Battery Sizing and Design for Electric Vehicles
Mike Sasena Danielle Chu
Automotive Product Manager Simscape Product Manager
msasena@mathworks.com dchu@mathworks.com
© 2023 The MathWorks, Inc.
1
Key Takeaways
▪ Problem description
– You can use an EV model to optimize battery pack size, then design the battery system
and validate its performance
Assess
Find Optimal Design Validate
System
Pack Size Battery Pack Performance
Performance
▪ Role of MathWorks tools
– Powertrain Blockset offers system-level models to quantify trade-offs in battery
performance, efficiency and cost
– Global Optimization Toolbox and Simulink Design Optimization efficiently optimize
the design while accounting for competing requirements
– Simscape Battery can be used to perform detailed battery design studies
– These products are complementary parts of the overall workflow
2
Agenda
▪ Context
▪ Vehicle model
▪ Battery sizing
▪ Battery design
▪ Summary
3
Automotive Powertrains Are Increasingly Electric
▪ The automotive sector is focused on reducing CO2 emissions
▪ Battery Electric Vehicles (BEV’s) are a promising option
– Localizes CO2 emissions to energy production source
– Can be charged from renewable energy
▪ But engineering challenges remain…
700 kWh 95 kWh
95 kg 700 kg EV battery
Credit: EPA.gov
Diesel tank
85 L 430 L
4
Vehicle-Level Targets
▪ Government agencies rate conventional, HEV and EV’s using
different standardized tests (US city / highway cycle, WLTP, etc.)
▪ Different metrics to define energy efficiency (MPGe, Wh/km, etc.)
▪ Vehicle program sets targets → requirements for subsystem teams
Extra High
WLTP Class 3
High
Medium
Low
Credit: US Environmental
Protection Agency (EPA)
World harmonized Light-duty vehicles Test Procedure 5
Use System-Level Models to Assess System-Level Targets
Target How to evaluate
Fuel economy Perform drive cycle test
Range Perform drive cycle test
Acceleration Perform Wide Open Throttle (WOT) test
Cost Assume $ / kWh
Simulations used to frontload
design / save money 6
Credit: 4x4 Dynamometer by Adam Navrotny / CC BY-SA 3.0
Right-Level Modeling
▪ We can answer system-level questions using system-level
models, but what level of fidelity is appropriate for the task?
▪ Initial estimates use simplifying assumptions
– Fast running 1D models CFD and
– Neglect thermal / spatial effects FEA
Computation
– Simplified controls Time Lumped
Parameter
Spreadsheet Network
▪ Design-oriented tasks require higher fidelity
Model Fidelity
– Slower running multidomain models
– Include thermal / spatial effects
– Production-oriented controls
7
MathWorks Offering for Virtual Vehicle Simulation
Engineering Tools + Application Expertise
Create Integrate Author Simulate & Deploy
Vehicle Software Scenarios Analyze Simulation
Vehicle Templates C/C++ Interface Scene & Scenarios Visualization Cloud Integration
Subsystem Libraries Reduced Order Models Open Standards Data Analysis Datalake Integration
Modeling Guidelines FMU Integration Drive Cycles Report Generation HIL Deployment
Value proposition:
▪ Proven tools for modeling of physics and software
▪ Reference applications for reduced time-to-simulation
▪ Common platform for model reuse
▪ Solutions for large-scale modeling and simulation
▪ Flexible platform for growth / new use cases
8
Agenda
▪ Context
▪ Vehicle model
▪ Battery sizing
▪ Battery design
▪ Summary
9
Powertrain Blockset
Library of blocks Virtual Vehicle Composer app
Pre-built reference applications
10
Virtual Vehicle Composer App
▪ Unified interface to quickly
configure a virtual vehicle,
select test cases, and review
results
▪ Available with Powertrain
Blockset and / or Vehicle
Dynamics Blockset
▪ Includes options for detailed
powertrain models, vehicle
dynamics and controls
▪ Generated models are
customizable
11
EV Model
1. Set target speed and ambient conditions
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EV Model
1. Set target speed and ambient conditions
2. Set brake, accel, shift commands to achieve target speed
13
EV Model
1. Set target speed and ambient conditions
2. Set brake, accel, shift commands to achieve target speed
3. Set lower-level control commands (e.g., motor torque)
14
EV Model
1. Set target speed and ambient conditions
2. Set brake, accel, shift commands to achieve target speed
3. Set lower-level control commands (e.g., motor torque)
4. Calculate vehicle response
15
EV Model
1. Set target speed and ambient conditions
2. Set brake, accel, shift commands to achieve target speed
3. Set lower-level control commands (e.g., motor torque)
