 4 Results

Cell A Cell H

Cell N
Cell M

Figure 4.2: Look-ahead charge and discharge power limits established by using a
R+2RC ECM and comply with both maximum current and voltage
limits.

current used during the pulse discharge test. The model now have both OCV
and R,C to vary with SOC, leaving temperature on the side at the moment.
A sensitivity analysis of keeping OCV and/or R,C values constant is shown in
Fig. 4.6. The RMSE between measurement and model is used to define model
error. This method is a way of validating the importance for model accuracy
to include the SOC dependence in OCV than it is to incorporate it for the
SOC dependence in the R and the C values. It also shows results from both a
simple Thevenin ECM (Fig. 2.6a) and the extended Thevenin R+2RC ECM
(Fig. 2.6b). For the best case in Fig. 4.6, SOC=50% all variables are SOC
dependant, the R+2RC ECM results in 3.4 mV RMSE, and the R10 ECM
71.2 mV RMSE. This equates to that best R10 ECM shows 21 times higher
error in voltage prediction. The corresponding number, when evaluated in a

46
 4.1 Battery modeling

long drive cycle is 10.7 mV and 28.4 mV RMS voltage error for R+2RC and
R10 respectively, as seen in Paper 1, Table III.
The second method of verification includes using a realistic, long, dynamic
load cycle that represents how the cell is aimed to be used in its end applica-
tion. This method is used and presented in Paper II ad Paper II. For a over
1.5 hour long drive cycle, without any feedback, the proposed R+2RC ECM
performs an RMSE of 15.5 mV (Paper II cell B), 20.3 mV (Paper II cell C),
and 10.7 mV (Paper II cell H). No such low RMSE values are found elsewhere
in the literature for long dynamic drive cycles.

Figure 4.3: Open circuit voltage sample points acquired after 1 h of relaxation
between pulse discharge measurements. Inter- & extrapolated lines.

High-level comparison
Fig. 4.8 shows the comparison with a selection of the analyzed cells for the
size-independent specific energy versus specific power, where the maximum
power is specified for a typical 10 s discharge pulse at room temperature.
Each straight line intersecting origo in this chart represent the rate of dis-
charge (C-rate) in (hours)−1 . Since the cell manufacturers’ maximum peak

47
Chapter 4 Results

Figure 4.4: Parameters results for R0 element in the R+2RC ECM (Fig. 2.6b)
at room temperature and 5 C discharge. Resistance values are scaled
with charge capacity.

48
 4.1 Battery modeling

Figure 4.5: Parameters results for R+2RC ECM (Fig. 2.6b) at room temperature
and 5 C discharge. Resistance values are scaled with charge capacity.

49
Chapter 4 Results

OCV=f(SOC) OCV=f(SOC) OCV=K OCV=K

R,C=f(SOC) R,C=K R,C=f(SOC) R,C=K

SOC ≈ 20%
SOC ≈ 50%
SOC ≈ 80%

Figure 4.6: The variation of accuracy using both models in R+2RC (Fig. 2.6) while
letting OCV and R,C values remain constant (at SOC=50% value) or
vary with SOC. X axis is time in seconds. Example for cell H.

50
 4.1 Battery modeling

(a) (b)

Figure 4.7: Equivalent R10 resistance for ECM in Fig. 2.6a as a function of SOC
(left column) and temperature (right column). Resistance is typically
flat between 20-95% SOC. Low temperature has a very strong effect
on resistance. Cell names matching Table 3.1 is found in the plot tile.

51
Chapter 4 Results

discharge C-rate is used to calculate the power, it should be noted that safety
margins to ensure long lifetime plays in as a penalty for automotive cells,
which are expected to withstand thousands of cycled in harsh environment.
Semiprofessional cells are typically specified for a few hundred cycles in ideal
conditions.

Figure 4.8: Ragone chart over tested batteries (circles) and examples of reference
battery cells from datasheet values (squares). The Maxwell super-
capacitor is found on coordinate [8500, 7.6] outside the plot.

4.2 Inverter results

The two inveters are tested at 100 kHz fsw continuously up to a current
level where either the temperature of the MOSFET packages is close to the
maximum allowed, or a power limitation of the power supply or load is reached.
For prototype 1, 45 A RMS is reached. The efficiency could not be established

52
 4.3 Electric machine results

due to very low power factor of the load. Prototype 2 is tested up to 220 A
RMS, mainly active current, resulting in 9.0 kW. The available DC power
supplies was limiting the possibilities of achieving higher powers. An efficiency
of 95.6% is measured, excluding the significant losses in power cables to and
from the inverter. This is considered to be successful results considering the
challenges with high switching frequency and high currents.

4.3 Electric machine results

Winding layout
The resulting balanced winding layout for a three-phase 12-slot, 10-pole TCWM
is visualized in Fig. 4.9. The smallest individual phase element is a coil group,
consisting of two adjacent tooth-coils connected in series. Each phase contains
two coil groups, which can be configured in a drive system wither individually,
in series, and in parallel.

Machine construction and results

Two mechanically identical machines are built, as presented in Paper 8, one
with windings optimised for 600 V, and the other optimized for 48 V. Results
from testing the 600 V machine can be found in Paper 6-8. The 48 V ma-
chine test results are presented in this chapter. All ECM parameters in this
chapter are measured for one coil group, meaning the machine is considered
to operate in six-phase mode. Voltages and resistances are measured indi-
vidually on all six phase groups, and the mean (µ) and standard deviation
(±1 σ) is presented in Table 4.1. ΨP M is calculated using (2.9) from voltage
measurements at 1027 rpm mechanical speed. Inductance measurements are
made with an LCR meter at 1 kHz excitation while step wise moving the
rotor to find minimum and maximum values within one electrical period. The
measured torque output for the 48 V machine is seen in Fig. 4.10 together
with simulated average torque output beyond maximum thermal limits. The
available motor controller was limited to 110 A RMS phase current at the
time of measurement. To illustrate the expected performance with a more
powerful inverter drive, the measurements from the 600 V machine presented
in Paper 7, figure 14, at 90◦ current angle are re-scaled for the current axis
with the coil turn ratio: N600 V /N48 V = 28/3.

53
Chapter 4 Results

Figure 4.9: Winding phasors and winding layout using Cros’ method. Slot per pole
per phase (q) and winding factor is displayed. The dotted vertical red
line marks the line of anti-symmetry in the stator winding.

Table 4.1: Parameter results from EM ECM extraction

Symbol Parameter Value Unit
nph Phase number 6 -
np Pole pairs 5 -
Ld Stator d inductance 20.9 µH
Lq Stator q inductance 40.5 µH
µ(Rs ) Coil group resistance 2.18 mΩ
σ(Rs ) Standard deviation 47.3 µΩ
µ(ΨP M ) PM linked flux 7.74 mWb
σ(ΨP M ) Standard deviation 19.8 µWb

54
 4.3 Electric machine results

Figure 4.10: Output torque over one electrical period at 150 rpm, 90◦ current ad-
vancement, measured and simulated with FEA at 48 V, and measured
fr the 600 V machine and re-scaled with the coil tun ratio.

55
 CHAPTER 5

Conclusions

5.1 Main conclusions

The following claims, found during the work presented throughout the thesis,
including the appended papers, are:

• For battery models used in time scales relevant to vehicle drive cycle
simulations, i.e. 0.1-1000 s, a linear, two-time-constant equivalent circuit
model offers a very appealing accuracy compared to all other options
found in literature
– The two time constants should both represent the diffusion phe-
nomena, but still have explicitly separated time constants by more
than an order of magnitude, e.g. τ1 =10 s and τ2 =200 s
– During LIB testing, it is important to allow for plenty of relaxation
between operating points in order to make sure the diffusion effects
have stabilized. In this work, a 1 h rest time is used for room tem-
peratures. Testing at lower temperatures than room might requires
more relaxation time. Some cells might need even longer relaxation
times, this is believed to be associated with optimization towards

57
Chapter 5 Conclusions

high energy density, e.g. thick electrodes

– For ECM circuit elements, the temperature is the most important
variable to take into account in order to keep model accuracy high
, except for OCV where SOC has the higher impact on model ac-
curacy.
– Using more than two RC networks in the circuit model does not
necessarily increase the accuracy in a car drive cycle evaluation,
but rather increases the difficulty of achieving robust parameter
fits.
– The model voltage deviation, measured as RMSE in a cell load
cycle, reaches as low as 11 mV for a 2RC equivalent circuit. This
is the lowest deviation (e.g. highest accuracy) found in literature
for linear circuit models without feedback.
– An RMSE of 15-20 mV is reached by using EIS to identify cir-
cuit parameters instead of pulse discharge, which is still among the
lowest deviations found in literature.
• The temperature dependence in the measured LIBs, using EIS and
frequency-domain analysis, is by far dominated by the medium-frequency
spectrum (ca 1 Hz to 1 kHz). This is attributed to charge transfer pro-
cess in the cells. The charge transfer is shifting the lower-frequency
impedance higher, but the delta resistance between 10 mHz and 1 Hz
does not change much in comparison.
• LIBs typically, in room temperature, exhibit a global resistive minimum
at 0.5-2 kHz. Additionally, for cells with graphite anodes, a local mini-
mum in reactance is usually displayed around 1 Hz. These features can
be interesting when modeling electrical properties in traction systems.
• The reversible entropy heat can dominate over the irreversible joule
losses for some LIB types and some operating points, shown with ex-
periments of a NMC/G cell and experienced even stronger in several
experiments with LCO/G cells. The entropy heat is an essential com-
ponent in any high-accuracy thermal model for LIBs.
• For a mild hybrid powertrain, using a well designed P2 topology, rather
than a P0, can save 21% to 35% more fuel in a rural and city drive cycle
respectively.

58
 5.1 Main conclusions

• For a mild hybrid powertrain, a 20 kW peak power rated electric machine

will capture >98% of the use cases in the tested drive cycles. For accel-
eration purposes, 50 kW peak capability is needed for the rural/highway
cycle tested if the electric machine is to power the car alone.

• Compiling a visually navigational map for three-phase double-layer tooth-

coil wound machines and their most important electromagnetic proper-
ties.
– Defining and visualizing key performance indices: key winding fac-
tor, cogging multiplier, fundamental winding factor and harmonic
leakage factor .
– Grouping all TCWM into categories using key winding factor, and
showing they share electromagnetic features.
– Declaring, by analytical means, that many winding configurations
display excessive inductance (harmonic leakage factor) due to the
magnetisation of sub- and super-harmonics over the airgap that are
not necessarily contributing to net torque output.

• Design, build and test a direct-oil cooled three-phase tooth-coil wound

machine and verify the performance using FEA with very good agree-
ment of torque and Back-EMF.
– The efficiency, measured both as mechanical power out divided by
electrical power in, as well as by direct thermal loss (calorimetric),
is verified as high as 95%. This point agrees with FEA within 0.9
percent units.
– The verified FEA model predicts a large peak efficiency area of
95%, which is higher than most automotive machines reported in
the academic literature, and it is on par with the state-of-art au-
tomotive traction machines use by Toyota, BMW, Nissan.
– The net power density of the presented machine, accounting for
active iron volume, is on par with mass-produced state-of-the-art
traction machines from BMW and Toyota, and it is higher than
the vast majority of machines presented in the academic literature.
– The design and validation of an electric machine for automotive
application with the combination of high efficiency (>90%) and

59
Chapter 5 Conclusions

high net power density (>15 kW/l) has not been previously found
reported in the academic literature.
– The construction and validation at the design target max torque
output of a direct-liquid cooled automotive traction machine is
rarely found in the literature.

60
 5.2 Future Work

5.2 Future Work

The following topics have been made salient during the process of finalizing
this thesis:

• Unifying the LIB test methodology and ECM to work on super capac-
itors and offer the same level of high model accuracy. Super capacitors
might display both high self-discharge and very slow mass transport,
which can make the proposed LIB model inaccurate.

• Designing a six-channel compact inverter power module that fits directly

on the machine housing and thus share oil cooling with the machine.

• Experimental evaluation of driving the EM with a six-leg or six-H-bridge

inverter and utilizing PWM carrier wave phase shift to minimize DC
capacitor current ripple.

• Experimentally establishing the rotor (magnet) losses in the prototype

TCWM at high rotational speeds. Magnet segmentation is used to limit
the harmonic losses, but the theoretical loss calculations have not been
verified. The temperature coefficient of the magnet material remanent
flux can be used to establish the average magnet temperature on-line at
no-load by measuring the BEMF.

• Continue to develop the theoretical framework for key performance in-

dices to include TCWMs with more than three phases.

• Verify the harmonic leakage inductance for different TCWM types by

using FEA. It is believed that the rotor geometry, especially reluctance
rotors, can reduce the effect of spacial harmonics magnetizing over the
airgap.

• Evaluate the extra machine losses due to time harmonics in TCWMs

when switching with 10 kHz and 100 kHz through FEA.

61
 APPENDIX A

Linear equivalent circuit model

This appendix presents the basic mathematical analysis of linear equivalent

circuit models with RC links used for LIBs. The ideal voltage source in the
simple Thevenin ECM of Fig. A.1a is trivial to model, this analysis will focus
on modeling one series RC link in Fig. A.1b. Fig. A.2 isolates one RC links
from the ECM, and from here one can apply nodal analysis:

i = iR + iC (A.1a)

iR = v/R (A.1b)
dv
iC = C (A.1c)
dt
From here, we can establish an ordinary first order linear homogeneous
differential equation (ODE):

dv v i
+ = (A.2)
dt RC C
It is important now to note that both v and i are function of time. Since

63
Appendix A Linear equivalent circuit model

it is hard to find a general analytical solution for the differential equation

to the arbitrary function i(t), we instead find solutions for two special cases:
Zero-state (Fig. A.2a) and zero-input (Fig. A.2b). Zero state means that
no energy is stored in the system at t = 0, but an external signal is applied
starting at positive time. Zero-input means that there is indeed stored internal
energy expressed as voltage over the capacitor, but no external excitation to
the circuit.
One solution to the zero-state form ODE is the sum of the homogeneous
solution and the particular solution:

vzs = vh + vp (A.3)

The boundary conditions for this homogeneous case is


v(t ≤ 0) = 0
(A.4)
i(t ≤ 0) = 0

and the differential equation becomes

dv v
+ =0 (A.5)
dt RC
with the homogeneous solution
t
vh (t) = K2 e− RC . (A.6)

However, the constant K2 cannot be determined until the particular solution is

found. The boundary conditions for the particular solution for the zero-state
circuit is defined by applying a step response in current after zero time:

v(t ≤ 0) = 0
(A.7)
i(t > 0) = i0

and the ODE for Fig. A.2a becomes

dv v i0
+ = . (A.8)
dt RC C

64
A solution of the same order as the right-hand side can be found, e.g.
(
vp = K3
dvp (A.9)
dt = 0

Combining (A.9) into (A.8) yields K3 = R i0 . Now (A.3) becomes vzs =

t
K2 e− RC + R i0 and applying the operating point t = 0 in (A.4) to this
solution, K2 can be found:
0
0 = K2 e− RC + R i0 ; (A.10a)

K2 = −R i0 ; (A.10b)
The full solution to the zero-state problem becomes
 t

vzs (t) = R 1 − e− RC . (A.11)

As this is true for a charging process of the capacitor, we can also find out
the discharge profile trough the zero-input case, which is defined through the
conditions corresponding to storing energy at time zero, but with no external
stimuli: 
i(t) = 0
(A.12)
v(t = 0) = V0
which makes the ODE to solve the same as in (A.5), and the solution vzi
has the same form as in (A.6), however, a different constant: K1 . With
the operating point t = 0 and the initial condition in (A.12), the solutions
becomes:
t
vzi (t) = K1 e− RC (A.13a)
0
− RC
V0 = K1 e = K1 (A.13b)
t
− RC
vzi (t) = V0 e . (A.13c)
Eq (A.11) or (A.13c) can be used to represent the charging and discharging
procedure of one RC link, respectively. For example, the charging or discharg-
ing pulse on a LIB. Since the system is assumed to be linear time invariant,
two series connected RC links can be superimposed and treated independently
during analysis. It should also be noted that the denominator of the expo-

65
Appendix A Linear equivalent circuit model

R0
i
+ v0 − +

+ vOCV v
−

−
(a) Simple R0 Thevenin ECM.

R1 i R2 i
R1 R2

R0
i
+ v0 − C1 C2 +
iC1 iC2
+ vOCV + − + − v
v1 v2
−

−
(b) Extended R+2RC Thevenin ECM.

Figure A.1: Reference ECMs for LIBs.

nent in the natural logarithms in the solutions to the ODE in e.g. (A.11)
and (A.13c) is equivalent to the time constant of the corresponding RC link:
τ = R C.

State space model

From the model in Fig. A.1b, it is straight-forward to express the output
voltage equation as
v = vOCV − v0 − v1 − v2 . (A.14)
The voltages over each of the two individual RC links with subscript x = 1, 2
can be derived by Kirchhoff’s current law within the RC link as:

vx dvx
i = iRx + iCx = + Cx (A.15a)
Rx dt

66
 i i

iR + iR
+ iC iC

v R C v R C

−
−

(a) One RC link at zero state. (b) One RC link at zero input.

Figure A.2: Simplified RC circuit used for analysis and formulation of equations.

dvx i vx
= +− (A.15b)
dt Cx Rx Cx
Z 
i vx 
vx = +− dt . (A.15c)
Cx Rx Cx
Equations in state space form can now easily be generated from (A.15b).
(A.15c) makes it very intuitive to implement in model based graphical pro-
gramming environments such as Matlab Simulink. Fig. A.3a shows a such
implementation with two subsystems of RC links depicted in Fig. A.3b.

67
Appendix A Linear equivalent circuit model

(a) Total Simulink implementation of (A.14), where

each of the two subsystems represent an RC link
as in Fig. A.3b

(b) Simulink model implementation of one RC link as

depicted in Fig. 2.6b and defined in state-space
form in (A.15c).

Figure A.3: Implementation of ECM in state-space form in Matlab Simulink.

68
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75
 Part II

Included Papers

77
 Paper I
Parameterization of equivalent circuit models
for high power lithium-ion batteries
in HEV applications
Presented 2016-09-06 at
EPE2016, Karsruhe, Germany

Published 2017-05-18 in IEEE Xplore:

http://ieeexplore.ieee.org/document/7695340/

79
80
Parameterization of Equivalent Circuit Models for High Power Lithium-Ion
Batteries in HEV Applications

Stefan Skoog
Div. of Electrical Power Enegineering
Dept. of Energy and Environment
Chalmers University of Technology
Gothenburg, Sweden
Email: stefan.skoog@chalmers.se

Acknowledgment
This work is sponsored by the Swedish Governmental Agency for Innovation Systems (VINNOVA).

Keywords
Automotive application, Automotive component, Batteries, Device characterisation,
Device modeling, Hybrid Electric Vehicle, Energy storage, Impedance measurement

Abstract
Three different linear equivalent electrical circuit models for power optimized lithium-ion batteries are
parameterized and compared in a long dynamic load cycle representing typical hybrid electric vehicle
usage. The goal is to estimate the voltage on the battery terminals by only using an open-loop electrical
model. Model parameters are extracted trough a simple discharge pulse test and the parameter results are
presented for five different types of batteries. A quantification of the model fit is presented and compared
with similar studies.

Nomenclature
Table I: Glossary

Acronym Explanation
ECM Equivalent Circuit Model
G Graphite, anode material
LCO Lithium-Cobalt Oxide (LiCoO2 ), cathode material
LIB Lithium-Ion Battery
LMO Spinel Lithium-Manganese Oxide (LiMn2 O4 ), cathode material
LTO Spinel Lithium-Titanate Oxide (Li4 Ti5 O1 2), anode material
MSE Mean Squared Error
NMC Nickel-Manganese-Cobalt Oxide (LiNiMnCoO2 ), cathode material
NMO Lithium-Nickel-Manganese Oxide (Li2 Mn3 NiO8 ), cathode material
OCV Open-Circuit Voltage
PHEV Plug-in Hybrid Electric Vehicle
SOC State of Charge

Introduction
Electrification of light-duty personal vehicles has the potential to offer significant fuel savings and re-
duction in emissions. Increasing the amount of electrification is an attractive method for vehicle manu-
facturers on reducing the fleet-average fuel consumption. This can be done with electric hybridization of
the powertrain, where the key components are; a small but efficient battery, and an electric machine to
assist the combustion engine. This setup typically require a power-optimized battery and several modern
lithium-ion battery (LIB) chemistries can deliver the required performance in terms of power density.
Since LIBs are one of the most expensive and critical components in a hybrid electric powertrain, it is
very important to dimension it adequately. A good sized LIB operates close to its limits of performance,
whenever needed, without taking permanent damage. Adequate sizing requires accurate and efficient
model-based development simulations to run through anticipated scenarios of operation. Representing
the electrical behavior of LIBs can be done with physics-based modeling, empirical modeling or a com-
bination of the two methods. In this study, an empirical method is explained, used and applied to several
commercially available LIBs. The test method is a simple but efficient method of analyzing single cells
of power optimized LIBs using only square wave discharge current pulses as the main stimuli. The result
is a set of parameter for an ECM, and the model is then implemented in a simulation environment and
the output of the model is compared with measurements from a dynamic load cycle. The chemistries of
the tested cells are NMO/LTO, LMO/LTO, NMC+LMO/G and LCO/G and the nominal capacity ranges
10-28 Ah. All test objects are new and healthy, ageing is not considered in this scope. The parameter
extraction is limited to room temperature.
Previous work in fitting equivalent circuit models to LIBs from time-domain data is reported in [1,
2, 3, 4, 5, 6, 7]. However, quite few papers quantify the total variance in dynamic load cycles and
rarely compare model results for more than one cell and/or cell chemistry. The main contributions of
this paper is the simplicity of the test method explained, the application of the test method on several
commercially available LIBs, and the quantification of model variance in a long dynamic load cycle with
a wide operating window.

Method
The test is based on high-current discharge pulses with well-defined pulse length and depth. All test are
performed in room temperature (20±3◦ C). Any possible aging effect of the test objects is not considered.
The method is suited for analysis of electrical time dynamics from 0.3 mHz to 10 Hz, focusing mainly
on electrical dynamics caused by electrochemical mass transport, more precisely diffusion[8].
Discharge pulse test
It is well known that LIBs show significant polarization behavior when subjected to large changes in
charge due to high currents or long pulses. To capture this phenomenon, a discharge pulse test is designed
according to Fig 2 to expose a strong polarization for ten different operating points over a charge window
defined as safe by the LIB manufacturer through upper and lower terminal voltage limits (Vmax and Vmin ,
see Table II). The magnitude of the discharge pulse must be strong enough to reliably capture the voltage
response, but within the limits of risking permanent degradation of the cell performance by causing
excessive chemical side reactions, depletion or saturation[9].
Equivalent Circuit Model
Three different equivalent circuits are considered, as seen in Fig 1. Each of the circuit alternatives are
aimed to approximate the electrochemical diffusion dynamics normally represented by a Randles circuit.

(a) ”R” (b) ”R+1RC” (c) ”R+2RC”

Fig. 1: Equivalent Circuit Models considered.

 Fig. 2: A typical high-current discharge pulse. Ten consecutive pulses forms one full discharge cycle.

Fig. 3: Curve fit for battery E, pulse no 6 (ca 44 % SOC). The time vector is re-aligned to focus on the
relaxation part of the voltage response.

However, to keep the model simple, the circuit elements are constricted to piece-wise linear electrical
passives. All parameters are a function of the test objects State of Charge (SOC) and for the purpose
of simulation, the parameters are stored in look-up-tables and linearly interpolated between the sampled
values. The Open Circuit Voltage (OCV) represents the cells internal average electromotive force, which
is also strongly dependent on SOC.
For each discharge pulse, a corresponding voltage response is expected according to Fig 3. For the more
complex of the three ECMs (Fig 1(c)), the corresponding electrical parameters to be extracted is OCV ,
R0 , R1 , C1 , R2 , C2 . All parameters are a function of SOC. The parameter extraction is applied on the
relaxation part of the pulse only, due to simplicity of having the average cell SOC as constant as opposed
to during the discharge pulse. It is assumed that fitting the model to the relaxation part will also give a
representative behavior during the discharge part, which is verified later on.
R0 is extracted by measuring the instantaneous voltage re-bounce from the discharge pulse the first few
samples (within 20 ms) of the current turn-off. Knowing the magnitude of the current applied just before
the turn-off and the magnitude of the voltage drop gives the resistance through Ohm’s law.
The remaining relaxation pulse Er , short of the R0 re-bounce, is fed into a curve fitting procedure. A Non-
linear Least Square method is used to fit the best curve to the measurement data assuming the following
behavior:

Er = a0 − a1 e−b1t − a2 e−b2t , (1)

where t is the time vector (t0 is at the current interrupt), a0 is the steady-state voltage after complete
relaxation, ax is the maximum polarization voltage at t0 , and bx is the time scaling for link x. ax and bx
are positive. Time constants for the corresponding RC links are extracted as

τx = 1/bx , (2)
where bx is the time scaling and x is the index of the RC link to be identified. Extraction of the resistance
parameters for the RC links is done using
ax
Rx = , (3)
i(1 − e−bxtch )

where tch is the time spend in constant-current discharge before current interrupt, and i is the magnitude
of the current used for discharge. In all tests here, tch = 72 s and i = 5 C as shown in Fig 2. The exponential
function in the denominator represents the amount of bias on the RC link that has been build up during
the discharge pulse. Now the equivalent capacitance for the corresponding links is

Cx = τx /Rx . (4)

These parameters are extracted separately for all pulses and stored in tables as a function of SOC for
each battery type. For the single time dynamics ECM in Fig 1(b), the parameters are extracted for two
RC links, but the slower one is dismissed. The OCV is sampled at the end of the relaxation; 60 min after
the current interrupt event.

