I NSTITUTE OF E NERGY T ECHNOLOGY

VECTOR CONTROL OF PMSG FOR

GRID-CONNECTED WIND TURBINE
APPLICATIONS

C ONDUCTED BY GROUP W PS4 − 1050

S PRING S EMESTER , 2009
 Institute of Energy Technology
Pontoppidanstræde 101
Phone number 96 35 92 40
Fax 98 15 14 11
http://www.iet.aau.dk/

Title: Vector control of PMSG for grid-

connected wind turbine applications Abstract:
Semester: 4th Semester, Spring 2009
Semester Theme: Master’s thesis
Nowadays, wind energy is a promising alter-
Project period: 02.02.09 to 03.06.09
native to the traditional energy sources. Due
ECTS: 30
to the increasing wind power penetration, the
Project group: W PS4 − 1050
improvements of the control strategies become
Members:
a new challenge for the manufacturers in or-
der to comply with the grid interconnection re-
quirements. This project focuses on the con-
Daryoush Mehrzad
trol of the grid side converter which let the
full controllability of the DC-link voltage and
the reactive power delivered to the grid. Syn-
chronous and stationary reference frame con-
Javier Luque
trol strategies are implemented to control the
power converter. Modeling and simulation of
the grid side of the wind turbine system are
performed. MATLAB/Simulink has been used
Marc Capella Cuenca
to implement the models. Different tests have
been done in order to analyze the control sys-
tem. In addition, a small scale version of the
Supervisor: Mihai Ciobotaru / Florin Iov
system has been implemented for the labora-
tory. Two different control strategies are com-
Number of prints: 6
pared and the results are verified in the labora-
Number of pages: 87
tory.
Finished: 03.06.2009

By signing this document, each member of the group confirms that all participated in the project
work and thereby all members are collectively liable for the content of the report.
 Preface

This 10th semester report is conducted at The Institute of Energy Technology in Aalborg Univer-
sity. It is written by group WPS4-1050 during the period from 2nd of February to 3rd of June
2009. The project theme with the title "Vector control of PMSG for grid-connected wind turbine
applications" is the continuation of the 9th semester project which was proposed by SIEMENS
Wind Power. The motivation of choosing this project is the increasing wind energy penetration
into the power networks and therefore the necessity to implement proper control systems.
The authors are especially grateful to Mihai Ciobotaru, the supervisor of this project, which pro-
vided great help to the development of this work. Furthermore the help of Florin Iov is appreciated.
We also acknowledge the help of our college Anca Maria Julean.

I
 Nomenclature

List of symbols

Vdc DC-link voltage [V]

C DC-link Capacitance [F]
Da , Db and Dc switching status of inverter [0 1]
vab , vbc and vca Line to line voltages of the power inverter [V]
ia , ib and ic Line output currents of the power inverter [V]
iDC DC current [A]
ha (t), hb (t) and hc (t) signal gates [0 1]
vre f Voltage reference [V]
v1 and v2 Adjacent voltages of vre f [V]
SA , SB and SC Duty cycles []
Lfi Filter inductance inverter side [H]
Rfi Filter resistance inverter side [ohm]
Lfg Filter inductance grid side [H]
Rfg Filter resistance grid side [ohm]
Cf Filter Capacitance [F]
Rd Capacitor resistance [ohm]
Vi Per phase voltage of inverter [V]
VPCC Voltage at the PCC [V]
ii Inverter current [A]
ig Grid current [A]
VH Voltage at high side of the transformer [V]
VL Voltage at low side of the transformer [V]
IH Current at high side of the transformer [A]
IL Current at low side of the transformer [A]
NH Number of turns at high side of the transformer []
NL Number of turns at low side of the transformer []
k transformation ratio of the transformer []
Lm mutual inductance between primary and secondary sides of transformer [H]
P Active power [W]
Q Reactive power [W]
Pt Wind turbine side power [W]
Pg Grid side power [W]

III
 vd vq dq-axis voltages [V]
id iq dq-axis currents [A]
θ PLL output angle [rad]
γ grid angle [rad]
ωgrid grid angular frequency [rad/s]
Kp Proportional gain []
Ti Integral time []
Ka Anti-windup gain []
e(t) error in time domain []
Kpv Proportional gain of voltage controller []
Kpc Proportional gain of current controller []
Tsw Switching period [s]
m Modulation index []
Ts Period of the sampling frequency [s]
Tpwm Period of the switching frequency of the PWM [s]
fs Sampling frequency [Hz]