4. Calculate vehicle response
5. Report results
16
Summary: Vehicle Model
▪ Key takeaways
– Virtual Vehicle Composer app can quickly configure a closed-loop EV model
– Generated model can be customized for your application
▪ Next step
– Perform optimization study to identify battery size that meets requirements
17
Agenda
▪ Context
Assess Optimize Design Validate
▪ Vehicle model
▪ Battery sizing
▪ Battery design
▪ Summary
18
Component Sizing Problem Statement
▪ Objective:
– Design a BEV that provides a good
range at a reasonable price
▪ Constraints:
– Meets typical driving demands
– Reasonable electric range
– Reasonable acceleration
▪ Design Variables:
– Number of battery cells in parallel (Np)
– Number of battery cells in series (Ns)
– Gearbox ratio (Nd)
{Nd}
{Np, Ns}
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Component Sizing Problem Statement
▪ Objective:
– Design a BEV that provides a good
min f(x) = w1*Cost - w2*Range
range at a reasonable price
▪ Constraints:
– Meets typical driving
g1: DriveCycleFault <0demands
– Reasonable
g2: Range > 400 electric
km range
– g3: t0-100 kph < acceleration
Reasonable 7s
▪ Design Variables:
– Number of battery cells in parallel (Np)
x1: 10 < Np < 50 (Integer)
– Number of battery
x2: 80 < Ns cells in series (Ns)
< 140 (Integer)
– x3: 7 < Nd
Gearbox < 10
ratio (Continuous)
(Nd)
{Nd}
{Np, Ns}
20
Initial Assessment
Default component sizes don’t
achieve system-level requirements.
Time for a redesign!
Metric Target Results
Battery cost [$] min 7537
Range [km] > 400 371
t0-100 [s] < 7.0 6.8
WLTP test WOT test 21
Initial Assessment
Range
▪ Performed initial parametric study
– Sweep of Np, Ns, and Nd
– Study problem statement before
Cost
launching long optimization study
▪ Lessons learned
– Range helped by large pack with
higher voltage (Ns) / lower losses (Np)
– Cost scales linearly (as expected)
– Battery pack size has nonlinear t0-100
impact on performance
22
Optimization Workflow
Modify Design
Variables
Initial Design No
Variables
System
Optimal
Simulation Yes
▪ Num. of parallel cells Objectives Design
▪ Num. of serial cells met?
▪ Gearbox ratio
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Selecting the Appropriate Optimization Solver
▪ MATLAB can indicate applicable optimization solvers
▪ Design variable space
– Continuous
– Integer (discrete)
– Mixed Integer
▪ Local / global search space
– Optimization Toolbox (local)
– Global Optimization Toolbox continuous discrete
Objective with multiple minima Objective with single minimum 24
Solve Expensive Nonlinear Problems with surrogateopt
▪ Concept
– Create a surrogate model of the objective /
constraints
– Find the best point on the surrogate model,
then sample new points
▪ near the best point found so far (refine solution)
▪ far from any sample (improve model accuracy)
▪ Benefits
– Automatically builds a cheap-to-evaluate
surrogate model
– Searches for global solution
– Uses fewer function evaluations than other
global solvers
– Works with continuous and integer variables
– Accepts nonlinear and linear constraints 25
Simulink Design Optimization Makes Problem Setup Easy
Select continuous or
discrete design variables
Select algorithm Speed up
optimization
26
Optimization Results
Search focused
around range
constraint boundary
Range < 400 km
(infeasible)
27
Optimization Results
Metric Baseline Optimized
(% change)
Cost [$] 7537 8297 (+10%)
Range [km] 371 406 (+9.4%)
t0-100 [s] 6.77 6.83 (+0.9%)
Nd 9 7
Battery cells 96s31p 91s36p
Bus voltage [V] 357.8 339.2
Capacity [kWh] 60.3 66.3
Performed 300 function calls
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Summary: Battery Sizing
▪ Key takeaways
– Formal optimization tools can iterate on model parameters to meet conflicting
requirements and optimize design performance
– Set up and automate the process easily using Simulink Design Optimization or
MATLAB scripts
▪ Next step
– Use the information from optimization study to perform more detailed design-
oriented analysis on the battery system
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Agenda
▪ Context
Assess Optimize Design Validate
▪ Vehicle model
▪ Battery sizing
▪ Battery design
▪ Summary
30
Design Study Workflow
1 2 3 4 5
Create lumped
Size battery pack battery pack model Design battery Select appropriate Evaluate battery
within context of full in Simscape Battery system in Simscape model fidelity for full design in full
system operation and demonstrate Battery system evaluation system
equivalence