Fig. 4: Implementation of parameter variation over OCV in SimScape

Verification and Validation

After the pulse tests and data processing, a simulation model is populated with the extracted parameters.
This simple LIB model is simulated with the same current input as the measurements to visualize pulse-
per-pulse model fit, as illustrated in Fig 5. The validation method consists of loading the real cell with a
dynamic load cycle and comparing with simulation results. The simulation model implements variable
linear passive elements with Simscape as shown in Fig 4. The battery charge level is estimated by
coulomb counting during the load cycle and the ECM parameters are extracted from look-up tables using
linear interpolation between the discrete SOC points. The load cycle is compiled with test sections for the
battery category PHEV min from [10]. The LIB is 90% charged at the start of the test and dynamically
loaded with the charge depletion cycle until a SOC of about 20 % is reached, when the test switches over
to the charge sustaining cycle. The original cycles consist of constant-power steps cycles with duration
of 90 or 360 seconds. These test cycles are repeated to form a test of 2 hours. The result for cell E
is shown in Fig 8. The recorded current profile from the physical test is then fed into the simulation
model for each of the three ECMs so that the model accuracy for the voltage response can be evaluated.
A sampling rate of 10 Hz was used for the current and voltage recording during the physical test. The
instantaneous error for each model voltage output (v̂) compared to the measurement (v) is defined as:

E = v̂ − v. (5)

The variance of the voltage outputs is defined as the mean of the square of the instantaneous error

1 n 2
n i∑
V= Ei , (6)
=1

where n is the number of measurement points. The standard deviation of the voltage estimation is defined
through the root-mean of the square of the instantaneous error:
√
RMSE = V . (7)

Test Setup
Test objects
Five different LIB variants are tested in this scope, as presented in Table II. All LIBs share the common
feature of being power optimized, allowing for repetitive pulse discharge rates up to 10 C. They are all
used as energy sources in various kinds of mobile electric propulsion systems. The brand of cell E is
obscured by the discretion of a major manufacturer of high-performance automotive cells. In Table II,
Qnom is the manufacturer specified charge capacity, Vmax and Vmin is the upper and lower cut-off voltages
respectively, Itest is the selected 5 C test current. Um is the measured usable energy density, derived by
measuring the available constant-current energy within the voltage limits at 1 C current, divided by the
volume of the smallest cuboid that can contain the active parts of the cell, i.e. excluding the tabs.

Table II: Test objects overview

Test object A B C D E
Brand Melasta Electric Power Tiankang Tiankang -
Form factor Pouch Pouch Prismatic Prismatic Pouch
Chemistry LCO/G LCO/G LMO/LTO NMO/LTO NMC+LMO/G
Qnom [Ah] 10 10 26 28 26
Vmax [V ] 4.20 4.20 2.75 3.00 4.15
Vmin [V ] 3.00 2.75 1.60 2.00 2.80
Itest [A] 50 50 130 140 130
Um [W h/dm3 ] 458 445 152 172 399

Test parameters
New cells are cycled at least 10 time with 1 C constant-current charge-discharge cycles to ensure a
minimum of formation[11, 12]. Before each batch of discharge pulses, the cell is charged to Vmax at 1C
constant-current, followed by constant-voltage phase until current falls below C/20. The cell i rested
for 1 hour. Each individual cell is tested with the current corresponding to 5 C according to the nominal
capacity specified in the manufacturer datasheets, see Itest in Table II. All pulse tests are performed with a
Digatron BTS-600 battery tester, Matlab is used for data processing and Simulink with Simscape is used
for model verifying simulations. The lab setup is programmed to perform intense logging of the voltage
response close to the current transients, and declining logging frequency further from current transients
in order to save data storage and computational power. Temperature control of the devices under test is
limited to passive convection for pulse tests and forced convection for verification load cycle tests.

Results
The exponential curve fit shows high robustness during the capacity extraction procedure. The per-pulse
verification displayed in Fig 5 shows a good fit also during the discharge pulse. The initial assumption
that the electrical dynamics can be represented with the same linear elements for discharge and relaxation
seems to be reasonable.
Looking at the behavior of the time constants for the two RC links over SOC, there is a large variation for
especially the slower of the two, as seen in Fig 6. The general behavior can be seen for all chemistries
tested. The cells tested during this experiment have not only different chemical properties, but also
 Fig. 5: Per-pulse model verification. Results from cell E.

Cell A
Cell B
Cell C
Cell D
Cell E

Fig. 6: Extracted time constants for a two-RC-link ECM (1(c)), results for all cells.
 Cell A
Cell B
Cell C
Cell D
Cell E

Fig. 7: ECM parameters for all tested cells, using parameter names from 1(c). The parameters are scaled
with cell capacity. Circles are sample points and dashed lines are interpolated trends between sample
points. A0 represents the OCV.

different physical sizes and charge capacity. In an effort to present the results in a size- and capacity-
neutral manner, the parameters in Fig 7 are scaled linearly according to their nominal capacity.
Running model verification with long dynamic load cycles comprised of test sections chargedepletion
and chargesustaining for PHEV min type LIBs from [10] yields a results as in Fig 8. The temperature
variation of the cell surface within this cycles is measured to 4.3 ◦C. An error analysis of the same test
can be seen in Fig 9 and the key numbers for model performance for that particular cell is gathered in
Table III together with results from similar studies. All of them utilize simple linear ECMs and evaluate
voltage error in automotive inspired test cycles.

Conclusion
This study used a simple discharge-pulse technique as the only test method to obtain a large-signal
equivalent circuit model for high-power LIBs aimed for automotive applications such as HEVs. Three
different ECMs are compared and parametrized through the same test procedure. The parametrized

Table III: Model Performance Evaluation Comparison for LIB ECMs used in drive cycles

ECM type Max(|E|) V RMSE Source

[mV ] [10−4 V 2 ] [mV ]
R 321.8 8.1 28.4 This study
R+1RC 269.1 6.9 26.25 This study
R+2RC 258.8 1.1 10.65 This study
R 1623 762 276 [6]
R+1RC 296.7 220 148 [6]
R+2RC 218.3 21 45.8 [6]
R+1RC 48.9 1.199 10.9 [4]
R+2RC - 6.76 26 [7]
Fig. 8: Voltage response of long dynamic load cycle of cell E. Measurements compared to the three
ECMs. The two zoomed-in areas displays the situation where the strongest polarization for charge de-
pletion (lower left) and charge sustaining (lower right) mode occurs. The power scaling is 500 W per
cell according to the test procedure[10].

Fig. 9: Error analysis of dynamic load cycle for cell E, comparing measurements with all three ECMs.
model is then compared with measurements of a real cell in a long, dynamic load cycle representing
typical HEV usage (Fig 8). The comparison shows that representing diffusion dynamics with two RC
links (Fig 1(c)) rather than with a single RC link (Fig 1(b)) decreases the model voltage standard deviation
(RMSE) drastically, from 36 mV to 12 mV worst-case in a long load cycle (Fig 9). The accuracy of the
model is among the better when compared to other similar studies, as can be seen in Table III. This
is even without having any correction for temperature included in this study. To improve the model
accuracy further, the parameter extraction can be continued for different cell temperatures.
Regarding the extracted time constants presented in Fig 6, the fast time constant RC link is typically 10
seconds regardless of cell chemistry. The slow RC link tends to capture behavior with a time constant
around 100-200 seconds except for cells composed with graphite anodes. It is believed that the active
elements in the cell undergoes phase changes associated with graphite at about 70 % SOC that affects the
electrical dynamics in this significant way (see also R and C in Fig 7). The corresponding time constant
peaks are absent in cells that carries a LTO anodes in this study.
Charge transfer dynamics is not represented by the RC links in this model, but is likely included in the
measurement of the R0 parameter due to the limited bandwidth of the equipment used. The time dynam-
ics for charge transfer for typical LIBs are concentrated to the 10-100 Hz region at room temperature
and therefore not particularly interesting when simulating load cycles stretching over hours. For long
load cycles that exposes the LIB for a net movement in SOC, typically charge depletion usage, the model
accuracy will benefit significantly by implementing a slow time-constant RC link to represent diffusion
with very slow behavior.
The limited complexity of the R+2RC equivalent circuit, as presented in Figure 1(c), is a benefit com-
pared to more complex non-linear constant-phase element-based circuits or partial differential equation
based physical models when it comes to implementing. This benefit is important when it comes to im-
plementing algorithms to run in real-time in on-board vehicle battery management systems. Estimating
the OCV accurately with this kind of model is an important first step in order to estimate the SOC and
dynamic current and power limit for a battery in automotive applications.

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thermal modeling of lithium-ion cells for use in hev or ev application,” World Electric Vehicle
Journal, vol. 3, pp. 1–10, 2009.

[3] R. Ahmed, J. Gazzarri, S. Onori, S. Habibi, R. Jackey, K. Rzemien, J. Tjong, and J. LeSage,
“Model-based parameter identification of healthy and aged li-ion batteries for electric vehicle ap-
plications,” in Proceedings of SAE 2015 World Congress, 2015.

[4] F. Sun, R. Xiong, H. He, W. Li, and J. E. E. Aussems, “Model-based dynamic multi-parameter
method for peak power estimation of lithium–ion batteries,” Applied Energy, vol. 96, pp. 378–386,
2012.

[5] T. Huria, M. Ceraolo, J. Gazzarri, and R. Jackey, “High fidelity electrical model with thermal
dependence for characterization and simulation of high power lithium battery cells,” in Electric
Vehicle Conference (IEVC), 2012 IEEE International. IEEE, 2012, pp. 1–8.

[6] H. He, R. Xiong, and J. Fan, “Evaluation of lithium-ion battery equivalent circuit models for state
of charge estimation by an experimental approach,” Energies, vol. 4, no. 4, pp. 582–598, 2011.

[7] Y. Hu, S. Yurkovich, Y. Guezennec, and B. Yurkovich, “Electro-thermal battery model identification
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ness Media, 2007.
 Paper II
Electro-thermal modeling of high-performance
lithium-ion energy storage systems including
reversible entropy heat
Presented 2017-03-27 at
APEC2017, Tampa, Florida, USA

Published 2016-10-27 in IEEE Xplore:

http://ieeexplore.ieee.org/document/7931031/

91
92
 Electro-Thermal Modeling of High-Performance
Lithium-ion Energy Storage Systems Including
Reversible Entropy Heat

Stefan Skoog
Electric Power Engineering
Chalmers University of Technology
Gothenburg, Sweden

Abstract—Two of the major heat sources in a high- attempts of measuring the entropy heat coefficient on full cells
performance automotive lithium-ion battery cell are parametrized in the literature. This paper offers a method to achieve a high-
in this study: Joule heat and entropy heat. Established electro- resolution entropy coefficient over virtually unlimited SOC
chemical models are investigated and experiments are designed points and over many temperature points.
to acquire the relevant parameters such as open circuit voltage,
entropy coefficient and internal impedance from ohmic losses and Calorimetric measurements is a very sensitive and suitable
mass transport. It is shown that the irreversible joule heat and method to measure the entropic effect at small currents, as
the reversible entropy heat has a similar magnitude at many showed in [3]. However, the limitation is that the method is
operating points for the device tested. The strong influence of generally limited to small currents only, which makes it hard
irreversible entropy heat has the potential to absorb all the joule to verify the effect in combination with large LIB currents.
heat in currents up to 135 A (C-rate of 13.5) charging and 66
A (6.6 C) discharge in a power optimized automotive lithium- This paper investigates the theory behind the reversible en-
ion cell. It is also shown that, by including the entropy heat in tropic heat effect and aims to establish the relevant coefficients
a simple thermal model, the temperature error can be reduced through high-precision, non-invasive voltage measurements on
down to 28 % and 44 % for under charging and discharging commercially available automotive battery cells. The magni-
with high currents, respectively. tude and significance of the reversible heat is set in to relation
to the joule heat. The joule heat is established experimentally
I. I NTRODUCTION by parametrization of a piece-wise linear electrical equivalent
For high-performance electrochemical energy storage sys- circuit model.
tems (ESS) comprising lithium ion batteries (LIBs) in mobile
application, thermal management is a central attribute to design II. T HEORY
for. Model-based design of battery systems accelerates the de- A high-performance automotive battery is a delicate piece
sign process for complex ESSs, but requires an understanding of interdisciplinary engineering. In this study, the electro-
of how the LIBs behave electrically and thermally under a chemical-thermal relations will be studied in order to quantify
range of load conditions. Very often, the thermal limits of the the reversible and irreversible heat that is generated when the
cell are specified from a safety point of view to prevent thermal battery system is used with high currents (above 1 C) and over
runaway and permanent damage, and even more conservatively a wide State of Charge (SOC) window.
set in order to preserve the life time of the LIBs. Basic
thermal modeling of ESSs are usually limited to include only
A. Electrical modeling
irreversible joule losses caused by the internal voltage drop in
the battery as a current is driven through the system. On the There is already vast number of methods to electrically
electrochemical level, more sources of heat are present, and represent the behavior of the cell in the literature. The scope
particularly interesting is the reversible effects that can both of this study promotes the use of empirical equivalent circuit
absorb and emit heat depending on the operating point. models. A simple Thevenin equivalent circuit (Figure 1(a))
and an extended R+2RC network (Figure 1(b)) is chosen to
The basics of entropic heat modeling is described by
represent the electrical properties of the cell. The Open Circuit
Gibbard[1] and Bernardi[2]. The entropic effect is reported
Voltage (OCV) is represented by a variable ideal voltage source
to be strong enough to cancel the joule effect, at least at very
mapped with a look-up table as a function of SOC. A R+2RC
low currents (C/5), as reported in [3] and [4]. However, as the
network provides higher accuracy of the internal voltage drop
technology and performance for especially automotive LIBs
than a simpler 1RC model, especially when using the cell with
is changing fast, the amount of joule heat is decreased per
large SOC windows as proven in[6]. The time constants of the
unit of output power the LIB is exposed for. This study aims
two RC networks (τx = Rx Cx ) are chose to represent two
to find, theoretically and experimentally, if the entropic effect
different time regions of the mass transport and diffusion part
can dominate even at reasonably large currents.
of a typical cell dynamics[7], [6]. In this case τ1 is in the
A recent and comprehensive review of the magnitude and range of 5-15 seconds and τ2 about 50-200 seconds depending
effect of entropy heat coefficient is presented by Viswanathan on SOC and temperature. The time constants typically vary
et.al[5]. However, it is hard to find successful non-invasive with temperature as especially the R’s are highly temperature
dependent [8]. Charge transfer impedance is neglected in of the sign of entropy coefficient and current determines if the
this scope as the time dynamics at room temperature and entropy heat (q˙E ) becomes exotermic (positive) or endotermic
above is typically 1 second and not relevant in relation to (negative). For all operating points in SOC, there exist two cell
the much slower thermal processes investigated here. Instead, currents i where the joule heat and the entropy heat cancel
the charge transfer dynamics is included in R0 so that the each other and no net heat is developed in the cell to alter its
steady-state dynamics above charge transfer becomes accurate. average temperature, (2) rewritten:
All electrical parameters are measured with pulse testing, also
∂U
known as current interrupt method. The data is extracted from q̇ = 0 ⇒ iT = −i2 Rtot . (3)
voltage responses and stored in look-up tables which can easily ∂T
be implemented with piece-wise linear interpolation in on-line The first solution is the trivial i = 0, and the second solution
models. becomes:
T ∂U
i=− . (4)
B. Thermal modeling Rtot ∂T

A rudimentary way of describing the heat transfer between III. M EASUREMENTS

a cell and its environment is with a 1D lumped-parameter (also
known as lumped-capacitance) model such as An automotive high-power pouch cell is used as a base
for parameter identification and verification. The chemistry
∂T is based on a NMC+LMO cathode matched with a graphite
q̇ = cp m + kA(T − T∞ ), (1)
∂t anode. The nominal voltage is 3.70 V and the rated charge
capacity is 10 Ah. The experimental procedure consists of four
where q̇ [W ] is the rate of heat generation by the cell, steps as described below.
cp [J · kg −1 · K −1 ] is the mass-specific heat capacity of the
cell, m [kg] the mass of the cell, T [K] the cell temperature, A. Determine entropic coefficient
T∞ [K] the ambient temperature, k [W m−2 K −1 ] the heat
transfer coefficient incorporating both convection and conduc- A high-precision potentiostat (Gamry Reference 3000) is
tion effects, and A [m2 ] the equivalent heat transfer area. used to charge and discharge the cell over the entire usable
Radiation is not considered in battery systems since it is of SOC window with a rate of 0.1 C (10 hour sweep). The pro-
no significant magnitude due to thermal difference between cedure carried out in a thermal chamber in thermal steady-state
cells and ambient is typically low. The heat generated by the and is repeated for five relevant temperatures: 5,14,25,34,45◦ C.
cell is defined as For each temperature, new curves are established and a small
∂U but significant difference is expected in OCV. The charge
q̇ = q˙J + q˙E = i2 Rtot + iT , (2) and discharge voltage for each temperature is compared and
∂T an average curve is established as the pseudo-OCV vs SOC
where q˙J [W ] denotes joule heat, q˙E [W ] entropy heat, curve, see Figure 4. The cell manufacturer’s voltage limits are
i [A] current through the cell with charging currents as positive, slightly overridden in order to guarantee that the average curve
Rtot [Ω] the total resistance of the cells’ ECM (Figure 1) after contains data at the extreme points 0 % and 100 % SOC. The
considering the impedance and the history of the current. The difference between any two adjacent OCV curves multiplied
entropy coefficient ∂U/∂T [V /K] is the temperature derivative by the average temperature for the two curves (T ∂U/∂T )
of the open circuit voltage, which is experimentally established forms the entropic potential, and is illustrated in Figure 5.
in this paper. The entropy coefficient can be both positive and
negative and depends on the SOC of the cell [5]. The product B. Identification of thermal parameters
The cell is equipped with an external controlled heat source
consisting of enameled copper wire with known length and
diameter. The assembly also contains a small aluminum plate
which also is included in the calculations. Several thermocou-
ples are attached to various points on the cell setup in order to
get reliable and comparable measurements. The cell setup is
thermally insulated with expanded polystyrene foam and then
placed in a passive thermal chamber. The thermal parameters
(a) ”R” in (1) are successfully identified using a first order exponential
curve fit to the controlled heating up process through the
copper wire. The setup can be seen in Figure 2 and the
resulting thermal parameters are presented in Table I.

C. Identification of electrical parameters

High-current pulse testing is carried out with a Digatron
(b) ”R+2RC” BTS-600 in order to identify electrical parameters within the
relevant temperature span. Parameters are stored as 3D look-up
Fig. 1. Equivalent Circuit Models considered. The 2RC network model tables (typically resistance vs Temperature and SOC), which
represent slow-acting diffusion, which is not captured in the simpler model. can be interpolated for in between measurement points. The
procedure of extracting the parameters is explained in detail
in [6]. The results for the simple ECM in Figure 1(a) can be
seen in Figure 3.

D. Verification of electro-thermal model

The LIB is charged and discharged with a constant current
of 4 C (40.0 A) with the battery testing equipment, while in the
thermal setup as illustrated in Figure 2. An open-loop model is
developed in Matlab Simulink to mimic the behavior defined
by (1), including optionally both joule heat and entropy heat
from (2). The result from the simulation and measurements
is shown in Figure 8. An error analysis is performed using
root-mean-square on the difference between measurement and
simulation and presented in Figure 9.

E. Results
The total entropy potential, as shown in 5, has a very Fig. 3. Equivalent electrical internal resistance of the cell during 10-second,
distinct drop between 0-15 % SOC. This area is particularly 2 C discharge pulses. Parameters represent the R0 resistance in Figure 1(a).
interesting to study because it means that the entropy heat
at this operating point has the possibility to dominate the
joule heat. Similar results are theoretically reported in [5] and
measurements in [9] agree with our results. For a fixed current
and internal resistance, the relation between entropic heat and
joule heat can easily be theoretically established, as in Figure
6. Using (4), the net-zero heat current is calculated for a fixed
R0 at room temperature and shown in Figure 7.

IV. C ONCLUSIONS
In the experiments, it is shown how large influence the
entropy heat has on the net thermal development of the cell.
In the case of a high-power LIB, as theoretically shown here,
the cell can act net endothermic for a large portion of the SOC
window and for current up to 13.5 C. Similar experiments has
also been carried out in our lab on more energy-optimized cells
and the result are matching, but the currents are not as high
due to a relatively higher internal resistance.
Fig. 4. The process of establishing OCV vs SOC by averaging the two curves
Measurements to acquire the entropic coefficient are suc- from 0.1 C charge and discharge respectively. 0 and 100 % SOC is defined, in
cessfully carried out and the results presented in Figure 5. this scope, as where the average OCV line intersects the manufacturer voltage
limits
The shape and magnitude matches with what is reported
previously[5] in the literature for this specific LIB chemistry.
The results here have shown an alternative way of measuring
the entropic heat coefficient by sweeping voltage with a
high-precision potentiostat while keeping the cell temperature

(a) Cell setup (b) System setup Fig. 5. The established entropic heat potential for all temperatures and
all SOCs: T ∂U
∂T
in (2) for each temperature case. A negative entropic heat
Fig. 2. Cell setup (left) with thermal sensors and including the added copper potential together with a positive (charging) current leads to an endotermic
wire as a reference heat source. System setup (right) in thermal chamber with entropic heat reaction.
expanded polystyrene as thermal insulation around the cell.
 TABLE I. T HERMAL PARAMETERS IDENTIFIED FROM (1)
Parameter Value
q̇ 16.7 W
cp m 536 J/K
kA 0.167 W/K

Fig. 6. A simulation with entropy and joule losses compared. The highlighted
green areas are operating points where the cell has a net endothermic heat
development. Joule losses developed over R = 2.00 mΩ in this example
and all heat is calculated with a 20 A steady-state charge current, which
corresponds to C-rate of 2.0.

Fig. 9. An error analysis on the output showed in Figure 8. The running root-
mean-squared error is displayed for each combination of simulation output,
using the measurement as the reference signal.

constant, providing higher resolution over SOC than other

easily accessible methods.
In the verification step (Figure 8-9), it can clearly be seen
that the entropy heat explains fully why there is a asymmetry
in the temperature rise of the battery in two scenarios when
the LIB is charged and discharging with current of the same
magnitude. When using a simulation model with entropy heat,
and the parameters presented in Figure 5, the temperature
RMSE is reduced from 1.24◦ C to 0.35◦ C, a decrease to 28 %.
The discharge error is, under the same conditions, decreased
Fig. 7. Cell current where the net heat developed by the cell is zero according from 0.68◦ C to 0.30◦ C, a reduction down to 44 %.
to (4), i.e. entropic heat cancels the joule heat. The largest charging current
(positive) is 135 A at ca 5 % SOC and largest discharge current 66 A at ca The results show that it is highly relevant to include
80 % SOC. The joule heat is calculated using an Rtot of 2.00 mΩ, which is entropic heat while designing thermal models over LIBs, es-
measured for 10-second pulses at 25◦ C and an average value for all SOCs. pecially when the operation of the battery includes movement
over large SOC windows since the entropic heat coefficient
vary significantly over SOC. For small SOC windows and
repetitive alternating currents, the entropy change will cancel
itself within a time frame represented by a thermal time con-
stant, usually in the range of many minutes and few hours for
LIBs. The entropy information can be used to optimize charge
and discharge rate limiting strategies for all types of electrified
vehicles where the temperature of the battery is considered as
a performance limitation. A reason of why the entropy heat
have not been given much attention in the literature might be
that for many battery types it is an insignificant heat source
compared to the joule heat. With the latest commercially mass-
produced high-power LIBs, this is not the case as their internal
resistance is so small that the entropic heat is dominating
in many operating points. The magnitude of the entropic
coefficient varies with type of chemistry rather than geometry
and performance, as opposed to the joule losses. Cells with
Fig. 8. A comparison of the temperature rise between a thermal simulation graphite anodes typically have pronounced entropy effects, as
model and measurements. The simulation model is executed both with and opposed to those with lithium-titanium-oxide (LTO) anodes.
without the entropy heat component, keeping all other parameters the same.
The current used is 4.0 C and SOC window about 4 − 95 % Further on, a combination with lithium-cobalt oxide (LCO) as
cathode gives the strongest entropic effects for all common
LIBs on the market. The chemistry analyzed in this work,
NMC + Graphite, has a less pronounced entropic effect than
LCO + Graphite[5].
An apparent challenge to verify the entropic effect is the
challenge of measuring very small changes in temperature
within a time frame of seconds. The inherent high thermal
inertia posed by the large heat capacity of the cell, makes
temperature changes from entropic phenomenas very slow
and small. A better measurement setup and/or cell-internal
temperature probing might be needed to achieve more robust
results.
In excess of the thermal consequences of entropic heat, it
has apparent consequences on the OCV as well. Variation up to
35 mV are observed during OCV measurements between the
5◦ C and 45◦ C at low SOCs. At high SOC, a peak of 11 mV
of difference in the other direction can be observed at the
same temperature conditions. This information is very relevant
when designing a high-performance SOC estimator that relies
on voltage measurements, regardless of the secondary thermal
phenomenas.

ACKNOWLEDGMENT
This work is sponsored by the Swedish Governmental
Agency for Innovation Systems (VINNOVA).