IV
Abbreviations

PMSG Permanent Magnet Synchronous Generator

DC Direct Current
SV M Space Vector Modulation
V SC Voltage Source Converter
AC Alternative Current
IGBT Insulated Gate Bipolar Transistor
PCC Point Common Coupling
p.u. per unit value
PW M Pulse Width Modulation
PI Proportional Integral controller
PID Proportional Integral Derivative controller
B2B Back to Back
PS Phase shift
UHF Upper limit full load
ULF Lower limit full load
PLL Phase Locked Loop
PR Proportional Resonant
DPGS Distributed Power Generation Systems
GUI Graphical User Interface

V
 Contents

1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Project goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Project limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.5 Project outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 System description and implementation 5

2.1 Premise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Power converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Space Vector Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Grid Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.5 Wind turbine system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Grid Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Control of the system 19

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Grid side converter control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Phase Locked Loop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 PI controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5 PR controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.6 Tuning of the controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4 Simulation and analysis 39

4.1 Simulation and analysis of 2.4 MW model . . . . . . . . . . . . . . . . . . . . . 39
4.2 Analysis and comparison of 11 kW model . . . . . . . . . . . . . . . . . . . . . 60

5 Experimental setup 81
5.1 Setup description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Study cases and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6 Conclusions 87

A Matlab models 90
A.1 Voltage Source Converter model . . . . . . . . . . . . . . . . . . . . . . . . . . 90
A.2 Space Vector Modulation model . . . . . . . . . . . . . . . . . . . . . . . . . . 91
A.3 Grid model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
A.4 PLL tuning model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
A.5 dq and αβ control models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

VII
CONTENTS

A.6 Complete model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

B Project proposal 97

VIII CONTENTS
 Introduction
1
In this chapter, the background gives to the reader a general vision of the project. The problem
is defined, the goals are listed, project limitations are mentioned and finally the project outline
summarizes the structure and content of the report.

1.1 Background
The renewable energy sources are one of the biggest concerns of our times. High prices of oil
and global warming make the fossil fuels less and less attractive solutions. Wind power is a very
important renewable energy source. It is free and not polluter unlike the traditional fossil energy
sources. It obtains clean energy from the kinetic energy of the wind by means of the wind turbine.
The wind turbine transforms the kinetic wind energy into mechanical energy through the drive
train and then into electrical energy by means of the generator.

Although the principles of wind turbines are simple, there are still big challenges regarding the ef-
ficiency, control and costs of production and maintenance.Wind power is growing and most of the
wind turbine manufactures are developing new larger wind turbines. The power of wind turbines
built in 1980 was 50 kW and the rotor diameter was 15 m long. In 2003 they had the power of 5
MW and the size of the rotor diameter was 124 m [7].

There are different wind turbine configurations. They can have or not gearbox, the generator can
be synchronous or asynchronous and finally the connection with the grid can be through a power
converter or be directly connected. Different modes of operation can be used depending on the
wind turbine configuration. They are classified in variable-speed and fixed-speed. For fixed-speed
operation, the system is very simple and thus the cost is usually low. As a drawback, the conver-
sion efficiency is far from optimal. Normally an asynchronous generator is used and it is directly
connected to the grid. For the variable-speed operation, maximum efficiency is obtained; the sys-
tem is controlled to maximize the power extracted from the wind. Normally they are connected to
the grid by means of a power converter. It increases the cost of the whole system but allows full
controllability of the system. Among all these configurations, the trend is to use variable-speed
wind turbines because they offer more efficiency and control flexibility which is becoming very
important to comply with the grid requirements.

Permanent Magnet Synchronous Generator, (PMSG), is an interesting solution which is based on

variable-speed operation. Since the speed of wind turbine is variable, the generator is controlled
by power electronic devices. With permanent magnets there is no need for a DC excitation sys-
tem. With a multipole synchronous generator it is possible to operate at low speeds and without
gearbox. Therefore the losses and maintenance of the gearbox are avoided.

The generator is directly connected to the grid through a full scale back-to-back power converter.
The power converter decouples the generator from the grid. With a full scale power converter,
there are more losses which may be a drawback but it allows a full controllability of the system.
With the use of the power converter it is possible to comply with the grid connection requirements.