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Simscape Battery
▪ Design and simulate battery and
energy storage systems
– Electrothermal cell behavior
– Battery pack design
– Battery management systems (BMS)
▪ With Simscape Battery you can
– Evaluate pack architectures for electrical
and thermal requirements
– Verify robustness of discharge, charge and
thermal management algorithms
– Validate algorithms using HIL testing
32
Create Lumped Battery Pack Model in Simscape Battery
and Demonstrate Equivalence
33
Create Lumped Battery Pack Model in Simscape Battery
and Demonstrate Equivalence
Unit Test
Simulink Voltage
Simscape Battery Voltage
Voltage Relative Error
34
Create Lumped Battery Pack Model in Simscape Battery
and Demonstrate Equivalence
System Test
Simulink Voltage
Simscape Battery Voltage
Voltage Relative Error
35
Design Battery Systems in Simscape Battery
▪ Create battery pack with higher resolution
Lumped (1 cell model for entire pack) Grouped (1 cell model for each parallel assembly)
96 cell models
36
Passive Cell Balancing
▪ Cells within a parallel assembly will naturally balance
▪ One cell balancing circuit for each series-connected parallel assembly
No external charge cycle - all
SOCs bleeds to lowest SOC level
Constant Current Constant
Voltage (CCCV) charge cycle
37
Passive Cell Balancing During CCCV
▪ Animation can bring further clarity to a
large number of time-series responses
38
Thermal Management
▪ Change the simulation strategy of cooling plates to meet your
model resolution needs
Connections dependent on
cooling plate architecture
39
Thermal Management
▪ Parallel cooling channels oriented along the x-axis
40
Thermal Management
▪ Parallel cooling channels oriented along the y-axis
41
Select Appropriate Model Fidelity for Full System
Evaluation
▪ For many scenarios, lumped battery model is
sufficient for system integration
▪ Other fidelities can be
incorporated as needed
42
Evaluate Battery Design in Full System
MPGe
180
Cooling activates near the end of the cycle
90
No Cooling
WLTP (Class 3) Drive Cycle
43
Summary: Battery Design
▪ Key takeaways
– Matching model fidelity to the engineering question being asked enhances
overall workflow execution
– Design information is effectively shared across different engineering teams
▪ Next step
– Where to go for more information
44
Agenda
▪ Context
▪ Vehicle model
▪ Battery sizing
▪ Battery design
▪ Summary
45
MathWorks Training Can Increase Your Productivity
▪ General purpose training courses
– Optimization free online onramp
– Optimization paid training services
– Simscape free online onramp
– Simscape paid training services
▪ Automotive-specific training
– Simulink Fundamentals for Automotive Applications training services
– Battery Modeling and Algorithm Development with Simulink training services
– Powertrain Blockset jumpstart training services
Learn more:
MathWorks Training Services 46
MathWorks Consulting Services Can Support You
Model assessment ▪ Provide expert-level guidance
Model Simulation performance
▪ Automate workflows
Architecture Interface standardization
▪ Develop custom UI’s
…
Build process automation
Database/Repo interface
Construction Model-Building know-how
…
GUI driven workflow
User Tool compatibility support
Experience Artifact creation
…
Learn more:
MathWorks Consulting Services 47
Additional Resources
▪ Overview of MathWorks’ automotive solutions:
– MATLAB and Simulink for Electric Vehicle Development
– Building Your Virtual Vehicle with Simulink
– Upskill for the Electric Vehicle Transition
▪ Products highlighted in this study:
– Powertrain Blockset
– Simscape Battery
– Global Optimization Toolbox
– Simulink Design Optimization
48
Key Takeaways
▪ Problem description
– You can use an EV model to optimize battery pack size, then design the battery system
and validate its performance
Assess
Find Optimal Design Validate
System
Pack Size Battery Pack Performance
Performance
▪ Role of MathWorks tools
– Powertrain Blockset offers system-level models to quantify trade-offs in battery
performance, efficiency and cost
– Global Optimization Toolbox and Simulink Design Optimization efficiently optimize
the design while accounting for competing requirements
– Simscape Battery can be used to perform detailed battery design studies
– These products are complementary parts of the overall workflow
49
Thank you
Mike Sasena Danielle Chu
Automotive Product Manager Simscape Product Manager
msasena@mathworks.com dchu@mathworks.com
© 2023 The MathWorks, Inc.
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