R EFERENCES
[1] H. F. Gibbard, “Thermal properties of battery systems,” Journal of the
Electrochemical Society, vol. 125, no. 3, pp. 353–358, 1978.
[2] D. Bernardi, E. Pawlikowski, and J. Newman, “A general energy balance
for battery systems,” Journal of the electrochemical society, vol. 132,
no. 1, pp. 5–12, 1985.
[3] H. Vaidyanathan and G. Rao, “Electrical and thermal characteristics of
lithium-ion cells,” in Battery Conference on Applications and Advances,
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[4] C. Alaoui, “Solid-state thermal management for lithium-ion ev batteries,”
IEEE Transactions on Vehicular Technology, vol. 62, no. 1, pp. 98–107,
2013.
[5] V. V. Viswanathan, D. Choi, D. Wang, W. Xu, S. Towne, R. E.
Williford, J.-G. Zhang, J. Liu, and Z. Yang, “Effect of entropy change
of lithium intercalation in cathodes and anodes on li-ion battery thermal
management,” Journal of Power Sources, vol. 195, no. 11, pp. 3720–
3729, 2010.
[6] S. Skoog, “Parameterization of equivalent circuit models for high power
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[7] A. Jossen, “Fundamentals of battery dynamics,” Journal of Power
Sources, vol. 154, no. 2, pp. 530–538, 2006.
[8] C. Fleischer, W. Waag, H.-M. Heyn, and D. U. Sauer, “On-line adaptive
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Sources, vol. 260, pp. 276–291, 2014.
[9] C. Forgez, D. V. Do, G. Friedrich, M. Morcrette, and C. Delacourt,
“Thermal modeling of a cylindrical lifepo 4/graphite lithium-ion battery,”
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 Paper III
Experimental and model based evaluation of
mild hybrid fuel consumption gains and electric
machine utilization for personal vehicle application
Presented 2017-08-08 at
ITEC-AP2017, Harbin, China

Published 2017-10-26 in IEEE Xplore:

http://ieeexplore.ieee.org/document/8080842/

99
100
 Experimental and model based evaluation of mild
hybrid fuel consumption gains and electric machine
utilization for personal vehicle application
Stefan Skoog
Div. of Electrical Power Enegineering
Chalmers University of Technology, Gothenburg, Sweden
Email: stefan.skoog@chalmers.se

Abstract—A mild hybrid electric-diesel powertrain for personal driving with fast re-fueling through a widely standardized
vehicles is modeled with respect to longitudinal vehicle dynamics energy delivery network (i.e. fuel stations).
in real-world recorded drive cycles. The potential in terms of fuel
consumption reduction in an ideal P0 and P2 mild hybrid electric A. Motivation
system is evaluated in order to define the outer boundaries of how
much the hybrid topologies can offer. The results are compared In order to successfully design an automotive traction assist
with logged data from real-world driving with a prototype vehicle electric machine (EM), it is crucial to in detail understand
in rural/highway and city drive cycles. The near-ideal powertrain the intended operation, otherwise requiring an unnecessary
model based simulations offer higher fuel consumption reductions number of design iteration loops[8] or a compromise in end
than the prototype vehicle due to the ability of aggressively
shutting off the combustion engine during low power requests. system performance. A common way of designing electric
The largest reduction of fuel consumption calculated is 41% for a machines is with incremental improvements; to start with
P2 configuration in city driving with a micro hybrid topology as something known and tweak the geometry and performance
reference. While quantifying the potential gains from an ideal P2 until it fits the application with acceptable performance. The
system, the resulting load profile for the traction assist electric intent of this paper is to, instead, initiate a top-down approach;
machine is also extracted, giving valuable information for the
detailed design process of a such machine. Fast cranking of the to try to quantify the power requirements on the ideal traction-
combustion engine is a key feature for mild hybrids, torque and assist EM will behave in a mild hybrid system, serving as
energy requirements for this procedure is quantified: 1.1 kJ is input requirements for further design studies of EM, power
needed during 300 ms, which is also verified by measurements. electronics and energy storage. As a measure of finding EM
properties that gives compelling system properties, the vehicle
I. I NTRODUCTION
fuel consumption is compared as the figure of merit.
A very appealing topology is to combine the relatively
high efficiency of a diesel powered internal combustion en- B. Contributions of this work
gine (ICE) with a mild hybrid electric system, to offer a A model-based design of a parallel hybrid powertrain is
fuel efficient system both at high-speed and at transient city investigated, and its results is compared to log data from a
driving[1]. A general study about the effect of electrification prototype car equipped with a 48 V hybrid P0 mounted system.
through the deployment of a parallel hybrid powertrain in a The energy and torque cost of cranking is quantified and
personal vehicle is presented in [2] and [3], yielding promising put into relation to other hybrid features. Fuel consumption
results. In [4], a diesel powertrain is electrified with mild reductions are calculated and compared.
hybrid components offering large CO2 savings and using
drive cycle simulation and evaluation. Similar case with a C. Mild hybrid topology
small gasoline ICE is presented in [5] and [6], but the latter A mild hybrid electric powertrain is in this scope designed
without any quantified fuel or performance improvements. as a parallel hybrid with one EM assisting a diesel ICE. The
According to [7], 48 V P2 systems have the potential to be electric power distribution net is limited to 48 V and supported
very cost-effective solutions in increasing the drive cycle ef- by a high-performance lithium-ion battery. By assuming a
ficiency of combustion engine based powertrains compared to practical upper limit of ±310 A peak in the 48 V electric
the otherwise mainstream solution of incremental technology system, a peak power of ±15 kW is established, which is
enhancements of the combustion engine such as downsizing, an important key figure included in the definition of mild
overcharging and friction reduction of ICE components. While hybrid powertrain in this context. The EM is assumed to
plug-in hybrid end electric vehicle will most likely offer larger be a multiphase machine controlled by an adequately sized
environmental alleviations than mild hybrids during the use inverter capable of high-performance current feedback control.
phase, thy are not yet mature enough to reach appealing mass- The electrical round-trip system efficiency is assumed to be
market prices while maintaining the availability of long-range 90%. Different topologies for mild hybrids (P0, P1, P2) are
978-1-5386-2894-2/17/$31.00 c 2017 IEEE explained in[9] and [10]. Fig. 1 shows an overview of the
two configurations studied in this scope. C1 and C2 are A. Vehicle powertrain topologies and features
controlled clutches, which in the case of a P2 setup offers In order to quantify energy gains with the two different mild
the ability to disconnect the combustion engine and run solely hybrid topologies, a small number of features are specified as
on electric power for as long as the energy storage and power seen in Table I. One important differentiation between a P0
limits permits. Table I shows a summary of hybrid powertrain and a P2 topology is that the ICE friction losses makes the P0
features that can be expected from three different layouts. inappropriate to propel the vehicle with electric power only.
A micro hybrid is the baseline and represents most modern For the same reason, only a fraction of the regenerative power
premium cars today equipped with automatic start/stop of will be available during soft vehicle deceleration. Further on,
the ICE. A P0 mounted EM has the disadvantage of being the P2 hybrid assumes to have most of the essential vehicle
permanently connected to the crankshaft of the ICE, hence support functions transferred to electrical power, e.g. power
forced to overcome the considerable internal friction of the steering and brake servo. For a P0 hybrid, it is inconvenient
ICE during regeneration and motoring of the wheels. However, to shut off the ICE at higher speeds than 50 km/h due to
the P0 position offers significant benefits during installation these essential auxiliary loads. In the feature definition in
and integration of the powertrains from the vehicle OEM Table I, Torque (τ∗ ) and Power (P∗ ) refers to the request at
perspective, making it an attractive topology to implement the input of the gearbox seen from the ICE, and the speed
mild hybridisation. The P2 topology is the single-machine (v) is the linear vehicle speed. The ∗ in the table means very
setup that offers most functionality and the only setup within limited regeneration capabilities through the 12 V system. For
this scope that offers limited-power full hybrid features such all models, an ancillary average electrical load of 1.0 kW is
as electric driving and extensive regenerative braking. These assumed as a reference load to the hybrid functions, see Fig. 3.
features are summarised in Table I. ICE shutdown and re-start is assumed to be fast and seamless
in the simulation, however, a filter is implemented to guarantee
that the ICE is only shut down when it can remain so for the
upcoming two seconds.

ICE C1 C2 GB B. Internal Combustion Engine Modeling

The fuel consumption of the target vehicle’s five-cylinder in-
EM

DIFF

line diesel ICE is represented by proprietary fuel consumption

map supplied by the vehicle manufacturer. Maximum torque
EM

limits as well as internal friction maps are also represented,

P2 making the engine model work in two quadrants for positive
speeds. The negative torque component, corresponding to base
P0 friction in the engine, is an important factor during evaluation
of possible regenerative power, see Fig. 2.
Figure 1: Two parallel hybrid electric topologies suitable
for mild hybrids: P0 and P2 are possible positions for one C. Gearbox and its controller
electrical machine. C1,2 notes possible position of controlled A six-speed automatic gearbox is implemented together
clutches. with a controller. The efficiency is fixed at 94 %, which is in
line with the literature for similar systems[13], [14], [15]. The
gearbox controller consists of a rule-based approach which
II. M ODEL selects the gear that will put the ICE as close as possible to
A numerical model covering the fundamental longitudinal its ideal operating speed, given that it is able to supply the
vehicle dynamics of a typical personal vehicle using Matlab requested torque output and stay within an allowed band of
Simulink is utilized in this study. The concept is described rotational speed. The ideal operating speed is a fixed value as
in[11] and an open version of the toolbox is available[12]. The illustrated in Table II.
main inputs to the model is a driving cycle describing driving
speed versus time profile. For each component represented D. Electric Machine and Energy Storage
in the vehicle model, relevant speeds, torques and losses are The electric machine (EM) performance in the model is
calculated from input parameters. A backward model approach determined by two high-level parameters: The maximum
is used for simplicity, implying that for each sample point, power (EM Pmax ), and the field weakening range (EMFW R ). A
the requested drive cycle speed explicitly represent a vehicle P2 position implies direct coupling to the crankshaft, hence
force and hence an engine torque. This setup is suitable the rotational speed dynamics is closely coupled with the
for early concept studies when the component models only limitations in the ICE performance. The EM performance is
represent limited dynamics The backwards vehicle model does illustrated in Fig. 2 with the parameters from Table II. In
not require a driver model nor a vehicle feedback controller, the simulations, the EM is allowed an infinite energy storage.
as long as the requested speed profile is reasonably aggressive, At the end of the drive cycle, any energy deviation in the
which is the case during the used drive cycles. energy storage is converted to fuel, taking the drive cycle mean
efficiency of the ICE and the electrical efficiency into account.
This scheme represents an efficient predictive control of energy
storage charge balance.
E. Cranking and rotational inertia
The ICE can be shut down in order to save fuel otherwise
lost in idle losses. One of the major benefits with a mild
hybrid system is that the ICE can be re-activated automatically
fast enough without causing noticeable toque delays for most
drivers. In warm ICE conditions, a fast cranking of the com-
bustion engine requires an average torque τcrank to accelerate
the ICE and all ancillary rotating mechanical components from
standstill up to ignition speed ωi within target cranking time
tc . This includes overcoming internal friction in the ICE, τ f ,
as well as priming considerable rotating inertia I with kinetic
energy:
dω
τcrank = I +τf . (1) Figure 2: Overview of the torque requested from the ICE
dt
The total amount of energy needed to fulfil the crank Ecrank during driving of the city cycle according to P2 system
can be estimated assuming a linear increase of speed from 0 simulations. Only a small portion of the ICE rotational speed
to wi as dynamics is used due to an efficient gear shifting strategy. No
Z negative ICE torques appears due to immediate ICE shutdown
I ω2i tc I ω2i τ f ωi tc during braking.
Ecrank = + τ f ω dt = + . (2)
2 0 2 2
The model used for ICE is based on mean torque over one
combustion cycle, hence assuming a fixed number for the base and city driving as seen in Fig. 3. Each drive cycle is driven
friction τ f to overcome. The inertia of the ICE is assumed twice for micro hybrid and P0 hybrid reference measurements
as 60 gm2 , torque converter pump and impeller and flexplate and the repeatability is analysed for consistency. The logged
total 159 gm2 and lastly the EM rotor inertia translated to vehicle speed is used as input to the model based calculations
equivalent ICE inertia through the belt gearing: 12.7 gm2 . The for a fair comparison. The speed and aggressiveness of the
total crankshaft-equivalent inertia equals 0.232 kgm2 . For the logged drive cycles is comparable with official drive cycles
specific case of cranking, the inertia must be considered, how- such as Worldwide harmonized Light vehicles Test Procedure
ever, the rest of the vehicle model ignores rotating inertia with (WLTP) and New European Driving Cycle (NEDC).
the motivation that mass inertia of the vehicle is dominating IV. R ESULTS
the driving dynamics.
Despite allowing an infinite amount of energy buffer in the
III. T EST V EHICLE electrical distribution net, the limited power range and aggres-
A premium mid-size (C-segment) premium station wagon sive re-gen strategy, the energy storage energy buffer needed
with a five-cylinder 2.0 l diesel engine and a 6-way automatic is in the range of 1 MJ (0.28 kWh) when complemented with
gearbox is equipped with a 48 V mild hybrid system consisting a re-charge strategy as soon as the ICE is enabled by high
of a P0 mounted (see Fig. 1) EM with integrated controller propulsion power request by the drive cycle speed profile.
and inverter, a high-performance li-ion battery and a DC/DC However, the amount of energy turnaround during a drive cycle
converter. The ladder component replaces the task of a 12 V is many times the required capacity: 7.0 MJ (1.9 kWh) in P2
generator. The hybrid control system allows to emulate a base- highway/rural according to Fig. 3c. This makes the design
line micro hybrid for the sake of reference comparisons, which requirements of the energy storage quite different to those in
has been utilized to create the reference fuel consumption electric and plug-in electric vehicles.
presented in Table III. The vehicle is equipped with extensive The fuel savings for logged P0 and modeled P0 powertrain
logging capabilities concerning powertrain signals. For this presented in Table III are within 0.4 and 1.4 percent unit for
study, mainly the energy flow to and from the EM is studied. rural/highway and city cycle respectively. This is considered
The car model is design to represent the test vehicle and good modeled accuracy for such a complex mechatronic
the key properties for vehicle dynamics are summarized in system as a full car. However, the modelled controller allows
Table II. for much more aggressive start and stop of the ICE compared
to the real car, explaining the larger fuel saving for the
A. Drive Cycles model. The remarkable feature is, however, the P2 system
The expected driving behavior has a large impact on the performance in terms of fuel saving of 27% and 41% for
requirements on the design of the electric machine. The pro- rural/highway and city driving respectively. This is aligned
totype car is driven in two different drive cycles; rural/highway with previous reported results for a similar system running
 Table I: Hybrid topologies and features
Feature Micro hybrid Mild P0 Mild P2 Rule
Auto-crank X X X v < 10 km/h, τ∗ <= 0
Limited re-gen ∗ X X Pf < P∗ < PEMmax
Extensive re-gen - - X P∗ < 15 kW
ICE shutoff in speed - - X v > 50 km/h, τ∗ <= 0
E-driving - - X P∗ < 0.7 PEMmax

Table II: Vehicle specifications covered by the EM well, but the small glitch of uncovered,
Property Value low power request are likely missed due to the persistence
rule of not shutting down the ICE too often as explained in
Car weight 1700 kg
Section II-A. Lastly, each graph displays two extra spikes in
Aero drag (Cd A) 0.661
occurrence. The leftmost at full regenerative power is due
Rolling friction 0.009
to the EM is absorbing braking power at its power limits,
Wheel rolling radius 0.312 m
and the remaining is taken care of with friction brakes. The
ICE displacement 2.0 l
second spike in occurrence is due to the need of re-charging
ICE max torque 400 Nm
the energy storage once the ICE is enabled by the request of
ICE max power 140 kW
high propulsion power.
ICE idle speed 800 RPM
ICE ideal speed 1250 RPM A. Cranking and ICE base friction
ICE max speed 4700 RPM Assuming the ICE idle speed as ignition speed (wi =
ICE base friction 28 Nm 800 RPM = 83.8 rad/s), a target crank time duration
EM Pmax 15 kW tc = 300 ms, and an ICE base friction of τ f = 28 Nm, (1) yields
EMFW R 3.0 τcrank = 92.8 Nm using crank shaft reference frame, and (2)
equals 1166 J. Analysis of the logged data during cranking by
the 48 V EM results in cranking energies of 1060 ± 270 J (one
standard deviation). Hence, the base friction power of the ICE
NEDC[4], and for a gasoline engine in NEDC[3]. The large equals 2.35 kW at τ f ωi . Through the evaluation of the drive
savings can be adressed to the controllable clutch C1 in Fig. 1, cycles, the number of cranking events and the required energy
the ICE can be disconnected and disabled at any time during to support those are analyzed and presented in Table III. The
the drive cycle when it is not needed. The the mild hybrid accumulated crank energy over the drive cycle is too small to
system is able to propel the vehicle for the majority of the be displayed in Fig. 3 together with the other hybrid functions.
time in both drive cycles with the allowed 70% of EM max The mechanical energy needed to overcome engine friction
power (10.5 kW). The electrical energy needed to perform this at ICE idle speeds surpasses the cranking energy already after
work must be generated at the operating points when the ICE 0.50 seconds of stand-still. Ideally, it means that ICE shut-
need to start due to high propulsion demand, and the EM adds off should be utilized as soon as the control system can
a generator load of 37 Nm and 3.6 Nm for highway/rural and anticipate a driving situation where the ICE is not needed for
city cycle respectively. the next 0.5 seconds. At higher ICE speeds than idle with low
The decrease of fuel consumption is explained by two loads, the break-even shut-down can be even shorter due to
factors, using the ICE efficiency as a support variable. During higher friction losses, which motivates an aggressive strategy
idling (wheel axle propulsion request equals or below zero), of ICE shut-down. However, in the physical test vehicle, many
the propulsion efficiency of the ICE is per definition zero due obstacles exists which inhibits aggressive in-speed ICE shut-
to the need of overcoming considerable amounts of internal down.
friction. The mild hybrid system is able to eliminate the vast It is also obvious that the amount of energy needed to crank
majority of those operating points by immediately shutting the engine in speed is far below what can be recuperated within
down the ICE. Secondly, when the ICE is enabled due to high the same drive cycle: The extreme example is city driving: 202
propulsion demand, the load is higher due to the additional crank occurrences (7 times per minute of driving in average)
generator load to re-charge the energy storage, increasing consuming 214 kJ for a P2 model, while the ideal recuperation
average ICE efficiency generally. energy is 3.84 MJ: 18 times the needed cranking energy.
Fig. 4 shows the power profile of the P2 mounted EM
compared to the total requested propulsion power. The first V. C ONCLUSION
observation is that zero and very low power requests are the The results here shows that a mild hybrid system with a P2
most common operating points in drive cycles. Next, it can configuration has a large potential for energy saving, and even
be seen how efficiently the EM is capturing all braking power pure electric driving, if it is deliberately designed to overcome
within its operating range. Positive power requests are also functions that might otherwise inhibit the shutdown of the ICE.
 Table III: Hybrid topologies and features
Drive scenario Cranking Total crank Amount of time Fuel
instances energy with ICE off consumption
Micro hybrid log rural/highway 7 N/A 6.4 % 5.529 l/100 km
P0 log data rural/highway 6 6.36 kJ 4.8 % -5.92 %
P0 model rural/highway 25 26.5 kJ 15.0 % -6.30 %
P2 model rural/highway 163 173 kJ 69.1 % -26.7 %
Micro hybrid log city 13 N/A 8.4 % 7.217 l/100 km
P0 log data city 26 27.6 kJ 9.2 % -5.89 %
P0 model city 95 101 kJ 28.1 % -7.28 %
P2 model city 202 214 kJ 76.9 % -40.7 %

It makes sense from a fuel consumption perspective to, even [2] S. M. Lukic and A. Emadi, “Effects of drivetrain hybridization on fuel
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is likely the opposite. machine’s fuel saving potential in parallel hybrid drive trains,” in Electric
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challenging with respect to ancillary systems and transmission [4] D. Gagliardi and C. Wren, “diesel hybrid powertrain for passenger
systems, and the performance reserve required by the EM and light commercial vehicles,” MTZ worldwide eMagazine, vol. 72,
no. 3, pp. 4–10, 2011. [Online]. Available: http://dx.doi.org/10.1365/
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study. Especially the transmission system control need to be and power net architectures,” MTZ worldwide, vol. 77, no. 9, pp. 48–53,
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optimized to take advantage of the EM properties instead of [6] Z. Yafu and C. Cheng, “Study on the powertrain for isg mild hybrid
only focusing on supporting limitations of the ICE. Further on, electric vehicle,” in Vehicle Power and Propulsion Conference, 2008.
to maximise the regenerative braking, an intelligent blending VPPC’08. IEEE. IEEE, 2008, pp. 1–5.
[7] J. M. German, “Hybrid electric vehicles, technology development and
system between EM and friction brakes is needed, which is cost reduction,” International Council on Clean Transportation, vol. 1,
hard to implement in real vehicles, but very easy in models. 2005.
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dissertation, Lund University, Lund, Sweden, 2014. [Online]. Available:
consumption, although it should be noted that some aspects http://www.iea.lth.se/publications/Theses/LTH-IEA-1072.pdf
of the strategy might be in conflict with minimum emissions [9] Y. Yang, X. Hu, H. Pei, and Z. Peng, “Comparison of power-split and
or perceived driving performance[16]. parallel hybrid powertrain architectures with a single electric machine:
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functions, in our case 1 kW, can be absorbed by maximising [10] M. U. Lampérth, A. C. Malloy, A. Mlot, and M. Cordner, “Assessment of
the regenerative braking capabilities. This is only possible axial flux motor technology for hybrid powertrain integration,” EVS28,
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ICE disconnect-and-shutdown control strategy with the options 2007, vol. 1.
considered here. The remaining energy needed to propel [12] L. Guzzella and A. Amstutz, “The qss-toolbox v2.0.1,” http://www.idsc.
ethz.ch/research-guzzella-onder/downloads.html, accessed March, 2017.
the vehicle electrically during ICE off mode can easily be [13] A. Irimescu, L. Mihon, and G. Pãdure, “Automotive transmission
replenished through an added generator load once the ICE efficiency measurement using a chassis dynamometer,” International
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[14] D. H. Park, T. S. Seo, D. G. Lim, and H. B. Cho, “Theoretical investiga-
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 (a)

(b) (a)

(c)

(b)
Figure 4: Power distribution during entire drive cycle for
highway/urban (a) and city (b). The green background data
is requested propulsion power by the vehicle in order to fulfil
the drive cycle speed profile. The orange data is requested
power by the P2 mounted EM.
(d)
Figure 3: Speed profile for the two logged driving cycles ru-
ral/highway (a) and city (b) and their corresponding electrical
energy profile (c) and (d). The speed profile is marked with the
instances the ICE is needed to operate in P0 and P2 modelled
topologies.
 Paper IV
Parameterization of linear equivalent circuit models
over wide temperature and SOC span for
automotive lithium-ion cells
using electrochemical impedance spectroscopy
Submitted 2016-10-06 to Elsevier Journal of Energy Storage
Published in Volume 14, Part 1, December 2017
Published 2017-09-22 in ScienceDirect:
https://doi.org/10.1016/j.est.2017.08.004

First author contributions

Idea generation, experiment design, paper structure and content,
data processing and analysis, figure generation, corresponding author.
Second author contributions
Data acquisition, EIS data analysis, model fitting and plots.

107
108
 Parametrization of Linear Equivalent Circuit Models
over Wide Temperature and SOC spans for Automotive
Lithium-Ion Cells using Electrochemical Impedance
Spectroscopy
Stefan Skooga,∗, Sandeep Davida
a
Electric Power Engineering,
Chalmers University of Technology,
Horsalsvagen 11, 412 96 Gothenburg, Sweden

Abstract

Three different types of automotive lithium-ion pouch cells are analyzed

with electrochemical impedance spectroscopy over a wide range of operat-
ing points in SOC (10-90 %) and temperature (-10 to +40◦ C) with the goal
of establishing parameters for an accurate linear equivalent circuit model.
The impedance vs frequency is analyzed and attributed to physical behav-
iors from current collectors, electrode and electrolyte, charge transfer and
diffusion. The change of resistance is statistically analyzed as a function of
SOC and temperature in an effort to quantify if there is any monotonic pat-
terns. Results show that the charge transfer resistance versus temperature
represent the largest relative change of resistance, followed by diffusion re-
sistance versus temperature and the electrolyte resistance over temperature.
Only weak correlations with resistance versus SOC are found irregardless of

∗
Corresponding author
Email address: stefan.skoog@chalmers.se (Stefan Skoog)

Preprint submitted to Energy Storage March 6, 2017

frequency range. Frequency-domain fitted equivalent circuit model parame-
ters are evaluated by comparison of physical measurements in long dynamic
load cycles using root-mean-squared of the voltage error between model and
physical measurements as performance index. A simple R+2RC model cap-
turing diffusion dynamics performs best at RMSE 15.46 mV , better than
most similar studies and better than the more complex R + 6RC also evalu-
ated.
Keywords: Battery impedance, Electric impedance spectroscopy,
Automotive lithium ion battery, Equivalent circuit model, Charge transfer

1. Introduction

1.1. Background

Vehicle electrification is a powerful method of reducing greenhouse gases

emissions while preserving the availability of personal mobility. A key com-
ponent in an electric or hybrid electric vehicle is the Energy Storage System
(ESS), which in most modern cases is constructed by a plurality of lithium
ion cells forming a Lithium Ion Battery (LIB). An important challenge in mo-
bility applications is to maximise the reliability and electrical performance
of the LIB at the same time as minimising the size and weight. The vehicle
installation cost of a LIB can be kept at competitive levels if the number
of cells as well as the size of each cell is kept at its minimum for the given
use case. In order to optimize the electrical usage of the battery in terms of
power and allowed energy window during the design process, a model based
design methodology is advantageous. Selecting the right model and popu-
lating it with parameters through reference measurements is critical for the

2
design process of the ESS. Knowing how the battery cells will behave as an
electrical component over a wide range of temperatures and State of Charge
(SOC) levels is therefore very relevant early in the design process. When
the LIB is operating in the vehicle, an on-line Battery Management System
(BMS) must be employed in order to guarantee safety and preservation of
performance of the cells. Real-time, accurate electric models are needed to
execute as a part of the BMS software to fulfil its objectives.
Equivalent Circuit Models (ECMs) are commonly used to represent the
electrochemical behavior of a LIB. ECMs are suitable as an alternative to
physics-based partial-differential equation (PDE) modeling. If the elements
in the ECM are chosen as standard linear elements, and its parameters stored
in look-up-tables (LUT) or simplified linear relationships, they are much more
suitable to run on-line in vehicle applications for the purpose of estimating
SOC and maximum power. One challenge with this setup is to keep the
complexity of the parameters on a reasonable level, as they vary with fre-
quency, temperature and SOC as shown in this study. Even though ECMs
would normally be considered as black-box models without any physical rep-
resentation of its parameters, careful investigation and analysis can lead to
connecting the circuit elements to the electrochemical properties of the cell.
Electrochemical Impedance Spectroscopy (EIS) is a powerful, non-invasive
method of measuring the internal impedance of a LIB. The data acquired
from EIS can be analyzed and used to populate circuit elements in ECMs in
parallel with identifying high-level electrochemical phenomena. An obvious
challenge for real-time implementation is the balance between complexity of
the model (execution time) and the amount of parameters stored in look-up

3
tables (storage memory).

1.2. Previous work

EIS has been used for LIBs previously in the literature for various pur-
poses. A nice introduction to EIS for the purpose of analyzing LIBs can be
found in [1, 2, 3, 4, 5]. Fitting EIS data to ECMs are discussed in [6, 1] for
linear models and [7, 8, 5, 1] for non-linear models. A comprehensive review
of utilizing EIS for LIB state-estimation can be found in [9, 10]. However,
there is room for debate in the literature between the complexity of the ECM
used and the performance in terms of minimizing the estimated mean voltage
error of the LIB model.
Low temperature performance of LIBs have been investigated in [11, 12],
and specifically for NMC/G in [13]. An overview of the specifics of charge
transfer dynamics for a few variants of LIBs is presented in [11]. However,
little information is found about the electrolyte and diffusion dynamics for
commercial cells as a function of temperature.
Ageing is not considered in our scope, however, good sources for impedance
implications of ageing in high-performance lithium-ion cells in automotive
applications exist for NMC[14, 15], LFP[16], LNO[17], LTO[18]. Also, spe-
cific calendar ageing for several commercially available cell types (NMC,
LMO/NMC, NCA, LFP) are evaluated in [19].
In [14], measurements on high-performance automotive cells and their
change in impedance over large variations in both state of charge and tem-
perature are evaluated. It is, however, still rare in the literature to present
results on different variants within the lithium-ion family of batteries, using
the same methods, analysis and tools to measure impedance, acquire ECM

4
parameters and state estimation. Due to the high sensitiveness of EIS equip-
ment, it is according to our understanding and experience hard to compare
measurement results from different labs using slightly different methods and
machinery.