1
1.2 Problem definition

The full scale back-to-back converter can be divided in two parts: the generator side converter
and the grid side converter. The generator side converter is mainly used to control the speed of
the generator in order to maximize the output power at low wind speeds. The grid side converter
is mainly used to keep the voltage in the DC-link capacitor constant and also to control the reac-
tive power delivered to the grid. Nowadays different techniques are used to control the grid side
converters. In this project vector control has been used.

1.2 Problem definition

The amount of wind energy supplied to the electrical network is considerably increasing, therefore
having an efficient and a reliable control system is very important. Modeling the power system
and performing the simulation helps to have a better understanding of the system. Furthermore in
this way is possible to avoid any damage to the equipment.

In the first part of the project, 9th semester, the focus was on the speed control of the PMSG
and to maximize the obtained power. In this project, 10th semester, the focus is on the control
of the grid side converter, in order to control the power delivered to the grid and to comply with
the grid requirements. PMSG studied in the previous project works in variable speed range and
it is connected to a full scale power converter. The power converter is controlled so that the
output power is maximized and the power delivered to the grid complies with the interconnection
requirements. Consequently it is clear the importance of an efficient control strategy. This is very
much important especially in the case of wind power applications in which the wind varies quickly
and in an unpredictable way. With a full scale back-to-back power converter is possible to have
the generator running at any speed within some certain range and to have a fixed frequency on the
grid side.

1.3 Project goals

The main goals of this project are described below.
• Implementation of the grid side converter control strategies and the analysis and comparison
between dq and αβ reference frame;
• Analysis of the behavior of the grid side of the wind turbine system under different grid
conditions considering the grid connection requirements;
• The implementation in the laboratory and the analysis and verification of the results by
scaling down of the wind turbine system.

1.4 Project limitations

The most important limitations of this project are described below.
• The exact parameters of some of the components of the 2.4 MW system, such as the filter,
transformer and grid were estimated due to the fact that no data was available.
• The laboratory work cannot be carried out in the same power range.
• Only the power flow study cases have been analyzed in the laboratory.
• In the modeling and simulations, some components such as converter, transformer are con-
sidered as ideal.

2 1. Introduction
 1.5 Project outline

1.5 Project outline

This project studies the grid side connection of a large wind power system. All of the components
of the systems are implemented by MATLAB/Simulink software. Finally the the model is scaled
down for the laboratory tests.

The system implementation chapter describes the components of the system. The generator is
connected to the grid through a back-to-back converter, a filter and a transformer. The basics of
each one are explained by means of the main equations and schemes. Finally this chapter ends
with an overview of the Danish grid codes.

The control system chapter describes the two main control strategies used in the project. Later the
method used to synchronize the grid voltage with the control is explained and tested. Finally, the
procedure to tune the controllers in both strategies is explained and the obtained results are shown.

The analysis and simulation chapter is composed of a 2.4 MW model which is analyzed accord-
ing to grid requirements. Next, it will be shown the analysis and comparison of the two control
strategies for a 11 kW model, ending with a table which shows which strategy suits better in each
study case.

The experimental setup chapter, shows the implementation of the control strategies in the labora-
tory setup and the analysis of the obtained results.

Finally, the project ends with the conclusions and future work.

1. Introduction 3
1.5 Project outline

4 1. Introduction
 System description
and implementation
2
In this chapter the main components of the system together with equations and schemes are ex-
plained. The system description contains the power converter, the Space Vector Modulation (SVM)
and the components of the grid connection. Finally the chapter ends with the explanation of some
grid requirements based on Danish grid codes.

2.1 Premise
The vector control of PMSG is divided in two parts, the generator side control and the grid side
control by considering a constant value for the DC-link voltage. The scheme of the wind turbine
system is shown in Fig. 2.1.

Wind Turbine Generator Side Grid Side

Grid
Generator Side Grid Side
Converter Converter Voltage
Transformer
PCC source
wind AC DC Filter Impedance

PMSG
DC AC

Pitch Control Generator Side Control Grid Side Control

Figure 2.1: Block diagram of PMSG based wind turbine.

In the first semester of this academic year, the first part, which includes is the generator side
control, has been treated. The DC-link voltage has been considered constant [13]. In the second
semester the grid side control is treated.

2.2 Power converter

Nowadays the Back-to-Back (B2B) converter is widely used in wind turbine applications. The
B2B converter is composed by two identical Voltage Source Converters (VSC) and a capacitor
which is connected in between them. The Fig. 2.2 depicts the B2B converter layout.