1.3. Contributions of this paper

1. Measurement and analysis of LIB impedance behavior over a wide range
of frequencies (10 mHz to 10 kHz), SOC (10-90 %) and temperatures
(-10 to +40◦ C) relevant for automotive usage
2. Performance comparison of three mass-produced automotive LIBs, us-
ing identical methods and evaluation techniques
3. Quantification of the impact from SOC and temperature on resistance,
and addressing it to the three main physical phenomena simplified
through frequency range decomposition: Electrolyte, Charge Transfer
and Diffusion
4. Parametrisation of linear ECMs through EIS measurements, validation
of model error through long drive cycles with successful results com-
pared to literature.

2. Cell impedance modelling in the frequency domain

2.1. Electrochemical Impedance Spectroscopy (EIS)

EIS is a valuable tool for non-destructively observing and quantifying var-
ious phenomena occurring within a electrochemical cell. It involves imposing
a small sinusoidal voltage at a given frequency on the cell, while measuring
the resulting current. With the fair assumption of a linear impedance re-
sponse, the fundamental impedance signal with both phase and magnitude

5
Figure 1: Linear equivalent circuit model used to fit the measured impedance of the cells.
By including only a sub-set of the RL adn CL links, the two models used in this tudy can
be formed. The blue curve is a measurement from cell A at 51 % SOC, 24◦ C

can be extracted for any given excitation frequency. By sequentially applying

a wide range of frequencies, normally a few millihertz to a few kilohertz, a
characteristic impedance spectrum can be obtained and illustrated through
a parametric frequency response plot (Nyquist plot), see Figure 1 on page
6. This method is time consuming but can be automated with modern tools
and equipment.
An ECMs structure using a plurality of linear circuit elements to mimic
the measured frequency response from LIBs is also illustrated in Figure 1

6
on page 6. Several circuit elements are generally needed in order to cover
the wide frequency dynamics of LIBs. Both linear and non-linear circuit
elements can be used to model the behavior depicted by the spectroscopy
measurements.

2.2. Linear vs non-linear models for the frequency domain

While trying to design ECMs which replicate EIS measurements accu-

rately in the frequency domain, researchers generally include at handful of
Zarc elements. Each Zarc element consists of a Constant Phase Element
(CPE) in parallel with a resistor[7, 12, 16, 15]. The resulting non-linear
models used in the frequency domain are not trivial to transfer in time-
domain simulations. Approximation using several linear elements can be
used[7, 1, 4]. In order to be able to use detailed models on-line in vehicle
battery-management systems, it is favorable to keep them simple with as few
parameters as necessary. However there is no accurate and simple represen-
tation of CPEs in the time domain and therefore most researchers utilizing
EIS find it hard to physically interpret their results, especially at lower fre-
quencies (below 2 Hz). Understanding cell behavior from EIS measurements
at lower frequencies is crucial for automotive applications where drive cycles
which typically lasts dozens of minutes.

Buller[4] found that it is possible to find approximations for a Zarc using

only resistive (R) and capacitive (C) elements. He suggests both five RC and
three RC link based networks whose values when chosen suitably become
equivalent to a Zarc. The five RC link based model is more accurate in the
frequency domain, but the three RC link based one is more computationally

7
efficient since it involved lesser number of parameters. In addition, Buller
validates both models in his work and suggests that the three RC network is
recommended as the general simulation tool for replicating the behavior of
a Zarc. With these conclusions, our template for a general ECM as shown
in Figure 1 on page 6 consists of six RC links in total, wherein links 1 to 3
are used to model the mid frequency range and links 4 up to 6 are used to
model the low frequency range. This R + 6RC model is an approximation of
a 2-Zarc circuit.

The resulting six RC link based ECM still contains a lot of information if
one consider that all the parameters can depend on both SOC and temper-
ature, and according to some studies, also current[9, 4]. In [7], the authors
introduce a simple ECM based on three RC links. Their work concludes
that even though their simple ECM is not able to accurately reproduce the
impedance in the frequency domain, it performs very well in predicting cell
voltage and cell performance in the time domain. Working along the simi-
lar lines of linear simplified ECMs, a further simplified R + 2RC link based
model is proposed in this paper, wherein a fixed resistance RDC and two
RC links are together used to represent the EIS measurements at low fre-
quencies alone, since frequencies higher than 2 Hz are not very relevant in
automotive applications. Here, the first three RC links from the R + 6RC
model are removed and their resistances alone are added to the value of the
ohmic resistance, so that the previously denoted R0 is replaced by RDC . The
capacitances which are associated with the first three links are representa-
tive of the double layer capacitance (Cdl ) [16, 15] and charge transfer, and

8
are neglected in this simplified low-frequency model. Time constants of the
diffusion dynamics in the cell are significantly slower than the double layer
and charge transfer dynamics, but matches better with the fundamental fre-
quency content of automotive drive cycles. Hence two RC links are dedicated
to replicate this region of the spectra. The proposed simplified ECM con-
sisting of a series combination of a single resistor and a pair of RC links is
commonly referred to as the dual polarisation (DP) model. The DP model is
generally parametrised using time domain techniques such as pulse testing.
However the contribution from this paper is using EIS data within a limit
frequency range from the spectra to parametrise it.

2.3. Comparing impedance points

When comparing impedance points of interest within a cell for different

operating points (SOC, temperature), a statistical approach is used using
the arithmetical mean (µ) and the associated standard deviation, which is
defined for N number of xi individual sample values as
v
u N
u 1 X
σ=t (xi − µ)2 . (1)
N − 1 i=1

2.4. Quantifying model-fitting

In order to quantify the model fit or in other words the error between
the measured (xi ) and modelled (x̂i ) results, the root-mean-squared error
(RMSE) is calculated as
v
u N
u1 X
RM SE = t (x̂i − xi )2 . (2)
N i=1

9
3. Measurements

3.1. Test setup

All measurements are performed on single li-ion cells. Three different,
automotive classed, high-performance li-ion cells are evaluated. All of them
are pouch form factor with both tabs on a short side of the pouch. The
list of the Devices Under Test (DUT) for the experiments performed in this
paper, together with their basic properties is shown in Table 1 on page 10.
Unfortunately, only a limited set of data can be shared about the cells due to
supplier confidentiality. Previous ageing of these cells is limited to calendar
ageing during storage. Apart from that, the cells are assumed to be at their
beginning of life state, and no considerations have been done to address the
aging effects into the interpretations of our measurements.
EIS measurements on the selected cells are performed using a high-precision
potentiostat; Gamry Reference 3000. The thermal chamber used is a Pol-Eko
ILW53. High current tests are done with a Digatron BTS-500.

Table 1: Test objects used

DUT Capacity [Ah] Nominal Voltage [V] Form factor Chemistry

A 30.0 3.7 Pouch NMC/G

B 25.7 3.7 Pouch NMC+LMO/G
C 19.5 3.3 Pouch LFP/G

3.2. Procedure
EIS is performed with 61 frequency points distributed evenly in a log-
arithmic scale between 10 mHz to 10 kHz. The potentiostat excitation is

10
typically 1.5-2.0 mV RMS and below 3 A. Before the EIS experiments, the
cells to be tested were subjected to basic forming which consisted of at least
10 full charge-discharge cycles at 1 C at room temperature. Each EIS sweep
is performed at about 12 SOC points per temperature, and for ca 7 different
temperatures between -10◦ C and +40◦ C for each cell, resulting in 259 EIS
curves, in total 16000 individual impedance sampling points.
Before each experiment, the cell is placed in a dedicated holder and then
housed in the thermal chamber, which maintains the desired temperature,
and is allowed up to six hours of rest to ensure thermal equilibrium. A
constant-current charge/discharge at C/10 is performed to reach either the
upper or lower voltage limits specified by the cell supplier. An electrical
resting period of 30 minutes is necessary before the actual EIS sweep starts.
After each frequency sweep, the cell is charged or discharged at C/10 to
reach a new desired SOC level, and then again rested for 30 minutes, and the
sequence of tests is repeated until it reaches the cut-off voltage. EIS sweeps
are subsequently alternated between high SOC to low and from low to high
between different temperature set points, which saves test time. Since the
capacity is expected to change slightly with temperature, a new SOC and
capacity was estimated and corrected for each sweep by automated scripts
by correlating the Open Circuit Voltage (OCV) measurements.
The geometric details of the electrodes are identified by, after the com-
pletion of all electrical test, opening up the cell packages and measure the
sizes of the current collectors with a micro meter.

11
4. Analysis

All EIS measurements share a similar impedance behavior, as can be seen

in Figure 1 on page 6. The general behavior as an inductance (Im(Z) > 0)
at higher frequencies, above 1 kHz, arise mainly from geometrical proper-
ties of the electrodes. For medium frequencies, 1-1000 Hz, a half-circle in
the complex impedance plane is generally found that originates from double
layer effect such as charge transfer in the electrodes[2], which originates from
porous electrodes[20]. Only one half circle is observed in all test cases in
this study. From the literature, some cells display one smaller and one larger
half-circle in this frequency range, where the smaller half-circle originate from
SEI layer effects on one of the electrodes [3, 15]. For warmer temperatures,
above 30◦ C, the only half-circle observed is generally so depressed that it is
indistinguishable from other impedance patterns and not easily identifiable
with the methods used here.
After the charge transfer half-circle, moving down in frequency and to
the right in the complex impedance plane, a tail shows up which seems
to be growing with an angle approximately at 45 degrees until the lowest
measurement frequency occurs, in our case 10 mHz. Mass transport such
as ion diffusion is responsible for the sloping tail behavior. The frequencies
and the absolute impedance values of where all of these typical phenomenas
occurs depends strongly on temperature and weakly on SOC.

4.1. Points of interest

An effort has been made in order to quantify the SOC and tempera-
ture dependence of the impedance for all cells specified in this work. For

12
all measurements, the most interesting points in the impedance spectrum
have been automatically identified and analyzed. Each impedance point (Z)
contains information of frequency (f ), resistance (r = Re(Z)) and reactance
(x = Im(Z)). Re and Im symbolizes, respectively, the real and the imag-
inary operator on an impedance (Z) represented by a complex number. In
a similar fashion, ra represent the real (resistive) part of Za , which in hand
represents the impedance at frequency point a. The points of interests are
graphically represented in Figure 2 on page 16 and are explained here:

• Zcc
The resistance of the metal parts of the electrodes; the current col-
lectors. In this study, this resistance cannot be measured separately
but is instead modeled from the known geometry of the electrodes, see
section 4.2.

• Za
Minimum resistance measurement point, occurs typically around 1-
3 kHz according to our experience. The resistance at this point is
physically represented by the contact resistance in the current collectors
(rcc ), the electrode active material, separator and the electrolyte [11, 3].
For ECMs including high frequency dynamics, this point should be
used to extract the minimum resistance while simultaneously respect-
ing the resistance contributed from equivalent capacitors and inductor
networks. It is identified in the EIS sweep as min(Re(Z))

• Zb
Zero-reactance point. This is the only point within the evaluated fre-

13
 quency range where the impedance crosses the imaginary axis, i.e.
translates from inductive to capacitive behavior with decreasing fre-
quency. Many ECMs in the literature focus on low to medium frequen-
cies use this point as the lowest resistance. This point is also often
referred to as RΩ by others. Identified as Im(Z) = 0.

• Zc
The local maximum in (capacitive) reactance for the charge transfer
half-circle. This points does not exist for all cells at all temperatures,
but it is generally prevalent at room temperatures and below. The
physics behind this point is impedance in SEI layer and charge transfer
impedance which occurs when the Li+ ions move from the electrolyte
to the electrode[11]. Identified as max(−Im(Z)), f (b) < f (c) < f (d).

• Zd
Local minimum (reactance) of charge transfer half-circle. This valley
in the complex impedance plane is usually wide from a frequency per-
spective, where a lot of EIS sampling points are focused. It physically
represent the transition between double layer effects and mass transport
effects and it is known to vary widely with temperature and age[15].
Identified as min(−Im(Z)), f (d) < f (c).

• Ze
This point is a fixed-frequency point rather than coupled to a specific
physical phenomena or breakpoint. The 100 mHz impedance can be
of significance for rudimentary Thevenin-based ECMs comprising of
only one internal resistance. This would represent the fundamental

14
 frequency of a 10-second current pulse. The 10 second time window
is particularly interesting in vehicle applications since it represents the
length of a typical acceleration or deceleration of the vehicle. Since this
is a fixed-frequency point, it might end up en either side of point d in
the Nyquist diagram depending on temperature and SOC of the cell.

• Zf
The slow-diffusion impedance is interesting particularly when compared
in relation to point d. The slope and length of the diffusion tail typically
varies with SOC and temperature. The point is identified as min(f ),
in our case 10 mHz.

In addition to the measurement points, composite variables are formed

that will form the basis of our analysis.

• rele = ra − rcc
This represents the resistance in the electrolyte, SEI layer and active
material in the electrodes. It is based on the minimum-resistance mea-
surements in point a, but with the modeled current collector metallic
resistance subtracted.

• rct = rd − ra
Charge transfer resistance isdefined as the diameter of the half-circle
along the real axis in the Nyquist diagram[21, 10].

• rdif f = rf − rd
The resistance of the diffusion tail is formed by taking the difference
between the lowest frequency impedance measurement (point f) and
the end of the charge transfer half-circle (point d).

15
 f
rct
r0
c

rcc rele e
d
b

a rdiff

Figure 2: Point of interests on a typical EIS sweep. Measurement are for cell B at 41 %
SOC and 6 ◦ C with linear interpolation between sample points.

4.2. Electrode and Current Collector

As mentioned in section 4.1, the current collectors constitute a part of the

measured ra resistance. By analyzing the internal geometry of the DUTs and
assuming an even current distribution along the current collector, the resis-
tance for the current collectors (rcc ) can be estimated. It is assumed in this
scope that the current collectors have no impedance change with the level
of charge in the cell and no impedance change over the relevant frequency
range. The exact sizes of the current collectors used for calculation cannot
be disclosed due to discretion of the manufacturers. However, common thick-
nesses for automotive pouch cells is 20 µm for positive aluminum cathode[22]
and 12 - 14 µm for negative copper anode[23, 22] are relevant numbers to
use. Dozens of layers of full electrochemical cells are usually stacked within

16
one pouch, forming many parallel strands of individual current collectors.
The temperature dependence of the current collectors are included in the
resistance estimation as

l  
rcc = ρ20 1 + α20 (T − 20) , (3)
As

where ρ20 is the material resistivity at 20◦ C, l is the equivalent length of

the current conductor, A the cross section area, s the number of stacked
full-cells in one pouch package, α20 the material temperature coefficient at
20◦ C, and T is the material temperature. For the two relevant materials,
ρ20 = 4.30 · 10−3 K −1 and ρ20 = 3.90 · 10−3 K −1 are used for aluminum and
copper respectively. The material resistivity numbers used are 2.65·10−8 Ωm
and 1.72 · 10−8 Ωm for aluminum and copper respectively. For the equivalent
length, it is assumed that half of the current collector height is effectively
used to transport current to the tab(s). Since two full cells inside a typical
pouch cells share one electrode and current collector, the effective thickness is
halved in the calculation of the cross area A. The calculated current collector
resistance at room temperature constitutes about 19 % of the total measured
ra .

4.3. Diffusion resistance

The difference in resistance between the 10 mHz sample point f and

the end of charge transfer point d in Figure 2 on page 16 symbolises the
isolated diffusion resistance of the cell: rdif f . Analysing the impedance trend
of point f only gives little understanding of diffusion dynamics, since the
charge transfer dynamics rct is dominating for most operating points.

17
 (a) Cell B at 49.3 ± 1.61 % SOC (b) Cell C at 49.4 ± 3.02 % SOC

Figure 3: Resistance measurements for point of interest a,d and f. Charge transfer can
also be found in this diagram as rd - ra .

The diffusion phenomena forms as the mobility of ions in the electrochem-

ical cell is limited. The longer a charge or discharge pulse is applied (i.e. lower
fundamental excitation frequency), the further the movement needed for the
average ion to form the necessary reactions. Example results are shown in
Figure 3 on page 18 for cell B and C, which have quite different absolute
magnitudes of resistance despite being similar rated in charge capacity and
power. It can be seen that the magnitude of diffusion resistance is in the
same range as the minimum resistance measured at point a. The tempera-
ture has very small influence on the resistive part of the diffusion impedance,
although in closer analysis the temperature dependence in clearly according
to an Arrhenius behavior with a negative temperature correlation.

18
4.4. Relative resistance change

In order to analyze and quantify how much temperature and SOC is

contributing to the change of resistance, a relative increase scenario is set
up. The operating point of 24◦ C and 50 % SOC is selected as the reference
and from here the relative change of resistance is calculated for all compos-
ite resistances; rcc , relec , rct and rdif f . All measurement values outside the
SOC window 10-90 % are disregarded as they are not very relevant operating
points for normal automotive usage and it is known that resistance and reac-
tance increases drastically at these extreme points. Four specific operating
points are selected to analyze the impact of temperature and SOC: 10 %,
90 %, -10◦ C and +40◦ C. For each operating points, the arithmetic mean and
the standard deviation from (1) is calculated with all available measurement
points in order to differentiate measurement noise from variable relation. An
example of the process is shown in Figure 4 on page 20. In this example,
it also be seen that the SOC has an impact as the resistance monotonically
decreases with increasing SOC for rct (Figure 4a). It can also be seen that
temperature has the largest impact on resistance change for rct , irregardless
of SOC level. For diffusion resistance, rdif f as seen in Figure 4b on page
20, resistance increase for low temperatures is unambiguous. Diffusion re-
sistance versus SOC, however, has only a weak trend flawed with random
measurement noise. The process of isolating operating points in this manner
is repeated for all cells and all composite resistances and displayed in Figure
6 on page 23. Bars represents the mean value (µ) and error bars indicate one
standard deviation (±σ) as defined in (1).

19
 (a) Cell B: rct

(b) Cell B: rdif f

Figure 4: Statistical analysis relative change for rct and rdif f . 24◦ C and 50 % is the
reference operating points. The measurement points closest to 10 %, 90 %, -10◦ C and
+40◦ C are selected (cross marked) to be included in the mean and standard deviation
calculations.

20
4.5. Analysis Results

Plotting the absolute resistance for the different regions, as showed in

Figure 2 on page 16, per cell and temperature gives an overview that clearly
shows how the charge transfer resistance is negligible at the higher temper-
atures, see Figure 5 on page 22. However, at 0◦ C and below, the charge
transfer resistance is dominant. Figure 6 on page 23 shows that for some of
the trends, there is no simple relation between resistance, SOC and temper-
ature, or the measurement noise is larger than the trend, indicated by very
large error bars. Trends for cell A (not displayed here) are aligned with cell
B (Figure 6a on page 23).
Current collector resistance (rcc ), represented by the metallic tempera-
ture coefficient in the non-chemically active parts of the electrodes, has the
smallest impact over the measured temperature span for all cells. Since it is
ideally modeled, there is no error bars included in the displayed data.
Minimum-resistance point ra ha a small, but vaguely significant impact
from SOC. However, a significant impact from temperature, increasing typi-
cally 20-50 % at -10◦ C compared to the reference at 24◦ C.
Charge transfer resistance, rct , shows large and significant change of both
SOC and temperature. rct is decreasing with increasing SOC for all cells. The
largest impact is from temperature, where rct increases with 1500-3300 %
from 24◦ C to -10◦ C. At higher temperatures, the resistance typically de-
creases to a degree where it virtually disappears in comparison to the other
resistances.
Diffusion resistance, rdif f has no statistically significant correlation with
SOC when looking over all the battery types. There is a clear resistance

21
Figure 5: Distribution of absolute resistance between the defined circuit elements at 50 %
SOC, for all three cells. The y axis is broken to capture the large difference between rct
and the other elements at low temperatures. Cell A has an extended temperature range
of 49◦ C compared to the other cells.

decrease with increasing temperature. rdif f can be 20-200 % higher at -10◦ C

than at reference room temperature.

5. Model fitting

As described in Section 2, the two approaches to linear model fitting of

the frequency domain impedance data is to use R + 2RC and R + 6RC based
models. The ECMs are fitted to the measured data in the frequency domain
using numerical optimization in MATLAB. For each spectrum, a nonlinear
curve-fitting optimization based on the method of least-squares was used.

22
 (a) Cell B

(b) Cell C

Figure 6: Analysis results of relative resistance change with 24◦ C and 50 % SOC as
reference point for each cell individually. Legend order from left to right in each bar
group: Rcc , Ra , Rct , Rdif f . Error bars show ±1 standard deviation.

23
The estimated parameters are then implemented into the corresponding cell
model, verified in the frequency domain and finally validated through a time-
domain drive cycle test. Figure 7 on page 25 shows a few examples of the
accuracy of impedance replication of the models to the original measurement
data. The RMSE of the impedance is used to quantify the accuracy of
the model in the frequency domain. The R + 6RC based model results in
a RMSE of 610 µΩ over the SOC and temperature range covered in the
tests. For the R + 2RC or DP model, upper frequency range is limited to
2 Hz considering the intended usage in vehicle applications. This type of
confined model, wherein the effort was made only to characterise the low
frequency aspects of the cell behaviour results in RMSE of 970 µΩ. It is
evident that the R + 2RC model performance much worse when trying to
reproduce the spectra. The RMSE based verification in the frequency domain
still showed that the parametrised ECMs could be further used for validation
with automotive drive cycles in the time domain. The RMSE values can be
compared with measured re (100 mHz resistance) at 24◦ C and 50 % SOC for
cell B and cell C respectively: 1.26 mΩ and 1.96 mΩ.

6. Model validation in time domain

Since there is a lack of established dynamic load cycles to be performed

on automotive cells on cell level, a combination of load cycles for performance
test defined in [24] are used. Physical tests are performed with cell B and
cell C at 8◦ C and 24◦ C in a climate chamber with forced air ventilation. An
additional large thermal mass in the form of a aluminum cell holder firmly
attached to the cell body in order to keep the temperature variations to

24
 -1.5 -1.5
8°C Fitted 8°C Fitted
8°C Measured 8°C Measured
24°C Fitted 24°C Fitted
24°C Measured 24°C Measured
-1 -1

-0.5 -0.5
Im(Z) [mOhm]

Im(Z) [mOhm]
0 0

0.5 0.5

1 1
0.5 1 1.5 2 2.5 3 0.5 1 1.5 2 2.5 3
Re(Z) [mOhm] Re(Z) [mOhm]

Figure 7: Model fitting with measurement data in the frequency domain using the R+6RC
model (left) and R + 2RC model (right). Data used is with reference to cell B at 50 %
SOC at two different temperatures

a low level. The cells starts at 90 % SOC and are loaded with dynamic
power profile, charge depletion from the profile P HEV min until a SOC
of about 20 % is reached. At this point, the battery tester switches to a
charge sustaining profile. The power level of the load cycles is scaled to
the maximum power the cells can handle during all operating points in the
test, according to the cell supplier, see Table 2 on page 26. The total load
cycle is just short of 100 minutes long. The cell test equipment records
voltage, current and temperature. The recorded current is fed into a Matlab
Simulink model corresponding to the three ECMs studied. In addition to the
two explained in Section 5, a rudimentary Thevenin model is also included in
the comparison, where the R10 value is extracted from point e (Figure 2 on
page 16 and Section 4.1) as a function of SOC for the relevant temperature.
An example of the load cycle results is shown in Figure 8 on page 27. The
final results in terms of maximum instantaneous voltage error estimation

25
between model and measurements, as well as the final RMSE according to
(2) is summarized in Table 2 on page 26, where the resulting errors can be
compared with similar studies.

Table 2: Setup and results from validation load cycle from this study (upper part) and
comparable RMS voltage errors from similar studies (lower part).

Test object Temp [◦ C] Power [W ] ECM max(E) [mV ] RMSE [mV ]

R10 160.3 33.38

B 24 630 R + 2RC 89.15 15.46
R + 6RC 108.2 18.77
R10 192.9 33.93
C 24 500 R + 2RC 139.3 20.31
R + 6RC 158.1 24.58

Source Method ECM max(E) [mV ] RMSE [mV ]

[10] Self-calibrating Non-linear R+2RC - 63

[25] Pulse Linear R+2RC - 26
[26] Pulse Linear R+2RC 259 10.65
[27] Pulse Linear R+2RC 218 45.8

7. Conclusions

7.1. Temperature trends

The largest resistance during operation of the tested cells between 10-
90 % SOC and -10◦ C to +40◦ C is due to charge transfer resistance, rct .
As shown in Figure 5 on page 22, it can vary from being virtually zero at

26
Figure 8: Load cycle measurements versus R + 6RC model for cell B at 24◦ C. Final RMSE
is 24.58 mV, see Table 2 on page 26

27
+49◦ C, to 90 % of the total resistance at -10◦ C, using cell A as an example.
This general behavior is common for all tested cells and well-known in the
literature. For low temperature performance, cell C displays an increase of
3 time, whereas cell A only displays 2 times higher rct at -10◦ C with room
temperature as reference. Figure 3a on page 18 shows the strong Arrhenius-
like increase of rct with falling temperature. Both electrolyte resistance rele
and diffusion resistance rdif f display similar Arrhenius trends, just not as
strong. According to our observations, the absolute value of the minimum-
resistance point ra is increasing significantly with decreasing temperature,
despite being partly canceled by the current collector’s positive temperature
coefficient. This might be in contrary to reported assumptions[10] about the
minimum-resistance point.

7.2. SOC trends

Studying the change of resistance over SOC, the only statistically signifi-
cant trend that can be generalized over all cell types tested is a reduction of
rct with increasing SOC. Other patterns are either too noisy (not statistically
significant) to draw a conclusion, or the trends show opposite slopes between
cell types due to chemical composition.

7.3. ECM design guidelines

When designing electrical equivalent circuits for general automotive lithium-

ion applications, our recommendation is to prioritizing the efforts of parametri-
sation is:

28
 1. rct (T ): The charge transfer resistance is dramatically increasing with a
decrease of temperature, here measured at 1500-3300 %.
2. rdif f (T ): Diffusion resistance is strongly increasing with a decrease of
temperature; 20-200 % compared to room temperature in our cases.
3. ra (T ): The minimum resistance at high frequency increases 25-60 % at
low temperatures, room temperature reference.
4. rct (SOC): Charge transfer changes in a linear fashion from 7-37 % at
low SOC to between -6 to -11 % at high SOC compared to mid-SOC.

No other trends with statistical significance is identified through our analysis

that is common for all tested cells. For the purpose of designing low-frequency
ECMs, the properties described by ra and rct can favorably be lumped to-
gether in one circuit element as long as the SOC and temperature dependence
is included.

Using EIS to extract ECM parameters to represent diffusion behavior of

the cell with a R + 2RC model is the most successful among the studied. For
the purpose of achieving low RMSE voltage error in automotive load cycles,
it makes more sense to focus model time constants towards the diffusion
part of the equivalent circuit. This is confirmed by the validation cycles in
Section 6 by a reduction of both peak error and RMSE by 40-80 % compared
to a rudimentary R10 model. These findings math similar setups using pulse
excitation for parameter extraction[26]. Similar results are also found in
[10, 25], but using more complex methods or models. Yet, the model accuracy
presented in this paper performs generally better in terms of average voltage
estimation accuracy than similar results found in literature, see Table 2 on

29
page 26.
A somewhat surprising finding is that an increase of the model complexity
by using a R + 6RC model to capture both charge transfer and diffusion very
accurately in the frequency domain (Figure 7 on page 25), did not result in
better time-domain model accuracy (Table 2 on page 26).

7.4. Drive cycle validation

Large proportions of the literature within BMS algorithms is focused on
estimating open-circuit voltage or charge transfer impedance, which is indeed
relevant for modeling in short time frames or as a tool to estimate tempera-
ture or age of the cells[16, 4]. Since typical usage of large automotive LIBs
involves dynamical loads for 20-60 minutes, where it is more beneficial for
estimation accuracy to include diffusion dynamics for the kind of open-loop
models used in this work.

The impedance measurements presented here are gathered from direct

measurements on mass-produced state-of-the-art automotive cells. The re-
sults can be directly transferred to industry applications to enhance initial
model based design approaches and BMS algorithm design for electric or
hybrid electric powertrains.

Acknowledgment

This work is sponsored by the Swedish Governmental Agency for Inno-

vation Systems (VINNOVA) in cooperation with Volvo Car Corporation.
Additional thanks to CEVT and Volvo Group ATR for their support with
test material.

30
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35
 Paper V
Pole-Slot Selection Considerations
for Double Layer Three-phase
Tooth-Coil Wound Electrical Machines
Presented 2018-09-03 at
ICEM2018, Alexandroupoli, Greece

Published 2018-10-25 in IEEE Xplore:

http://ieeexplore.ieee.org/document/8506772

First author contributions

Idea generation, literature review, theoretical evaluation,
data processing and analysis, FEA figures, corresponding author.
Second author contributions
Idea development, model verification.

145
146
 Pole-Slot Selection Considerations for Double
Layer Three-phase Tooth-Coil Wound Electrical
Machines
Stefan Skoog, Member, IEEE and Alessandro Acquaviva, Member, IEEE

Abstract—This work presents a combination of top-down machine topology studied in this paper. A non-overlapping
and bottom-up design procedures to select a suitable pole-slot stator winding, as offered by TCWM, allows for pre-winding
combination for a tooth-coil wound machine (TCWM), also of stator coils before installing them on the machine [6].
known as non-overlapped fractional slot concentrated winding
synchronous machine. Top-down features such as size and speed TCWMs are well suited for stator segmentation, and winding
are determined by the intended application and affect the coils directly on stator segments can offer fill factors of 60-
selection of slot and pole number. Bottom-up properties are 78% [3]. Combining TCWM with soft magnetic composites
quantified through key performance indicators (KPI) such as and pre-pressed windings, fill factors beyond 80% can be
fundamental winding factor, periodicity, cogging multiplier and reached [3], [7].
MMF harmonic leakage factor (HLF). Furthermore a compact
and intuitive graphical way of presenting the properties of the Performance indicators for high-performance TCWM are
double layer TCWMs is shown in this paper for slot number presented in [6], [8]–[11]. The inductance in TCWMs due to
up to 39, highlighting the similarities among machines through harmonics is studied in [12] and [1]. In [13], a comprehensive
the key winding factor concept. Analytical formulas for KPIs set of analytical equations are presented to analyze TCWMs,
are presented and the results are compared and visualized with independent of number of layers and number of phases, in
FEM simulations.
terms of finding the optimal rotor pole number for a given
stator slot number by acquiring the winding factors for all
Index Terms—Electric machines, AC machines, Brushless reasonable harmonics. An overview with some examples of
machines, Rotating machines, Permanent magnet motors, Elec-
tromagnetic modeling, Magnetic flux key winding factors, periodicity and torque ripple is given in
[14], [15].
This paper combines the most relevant performance in-
I. I NTRODUCTION dicators from the literature together with the basic analysis
A. Tooth-coil wound machines and presents it graphically together with a FEM verification
Tooth-coil wound machines (TCWM) [1], [2], also for a vast number of machine designs. The concept of coil
known as non-overlapped fractional slot concentrated wind- grouping, base machine and key winding factor is highlighted
ing (FSCW) synchronous machines, offer several benefits in order to group machines together in families with identical
compared to machines with a distributed winding [3], but key performance indicators (KPIs).
TCWMs are mainly used for Brushless DC (BLDC) and
they also present some special characteristics resulting in
Brushless AC (BLAC) applications, where one characteristic
design challenges not typical for classical distributed winding
difference between the two is the effective shape of the back
machines.
electromotive force (BEMF) due to the magnetic-geometric
One of the main challenges with TCWMs is that the
design. BLDC typically offer high flux linkage, but a BEMF
stator induced MMF wave contains both sub- and super-
with significant harmonic content, approaching trapezoidal
harmonics spatially along the air gap. Space harmonics affect
shape. BLAC designs typically offer very pure sinusoidal
the machine inductance and can induce significant losses in
BEMF, which is possible by harmonic elimination when
the rotor iron and in the rotor permanent magnets (PMs).
matching stator tooth tip and rotor pole geometries.
This kind of rotor losses is studied in detail in [4], [5].
Among the benefits of using a TCWM, is generally higher B. Pole-slot selection
torque density, which is a direct effect of achieving higher
stator slot fill factor, and minimization of end windings The aim of this paper is to guide the electrical machine
length and hence lower losses and lower parasitic effects. designer in the selection of a suitable pole/slot combination
The lack of end windings becomes a significant advantage for a specific application. The process is divided into two
in radially magnetized, axially short machines, which is the main steps:
• From application specifications, such as torque rating
This work is sponsored by the Swedish Governmental Agency for Inno- and speed, determine the acceptable range of pole pairs
vation Systems (VINNOVA) and The Swedish Energy Agency and slots. This is the top-down process.
S. Skoog and A. Acquaviva are both with Chalmers University of
Technology, Gothenburg, Sweden (e-mail: stefan.skoog@chalmers.se and • Verify which is the most suitable pole slot combination
alessandro.acquaviva@chalmers.se). based on KPIs, grouping design families together and

978-1-5386-2477-7/18/$31.00 ©2018 IEEE 934

 visualizing them in an intuitive manner. This is the How the periodicity affects the winding structure is illus-
bottom up process. trated in Figure 1a. Note that the value of t shown in the
picture can be either tsym or tasym depending on the winding
II. T HEORY configuration. Any viable TCWM need a t number above
unity in order to cancel radial forces induced in the rotor,
A. Pole-slot structures creating excessive noise and vibrations [14], [17].
A simple method of determining whether a machine with The high-level key performance indicator key winding
a certain pole - slot combination qualifies as an TCMs for a factor [10], [16] W , defined as
machine with nph phases is to look at the slot per pole per
phase number Qs Qs
W = = , (3)
Qs nph tasym nph GCD(2p, Qs )
q= . (1)
2p nph
fulfills two functions. W must be a positive integer to realize
where Qs is the number of slots and p is the number of a balanced machine with nph number of phases, W also
pole pairs. If q ≥ 1, the machine is a traditional dis- defines the number of coils from the same phase in each
tributed winding type, e.g. q = [1, 32 , 2] are common setups phase belt. In most high-performance machines (see Table I)
for overlapping distributed winding machines. Most 3-phase with Qs < 30, all coils from the same phase within a phase
TCWMs offering high performance fulfill 14 ≤ q ≤ 21 , a belt are positioned on adjacent stator teeth, as illustrated
comprehensive explanation of this is given throughout  the in Figure 1b. Typically for high-power-density (high speed,
paper. The TCWMs defining this boundary, q = 21 , 14 ,

low pole number) and production-friendly TCWMs, the key
are often referred to as traditional brushless PM machines, winding factor is low.
which have single-tooth per phase windings W = 1 (defined
in (3)) and with the highest possible periodicity (tsym ) for
any given number of slots. Machines with q = 12 are
the only TCWM where the working harmonic is also the
lowest harmonic, i.e. all other combinations of Qs and p
will generate MMF subharmonics, which will limit their
𝑡=2 𝑡=3 𝑡=4 𝑡=5 𝑡=6
electromagnetic performance.
(a) Machine layouts with unity key winding factor and varying
B. Base machine, periodicity and key winding factor periodicity.

Although there is a very large set of possible combi-

nations of slot and poles, only a small fraction of these
combinations can produce a viable machine. The winding
structure for many TCWMs are often repeated within a 𝑊=1 𝑊=3
mechanical revolution, creating symmetry with the smallest
symmetrical part referred to as phase belt [13] or as base
machine [12]. This is the smallest pole-slot structure that
defines the basic properties of the machine. Most parts of
the machine analysis can preferably be performed on the base 𝑊=2 𝑊=4
machine instead of the full machine, including FEM analysis
when using the right boundary conditions.
The machine electrical periodicity, or mode order [16], (b) Machine layouts with periodicity tsym =2 and varying key winding
defines how many symmetric parts the machine can be split factor.
into from an electromagnetic perspective. The periodicity Fig. 1: Winding layouts for an outer-rotor TCWM. The
also states the maximum number of parallel connections phase windings are represented by colored rectangles in
of coils possible. Machines can be both symmetric and blue, red, green for phase A,B,C respectively. The geometry
anti-symmetric, where the latter example means that each corresponding one electrical period is drawn for each variant,
second phase belt is repeated with the coils phase shifted i.e. the base machine.
180 degrees, e.g. with coils electrically reversed. The greatest
common divisor (GCD) between pole pair number p and slot
number Qs is used to establish how many phase belts that are
possible in a balanced machine setup, i.e. the periodicity for C. Cogging torque
complete symmetry tsym or anti-symmetry tasym is defined
as Specifically for TCWM, a way of reducing the magnitude
tsym = GCD(p, Qs ) (2a) of cogging torque is to design for high cogging frequency,
so that the produced cogging torque is damped by the rotor
tasym = GCD(2p, Qs ) . (2b) inertia. The cogging frequency multiplication Mf depends

935
on the least common multiplier (LCM) between number of
slots and number of poles [10], [16], [18]:

Mf = LCM (2p, Qs ). (4)

D. Winding layout
Methods to derive the optimal winding layout for a given
pole, slot and layer number is widely covered in literature.
The main methods are the star of slots method [8], [9] or
(a) Q36p16, kw = 0.945 (b) Q36p14, kw = 0.902
the method presented in [10], [19], [20]. The latter is used in
this work and some examples are presented in Figure 1 and Fig. 2: Two TCWMs with W =3, with phase coils (a) grouped,
Figure 2. and (b) non-grouped.

E. Winding factor G. Stator generated MMF

With the assumption that the machine is fed by a sym-
The winding factor kw decides the linkage between the
metric multiphase current, that stator slots can be represented
coil current and any specific spatial MMF harmonic in the
as point like sources and the magnetic materials are acting
airgap. Once the stator winding is designed, the rotor pole
linearly, several methods can be used to estimate the stator
number locks to the matching spatial MMF harmonic which
induced airgap MMF [21]–[23], which are all similar by uti-
is defined as the working harmonic or the fundamental
lizing spatial Fourier series while keeping the time frozen for
harmonic kw,f . To make detailed estimations of stator MMF
the multiphase phase input. By using the same assumptions,
and total stator inductance, the winding factor have to be
a simplified numerical approach to draw the MMF waveform
calculated for all harmonics. Methods for this are reported in
can be used. Once the layout of the winding is defined,
[8], [9], [13] and are all similar in their structure. Generally,
starting from any of the slots, the number of ampere-turns
the winding factor kw consist of the product of winding
that are met around the mechanical angle are added up for
distribution factor kd and winding pitch factor kp , which
each slot (summing up the ampere turns within the slot) and
must both be evaluated for each spatial harmonic number.
then the average value is subtracted. With some further care
The skewing [18] factor is ignored in this scope.
the effect of the slot opening on the stator generated MMF
can be added.
kw = kd kp (5)

H. Magnetization inductance
The total stator coil inductance Ls can be split into airgap
F. Grouped coils within phase belt inductance Lδ and stator leakage inductance Lσ . The airgap
inductance represents all linked stator flux that travels over
Most TCWM combinations of Qs and p that offer high the airgap, whereas Lσ are all parasitic inductance generated
performance will automatically group together coils from the from slot, tooth tip and end winding lumped together. The
same phase so that they are placed next to each other within airgap inductance can, specifically for TCWMs be divided
any symmetric or anti-symmetric phase belt that forms the into synchronous magnetizing inductance through the funda-
base machine, Figure 1b and Figure 2a shows examples of mental harmonic Lms which is involved in the net torque
this. However, there is also examples of machines where coils production, and a parasitic magnetization of harmonics Lh
from the same phase are spread out over the phase belt in a which does little for net torque production [2]. Since the
seemingly random manner, but still providing high winding magnetic circuit for fundamental and harmonics are equal,
factor and reasonable losses as in Figure 2b. A condition it is feasible to express the harmonic inductance as propor-
presented in [21] is ameliorated into a simpler form by tional to the fundamental air gap inductance, introducing the
directly recognizing asymmetry as defined in (2) and included harmonic air gap leakage factor δσ .
in (3):
Q  Q  Ls = Lδ + Lσ (7a)
s s
round W = round W . (6)
2p 2p Lδ = Lms + Lh = Lms (1 + δσ ) (7b)
This condition holds true only when the machine can form a
winding where all coils from a phase are placed on adjacent The harmonic air gap leakage factor can be calculated
stator teeth within the smallest symmetric or asymmetric by summing together the relative amplitude of all harmonics
phase belt. h, either by using winding factors [2], [24] or the harmonic

936
spectrum [12] derived from distribution- and pitch factors or
by applying Fourier analysis on the winding function:
∞  ∞ 
X υf kw,υ 2 X hυ 2
δσ = = , (8)
υ kw,f hf
υ6=υf υ6=vf

where υ is the harmonic number, υf is the fundamental

(working) harmonic of the base machine. With this said, the
Fig. 3: PM flux shunting effect.
MMF harmonic spectrum will directly affect the performance
of the TCWM by increasing its inductance without linking
any torque producing flux. Increased inductance can be useful
with reserving space for a slot liner and isolation between
in some particular cases, such as limited short-circuit current
the two coils, the resulting gross fill factor will drop.
or increased field weakening range. Generally, increased
The opposite example with a large size machine and
inductance is an undesired property due to increased reac-
low pole number results in few but large slots. This should
tive voltage drop of the machine at high speeds, decreased
be avoided because the thermal design of the slot becomes
maximum torque and decreased power factor. The harmonic
critical, the end-windings are longer, and the overall design
air gap leakage factor is a particularly interesting indicator
of the machine becomes more problematic. Generally, a good
of the spatial harmonic content. This scaling effect with the
TCWM stator design presents slots that have a height and
harmonic order well represents the effect of the airgap, which
length that are within a ratio of 2.
acts as a low pass filter, when evaluating the flux density
harmonics generated by the stator MMF that in turn generate
eddy current losses in the rotor iron and PMs. Hence, δσ can B. KPIs and bottom-up design criteria
be used as an indicator of rotor losses. Note that the harmonic A step-by-step design procedure of how to establish a
leakage factor is calculated with the assumption that the coil suitable slot-pole combination for a two-layer, three-phase
pitch equals to slot pitch, i.e. a virtual tooth tip design with TCWM is summarized in Table I, with the most basic and
infinitesimally small slot opening. important design criteria in the top of the table, including
references to the relevant formulas. Additionally, some guide-
III. M ETHOD lines about the conditions are given. Machines with very high
number of poles compared to the slots (q < 0.25) might show
The selection of slot and pole number begins with the
good KPIs, however due to the flux shunting effect shown in
knowledge of the intended application of the machine.
Fig. 3, their performance is limited beyond what is reflected
in the theory in this paper.
A. Pole-slot range from top-down requirements
Brushless machines are by definition inverter fed, this TABLE I: TCWM design procedure
means there are no limitation tied to grid frequency or Attribute Characteristic Condition
voltage. From a system perspective, the pole selection affects Fractional slot pitch Slot/pole/phase (1) q≤1
the frequency of the fundamental which directly affects iron Phase symmetry possible Symmetric windings (3) W ∈ Z+
Avoid radial EM forces Periodicity (2) t≥2
losses and the switching frequency of the converter. High High torque per ampere Fund. winding factor (5) kw,f > 0.85
power density machines typically aim for high mechanical Low parasitic inductance Harmonic leakage (7b) Low δσ
speed, which makes it suitable to select a low rotor pole Low rotor losses Low space harmonics (7b) Low δσ
Avoid PM shunting effect Slot/pole/phase (1) q ≥ 0.25
number in order to keep the fundamental electrical frequency Low cogging torque Periodicity (4) (2) High Mf & t
within a certain range. This because standard laminated ma- Low torque ripple Large phase belts (3) W >1
terials result in reasonable losses with an excitation frequency Modular windings Grouped phase coils (6) Equality
Z+ = positive integer
of 0.1-1.0 kHz. Furthermore, to have an acceptable current
ripple, the switching frequency should be at least 20 times
the fundamental but it also directly affects switching losses.
By setting the maximum fundamental frequency ff,max the IV. R ESULTS
maximum number of poles is established as For bottom-up design, a table with formulas on how to
form high-performance pole-slot combinations with grouped
4πff,max
pmax = , (9) coils up to key winding factor seven is presented in Table
ωm II, together with their corresponding fundamental winding
where ωm is the mechanical angular speed. factor. Other TWCMs with satisfactory performance do exist
The machine size constraint also plays a role in the outside the range of this table, but with non-grouped coils
maximum number of poles that can be selected. A small sized (see Figure 2b) or key winding factor above seven.
machine with a high pole number equals small slots. This In Figure 5, a graphical representation of all slot-pole
leads to challenges in the winding procedure, and together combinations up to Q39p17 rendered. Distributed windings

937
TABLE II: Base machine and their derivatives for dual-layer, taken when evaluating the harmonic content based on this
three-phase TCWM. coefficient. The results of HLF between analytical and FEM
Winding Possible Possible Base
Example
method is presented in Table III, the time series and FFT of
W factor slot number pole number Machine the spatial MMF wave can be seen in Figure 4. The results
q
kw,f Q 2p Qs /2p
from the two methods match very good, verifying that the
3/2 1/2
1 0.8660 3x Q(1 + 2y) ± x winding configuration alone, and the selection of fundamental
3/4 1/4
2 0.9330 12x Q(1 + 2y) ± 2x
12/10 2/5 harmonic influence the HLF to a large degree and that the
12/14 2/7 analytical method gives a fair and accurate representation of
9/8 3/4
3 0.9452 9x Q(1 + 2y) ± x the stator induced MMF. Note that the MMF waveform is
9/10 3/8
24/22 4/11 derived from the flux density in the airgap.
4 0.9495 24x Q(1 + 2y) ± 2x
24/26 4/13
15/14 5/14
5 0.9514 15x Q(1 + 2y) ± x
15/16 5/16
36/34 6/17
6 0.9525 36x Q ± 2x
36/38 6/19
21/20 7/20
7 0.9531 21x Q(1 + 2y) ± 2x
21/22 7/22
x ∈ N+ (all real non-zero numbers)
y ∈ N0 (all real non-negative numbers)

of q = [1, 2] are included as a reference. For each slot-

pole combination, four of the KPIs are displayed: Funda-
mental winding factor kw,f , harmonic leakage factor δσ (8),
(a) Spatial MMF waveform in airgap for one symmetric electrical
asymmetric periodicity tassym (2b) and cogging frequency period.
multiplication Mf (4). Red boxes indicate that conditions
from Table I are not fulfilled. Yellow boxes signals passed
conditions, and more green means excellent performance in
each KPI. A dashed HLF number means that the machine
coils are unevenly grouped according to (6), which renders
the analytical procedures behind (8) inaccurate. Gray boxes
are disqualified due to flux shunting and very high HLF
numbers, which means that they will likely display inferior
performance, but also that the analytical methods presented
here are less accurate. Out of 208 possible design candidates
marked by the grid in Figure 5, 49 designs pass rule one (b) FFT spectrum of spatial MMF waveform in airgap. Working
through four from Table I, most of them grouped coil designs harmonic is 5.
belonging to any of the combinations possible from Table II.

A. FEM verification of HLF

A Q36 outer-rotor is selected and modeled in Ansys
Maxwell in order to verify HLF. The machine is normally
equipped with surface-mount permanent magnet, however,
for the study of stator induced magnetic field in the airgap,
the magnets are not included. A slot number of 36 is selected
since it offers many different machine variations with varying
W numbers without changing the stator geometry apart from
winding configuration. The machine is excited with a stator
current below saturation level of the magnetic iron and the
radial component of the magnetic flux density is evaluated
along an arc in the middle of the air gap, as displayed in (c) Magnetic flux density plot when
Figure 4a. The machines used for FEM analysis present a C winding (green) is carrying peak
very small slot opening in order to match the analytical current with a balanced 3-phase
method to calculate HLF, assuming a coil pitch that equals supply.
the slot pitch. From Figure 4c one can see how the tooth Fig. 4: Analysis of MMF by analytical Fourier series and air
tips saturate at nominal stator current which will result in a gap spatial flux density from FEM for a Q36p15 machine.
slot opening effect. It should be noted that HLF can differ
substantially with wide slot openings and some care must be

938
Fig. 5: An overview of TCWM configurations and their corresponding key performance indices.

939
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The int. journal for computation and mathematics in electrical and Stefan Skoog was born in 1985 and hold a M.S. degree from Lund
electronic engineering, vol. 30, no. 1, pp. 72–83, 2011. University, Sweden in Industrial Electronics and Automatic Control. He
[7] A. G. Jack, B. C. Mecrow, P. G. Dickinson, D. Stephenson, J. S. has been working professionally with embedded systems, electronics and
Burdess, N. Fawcett, and J. Evans, “Permanent-magnet machines with vehicle electrification for 10 years. Stefan is currently a PhD student at the
powdered iron cores and prepressed windings,” IEEE Transactions on Division of Electric Power Engineering, Chalmers University of Technology,
Industry Applications, vol. 36, no. 4, pp. 1077–1084, 2000. Sweden. His research project is affiliated with Volvo Cars with the ambition
[8] N. Bianchi, M. Dai Pre, L. Alberti, and E. Fornasiero, “Theory and to accelerate the electrification of passenger vehicle powertrains through the
design of fractional-slot pm machines,” in Conf. Rec. IEEE IAS Annu. use of low voltage mild hybrid systems.
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[11] A. M. El-Refaie and T. M. Jahns, “Optimal flux weakening in surface 2012 and is a PhD student at the Division of Electric Power Engineering,
pm machines using concentrated windings,” in Industry Applications Chalmers University of Technology since 2016. From 2012 to 2016 he has
Conf., 2004. 39th IAS Annual Meeting. Conf. Record of the 2004 IEEE, been working in the traction electrification industry. His current research
vol. 2. IEEE, 2004, pp. 1038–1047. interests include electric drives, electrical machine design and multiphysics
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 Paper VI
Design and Verification of
In-slot Oil-Cooled Tooth Coil Winding
PM Machine for Traction Application
Submitted 2019-12-20 to IEEE Transactions on Industrial Electronics
Published 2020-04-07 in IEEE Xplore:
https://ieeexplore.ieee.org/document/9059039

First author contributions

Lead machine design FEA, thermal and mechanical,
data processing and analysis, FEA figures, CFD and CHT analysis,
figure generation.
Second author contributions
Lead in design, construction and calibration of measurement setup,
idea development, verification of machine design with FEA,
corresponding author.
Third author
Paper review, paper structure, idea revision, supervision,
administration, resource allocation, funding.