As it can be seen in Fig. 2.2 the power flow can be bidirectional, either it can go to the generator
or to the grid. Therefore the VSC can work as a rectifier or as an inverter. At first step the AC is
converted to DC through the generator side converter. Next, the DC is converted to AC through
the grid side converter. Therefore in this case the generator side converter works as a rectifier and
the grid side converter works as an inverter. The DC-link voltage must be higher than the peak
main voltage and it is regulated by controlling the power flow to the AC grid. In fact one important

5
2.2 Power converter

Generator Grid
side converter side converter

AC + AC
Cdc Vdc
-

AC DC DC AC

Figure 2.2: Back-to-Back converter.

property of the back-to-back converter is the possibility of fast control of the power flow [15].

With the generator side converter it is possible to control the torque and the speed of the generator,
while the grid side converter keeps the DC-link voltage constant. The capacitor acts as filter for
the voltage variations or ripple produced by the VSCs [3].

The equivalent circuit of a VSC is shown in Fig. 2.3. In the circuit there is a full-bridge converter
having ideal IGBT’s as devices switches. The switching status variable D can have two values,
either 1 or 0. Conventionally in the conduction state the value of the switching function is 1 and
in the block state its value is 0. Based on the state of the switches, the VSC can assume eight
different configurations.

Grid
side converter
iDC
+
Generator Grid
side converter DA DB DC
Filter Transformer impedance V. source
AC ia
A
CDC VDC ib
B Y Δ
ic
C

-DA -DB -DC N

-
0 VON

Figure 2.3: Grid side VSC IGBTs.

Based on the equivalent circuit in Fig. 2.3, for a star connected transformer in the low voltage
side, the line-to-line voltages are described by the equations 2.1-2.3.

vAB = vAN − vBN (2.1)

vBC = vBN − vCN (2.2)

6 2. System description and implementation

 2.3 Space Vector Modulation

vCA = vCN − vAN (2.3)

vAN + vBN + vCN = 0 (2.4)

The equation 2.4 is based on the assumption that the system is balanced. Next, the equation 2.5
shows the relation between phase voltages and the DC-link voltage.
   
vAN DA
 vBN  = vDC  DB  (2.5)
   
vCN DC
where vAN , vBN and vCN are the average phase voltages and DA , DB and DC are the switches status
at each leg respectively. The voltage between the star connection point N and the neutral point 0
is defined as in the following:

1 vDC
v0N = (vAN + vBN + vCN ) = (DA + DB + DC ) (2.6)
3 3
Regarding the equations 2.1-2.3, the phase voltages can be written as follows [11]:
     
vAN 1 0 −1 vAB
 1
 vBN  =  −1 1 0  ·  vBC  (2.7)
   
3
vCN 0 −1 1 vCA
The current iDC is expressed in function of phase currents:

iDC = (DA ia + DB ib + DC ic ) (2.8)

Regarding the simulations in MATLAB/Simulink, the model of the converter has been taken from
the Wind Turbine Blockset in MATLAB/Simulink [9]. In Fig. 2.4 it can be seen the black box of
the VSC with its inputs and outputs. In order to complete a back-to-back converter, two VSC are
put together through a DC-link. However, for the purpose of this project only the grid side con-
verter is considered. The MATLAB/simulink model and the mask of the converter is represented

Dabc i DC
v DC VSC
v abc
iabc

Figure 2.4: Black box of VSC.

in appendix A.1. The modulation strategy used in this project is Space Vector Modulation (SVM)
with Pulse-Width Modulation (PWM) which is explained in the following section.

2.3 Space Vector Modulation

The VSC requires switching status DA , DB and DC applied to the IGBT gates in order to con-
trol the power flow through the converter. SVM represents three-phase quantities as vectors in

2. System description and implementation 7

2.3 Space Vector Modulation

a two-dimensional α-β plane providing the duty cycles necessary for the control of the power
flow through the converter. SVM is very suitable for field-oriented control, since provides accu-
rate control of voltage amplitude, frequency and phase within every switching period. Furthermore
does not require separate modulators and calculation of zero-sequence signals as in third harmonic
PWM and it has higher utilization of the DC voltage than the sinusoidal PWM method [12].

With SVM all three-phase waveforms are generated simultaneously which is a good advantage
compared with when the phases are considered separately. The reference voltage vector is shown
in the following equation:

2 0
α van + α1 vbn + α2 vcn


V re f = (2.9)
3
where α is - 12 +j 23 and van , vbn and vcn are the phase reference voltages.