155
156
SUBMITTED 2019-12-20 TO IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

Design and Verification of In-slot Oil-Cooled

Tooth Coil Winding PM Machine for Traction
Application
Alessandro Acquaviva, Student Member, IEEE, Stefan Skoog, Student Member, IEEE,
and Torbjörn Thiringer, Senior Member, IEEE

Abstract—Tooth coil windings, in particular when using this article, where the stator end sections of the machine
a double layer structure, present opportunities for in-slot are immersed in the cooling fluid and designed to generate
liquid cooling. Since the windings are not overlapping, turbulence and distribute the fluid in the slot and iron cooling
access to the slot from the end section for coolant liquids
is enabled. In this paper, a solution for in-slot and in- channels.
stator direct oil cooling for a tooth coil winding machine Tooth coil winding machines, also defined as non-
is presented. The coils are pre-wound on bobbins and overlapping fractional slot (pitch) concentrated winding
inserted on the stator teeth. The novelty of the design (FSCW) machines, are particularly interesting when it comes
consists in the integration of the cooling, using a thermally to high power density, high efficiency and flexibility in
conductive epoxy resin to create the channels within the
slot as well as the positioning of the stator yoke cooling manufacturing [10]–[12]. Furthermore, they present several
channels. A 50 kW machine for an automotive traction ap- opportunities also when it comes to cooling. Theoretical
plication is designed, manufactured and tested. Conjugate investigations on direct cooling in concentrated laminar wind-
heat transfer simulations are used in the design process ings are presented in [13]. The laminar winding, however,
in combination with finite element analysis for the loss presents manufacturing challenges and the solution is lacking
mapping. The thermal model is verified with measurements
at 6 l/min oil flow and 17.5 A/mm2 continuous and 35 A/mm2 experimental validation. In [14] a double layer tooth coil
30 s peak. The thermal model is then used to establish a winding machine concept with in-slot cooling between the
continuous operating point of 25 A/mm2 . coils is presented and partly evaluated. This solution uses
Index Terms—Cooling, Permanent magnet motors, Mod- the space in the slot not filled with copper to create cooling
eling channels by using water-soluble mould cores, a concept that is
hard to adopt for mass production. Directly cooled axial flux
PMSM using hollow conductors, and coolant flow in the axial
I. I NTRODUCTION direction, can also be found in literature [15]. The prototype
The development of electric drivetrains is primarily domi- presented uses Litz wire with a tube for liquid inside each turn,
nated by the permanent magnet synchronous machine (PMSM) which is complicated to manufacture and yet the maximum
[1], characterized by their high efficiency, high power and feasible current density 14 A/mm2 at 2 l/min is reported.
high torque density [2]–[4]. Liquid cooling is necessary to A comparison between tooth coil winding PM machines with
enable high torque density for continuous operation. Extensive cooling jacket and direct cooling using hollow conductors is
engineering efforts are devoted to develop automotive traction presented in [16]. A very interesting concept is used in [17],
machine cooling solutions, as summarized well in [5]–[7]. where a direct winding heat exchanger is used in between the
Design of electrical machines is a multiphysics (electric- coils of a double layer tooth coil would machine. This setup
magnetic-thermal-mechanic) challenge. The thermal modeling allows for direct, in-slot water-cooling of the windings without
is essential to establish the continuous and transient maximum exposing water to the winding copper wires. Current densities
performance. In classical machines, cooling jackets are used, of 25 A/mm2 continuous and 40 A/mm2 peak operation
which can be modelled with a simplified lumped-parameter are reported with this solution, with coolant flow rates up to
approach [8], [9]. However, with increased complexity of the 5.3 l/min and 5.1 kPa pressure drop. Copper heat exchangers
cooling solution, conjugate heat transfer (CHT) simulations in the slot, however, can be challenging when it comes to
are needed during the design process to evaluate the thermal slot insulation and manufacturing, and the authors have not
performance. This is the case for the machine presented in presented a complete rotating machine in hardware with their
cooling concept. The authors of [18], [19] presents an in-
The authors gratefully acknowledge the financial support from the
Swedish Energy Agency and the Swedish Governmental Agency for slot cooling for a SRM, with dramatically increased cooling
Innovation Systems (VINNOVA). performance using water mantle cooling as reference. The
A. Acquaviva, S. Skoog and T. Thiringer are with the Division concept is tested with DC current up to 22 A/mm2 and a flow
of Electric Power Engineering at Chalmers University of Technology,
Gothenburg, Sweden (e-mail: alessandro.acquaviva@chalmers.se, ste- rate of 6 l/min, but this concept comes with some challenges
fan.skoog@chalmers.se, torbjorn.thiringer@chalmers.se). regarding coolant leakage to the rotor.
SUBMITTED 2019-12-20 TO IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

The purpose of this paper is to demonstrate effective and internal to external stator diameter, is established to 0.62 to
manufacturable high-performance cooling solution for a trac- maximize the efficiency. The rotor geometry is chosen as an
tion machine. The cooling solution presented in this paper, internal V-shaped PM with air barriers to enable high saliency
which combines direct iron and direct in-slot oil cooling, which improves the field weakening characteristic. Embedding
and experimentally verifying operation at very high current the magnets in the rotor also limits magnet losses caused by
densities, is prior not found in the literature. The novelty harmonics in the airgap MMF [21], [22]. Magnet segmentation
consists in the integration of the cooling within the stator, axially is also utilized to further reduce the losses [22], [23];
using a thermally conductive epoxy resin to create the channels each rotor slot is axially filled with 20 equal units of Vacodym
within the slot as well as the positioning of the stator yoke 745DHR NdFeB-magnets.
cooling channels. Neither of these solutions have been found A stator design without tooth tips is selected to improve
in the literature. Additionally, the design of the end section manufacturability by allowing the coils to be pre-wound and
to properly distribute the oil flow forms a high turbulence inserted radially.The cogging torque and torque ripple are
region which leads to very high cooling capability of the end minimized by adjusting the PMs angle the pole pitch width and
windings. This is a clear advantage compared to an external the tooth width. The resulting machine geometry is presented
cooling jacket, where end winding cooling is typically an in Table II. The maximum phase current corresponds to a
issue. Regarding manufacturability, the machine is designed current density of 35 A/mm2 . The stator and rotor lamination
such that it is possible to use a linear winding machine to geometries as well as the coil disposition are shown in Fig. 1.
pre-wind the coils on a bobbin, leading to a significantly In Fig. 2 the disposition of conductors and the shape of
reduced manufacturing cost for high volume production. Also, the stator are shown, including the cooling channels and the
the procedure to create the cooling channels within the slot, plastic support (bobbin) used to pre-wind the coils. PT100
and extract the channel shapers, can be automated. temperature sensors (4 in the slots placed mid-axially and 3
A calorimetric setup is used to measure the iron losses and on the end windings) are all placed before the potting process.
to validate the CHT model of the machine and cooling at The end winding temperature sensors are placed as follows
different flow rates. The convection heat transfer coefficients with the same naming as in Fig. 1 and the legend in Fig. 16:
(HTC) from the CHT simulation are extracted and used in a • one between slot 1 and 2 on the drive end side (EW1-DE)
transient thermal finite element simulation to evaluate the op- • two between slots 5 and 6, one on the drive end (EW5-
eration of the machine in worst-case conditions. Measurements DE) and one on the non-drive end (EW5-NDE)
are performed on the machine in thermal steady state operation The coils of each phase are connected in parallel with the
at 17.5 A/mm2 showing good agreement with the thermal ones on the opposite side of the stator, as illustrated in Fig. 3.
simulations. The continuous operation at 25 A/mm2 is ver- This choice is made in order to allow a higher number of turns,
ified in the worst case conditions with a thermal simulation. and therefore reduce the size of each conductor, which helps
Results from both the transient simulation and measurements improving the manufacturing process as thinner and fewer
show that a current density of 35 A/mm2 can be kept for parallel conductors are easier to wind.
30 s peak operation without exceeding the thermal limits of
the machine components. B. Slot fill factor and cooling channels
The cooling channels are derived from unused space in the
II. M ACHINE DESIGN slot. The total slot area is 350 mm2 . The cooling channel
The electrical machine in this paper is designed as a traction area in the slot is 100 mm2 which gives a net slot area of
machine for a small passenger vehicle, assuming it will operate 250 mm2 . The copper area is 113 mm2 , yielding a net fill
with a fixed-gear reduction gearbox powering either of the factor of 0.45, while considering the total slot area yields a
vehicle wheel pairs. It is assumed that a liquid cooling circuit bulk fill factor of 0.32. The stator winding before and after
is available in the car, as in the vast majority of modern potting is shown in Fig. 4. A wire diameter of 1.6 mm is the
passenger electric vehicles on the market, and no additional largest possible wire size that can be fitted in 28 turns when
cooling infrastructure is therefore needed for this cooling using manual winding process for this prototype.
concept. The material used for the potting is an epoxy resin,
Lord CoolTherm EP-2000, with a thermal conductivity of
A. Electromagnetic sizing and design choices 1.9 W/(m · K).
The electromagnetic design is based on an analytical siz-
ing method combined with a finite element mapping and TABLE I: Electrical machine design specifications.
verification. A 12 slot 10 pole (Q12p10) machine is chosen Quantity Symbol Value Unit
based on characteristics presented in [11]. Prioritized features Peak torque τmax 140 Nm
Peak power Pmax 50 kW
are: high efficiency, high fundamental winding factor (0.933), Base speed nb 3 600 rpm
low harmonic leakage inductance factor (0.97), low cogging Max speed nmax 11 000 rpm
Coolant max temperature ◦C
torque, and low torque ripple. The machine is designed for the Θmax,c 60
◦C
Max winding temperature Θmax 180
specifications listed in Table I. DC bus voltage VDC 600 V
The analytical sizing procedure used is based on split ratio Maximum RMS current Imax 140 A
optimization [20]. The split ratio, defined as the ratio between
SUBMITTED 2019-12-20 TO IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

TABLE II: Electrical machine main dimensions and data.

Quantity Symbol Value Unit
Outer Stator diameter De 180 mm
Inner Stator diameter D 111.4 mm
Active length L 100 mm
Tooth width wt 17 mm
Stator Yoke width wsy 13 mm
Magnet thickness hm 3.5 mm
Diameter of each conductor dN 1.6 mm
Number of turns per coil N 28 -

Fig. 3: Winding disposition and connection for the

tooth-wound Q12p10 machine for balanced three-phase
operation.

Fig. 1: Stator and rotor laminations geometry, slot naming,

coil and temperature sensors disposition. [21] to reduce sub-harmonics, which in turn would reduce
both iron and PM losses in the Q12p10 machine. The main
difference is that the position of the yoke barriers in [21] are
C. Stator yoke cooling channels shifted one slot and hence blocking part of the main magnetic
A machine with an even key winding factor [11] (e.g. two flux within the adjacent coils in one phase. The drawback is
adjacent tooth-coils belonging to the same phase winding), a torque reduction, which for the Q12p10 used in this paper
such as the Q12p10 machine , presents negligible mutual would be substantial according to several FEA cases where the
inductance. This means that the flux generated by a single yoke barrier thickness is varied as a parametric variable. The
phase is enclosed between the two adjacent tooth coils and chosen thickness presents no torque reduction at full current
the yoke in between. A plot of the flux generated by 100 A in compared to the solution without barriers.
phase A and the PMs considered as air is shown in Fig. 5. The
yoke in-between coils of different phases has a very low flux D. End section
density. However, when the PMs flux is added, parts of the PM The stator end sections are filled with oil and flow stoppers
flux would also flow in between coils of different phases but are inserted as shown in Fig. 6 to redirect the oil in the two
still with flux densities below 1.3 T . To sum up, the yoke in parallel paths, as illustrated in Fig. 7. The oil flow splits evenly
between phases is oversized in this design and some barriers thanks to the symmetry of the geometry on the two sides of the
for direct iron cooling can be created as shown in Fig. 5. machine. The inlet and outlet are placed in correspondence to
A similar solution with stator yoke barriers is adopted in the iron cooling channels, which are a parallel fluid path with
corresponding slot channel. This is done mainly to minimize
the pressure drop from the whole flow passing through those
channels.

III. N UMERICAL EVALUATION

The electromagnetic performance of the machine, including
loss mapping, is evaluated using FEA. The losses are used as
input for evaluating the thermal performance. A flow chart
presenting how the models are built is shown in Fig. 8.

A. Electromagnetic FEA and loss mapping

The machine is mapped using equidistant operating points
on the d-q current plane, and for each of those a set of
2D quasi-static magnetic FEA is performed. The losses are
computed as in [24]. The eddy current and hysteresis loss
factors are extracted from the lamination data sheet (M235-
Fig. 2: Overview of a cross-section of the slot design 35). Copper losses are calibrated by measuring the total phase
showing in-stator cooling channel, winding layout, steel and resistance with a high-current 4-wire setup. The iron losses
potting material. are calibrated by measuring the heat generated while motoring
SUBMITTED 2019-12-20 TO IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

Fig. 4: Wound stator non-drive-end before (left) and

drive-end after (right) potting. The oil cooling channels can
clearly be seen as formed by the empty space between coils.

Fig. 6: Details of manufactured machine end section at

non-drive-end showing the flow barriers between the slots
and the phase connection terminals.

Fig. 7: Velocity streamlines showing the coolant flow path

and the temperature increase from inlet to outlet at 6 l/min,
inlet oil temperature of 30 ◦ C and winding loading of
60 ADC (15 A/mm2 ).
Fig. 5: Magnetic flux density generated by 100 A in phase A
with and without PMs, respectively lower and upper
B. Conjugate heat transfer model
sub-figure. The stator yoke cooling channels are actually
assisting in lowering mutual flux between phases. The rotor To verify the steady-state thermal performance of the ma-
position is chosen such that PMs are generating flux in the chine, a 3D CHT model is built and solved for different flow
same direction as phase A. rates. This multiphysics model combines CFD and thermal
FEA. The losses are assigned as domain distributed heat
sources and all the materials are assigned with thermal proper-
ties. Using a similar approach as in [8], the material modeling
the machine, with the dynamo at 3000 rpm and no electrical includes
load, with the calorimetric set up described in Section IV. This • Anisotropic thermal conductivity of iron lamination stack
resulted in an iron loss scaling coefficient of 2.0, meaning • Anisotropic thermal conductivity of coils
that the measured values of iron losses are twice the ones • Dynamic viscosity, heat capacity and thermal conduc-
estimated with FEA using the interpolated loss coefficients tivity of the coolant is considered as a function of
from the soft iron manufacturer. Typical values of iron loss temperature
scaling coefficients found in the literature [25] are in the range • The air in the airgap is modelled with an equivalent
between 1.5 and 2.0. thermal conductivity to account for the convection effect
The torque-speed iron and copper loss maps, after the at a given speed based on [26]
adjustments, are presented in Fig. 9. The winding and slot insulation/filler are modelled as a
SUBMITTED 2019-12-20 TO IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

each conductor and to decrease the complexity of the model. A

similar approach, with different material proportions, is used
for the end winding, resulting in a λslot,xy of 63 W/(m · K)
and λslot,z of 3 W/(m · K).
The resulting surface temperature distribution, at 2 l/min
and assuming only copper losses with a current of 60 ADC ,
is presented in Fig. 10. For the same loading condition the
temperature distribution in the middle of the axial length of
the machine for different flow rates is presented in Fig.11.

Fig. 8: Flow chart of development and calibration of FEA

and CHT simulation models.

Fig. 10: Surface temperature distribution with 60 ADC

(15 A/mm2 ), oil inlet temperature of 20 ◦ C and 2 l/min
flow rate.

Fig. 9: Iron and copper losses from FEA machine mapping.

unified material. In [27] a model is derived that predicts

the equivalent thermal conductivity of a composite material
consisting of aligned, infinitely long, equi-sized, rigid, circular
cylinders (i.e., the copper conductors) randomly distributed
in a medium with lower conductivity (i.e. slot filler). This Fig. 11: Motor temperature distribution with 60 ADC
value depends on the fill factor and the thermal conductivity (15 A/mm2 ), oil inlet temperature of 20◦ C and four
of the two materials. The value obtained is 4.8 W/(m · K), different oil flow rates. The simulated temperatures are
and this value of thermal conductivity is used for the plane symmetrical for the two motor halves and hence only one
parallel to the lamination (referred as x and y directions), half is shown per oil flow rate.
while a weighted thermal conductivity of copper and epoxy-
resin, resulting in 118 W/(m·K), is used in the axial direction The CHT model accounts for the effect of increasing
(referred as z direction). This method allows to avoid modeling resistance with temperature. The distributed heat source is a
SUBMITTED 2019-12-20 TO IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

function of the local temperature using the equation TABLE III: Software and mesh data
Physics Software Dimensions n. mesh nodes
Pcu,T = Pcu,T0 (1 + α(T − T0 )) (1) Electromagnetics FEMM 2D 41575
Complete CHT COMSOL 3D 231370
Trans. therm. Model COMSOL 3D 121179
where Pcu,T0 and Pcu,T are respectively the copper losses at
the reference temperature T0 at which the phase resistance
is estimated and at the temperature T of the winding which
is updated at each time step of the simulation; α is the IV. T EST SET UP
temperature coefficient of copper. End winding joule losses
The machine is tested in a lab environment consisting of a
are distributed to the corresponding domain.
electric dynamometer, power electronics, and a custom made
oil-to-water cooling system. The setup is illustrated in Fig. 13
and a photo is also shown in Fig. 14. Appropriate sensors
C. Transient thermal model are installed and calibrated to measure rotational torque (τ ),
The CHT model is computationally very demanding, about rotational speed (n), rotational position (θ), oil flow (ṁ),
9 hours to solve a single steady state operating point on a oil temperatures (T ), oil pressures (p) and electrical voltages
workstation with an Intel i7-6700K CPU operating at 4 GHz. (v) and electrical currents (i). The custom cooling system
Transient analysis using a standard workstation is not feasible. utilizes tap water which is flow-controlled with a feedback
However, it is possible to extract the convection HTCs for the PI-controller into a heat exchanger to cool the oil circulated
different solid to fluid surfaces and use them as a boundary in the machine. The low-viscous oil is circulated by a 100 W
condition for a thermal FEA simulation (without the CFD controlled gear pump capable of generating 3 bar overpressure
part), which has orders of magnitude lower computational or 7 l/min flow rate. An oil reservoir and a 10 µm particle
effort. A 60 s transient simulation, with 0.1 s time step- filter is also part of the oil cooling circuit. The direct heat
ping, can be solved in less than 10 minutes with the same measurement is based on measuring the temperature difference
workstation mentioned above. The transient thermal model of the inlet and outlet oil in the prototype machine together
has the same geometry, meshing, material characterization and with the oil flow. Redundant Swissflow SF-800 sensors are
loss distribution of the CHT model solid parts, but no fluid used for flow measurements, several NTC sensors as well as
modelled. 16 4-wire PT-100 class A sensors are redundantly measuring
The HTCs, extracted from the CHT simulation, at different oil temperatures to offer high accuracy and high reliability
flow rates are presented in Fig. 12. These are calculated as for the prototype setup. The entire test system is controlled
average over the surface of the specific part and in reference and monitored through a dSpace SCALEXIO-system. The
to the inlet temperature. The two halves of the machine are prototype machine is fed with a three-leg IGBT-based inverter
symmetrical, and hence the HTCs of the slots on the left and at 400 VDC , operating at 5 kHz Space Vector Modulation
right side of the machine are equal. closed-loop current control. The dynamometer is operating at
closed-loop speed control.

𝑛𝑟𝑒𝑓
𝜏 𝑛 𝜃
500 S1-S11
S2-S10
S3-S9 𝑇
400
S4-S8 𝑚
S5-S7 𝑝
HTC [W/(m 2 K)]

S6 - outlet
S12 - inlet 𝑖
+
300 EW −
Iron chan 𝑣
Iron sides
Fig. 13: Measurement system setup with dynamometer to the
200
left, prototype machine in the middle connected to a
calorimetric oil-to-water cooling system and controlled by a
100 dSpace rack.
2 3 4 5 6 7 8
Flow rate [l/min] The coolant oil used for the prototype machine is pro-
vided by ExxonMobil and specifically developed for electrical
Fig. 12: Convection heat transfer coefficients from coils in
machine cooling, featuring low viscosity and good thermal
slot number S to coolant oil, established by CHT simulation
properties as shown in Table IV.
at different flow rates.

The software used for the different physics as well as the V. R ESULTS
number of mesh nodes for the models built are presented in In order to validate the CHT model, the temperatures of
Table III. the different slots and end windings are compared with the
SUBMITTED 2019-12-20 TO IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

TABLE IV: Oil coolant properties (data from ExxonMobil).

40 ◦ C 80 ◦ C 100 ◦ C
Kinematic viscosity (cSt) 2.31 1.28 1.02 S9 Sim
Specific heat (J/kgK) 2.15 2.28 2.35 65
S9 Meas
S10 Sim
60 S10 Meas
S8 Sim
S8 Meas
55 S11 Sim

[deg C]
S11 Meas
50

45

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

[l/min]
Fig. 15: Measured and simulated slot temperatures.

60 EW1-DE Sim
EW1-DE Meas
EW5-DE Sim
55 EW5-DE Meas
EW5-NDE Sim
EW5-NDE Meas
[deg C]

50

45

40

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Fig. 14: Photo of calorimetric and dynamometer setup. [l/min]
Fig. 16: Measured and simulated end winding temperatures.
temperature sensors available in the machine. In the CHT
model the sensors are placed in a position which corresponds between the sensor and the surface of the cooling channel
to the ones presented in Fig. 1. greatly affects the temperature measurement. The uncertainty
on the placement of these sensors is the major source of error.
A. DC current measurements and CHT validation A similar measurement was performed in [8] on a machine
Both CHT simulations and physical measurements are per- with cooling jacket reporting errors between simulation and
formed at 60 ADC (ca 800 W copper losses) as the only sensor readings in the order of 3-5%. For the cooling solution
heat source, rotor at stand still, and with three different oil adopted in this paper, the highest temperatures are found at
flow rates. Results comparing the CHT simulation and the high machine load are found in the molded coils axially mid-
measurements are presented in Fig.15 for the slot sensors, way through the slot. The end-windings are extremely well
and in Fig.16 for end winding sensors. The measurements- cooled according to measurements and simulation results.
to-simulations relative error in percent is presented in Tab. V, To evaluate the pressure drop, a CFD simulation of the
defined as cooling path is built, considering the oil viscosity at 20◦ C and
Tmeas − Tsim modeling the bolts, which are generating turbulence in the end
dT% = ∗ 100 (2)
Tmeas − Tinlet section. The pressure drop from the CFD simulation and the
where Tmeas and Tsim are respectively the measured and measurements (pressure sensors placed at inlet and outlet of
simulated values and Tinlet is the oil inlet temperature (20◦ C). the machine) are presented in Tab. VI. The measured pressure
The winding temperature prediction is in good agreement drop is significantly higher than the simulated values. This is
considering that there has been no correction factor of ge- due to the fact that the CFD simulation does not include all the
ometry or material properties to fit the measurements. The parts in the end section, such as adjacent coil connection joint,
temperature sensors are buried in the potting material (in and the invasive presence of the temperature sensors cables
contact with the coil) and the thickness of the epoxy resin which are being partly routed through the cooling channel.
SUBMITTED 2019-12-20 TO IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

TABLE V: Percentage relative error temperature sensors. Measurements for continuous operation have been carried
Sensor 2 l/min 4 l/min 6 l/min out with 70 ARM S (17.5 A/mm2 ) and a constant speed of
S8 -0.4 4 9.2 1000 rpm, input oil at 20◦ C and oil flow rate at 6 l/min.
S9 -17.3 -11 -5.3
S10 -15.5 -9.5 -6.2
The simulated and measured temperature rise are presented in
S11 -8.3 9.7 23 Table VII.
EW1-DE 4.5 2.3 14.2
EW5-DE -13.4 -4.3 4.1 TABLE VII: Steady state temperature rise at 17.5 A/mm2 ,
EW5-NDE -9.3 3.8 10 speed of 1000 rpm and oil flow rate of 6 l/min
Measured Simulated
End Winding 26.0◦ C 32.6◦ C
Mid-Slot 35.2◦ C 42.1◦ C
These can significantly affect the turbulence, and consequently
the pressure drop. The measured pressure drop at the highest
flow rate of 6 l/min, is considered low enough for a standard
12 V automotive oil pump to be used. The electrical power
required by the pump at 6 l/min and oil temperature of 20◦ C C. Peak operation validation
is ca 10 W . To verify the peak operation condition, a transient simula-
tion is carried out at an initial temperature of 90◦ C and oil
TABLE VI: Oil pressure drops comparison. temperature of 60◦ C, constant flow of 6 l/min, rated speed
2 l/min 4 l/min 6 l/min 3600 rpm and 140 ARM S (35 A/mm2 ). As seen in Fig. 18,
CFD [kP a] 2.9 6.6 12.7 winding hot-spot reaches 180 ◦ C after 30 s, which defines the
Measured [kP a] 4.9 18.4 37.6
peak operating condition in worst case circumstances.

B. Continuous operation validation 200 Winding avg.

Having the oil flowing in close proximity to the winding Hot-spot winding
Stator iron
and directly in the stator iron significantly reduces the thermal 180 Rotor iron
transient of the stator. Two thermal time constants can be PMs
identified; the stator thermal steady state is reached after 30 160 End windings
[deg C]

minutes of operation, however due to the high thermal resis-

tance of the airgap the rotor thermal transient is about twice as 140
long. A thermal transient simulation is carried out to verify the
continuous operation condition with the following conditions: 120
initial oil temperature of 60◦ C, constant oil flow rate 6 l/min,
rated speed 3600 rpm, and 100 ARM S (25 A/mm2 ). As 100
seen in Fig. 17, all temperatures are below the 180◦ C limit
which validates the continuous operating condition in worst 0 10 20 30 40 50
[s]
case circumstances.
Fig. 18: Transient simulation for peak operating condition at
initial machine temperature of 90◦ C, oil temperature of
60◦ C, constant flow of 6 l/min, 3600 rpm and 140 ARM S
(35 A/mm2 ).
160
Measurements for peak torque, 140 ARM S , are carried out
140 at 150 rpm. The input oil temperature is approximately 20◦ C
and oil flow of 6 l/min. The readings of the warmest sensors
120
[deg C]

are depicted in Fig. 19 and compared to simulated values,

confirming that all temperatures are well within the limits. The
100 Winding avg.
Hot-spot winding winding temperature measurements are partly interrupted by
Stator iron interference of PWM operation at high currents in this setup.
80 Rotor iron The difference between simulated and measured temperatures
PMs is again mainly due to uncertainty in the placement of the
60 End windings
sensor.
0 20 40 60 80 100 120
[min]
VI. C ONCLUSION
Fig. 17: Transient simulation for continuous operating In this paper a novel design and construction of an in-slot
condition at initial and oil temperature of 60◦ C, constant and in-stator direct oil cooled tooth coil winding machine
flow of 6 l/min, 3600 rpm and 100 ARM S (25 A/mm2 ). is presented which enables current densities of 25 A/mm2
SUBMITTED 2019-12-20 TO IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

Stefan Skoog was born 1985, graduated as

M.Sc.E.E from Lund University, Sweden in 2010.
140 Stefan has a decade of professional experience
in R&D in advanced mechatronics and automo-
120 tive powertrains. He is currently a PhD student at
Chalmers University, Sweden, working on mild
100 hybrid electrification systems limited to 48 VDC
Slot meas aimed for personal vehicles. His interests in-
Slot sim clude modeling, design and verification of ad-
[degC]-[Nm]

80 EW meas vanced battery systems, power electronics and

EW sim electric machines.
60 Steel meas
Steel sim
40 Torque meas

20

0
0 10 20 30 40
time [sec]
Fig. 19: Peak torque operation (140 ARM S , 150 rpm) for
30 s at starting temperature and oil temperature of about
20◦ C. Solid lines showing measured values of the warmest
sensor for the part considered. Dashed lines are simulated
values.

continuously and 35 A/mm2 for 30 s peak operation at oil

flows of 6 l/min and 42 kP a pressure drop. Such high
current densities have not been found in the literature from
full rotating experiments for a similar sized machine. Although
the machine is tested at max 3000 rpm, the FEA models
indicate that the target of 50 kW can easily be met at slightly
higher speed. The hot spots of the motor is found mid-slot,
which proves that the end-windings are very well cooled by
the coolant oil flow.
The slot cooling channels are created using a high ther-
mal conductivity potting material and can be successfully
simplified in FEA modeling using an equivalent composite
material. A conjugate heat transfer simulation is developed to
characterize the cooling performance and run using the losses
from electromagnetic finite element simulations. Convection
heat transfer coefficients are extracted and used to simulate
the transient operating condition. The model-to-measurement
temperature deviations are within a few percent (and within
a few ◦ C), proving the usefulness of the simplified thermal
model.