Figure 2.5: State voltage vectors and V re f represented in sector 1 [9].

As mentioned in the previous section there are eight possible configurations for a three-leg VSC.
Six of them produce a non-zero output voltage and the other two produce zero output voltage [16].
The six non-zero voltage vectors can be represented as shown in Fig. 2.5.

Each voltage vector corresponds to a switch combination of the three switching status DA , DB and
DC explained previously. In Fig. 2.5 are depicted the six state voltage vectors with the needed
switching status to perform them. The areas between two state vectors are sectors, hence six
sectors are present. In this way the output voltage of the converter could be represented by an
equivalent rotating vector V re f with a counter clockwise direction, whose angle is represented by
θ [16]. Fig. 2.6 shows the switching pattern for the first sector.

where Tsw is the switching period. T0 is the time period left from a half switching period used
by the null voltage vectors. In sector 1 The pattern used is [0 0 0],[1 0 0], [1 1 0], [1 1 1] which
reduces the number of switching commutations in each transition. The time duration equation is
shown as follows:

8 2. System description and implementation

 2.3 Space Vector Modulation

Figure 2.6: Switching pattern for the first sector [9].

T0 Tsw
= − T1 − T2 (2.10)
2 2
This reference voltage vector can be considered constant, for each switching period, if there is a
high switching frequency.

Finally, in Fig. 2.7 can be seen the three duty cycles a,b,c, in a complete period. The black box
shows the inputs as voltages in α-β reference frame and vDC as well as the duty cycles as the
outputs.

1
0.9
0.8
v *α 0.7
Duty cycles

0.6
S abc 0.5
v*β 0.4
SVM 0.3
v DC 0.2
0.1
0
0.8 0.81 0.82 0.83 0.84
Time [s]

Figure 2.7: Black box and the provided duty cycles from the SVM.

In order to obtain the switching functions necessary to feed the VSC gates, PWM is necessary.
PWM produces the gate signals or switching functions, by comparing the duty cycles with a car-
rier signal. In Fig 2.8 can be seen the black box of the PWM and the signal gates to apply the VSC.

1.5

1
Gate Signal leg A

0.5

S abc H abc 0

PWM -0.5

-1

-1.5
0.6 0.602 0.604 0.606 0.608 0.61
Time [s]

Figure 2.8: Black box and signal gates supplied by the PWM.

The Models of SVM and PWM are taken from the Wind Turbine Blockset in MATLAB/Simulink
[9]. The subsystems of the models and the masks are shown in the Appendix A.2.

2. System description and implementation 9

2.4 Grid Connection

2.4 Grid Connection

When a considerable part of the electrical power is coming from the wind turbines, the network
operators will have many technical and economical problems to manage the system. Therefore it
is clear that one of the important aspects of research must be concentrated on the grid interaction
of the wind turbines. One of the main concerns of the network operators is the power quality
which depends on what kind of sources are connected to the grid. The wind energy has to be
grid compatible, because in any power system the operator has to control the frequency and the
voltage. These are the most important grid connection requirements [9].
The scheme of the plant which represents the connection of the wind turbine to the grid starting
from the grid side converter as shown in Fig. 2.9.

Grid
Grid Side
Converter Voltage
Transformer
PCC source
DC Filter Impedance

AC

Figure 2.9: The scheme of the plant.

The output currents of the grid side converter contain the ripple caused by the switching. There-
fore, it has to pass through a filter in order to have a lower current THD (Total Harmonic Distor-
tion). After the filter a transformer brings the voltage to a proper value for the connection to the
transmission line.

2.4.1 Filter
L-filter

In case of a simple L-filter, it will be represented by an inductance and a small resistance which
takes into account the losses of the inductance. The filter is shown in Fig. 2.10.

Grid Side
Converter
VPCC
DC Lf Rf

If
AC PCC
Vf

Figure 2.10: The representation of the filter.

The phasorial equation is as the following:

V f (t) = I f (t)( jωL f + R f ) (2.11)

In s-domain the following expression is valid:

V f (s) = I f (s)(sL f + R f ) (2.12)

The transfer function has the following expression:

10 2. System description and implementation

 2.4 Grid Connection

1
F(s) = (2.13)
(sL f + R f )

LCL-filter

The filter scheme used to filter the grid currents is shown in Fig. 2.11.