VII. B IOGRAPHIES

Alessandro Acquaviva received a double M.Sc

at Politecnico di Torino and KTH, Stockholm, Torbjörn Thiringer works at Chalmers univer-
Sweden in 2012. After four years in traction sity of Technology, in Gothenburg, Sweden, as a
electrification industry and completing an MBA professor in applied power electronics. He took
he is currently pursuing his Ph.D. at Chalmers his M.Sc and Ph.D at Chalmers University of
University of technology in Gothenburg, Swe- technology in 1989 and 1996 respectively. His
den. His areas of interest include the modeling, areas of interest include the modeling, control
control and design of electrical machines and and grid integration of wind energy converters
power electronics with focus on automotive ap- into power grids as well as power electronics
plications. and drives for other types of applications, such
as electrified vehicles, buildings and industrial
applications.
SUBMITTED 2019-12-20 TO IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

R EFERENCES [15] P. Lindh, I. Petrov, A. Jaatinen-Värri, A. Grönman, M. Martinez-

Iturralde, M. Satrustegui, and J. Pyrhönen, “Direct liquid cooling method
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[11] S. Skoog and A. Acquaviva, “Pole-slot selection considerations for ison of mtpa and minimum loss control for tooth coil winding pmsm
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 Paper VII
Electromagnetic and Calorimetric Validation
of Direct Oil Cooled Tooth Coil Winding
PM Machine for Traction Application
Submitted 2020-05-17 to MDPI Energies

First author contributions

Lead machine design FEA, thermal and mechanical, idea generation,
data processing and analysis, FEA figures, figure generation.
Second author contributions
Lead in design, construction and calibration of measurement setup,
data acquisition, idea development.
Third, fourth author
Paper review, paper structure, idea revision, supervision,
administration, resource allocation, funding.

167
168
 Article
Electromagnetic and Calorimetric Validation of Direct
Oil Cooled Tooth Coil Winding PM Machine for
Traction Application
Alessandro Acquaviva 1, * , Stefan Skoog 1, , Emma Grunditz 1, and Torbjörn Thiringer 1,
1 Chalmers University of Technology
* Correspondence: alessandro.acquaviva@chalmers.se; Tel.: +46-735704363

Version May 17, 2020 submitted to Energies

1 Abstract: Tooth coil winding machines offer a low cost manufacturing process, high efficiency
2 and high power density, making these attractive for traction applications. Using direct oil cooling
3 in combination with tooth coil windings is an effective way of reaching higher power densities
4 compared to an external cooling jacket. In this paper, the validation of the electromagnetic design for
5 an automotive 600 V, 50 kW tooth coil winding traction machine is presented. The design process
6 is a combination of analytical sizing process and FEA optimization. It is shown that removing iron
7 in the stator yoke for cooling channels does not affect electromagnetic performance significantly.
8 The machine is designed, manufactured and tested continuously at 105 Nm with 25 A/mm2 and at
9 145 Nm with 35 A/mm2 10 s peak during 6 l/min oil cooling. Inductance, torque and back EMF
10 are measured and compared with FEA results showing very good agreement with the numerical
11 design. Furthermore, the efficiency of the machine is validated by a direct loss measurements, using a
12 custom built calorimetric set-up in six operating points with an agreement within 0.9 units of percent
13 between FEA and measured results.

14 Keywords: Permanent magnet machines, Electromagnetic design, Model verification, Performance

15 evaluation, Calorimetric measurement, Oil cooling, Efficiency validation

16 1. Introduction
17 In recent years, research and development of automotive electric traction machines has greatly
18 intensified. Apart from high efficiency and low cost, a specific design target for these machines is
19 high power density (i.e. power per volume) [1–3]. Aiming for high power density means maximizing
20 the material utilization of the machine, which is essential to achieve cost-effective solutions for
21 mass-production, and low package volumes that enables effective system packaging.
22 Therefore, high-power density electric machines as well as power electronics, are seen by the
23 US department of energy as critical enablers of large-scale electric vehicle adoption [2]. The previous
24 technical target specified in the US DRIVE Technology Roadmap for 2020 was 5.7 kW/liter for a 55 kW
25 peak machine. However, the latest target for 2025 is 50 kW/liter for a 100 kW peak machine. Even
26 though existing solutions are well positioned for the 2020 target, significant challenges lies ahead to
27 live up to the next generation of traction systems in year 2025. This is exemplified in Table 1, which
28 provides a comparison of power densities, both net (total volume of active steel) and gross (volume of
29 complete electric machine casing), for state-of-the-art automotive electric traction machines.
30 High-power density electric machines can be achieved by utilizing factors such as:

31 • high mechanical speed [3], by a high electric frequency, or high pole number [4]
32 • high airgap flux density (i.e. magnetic loading), eg. by using high energy magnets, or a field
33 winding excitation, both in combination with core material with a high saturation[5]

Submitted to Energies, pages 1 – 18 www.mdpi.com/journal/energies

 Version May 17, 2020 submitted to Energies 2 of 18

34 • high current loading, or high current density, while simultaneously assuring a low thermal
35 resistance between the winding and coolant

36 For the sake of high magnetic loading, the development of electric drive-trains is primarily
37 dominated by the permanent magnet synchronous machine (PMSM) [6], characterized by its high
38 power density as well as high efficiency [1,7,8]. However, as identified in [2], to reach even higher
39 power density, more research is required regarding “improved thermal materials”, as well as “advanced
40 cooling/thermal management techniques to reduce size, cost and improve reliability”. Extensive
41 engineering efforts are devoted to solve these challenges, as summarized well in [9–11]. An apparent
42 aim is to try to bring the coolant medium closer to the main sources of heat, i.e. the stator core and
43 winding, as opposed to so called cooling jackets.
44 One possibility is then to use a tooth-coil winding machine (TCWMs), also known as
45 non-overlapping fractional slot concentrated winding (FSCW) machine. With this machine type,
46 it may be possible to devote some of the space that is normally used for active material, for
47 cooling channels instead, without sacrificing performance. Still, it offers high torque density and
48 high efficiency [12–14] when combined with a permanent magnet (PM) rotor, as well as low cost
49 manufacturing. In [15], a 12-slot 8-pole TCWM for traction application is compared with a distributed
50 winding (DW) interior-magnet, a switched reluctance, and an induction machine. The TCWM is shown
51 to perform best in terms of torque density, even without considering the shorter winding overhang.
52 Efficiency-wise, the two PM machines are comparable, TCWM being slightly better in the low speed
53 region and less efficient at high speeds compared to the DW machine. Other interesting traction motor
54 designs using TCWM are presented in [16–20], however, without the integration of direct cooling in
55 the stator, continuous current densities above 20 A/mm2 are hardly reached, which limits the torque
56 density.
57 Previous proposals of high performing liquid cooling techniques for TCWMs comprise examples
58 such as the following:

59 • using conductive pipes in the slots, with the drawback of generating large eddy current losses [21]
60 • theoretical evaluation of the concept of flushing the entire stator and rotor with oil coolant [22]
61 • direct-water cooled coils by winding a coolant carrying steel pipe with litz wire, validated in a
62 205 kW machine for a bus application [23]
63 • using fluid guiding structure and airgap sealing to allow for oil cooling within the slots [24].

64 Neither of these examples though, have reached the levels of power density and efficiency that is
65 presented in this paper, nor have they experimentally verified as high current densities.
66 Enabling high current density, which in turn means high copper losses at peak operation, does
67 not preclude the traction machine to achieve high energy efficiency. The reason is that during driving,
68 the machine operates most of the time in part-load, i.e. the low torque region, as shown for several
69 drive cycles in [25]. Achieving high energy efficiency can significantly extend the range of the vehicle
70 for a given battery pack.
71 This purpose of this paper is to present the electromagnetic design and verification of a high-power
72 density, high-efficiency 50 kW TCWM, sized for traction application of passenger vehicles. The high
73 power density is achieved by integration of direct-oil cooling in the stator yoke as well as in the slot
74 via a potting material with high thermal conductivity, which shapes the cooling channels. The details
75 of the design and verification of the cooling solution are presented by the authors in [26]. This paper
76 instead focuses on the electromagnetic design validation. Particularly, it is shown how the placement of
77 stator yoke oil cooling channels can be done without affecting the electromagnetic performance, which
78 has not been found in literature. Experimental validation of the torque, no-load EMF and inductance
79 present a very good match with simulations. Furthermore, the efficiency is verified through a direct
80 loss measurement in a custom-made calorimetric set-up, also showing a good match with simulated
81 results. Finally, the paper guides the reader through the main choices and steps for the design of a
82 traction PM-TCWM intended for high volume production.
 Version May 17, 2020 submitted to Energies 3 of 18

Table 1. Performance metrics for traction machines

Machine Net Power Gross Power Peak
Density (kW/l) Density (kW/l) Efficiency
Toyota HSD 2010 [27] 22 5.2 96% [27]
BMW i3 [3] 20 9.2 94% [28]
Machine presented here 19 6.7 95%
DoE Target 2020 [2] - 5.7 -
DoE Target 2025 [2] - 50 -

Q12p10 Q9p12

Q6p8 Q12p8

Figure 1. Smallest unique section of rotor and stator geometries for the four TCWM slot-pole
combinations evaluated through FEA.

83 2. Machine design
84 The target application of the machine in this paper is a traction motor for either a small passenger
85 vehicle, or an assist motor in a plug-in hybrid electric vehicle. The traction machine is assumed to
86 operate with a fixed-gear reduction gearbox, powering either of the vehicle wheel pairs, and able to
87 operate with a large field-weakening window. The design specifications are listed in Table 2.

88 2.1. Electromagnetic analytical sizing and design choices

89 The electromagnetic design is based on an analytical sizing method combined with a finite element
90 mapping and verification. Given the target power rating, a desired high power density, and the ability
91 to gear the machine, an axially long and radially small machine is selected to achieve high mechanical
92 speeds. A fundamental frequency of 1.2 kHz is assumed at maximum speed, limited by machine iron
93 losses and the maximum switching frequency (typically 10 kHz) together with a reasonable frequency
94 modulation index of a high-performance traction inverter. A pole-pair number of five or six will
95 now set the maximum mechanical speed to 14.4 and 12 krpm, respectively. Using the methodology
96 presented in [13], the only slot (Q) - pole (p) options left for a balanced three-phase machine are Q6p8,
97 Q12p8, Q12p10 and Q9p12, all illustrated in Fig. 1. A FEA comparison between these four feasible
98 pole-slot combinations in terms of output torque and iron losses at 300 Hz electrical frequency is shown
99 in Fig. 2. This comparison is done keeping the main geometrical parameters (material types, axial
100 length, stator external and internal diameter, airgap length, tooth embrace) and loading parameters
101 (current density, airgap flux density) constant in all the designs. The Q12p10 machine presents the
102 highest torque density and lowest iron losses among the machines compared, as can be seen in Fig. 2.
103 Furthermore the Q12p10 offers the best balance between high fundamental winding factor (0.933),
104 low harmonic leakage inductance factor (0.97), and high cogging frequency, all numbers are derived
105 in [13].
 Version May 17, 2020 submitted to Energies 4 of 18

Q12p10 cont
1.3
Q12p10 peak

Q12p8 cont

Normalized Torque [p.u.]

1.2
Q12p8 peak

Q6p8 cont

1.1 Q6p8 peak

Q9p12 cont

Q9p12 peak
1.0

0.9

0.8

2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75

Iron losses/output power [%]

Figure 2. Numerical comparison of the different pole slot combinations for peak and continuous
operation. The machines have the same volume, airgap flux density and current density. The torque is
normalized to the Q12p10 machine in continuous operation.

106 The analytical sizing procedure, presented in [29], is based on the split ratio optimization. The
107 split ratio, defined as the ratio between internal to external stator diameter, in fact can be used as a
108 main parameter to size the machine. The analytical model is built by writing the torque equation of
109 the brushless PM machine as a function of the main geometrical parameters and the two main loading
110 parameters, airgap flux density and current density. It is shown in [29] that the choice of the split
111 ratio is a trade-off between efficiency and torque density. In the design presented in this paper the
112 split ratio is chosen to maximize the efficiency, resulting in 0.62. The choice is also driven by thermal
113 considerations; a low value of split ratio leads to a high copper and slot area, which, for a fixed current
114 density, means critical cooling requirements. A stator design without tooth tips is chosen to improve
115 manufacturability by allowing the coils to be pre-wound outside the stator and inserted radially. The
116 rotor is chosen as an internal V-shaped PM with air barriers to enable high saliency which improves
117 the field weakening (FW) characteristic. Embedding the magnets in the rotor also limits magnet losses
118 caused by harmonics in the airgap MMF [30,31]. One additional measure taken to limit excessive
119 magnet losses is magnet segmentation [31,32] by using 20 equal Vacodym 745DHR NdFeB magnet
120 units stacked axially in each rotor slot.
121 The resulting machine parameters are listed in Table 3. The maximum phase current corresponds
122 to 35 A/mm2 current density in the copper conductors. The coil disposition and geometries of stator
123 and rotor with details about disposition of conductors and cooling channels are shown in Fig. 3. The
124 Q12p10 machine has a key winding factor [13] of 2, meaning each phase coil consist of two electrically
125 series connected coils on adjacent teeth. Each coil has 28 turns, which allows for a 1.6 mm diameter
126 enamel copper wire to be used and avoiding parallel strands in the coils. Having a bobbin which can

Table 2. Electrical machine design specifications

Quantity Symbol Value Unit
Peak torque Tmax 140 Nm
Peak power Pmax 50 kW
Base speed nb 3 600 rpm
Max speed nmax 11 000 rpm
Coolant max temperature Θmax,c 60 ◦C
Max winding temperature Θmax 180 ◦C
DC bus voltage VDC 600 V
 Version May 17, 2020 submitted to Energies 5 of 18

(b) The arrangement of copper conductors, potting

(a) Stator and rotor laminations geometry, coil material and oil cooling channel within one slot.
disposition and cooling channels.
Figure 3. Details of lamination geometry, cooling channels and conductor disposition.

127 be inserted, limiting the conductor diameter and avoiding parallel strands enables the use a linear
128 winding machine, which can drastically reduce the manufacturing cost at high volume production.
129 Each set of two series coils are then parallel connected to form a full phase winding, as shown in Fig. 4.

Table 3. Electrical machine main dimensions and data

Quantity Symbol Value Unit
Outer Stator diameter De 180 mm
Inner Stator diameter D 111.4 mm
Active length L 100 mm
Tooth width wt 17 mm
Stator Yoke width wsy 13 mm
Magnet thickness hm 3.5 mm
Diameter of each conductor dN 1.6 mm
Number of turns per coil N 28 -
Maximum RMS current Imax 140 A

Figure 4. Winding disposition and connection. For this prototype machine, both parallel connection
and Y connection is made outside the housing through six connection terminals.

130 2.2. Cooling channel size and electromagnetic effects

131 Introducing cooling channels in the stator back yoke by removing iron after the split ratio
132 optimisation might affect the electromagnetic performance negatively by increasing the reluctance
133 path for the rotor PM flux and/or the linked flux between stator coils. The Q12p10 machine features
134 low mutual inductance between phases by linking the vast majority of the flux generated by phase
135 windings in a loop contained within the two adjacent teeth belonging to the same phase group. This
 Version May 17, 2020 submitted to Energies 6 of 18

Table 4. Results from FEA evaluation of cooling barrier size at 3000 rpm, 40 A/mm2
Barrier Average torque Torque ripple
size pk2pk
(mm) (Nm) (%) (Nm) (%)
1.0 162.13 0 16.484 0
2.0 162.12 -0.01 16.633 +0.90
3.0 161.91 -0.13 16.973 +2.97
4.0 160.65 -0.91 19.135 +16.1
5.0 157.37 -2.94 23.933 +45.2

Figure 5. FEA established magnetic flux generated by 100 A in phase A without any remanence in the
magnets.

136 scenario is illustrated in Fig. 5 without any PM flux and 100 A in phase A. The reluctance change
137 for coil self-linked flux due to cooling channels positioned between the coil groups belonging to the
138 different phases, is believed to be negligible. In [30], a similar yoke barrier strategy is used to reduce
139 the flux of sub-harmonics which exist in this winding layout, aimed to reduce both iron and PM losses
140 in the Q12p10 machine. The solution in [30] evaluates yoke barriers situated between the teeth within
141 a phase, which leads to a large reduction on torque for the machine type preferred in our paper.
142 To find out the performance implications of flux barrier between the phases, including the PM
143 flux, a FEA parametric sweep is performed. The cooling channels thicknesses is swept from from 1 to
144 5 mm. As a reference, 2.0 mm is used in the final design shown in Fig. 5, and at 5 mm each, the two
145 channels cover 77% of the 13 mm yoke thickness. Note that the shape of the channels and the choice
146 of having four parallel channels instead of one is driven by flow split evaluation as explained in [26].
147 Average torque, torque ripple and iron losses are evaluated at rated speed, from zero up to to above
148 rated current; 3000 rpm and 160 A (40 A/mm2 ). The results for the highest current, which has the most
149 dramatic impact, are shown in Table 4. More than half (4 mm) of the yoke width can be cut out before
150 1% average torque loss is experienced. Torque ripple consequences are kept low at 3 mm or lower.
151 Regarding iron losses, no monotonic or clear change is found for the different barrier thicknesses;
152 increase of iron losses is less than 1% as a function of slot size. Using two 2 mm coolant barriers
153 positioned between the phase groups is considered to have negligible impact on electromagnetic
154 performance, and offer enough cross-section area for low-viscosity oil to flow without significant
155 pressure drop. This type of utilization of part of the stator yoke to introduce cooling channels can
156 be generalized for all the TCWMs with an even key winding factor, which represents the number of
157 adjacent coils of the same phase [13].
 Version May 17, 2020 submitted to Energies 7 of 18

Figure 6. Wound stator before (left) and after (right) potting. The white plastics in the left picture is the
bobbins used to pre-form the coils outside the machine.

158 2.3. Slot fill factor and cooling channels

159 The cooling channels are derived from the space in between the two coils, which is unused space
160 in the slot. These are shaped in the epoxy material with Teflon sticks that are extracted after the potting
161 process. The potting material is a epoxy resin, with a thermal conductivity of 1.9 W/(m · K ). The total
162 slot area is 350 mm2 . The cooling channel area in the slot is 100 mm2 giving a net slot area of 250 mm2 .
163 The copper area is 113 mm2 , therefore the net fill factor is 0.45 while the bulk fill factor considering
164 the total slot area is 0.32. The stator with the windings mounted before and after potting is presented
165 in Fig. 6. All thermal and cooling design considerations, including fluid dynamic analysis, for this
166 machine are presented in [26].

167 3. Numerical evaluation

168 The electromagnetic performance of the machine, including loss mapping, is evaluated using
169 FEA. The losses are used as input for evaluating the thermal performance and the efficiency.
170 Interior PM machines, when functioning as motors, are typically operated in the second quadrant
171 of the d-q current plane. This is done in order to use both the PM flux generated torque, the reluctance
172 torque and, at high speed operation, field weakening. The maximum negative d-axis current and
173 positive q-axis current are evaluated analytically and used as references to map the operating region.
174 For each point in the mapping, a set of 2D quasi-static magnetic FEA for one electric period is
175 performed.

176 3.1. Loss Mapping

177 In order to evaluate PM and iron losses, the information stored on each simulation is the B field
178 x and y component (Bx and By ) of the stator and rotor iron mesh elements and the magnetic vector
179 potential A, which in 2D FEA has only the z component, of the PMs mesh elements.
The iron losses are computed by performing the Discrete Fourier Transform (DFT) of Bx and By of
stator and rotor iron elements. For each harmonic i and mesh element j

B2f e,i,j = Bx,i,j

2 2
+ By,i,j . (1)

Iron losses are computed as the sum of all the contributions of the harmonics and all the m elements [25]

m n/2 Vj
Pf e,ω = Km ∑∑ γ (k e B2f e,i,j f i2 + k h B2f e,i,j f i ) (2)
j =1 i =1
ks f e

180 where k e and k h are eddy current and hysteresis loss factors that can be extracted from the lamination
181 data, γ f e is the mass density of the iron, f i is the electrical frequency corresponding to the ith harmonic,
 Version May 17, 2020 submitted to Energies 8 of 18

182 where the fundamental harmonic is the first harmonic present in the machine MMF for a certain speed
183 ω. Vj is the volume of the mesh element j and k s is the stacking factor. Furthermore, Km is a iron
184 loss scaling coefficient. This coefficient accounts, in the first place, for the effect of laser cutting of
185 non-oriented electrical steel causing structural changes at the cutting edge, which finally affect the
186 magnetic properties. Secondly, there is often a mismatch between the loss data found in the steel data
187 sheets and the measured values.
188 Copper and iron losses are calibrated with the measured phase resistance, and by measuring
189 the iron losses with the calorimetric set up described in Section IV, at 3000 rpm and no load. This
190 results in an iron loss scaling coefficient Km in eq. (2) of 2.0, meaning that the measured values of iron
191 losses are twice the ones estimated with FEA using the interpolated loss coefficients from the soft iron
192 manufacturer. Typical values of iron loss scaling coefficients found in the literature [22] are in the range
193 between 1.5 and 2.0.
To calculate the PM losses, the DFT of the vector potential A of mesh elements belonging to the
PMs is computed. The PM induced current density can be then calculated as

1 dA PM
JPM = − ω + C (t) . (3)
ρ pm dθ

194 where C (t) is an integration constant which forces the net total current flowing in each magnet to zero
195 at any time instant and ρ pm is the resistivity of the magnet material. The method is fully described
196 in [33]. PM segmentation in the axial direction is accounted for by considering an equivalent eddy
197 current resistance path. A flow chart summarizing the loss mapping procedure is shown in Fig. 7. The
198 torque-speed maps showing the different loss contributions are presented in Appendix A.

Figure 7. Loss mapping procedure flow chart

199 3.2. Inductance and linked PM flux

200 The d and q-axis inductance as a function of current are useful parameters for control purpose.
201 The flux linkage of each phase and for all operating points is known from the FEA. Using the Clark
202 and Park transformation the d-axis and q-axis flux linkage are derived. The PM flux linkage can be
203 calculated at id = 0 as a function of the q-axis current as

Ψ pm (iq ) = Ψd . (4)
i d =0

204 The d-axis and q-axis inductance can be computed as

 Version May 17, 2020 submitted to Energies 9 of 18

Ψd − Ψ pm
Ld = (5)
id
Ψq
Lq = . (6)
iq
205 The inductance maps as a function of the d-axis and q-axis currents are presented in Fig. 8.

10-3 10-3
1.4 2.5

1.2
2

Lq [H]
Ld [H]

1
1.5
0.8

0.6 1
0 0
0 0
100 -50 100 -50
iq[A] 200 -100 id[A] iq[A] 200 -100 id[A]

Figure 8. Inductance maps established through FEA.

206 3.3. Induced voltage

The induced phase voltage of the machine can be calculated from the derivative of the flux with
respect to the angle, using approximation of derivatives by finite differences, as

∆Ψ a,b,c
Va,b,c = ω + R DC i a,b,c . (7)
∆θ
207 where ∆Ψ a,b,c is the finite difference in flux linkage for a mechanical angle step of ∆θ, is the R DC is the
208 measured DC phase resistance, ω is the mechanical rotational speed and i a,b,c is the phase current.

209 3.4. Torque

210 The torque is computed through Arkkio’s method [34], which essentially averages out all Maxwell
211 stress tensor integration paths in a circular band in the air gap to improve the accuracy of torque
212 computation by cancelling out some numerical noise due to the differentiation.

213 4. Test set up

214 In order to evaluate the performance of the assembled traction machine, a calorimetric set up is
215 designed and constructed. The lab environment consists of a electric dynamometer, the test machine,
216 power electronics, a custom made oil-to-water cooling system and a dSpace SCALEXIO-rack. The
217 setup is illustrated in Fig. 9 and shown on photo in Fig. 10.
Sensors are installed and calibrated to measure DC and AC voltage (v), phase currents (i) output
torque (τ), rotational speed (ω), rotational position (θ), oil and water flow-rates (ṁ), oil and water
inlet and outlet temperatures (T) and pressures (p), water flows and pressures. Critical measurement
equipment is listed in Tab. 5. The dSpace rack acts as the control hub of the dynamo setup. With
the total setup, both electrical, mechanical and direct-loss power can be measured and displayed
continuously and reference values can be set via a PC GUI. Oil and water temperatures are measured
and converted to digital form with high resolution. The inlet-to-outlet temperature drop (∆T) of the
coolant oil is established. Together with the oil mass flow (ṁ), oil density (ρ = 821 kg/m3 ) and the
 Version May 17, 2020 submitted to Energies 10 of 18

𝑛𝑟𝑒𝑓
𝜏 𝑛 𝜃

𝑇
𝑚
𝑝
𝑖
+
−
𝑣
Figure 9. Calorimetric measurement system setup: A dSpace system is controlling the dynamo, the
prototype machine, and the custom made oil-to-water cooling system.

Figure 10. Picture of calorimetric test setup, showing the thermal insulation of the machine, oil hoses,
and phase cables.

oil specific heat capacity (c p = 2100 J/kg/K) the total loss heat transported out of the machine can be
calculated as
Pcal = ṁ ρ c p ∆T . (8)

218 The test machine and the oil system is thermally insulated towards ambient in order to minimise
219 thermal leakage and enable accurate calorimetric measurements. A glass fiber washer acts as a thermal
220 insulator between the machine enclosure and the mounting frame. The coolant oil is heat exchanged
221 with mass flow controlled tap water so that the inlet oil temperature to the machine is kept at 22◦ C, in
222 order to minimize leakage heat from the surroundings.
223 A three-leg IGBT based inverter, operating at 5 kHz SVM closed-loop current control is feeding
224 the test machine at up to 600 VDC . The dynamometer is operating at closed-loop speed control through
225 a thyristor converter, feeding back power to the grid when the test machine is operating in motor
226 mode.
 Version May 17, 2020 submitted to Energies 11 of 18

Table 5. Critical measurement equipment

Quantity Equipment
Torque ETH DRBK-500-n
Speed, Position Kübler 8.5020.2514.1500
Voltage LeCroy HVD3206A
Current LeCroy CP150
Power Analysis LeCroy MDA805
Mass flow Swissflow SF800

227 5. Results
228 In this section the results from the measurements are presented and compared to the simulated
229 values.