Grid Side
Converter
VPCC
DC Lfi Rfi Lfg Rfg

Ii Ig
AC PCC

Rd

Vi

Cf

Figure 2.11: LCL filter scheme.

Based on the Kirchhoff laws, the following equations can be written:

   
1 1
Ii sL f i + R f i + Rd + − Ig Rd + = Vi (2.14)
sC f sC f
   
1 1
Ig sL f g + R f g + Rd + − Ii Rd + =0 (2.15)
sC f sC f
The transfer function of the filter is obtained by operating with the equations 2.14 and 2.15 in
Ig
order to obtain H = out put
input = Vi . The resulting transfer function is as follows:

sRd C f + 1
H=






s3 L f g L f iC f + s2 L f g C f R f i + Rd + L f i C f R f g + Rd + s C f R f g R f i + R f g Rd + Rd R f i + L f g + L f i + R f g + R f i
(2.16)
In this this filter configuration, there is a resonance frequency and it occurs when the impedance
of the inductances becomes equal to the impedance of the capacitor. It can be calculated by using
the following equation:
s
Lfi + Lfg
ωres = (2.17)
L f i L f gC f

2.4.2 Transformer
At this point the voltage level has to be increased in order to be connected to the transmission line.
Therefore a transformer is used and it is connected to the PCC (Point of Common Coupling). The
ideal transformer has the following characteristics:

VL = jωLL IL + jωLm IH (2.18)

2. System description and implementation 11

2.4 Grid Connection

VH = jωLH IH + jωLm IL (2.19)

where LL and LH are the self-inductance of the primary and secondary. Lm is the mutual inductance
between the primary and secondary. In this project the primary is considered to be the low voltage
side and the secondary the high voltage side. Another important parameter of the transformer is
the turn ratio k which is given by the following expression [15]:

VH IL NH
k= = = (2.20)
VL IH NL
where NL and NH are the number of turns in the primary and secondary winding respectively. A
more detailed representation of the transformer is the equivalent circuit of the linear transformer
which is shown in Fig. 2.12.

IL RL LL LH RH IH

VL RM LM VH

Figure 2.12: The equivalent circuit of the linear transformer.

In this report, for the simulations and calculations, all the plant parameters are considered on the
low voltage side of the transformer. Fig. 2.13 shows the equivalent circuit of the linear transformer
when the impedances of the high voltage side are brought on the low voltage side.

IL RL LL L’H R’H IH

VL RM LM VH

Figure 2.13: The equivalent circuit of the linear transformer with all the parameters on the low
voltage side.

The new values of the resistance and the inductance on the low voltage side are calculated in the
following way:

RH
R0H = (2.21)
k2
0 LH
LH = 2 (2.22)
k
A three-phase transformer can be considered as three separate single-phase transformers. Further-
more, depending on the type of the connection of the windings in the primary and secondary, there
are 4 different possibilities depending on if the connections are delta or star. Another important
factor to consider is the phase shift that occurs in some of three-phase transformer connections
which consists of a phase shift between the primary and secondary line-to-line voltages [3].

12 2. System description and implementation

 2.4 Grid Connection

2.4.3 Grid

The grid can be presented with the Thevenin equivalent circuit. Each of the three phases can be
presented by the equivalent circuit shown in Fig. 2.14. The equivalent impedance (R-L) takes into
account the distribution lines.

Lg Rg

Ig

VPCC
Vg

Figure 2.14: The equivalent Thevenin circuit representing the grid.

The voltage equation per phase can be written as follows:

dIg
Vg = Rg Ig + Lg +VPCC (2.23)
dt
where Vg is the grid voltage and Vpcc is the voltage of the PCC. When there is a connection to the
grid many considerations have to be taken. There are important factors regarding the control of
the important values and the grid requirements that regulate the operations. The amount of wind
energy penetration in the network is always increasing which brings big challenges to grid oper-
ators. Especially with the growing of the big wind farms of large capacity, the network is more
dependent on the wind energy which is fluctuating and not completely predictable.

For the simulations in MATLAB/Simulink, the model of the grid has been taken from the Wind
Turbine Blockset in MATLAB/Simulink [9]. In Fig. 2.15 it can be seen the black box of the grid
model with its inputs and outputs.

f
Grid model V pcc
Phase

I abc

Figure 2.15: Black box of the grid model.

The inputs are A which is the amplitude of the grid voltage, f the frequency, phase the phase and
Iabc the grid current. The output Vpcc is the voltage of the PCC. The MATLAB/simulink model
and the mask of the grid model is represented in the appendix A.3.

2. System description and implementation 13

2.5 Wind turbine system

2.5 Wind turbine system

Finally, all Simulink models explained through this chapter has been connected in order to build
the grid side wind turbine model and therefore to be able to perform the simulations and analysis
of the system. The SVM and PWM models are included in the grid side controller. The model is
shown in Fig. 2.16.

GRID

Vw Twt ωm
Vw v abc
Wind Wind Turbine ω wt Drive-train PMSG

ω wt Filter

β v abc iabc v abc iabc

PITCH i DC v DC
CONTROL
DC
VSC v DC i DC VSC
Link

Pe habc habc
GENERATOR
GRID SIDE
SIDE
CONVERTER
CONVERTER
CONTROL
CONTROL

~
Vw ω m isd isq v DC iabc v abc

Figure 2.16: Complete model of the system.

The layout of the complete model in MATLAB/Simulink is shown in Appendix A.6.

2.6 Grid Requirements

In this section the interconnection requirements based on the Danish grid codes will be explained.
Topics that will be treated are local frequency control, active and reactive power control, design
voltages and frequencies, fault ride-through capability and finally power quality.

• Local frequency control

Fig. 2.17 presents the frequency control characteristics. The continuous line shows the range
where the wind turbine can operate. It can also be decided to set a down-regulation operation. The
figure shows an example where it has been decided a 50% down-regulation. It means that under
normal operation the wind turbine will deliver 50% of the rated power. If the network operator
needs more power due to a frequency drop, the wind turbine can deliver more power in order to
stabilize the frequency of the grid. It will act in the opposite way if the frequency of the grid
increases. Dead-band is the frequency between 49.85 and 50.15 Hz.

14 2. System description and implementation

 2.6 Grid Requirements

Figure 2.17: Frequency control characteristics [8].

• Active and reactive power

In Fig. 2.18 the blue band represents the working zone of the wind turbine. Depending on the
active power production, the reactive power has to be between -0.1 and 0.1 in p.u. values.

Figure 2.18: The reactive power exchange between the wind turbine and grid [8].

• Design voltages and frequencies

A wind turbine has to be designed to give power for voltages and frequencies as it is shown in
Fig. 2.19. It is observed that a wind turbine will be working in normal operation when the values
of frequency are between 47 and 53 Hz and the voltage values are between 95% and a bit above
105%. If in some moment the frequency and voltage values change and go out of the above
mentioned range, the wind turbine will be disconnected from electrical network after the time
indicated in Fig. 2.19.

2. System description and implementation 15

2.6 Grid Requirements

Figure 2.19: Voltages versus frequencies for design a Wind Turbine [8].

• Fault ride-through capability

In normal operation a wind turbine will be disconnected from the grid when it will be working out
of the white area, although, there is a vertical lines area where it is possible to choose if it will be
or not disconnect of the grid, as it shown in Fig. 2.20.

Figure 2.20: Requirements for disconnection of wind turbines under voltage dips/sags [8].

In case of fault, a wind turbine shall not be disconnected from the electrical grid in the following
situations because after the time of short circuit it will be working in a normal operation:

• 3-phase short-circuit for 100ms.

• 2-phase short-circuit with or without ground for 100ms followed after 300 − 500ms by a
new short-circuit for 100ms.

In Fig. 2.21 the following notation is used: UHF as the upper-limit full-load and ULF as the
lower-limit full-load.
A wind turbine should have sufficient capacity to satisfy the mentioned requirements for the next
sequences:

• at least two 2-phase short-circuit within 2 minutes interval.

• at least two 3-phase short-circuit within 2 minutes interval.

16 2. System description and implementation

 2.6 Grid Requirements

Figure 2.21: Fault ride-through capabilities of wind turbines connected to the distribution system
[8].

For this case it is the same as before, after the time of short-circuit will be working in a normal
operation.

• Voltage quality

The limits of rapid voltage variations and long term flicker severity for different levels of voltages
are shown in Fig. 2.22.

Figure 2.22: Levels of voltage quality [8].

In Fig. 2.23 the limits which can not be exceeded when the wind turbine is connected are pre-
sented. The first, third, ninth, fifteenth and twenty-first harmonics do not appear due to the fact
that the generator is using delta connection.