230 5.1. Machine parameters, back EMF and torque evaluation

231 The initial set of tests performed on the machine is to extract the main equivalent circuit model
232 parameters. Firstly, the DC resistance of each coil is measured using a 4-terminal method resulting in a
233 phase resistance of 62 mΩ. Secondly, the machine is connected with phase A in series with the parallel
234 of phase B and C. The inductance seen with this type of connection needs to be scaled by 2/3 to obtain
235 the synchronous inductance. By moving the rotor in small mechanical angle steps and locking it, the
236 inductance for each position can be measured using two methods:

237 • LCR tester at 1 kHz

238 • voltage step response from a fast power supply resulting in ca 19 A. The 20-80% rise time is
239 extracted with an oscilloscope and re-scaled to a first order time constant

240 The results of the two measurement methods compared to the predicted FEA synchronous
241 inductance as a function of the mechanical position are presented in Fig. 11. The maximum and
242 minimum values of the curves in Fig. 11 represent the q-axis and d-axis inductance respectively. The
243 machine presents a saliency Lq /Ld = 1.45 given by the V-shaped rotor geometry. Fig. 12 shows the
244 no-load back-EMF at 1016 rpm, with both FEA and measurements.

1.9
Meas-step
1.8 Meas-LCR
FEM
1.7
1.6
Inductance [mH]

1.5
1.4
1.3
1.2
1.1
0 50 100 150 200 250 300 350
Theta [deg]
Figure 11. Inductance versus electrical position by FEA and two different measurement methods
 Version May 17, 2020 submitted to Energies 12 of 18

100 Meas
75 FEM

50
EMF [V] 25

−25

−50

−75

−100
0 50 100 150 200 250 300 350
Theta [deg]

Figure 12. No-load back-EMF at 1016 rpm measured and simulated line-line voltage in Y-connection

245 The torque is measured, with the torque sensor, in two different operating conditions, pure
246 q-axis current (90 deg) and the MTPA angle at maximum current (115 deg). The results at 150 rpm
247 are presented in Fig 13. A current value of 100 A RMS corresponds to a copper current density
248 of 25 A/mm2 which can be kept continuously for this machine. If the machine would have been
249 equipped with a standard water jacket cooling, a current density of 10 A/mm2 is to be expected [7,24].
250 Maintaining the same fill factor and removing the cooling channels, the slots could theoretically fit 40%
251 more copper. Altogether, the maximum allowed continuous phase current would be 56 A (instead of
252 100 A), and according to Fig. 13, the maximum output peak torque limited to 62 Nm instead of 110 Nm.
253 Overall, by using direct oil cooling, the continuous power of the machine, for the same operating
254 speed, increases by over 75%.

140 Meas 90 deg

FEM 90 deg
120 Meas 115 deg
FEM 115 deg
100
Torque [Nm]

80

60

40

20

0
0 20 40 60 80 100 120 140 160
Current RMS [A]
Figure 13. Average torque output at 150 rpm rotor speed, 90 and 115 deg current angle. Measurement
and simulation comparison.

255 5.2. Calorimetric evaluation of efficiency

Electromagnetic efficiency through FEA, not including mechanical losses, is presented in in Fig. 14.
The six operating points where the efficiency of the machine has been measured with the calorimetric
 Version May 17, 2020 submitted to Energies 13 of 18

setup are marked with letters. The calorimetric method is presented in Eq. 8, and the measured
efficiency is calculated using the total AC electrical active power Pin from the power analyser as:

Pin − Pcal
η= . (9)
Pin

256 The output mechanical power is defined as Pmech = ω τ . The measured efficiency are presented
257 in Table. 6 and summarized in Fig. 16. The measured efficiency is within 0.9% of the simulated one.
258 The difference between the two can be attributed to two main reasons.

259 • Mechanical losses, such as friction in the bearings and windage losses, which are not included in
260 the FEA efficiency but are present in the measurements
261 • Leakage heat towards ambient air and through the shaft. Although, all possible precautions have
262 been taken to minimize the heat leakage it is not possible to completely remove this source of
263 error

264 The mechanical power can also be used to estimate the efficiency, however the accuracy of the torque
265 sensor reading is lower compared to the input power reading and would lead to a higher uncertainty.
266 Measurements above base speed are unfortunately not possible with the current dynamo setup.
267 In Fig. 15 the calorimetric run for point E is presented. It is of great importance to reach a thermal
268 steady state in order to have an accurate calorimetric reading.

140

120
10
40
70

100
94
Torque[Nm]

92
88

80
84
80

60
95

B D F

40

A 94 C E 95
20 94
70
10
40

92 92
88 88
84
84
80 80
0
0 2000 4000 6000 8000 10000
speed[rpm]

Figure 14. Efficiency map established with FEA while operating with a MTPA control strategy. Letters
A-F represent the points verified with calorimetric measurements presented in Tab. 6.
 Version May 17, 2020 submitted to Energies 14 of 18

Figure 15. Calorimetric run at 3000 rpm and 30 A RMS. The plots are showing: top left output torque,
top right oil inlet and outlet temperature, middle left mechanical speed, middle right oil flow rate,
bottom left d-axis and q-axis currents, bottom right calorimetric loss

Table 6. Results from calorimetric measurements

Point ω τ i Pmech Pin Pcal η η FEA η FEA -η
(rpm) (Nm) (A RMS) (kW) (kW) (W) (%) (%) (%)
A 1003 27.5 30.0 2.89 3.16 233 92.63 92.8 0.17
B 1005 56.0 60.0 5.89 6.65 660 90.07 90.8 0.73
C 1985 26.6 30.0 5.52 5.97 370 93.80 94.3 0.50
D 1990 56.6 60.0 11.78 12.65 860 93.20 94.0 0.80
E 3004 27.0 30.0 8.49 9.05 570 93.70 94.6 0.90
F 3007 57.0 60.0 17.96 18.74 785 94.66 94.9 0.24

Figure 16. Measured and simulated efficiency comparison. Emes is measured efficiency, EFE is
efficiency established with FEA.

269 6. Conclusion
270 This paper presents the design of a tooth coil winding PMSM machine for traction application,
271 focusing on the electromagnetic design and performance verification. The solution adopted integrates
 Version May 17, 2020 submitted to Energies 15 of 18

272 stator cooling, both thorough the slot and the stator yoke. The originality of the design consists on
273 the integration of the cooling, using a thermally conductive epoxy resin to create the channels within
274 the slot as well as the positioning of the stator yoke cooling channels. It is shown that for the Q12p10
275 machine, the electromagnetic performance is negligible affected by removing iron in the stator yoke for
276 cooling channels if the position is carefully selected. The machine is designed such that it is possible
277 to use a linear winding machine to pre-wind the coils on a bobbin, potentially leading to a reduced
278 manufacturing cost for high volume production.
279 The adopted cooling solution enables a continuous copper current density of 25 A/mm2 .
280 This allows for a 75% higher output torque and power density comparing with a corresponding
281 water-jacket-cooled machine. Inductance, torque and no-load back EMF are measured and compared
282 with FEA results, showing very good agreement. Furthermore, the efficiency of the machine is
283 validated in one operating point, using a calorimetric direct-loss measurement set up, matching
284 with FEA within 0.9 percent units. The peak efficiency according to FEA is a wide area above 95%,
285 which is on par state-of-the-art automotive traction machines for higher power levels. The overall
286 net power density (19 kW/l) is comparable with the current state-of-the-art traction machines on
287 the market, even with higher power ratings, despite this machine being an early prototype. Further
288 design improvements towards series production is likely to bring also the gross power density to
289 very appealing levels by minimizing the volumetric overhead of coolant interfaces and connection
290 terminals.
291 Author Contributions: Conceptualization, A.A.; methodology, A.A. and S.S.; software, A.A. and S.S.; validation,
292 A.A. and S.S.; formal analysis, A.A. and S.S.; investigation, A.A. and S.S.; resources, A.A. and S.S.; data curation,
293 A.A. and S.S.; writing–original draft preparation, A.A. and S.S.; writing–review and editing, A.A., S.S. and E.G.;
294 visualization, A.A. and S.S.; supervision, E.G and T.T.; project administration, T.T.; funding acquisition, T.T. All
295 authors have read and agreed to the published version of the manuscript.
296 Acknowledgments: The authors gratefully acknowledge the financial support from the Swedish Energy Agency
297 and the Swedish Governmental Agency for Innovation Systems (VINNOVA).

298 Abbreviations
299 The following abbreviations are used in this manuscript:
300
PMSM Permanent magnet synchronous machine
HTC Heat transfer coefficient
FEA Finite element analysis
TCWM Tooth coil winding machine
301
DW Distributed winding
MMF Magneto-motive force
FW Field weakening
SVM Space vector modulation
 Version May 17, 2020 submitted to Energies 16 of 18

302 Appendix A

Figure A1. Copper loss map from FEA.

Figure A2. Iron loss map from FEA.

Figure A3. PM loss map from FEA.

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380 c 2020 by the authors. Submitted to Energies for possible open access publication under the terms and conditions
381 of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
 Paper VIII
Manufacturing of in-slot cooled
tooth coil winding PM machines
Submitted to ICEM2020
Conference date: 2020-08-23 in Gothenburg, Sweden

First author contributions

Paper structure, lead machine design FEA, thermal and mechanical,
corresponding author, manufacturing support.
Second author contributions
Idea development, verification of machine design with FEA,
48 V machine responsible, picture generation,
manufacturing support.

187
188
 Manufacturing of cooled tooth coil winding PM
machines with in-slot oil cooling
Alessandro Acquaviva, Student Member, IEEE, Stefan Skoog, Student Member, IEEE,
and Torbjörn Thiringer, Senior Member, IEEE

Abstract—This paper presents a description of the man- • Fluid bath (oil)

ufacturing challenges and solutions of two 50 kW radial flux • Fluid spray (oil)
inner-rotor tooth coil winding PM machines with in-slot cooling
Some of these can be combined on the same machine.
for vehicle application. The two machines are designed for
different DC link voltages, 600 V and 48 V. The machines are Depending on the solution in use there are different
designed to achieve high efficiency and high power density. To options when it comes to the coolant fluid, as shown in [4].
enable this, liquid cooling is necessary. In the solution presented, However, most solutions use either oil or water (typically
the oil coolant is pushed through the stator yoke and in the mixed with glycol). The specific heat of water or water/glycol
slots with the intent of removing the heat close to the loss
is about twice that of oil, so a given flow rate of water absorbs
generation. The cooling channels in the slots are built during
the stator potting process using a high thermally conductive more heat per degree increase in temperature than the same
potting material. The stator is designed to be compatible flow rate of oil. The coolant chosen in the solution adopted
with automated manufacturing for high volume production. is oil, this because oil is a good electrical insulator, thus it
The machines presented in this paper are designed for high can be in direct contact with the conductors. In the machines
speed operation and capable to withstand current densities of
presented in this paper the coils are not in direct contact with
25 A/mm2 in continuous operation and 35 A/mm2 for 30 s peaks,
at 6 l/min oil flow and a inlet temperature of 20◦ C. the oil, but some fluid might penetrate through the potting
material. Additionally there is a direct contact in the end
Index Terms—Brushless PM machines, Cooling, Electric
section, where the connections between adjacent coils and the
Vehicles coil terminals are brought out of the machine. Also, an oil
leak from the cooling channel through the airgap would not
cause any hazard. If water should similarly leak, substantial
I. I NTRODUCTION
machine damage might occur, such as PM corrosion and steel
Tooth coil winding machines (TCWM) are widely used oxidation. Oil, is already often present as a lubricant in the
for mass produced low power industrial applications because transmission and naturally helps to prevent corrosion, which
of the low cost manufacturing process and good copper can be beneficial for the system compactness.
fill factor. These are becoming attractive also for traction In-slot cooling is an efficient way of removing the heat
applications [1], [2]. The cost saving comes mainly from the very close to the main source. Tooth coil winding, in par-
simple winding structure, which typically allows to use high ticular the double layer configuration, present opportunities
speed winding machines, such as linear winding machines of direct winding cooling. Firstly, the end winding is not
(also known as spindle winding machines), based on bobbin overlapping, meaning an easy access to the slot from the end
rotation and the wire is layered onto the bobbin. section. Secondly, typically it is convenient to have wound
Traction electric drives are designed for high power with a winding machine either by segmenting the stator or by
density, high efficiency and reliability. In order to achieve designing the stator without tooth tip to insert the pre-formed
this an effective cooling system for the electrical machine is coil. During this process often some space is left between the
needed, typically a closed loop forced liquid cooling. Several two coils, this can be used for the cooling, see Fig 2.
different forced cooling solutions found in industry can be In [5] a tooth coil winding machine concept using in-
categorized as [3], [4]: slot cooling is presented. This solution uses water-soluble
• Cooling jacket (oil or water) mould cores in the space in the slot not filled with copper to
• Hallow shaft (oil or water) create cooling channels, a concept that is hard to adopt for
• In-slot cooling (oil or water) mass production. Directly cooled axial flux PMSM, using
Litz wire with a tube for liquid inside each turn, can also
The authors gratefully acknowledge the financial support from the
Swedish Energy Agency and the Swedish Governmental Agency for In- be found in the literature [6]. This solution requires custom-
novation Systems (VINNOVA). made Litz wires which can be costly, complicated to wind
A. Acquaviva, S. Skoog and T. Thiringer are with the Division of Electric during manufacturing and yet a maximum feasible current
Power Engineering at Chalmers University of Technology, Gothenburg, Swe-
den (e-mail: alessandro.acquaviva@chalmers.se, stefan.skoog@chalmers.se, density of 14 A/mm2 is reported. A different concept
torbjorn.thiringer@chalmers.se). is presented in [7], where a direct winding copper heat
exchanger is placed in between the each of the coils of TABLE II: Main dimensions and data for both 600 V and
a double layer tooth coil wound machine. This solution 48 V machines
allows a direct, in-slot water-cooling of the windings without Quantity Value Unit
exposing the winding copper wires to water. Current densities Outer Stator diameter 180 mm
Inner Stator diameter 111.4 mm
of 25 A/mm2 continuous and 40 A/mm2 peak operation are Active length 100 mm
reported with this solution. The copper heat exchangers in Tooth width 17 mm
the slot add complexity when it comes to slot insulation and Stator Yoke width 13 mm
Magnet thickness 3.5 mm
manufacturing. Furthermore, a complete machine in hardware
validating the cooling concept is not presented.
In-slot cooling for a SRM is presented in [8], [9] show-
ing how the cooling performance is improved compared to
water mantle cooling. The concept, tested DC current up to
22 A/mm2 , comes with some challenges regarding coolant
leakage to the rotor.
The machine presented in this paper has been built,
tested and validated up to the maximum torque. The cooling
concept, using a high thermally conductive potting material
to create the slot cooling channels and the placement of
the stator yoke cooling channels, has not been found in the
literature. The design process and test results are described
and presented in [10], [11]. Both thermal and electromagnetic
experimental verification was carried out up to to the peak
torque of 145 Nm, showing that the machine can withstand
25 A/mm2 for continuous operation and 35 A/mm2 for
30 seconds with an oil flow rate of 6 l/min. The focus of this
paper is to show how the solution adopted has been manu-
factured, presenting the main issues and how these have been
solved. Furthermore, an analysis of how the manufacturing of
such solution could be made for mass production is presented. Fig. 1: Stator and rotor laminations geometry, coil
disposition and cooling channels (in yellow).
II. P ROPOSED SOLUTION
The electrical machine in this paper is designed as traction
motor for a small passenger vehicle, a two seater car with
a curb weight of 800 kg. The resulting machine design Acu
kf ill,bulk = (1)
specifications are presented in Table I. Aslot
and the net fill factor as
TABLE I: Electrical machine design specifications
Acu
Quantity Value Unit kf ill,net = (2)
Aslot − Acool
Peak torque 140 Nm
Peak power 50 kW where Acu is the copper area, which differs for the two
Base speed 3 600 rpm motors:
Max speed 11 000 rpm
Coolant max temperature 60 ◦C
• the 600 V machine has 56 (2x28) conductors with a
Max winding temperature 180 ◦C
diameter of 1.6 mm in each slot. Resulting in a total
DC bus voltage 600/48 V
copper area of 113 mm2 , yielding a net fill factor of
0.45, while considering the total slot area yields a bulk
The machine is sized using an analytical sizing process, fill factor of 0.32.
described in [12] and verified with FEA. The main geomet- • the 48 V machine has 54 (2x3x9) conductors with a

rical dimensions, outcome of the sizing, are presented in diameter of 1.5 mm in each slot. Resulting in a total
Table II and the details of the winding. copper area of 95.5 mm2 , yielding a net fill factor of
The coil disposition and geometries of stator and rotor as 0.38, while considering the total slot area yields a bulk
well as the cooling channel disposition are shown in Fig. 1. fill factor of 0.27.
The slot cooling channels are derived from unused space Figure 2 shows the slot and the conductor disposition for the
in-between the coils. The total slot area, Aslot , is 350 mm2 . two machines.
The cooling channel area, Acool , for a single slot is 100 mm2 Another feature of the 12 slot 10 pole machine, is that it
which gives a net slot area of 250 mm2 . The bulk fill factor presents the opportunity of inserting cooling channels also
is defined as in the stator yoke as described and analyzed in [11] and
 TABLE III: Winding design for the two machines
Quantity 48 V Mach. 600 V Mach. Unit
Diameter of each conductor 1.5 1.6 mm
N. parallel conductors per turn 9 1 -
N. turns per coil 3 28 -
Max. RMS current 1200 140 A

Fig. 3: Efficiency map established with FEA while operating

with a MTPA control strategy. In red one of the points
where the efficiency has been measured experimentally.

manufacturing. A flow chart showing the main steps of the

stator manufacturing process is presented in Fig 4.

Fig. 2: Slot design: upper 600 V machine with 28 turns,

lower 48 V machine with 3 turns of 9 parallel conductors

presented in Fig. 1. This allows to directly cool the stator iron,

which can have a significant amount of losses at high speed
operation. A fluid flow analysis and distribution in presented
in [10].
The machine is designed for high power density but the
main target is high efficiency. In [12] it is shown that by
writing the machine torque equation as a function of the split
ratio, inner to outer stator diameter ratio, there is a trade off Fig. 4: Flow chart of the stator manufacturing process. End
between efficiency and power/torque density. Efficiency was section barriers are placed after inserting the stator in the
privileged and has been evaluated in [11] and shown in Fig. 3. frame and not shown here.
The net power density is 19 kW/l and is comparable with
other traction motors found in industry [11].
A side view and cross section of the machine is presented
in 5.
III. M ANUFACTURING The prototypes have been built using single Polytetraflu-
In this section the manufacturing of the prototypes is oroethylene (PTFE) sticks for each slot as shown in Fig. 6.
discussed and described, analysing also the potential for mass PTFE is used for the cooling channels former because of the
 Fig. 7: PTFE ring with channel former sticks for automated
manufacturing of slot cooling channels

Fig. 5: Side and cross section view o the machine and

support

remarkable nonstick properties. In fact the material is self-

lubricated which allows to extract the channel former sticks
once the potting is cured without damaging the stator. For
series production, it is possible to have a PTFE ring with
Fig. 8: 600 V machine before potting and frame mounting
all the sticks inserted at once, shown in Fig 7. In order to
(non-drive end) of the left and after potting and mounting
make the extraction process of all the sticks at the same time
the frame on the right (non-drive end).
possible, these need to have a well defined draft angle; a
cross section which is slightly gradually reducing, wider at
the point of connection to the ring and thinner at the other
end. The difference between the two ends of the cooling using a steel coil former as a support for the bobbin, shown in
channel former needs to be very small to limit the effect of the Fig. 9. These avoid the collapse of the PTFE bobbin during
non-constant cross section on the fluid dynamics. The 600 V the winding when a significant pull to the wire is applied.
machine stator before and after the potting and extraction The coil former with the wound bobbin is placed in front
process is presented in Fig 8. of the tooth and then pushed radially in the stator. In a high
volume production process this could be automatized with a
more detailed analysis of the tolerances needed in the process.
Furthermore, the bobbins, which are now made by water
cutting, can easily be molded for high volume production.
The 12 slot 10 pole machine presents four coils for each
phase [13], the coils of the same phase are paired around
the stator core, as shown in Fig.10. The two adjacent coils
of the same phase cannot be parallel connected because
the induced voltages are not in phase [13] but need to be
series connected. The coils can be wound in pairs of two,
without interrupting the conductor, and inserted. This avoids
one connection point which is usually a costly and complex
Fig. 6: Insertion of PTFE barriers before potting process. process during manufacturing. Also, the parallel connection
Left non-drive end and right drive end. of the two pairs of parallel coils as well as the star connection
can be made internally, this guarantees additional cooling on
The coils for the two machine prototypes are hand wound the point of connection which can be otherwise a critical
Fig. 9: Bobbin and coil former for manual winding

hot-spot.

Fig. 12: Stator of 48 V machine after potting and after

connection of adjacent coils

Fig. 10: Diagram showing the disposition and connection of the cooling channel. This type of installation is quite invasive
the coils. For the prototypes 12 terminals are coming out of when it comes to flow distribution, however in an industrial
the frame and the star and parallel connections are made product these are typically not necessary.
externally. For mass manufacturing all this can be done
internally having externally only 3 connection terminals.

The series connected adjacent coils are soldered and

bundled, the connection point is immersed in oil during
normal operation. Pictures showing the connection points and
terminations of the two machines are presented in Fig. 11 and
Fig. 12.

Fig. 13: End section barriers to redirect flow

The end winding section, which is basically immersed in

oil, needs to be sealed with respect to the airgap. This is done
by using o-rings at the ends of the frame as shown in Fig. 13.
Fig. 11: Detail of adjacent coil connection for 600 V A big issue during manufacturing has been to seal of
machine leakage from oil cooling channels to the rotor area. In fact
leakage was detected via the stator sheets by performing
Fiber glass flow stoppers are installed in the end section a pressure test with air at 1.5 bar. There is a rather short
to redirect the coolant flux in two parallel paths. The end distance via the steel sheets from the cooling channels to
section is shown in Fig. 13. The temperature sensors installed the surrounding areas. Obviously, the back lack glue was not
in the mid-axial position of the machine are routed through sufficient and the molding material has not penetrated enough
into any voids. Finally, for the prototypes the leakages has started after testing the machine at high temperature. The
been resolved by using a penetrating glue, Loctite 420. thermal expansion during the testing has probably caused
A degree of leakage to the rotor is anyway accepted, in some openings of the sealing of the inner part of the stator
fact the end section presents a rotor leakage outlet, shown in and the oil leaks radially through the lamination sheets. This
Fig. 14. leakage, if controlled, could be beneficial for rotor cooling.
A possible solution to avoid this leakage completely is to
install a non conductive thin cylindrical sheet in the airgap
or a special coating of the inner stator. This, however, could
cause an increase in the airgap length needed for mechanical
tolerance.
The margins taken because of the hand-winding process
and the sub-optimal bobbins used during prototyping led to
a copper conductor of 1.6 mm and 1.5 mm in diameter
respectively for the 600 V and 48 V machine. However, with
a winding machine and an optimized bobbin design for series
production a copper conductor of 1.8 mm is feasible, which
would result in a net fill factor of 0.57 (600 V machine, 28
turns) and 0.55 (48 V machine, 3 turns with 9 conductors
per turn).
Regarding the terminations and end sections these have
been built keeping big margins. The flow stoppers can be
integrated in the end-cap, avoiding single insertion. There is
significant room to reduce the space in the end section, thus
reducing the total volume and in turn to further improve the
Fig. 14: Rotor leakage outlet power density.
The external frame is used just for mechanical support and
A list of the materials used to manufacture the different can be made thinner than the one built for the prototypes. This
parts is presented in Table IV would allow to further improve the weight and gross power
density.A summary of the suggested design improvements for
TABLE IV: Used materials mass production is presented in Table VI.
Part Material
Stator and rotor Lamination M235-35 Backlack TABLE VI: Design Improvements
Frame Aluminum A356 Temper
Prototype Mass production
Magnets NdFeB Vacodym 745 DHR
Star connection External Internal
Potting stator Lord CoolTherm EP-2000
Parallel coil connection External Internal
Potting rotor Elantas Elantron MC4260
Adjacent coil connection Soldered No interruption
Bobbin PTFE
Coil former Single Multi-former tool
Leakage sealing Penetrating glue Loctite 420
Bobbins Water cut Molded
Cooling channel former PTFE
Winding Manual Linear winding machine
End section barriers Fiberglass
Temperature sensors Yes No
Wire diameter 1.6 mm-1.5 mm 1.8 mm
End-section barriers Single parts Integrated in end-cap
The coolant oil used is provided by ExxonMobil and
specifically developed for electrical machine cooling, featur-
ing low viscosity and good thermal properties as shown in V. C ONCLUSIONS
Table V. However, any low viscosity oil could potentially be In this paper the design and manufacturing steps of two
used if compatible with the materials used. 50 kW in-slot cooled tooth coil winding machine prototypes
has been discussed and analyzed. The machines are meant
TABLE V: Oil coolant properties (data from ExxonMobil). for traction application and are designed to achieve high effi-
40 ◦ C 80 ◦ C 100 ◦ C ciency and high power density. This is done by designing the
Kinematic viscosity (cSt) 2.31 1.28 1.02 machine for high speed operation and capable to withstand
Specific heat (J/kgK) 2.15 2.28 2.35 current densities of 25 A/mm2 in continuous operation and
35 A/mm2 for 30 s. To enable this, cooling channels are
created in the slot using a high thermally conductive epoxy
resin. Additionally, the oil can flow through the stator iron
IV. D ESIGN IMPROVEMENTS and in the end sections. The process to create the cooling
The main issue found during testing is an oil leakage channels within the slot is potentially an interesting solution
of about 1% of the total volumetric flow towards airgap for industry and the overall machine design can be improved
and the rotor oil drainage worked as expected. The leakage and engineered to be compatible with mass manufacturing.
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Stefan Skoog was born 1985, graduated as Feb. 2020.
M.Sc.E.E from Lund University, Sweden in 2010. [12] A. Acquaviva, “Analytical electromagnetic sizing of inner rotor brush-
Stefan has a decade of professional experience in less pm machines based on split ratio optimization,” in ICEM ’18,
R&D in advanced mechatronics and automotive Alexandroupoli, 2018.
powertrains. He is currently a PhD student at [13] S. Skoog and A. Acquaviva, “Pole-slot selection considerations for
Chalmers University, Sweden, working on mild double layer three-phase tooth-coil wound electrical machines,” in
hybrid electrification systems limited to 48 VDC ICEM ’18, Alexandroupoli, 2018.
aimed for personal vehicles. His interests include
modeling, design and verification of advanced bat-
tery systems, power electronics and electric ma-
chines.

Torbjörn Thiringer works at Chalmers univer-

sity of Technology, in Gothenburg, Sweden, as a
professor in applied power electronics. He took
his M.Sc and Ph.D at Chalmers University of
technology in 1989 and 1996 respectively. His
areas of interest include the modeling, control and
grid integration of wind energy converters into
power grids as well as power electronics and drives
for other types of applications, such as electrified
vehicles, buildings and industrial applications.