Figure 2.23: Harmonics voltage level versus harmonic order [8].

So far the main components of the system have been explained, grid connection requirements
according to danish grid codes have been included and they will be taken into consideration in the
chapter 4. The following chapter will explain the grid side converter control.

2. System description and implementation 17

2.6 Grid Requirements

18 2. System description and implementation

 Control of the system

In this chapter two types of grid control strategies are explained. Then the PLL method to syn-
3
chronize the control with the grid is introduced and tested. Finally, the PI and PR controllers as
well as the process of tunning are described.

3.1 Introduction

The control system is an important issue for the wind turbine performance. It maximizes the
extracted power from the wind through all the components and also makes sure that the deliv-
ered power to the grid complies with the interconnection requirements. The control strategies are
applied in different parts of the wind turbine and they have different aims. The general control
scheme is shown in Fig. 3.1.

Generator Side Grid Side

Converter Converter

DC PCC
wind AC Filter
PMSG
DC AC
I v DC I

Control Generator Side Control Grid Side

β ωm CONVERTER CONTROL

ω m* PG*
*
v DC QG*

Pitch Control Speed Control VDC and Q Control

PPCC QPCC
Power Control VPCC
WIND TURBINE CONTROL

Figure 3.1: General control scheme [7].

One of the control strategies is located in the rotor blades. This control modifies the angle of
attack of the rotor blades so that the output power of the wind turbine can be controlled. This is
performed by the pitch control technique.

The other control strategy is applied to the converter. The PMSG is driven by advanced power
electronics. A back-to-back VSC is used to connect the generator to the grid and it allows the
full controllability of the system. It can be divided in two parts: the generator side and the grid
side. Both have different purposes. The first one controls the speed of the rotor so that the power
is maximized. The second one controls the voltage on the DC-link and also the reactive power
delivered to the grid. This project will focus on the control of the grid side converter.

19
3.2 Grid side converter control

3.2 Grid side converter control

There are different control strategies used to perform the control of the grid side converter. They
all are focused on the same topics: the control of the DC-link voltage, active and reactive power
delivered to the grid, grid synchronization and to ensure high quality of the injected power [2].

They can be classified depending on the reference frame used in the control structure. They are
shown in Fig. 3.2. In this project the focus is on the synchronous and stationary reference frame
control strategies.

VECTOR CONTROL

SYNCHRONOUS REFERENCE STATIONARY REFERENCE NATURAL REFERENCE

FRAME CONTROL FRAME CONTROL FRAME CONTROL

Figure 3.2: Classification of grid side converter control strategies.

In both cases, the control strategy contains two cascaded loops. The inner loops control the grid
currents and the outer loops control the DC-link voltage and the reactive power. The current loops
are responsible of the power quality, thus harmonic compensation can be added to the action of
the current controllers to improve it. The outer loops regulate the power flow of the system by
controlling the active and reactive power delivered to the grid [2].

The strategy used to control the power flow in both cases is the same. The equations of the active
and reactive power in dq-reference frame assuming that the reference frame is oriented along the
supply voltage are [5]:

3
P= (vd id ) (3.1)
2
3
Q = (vd iq ) (3.2)
2
Equations 3.1 and 3.2 show how to control the active and reactive power. It can be seen that
by changing the d and q-components of the current, the active and reactive power are controlled
respectively. Basically, the aim of the control is to transfer all the active power produced by
the wind turbine to the grid and also to produce no reactive power so that unity power factor is
obtained, unless the grid operator requires reactive power compensation. In order to transfer all
the active power generated by the wind turbine the DC-link voltage must remain constant. It can
be derived from the following equation [1]:

dvDC Pt Pg
C = − (3.3)
dt vDC vDC
where subscript g refers to the grid and t to the wind turbine.
If the two powers, the wind turbine and the grid, are equal there will be no change in the DC-link
voltage and all the power will be transferred to the grid.

20 3. Control of the system

 3.2 Grid side converter control

The difference between the two control schemes is in the inner loops where they use different
reference frames to perform the current control. In the first case, the currents are controlled in
the synchronous rotating reference frame using PI controllers. In the second case the currents and
voltages are transformed into the stationary reference frame and PR controllers are used instead.

The structure of the synchronous rotating reference frame control is shown in Fig. 3.3.

va
θ vb
PLL
vc

vd dq

vq
abc

θ
Filter
θ
id dq
ia
ib
vd iq ic
* abc
vDC id* vd*
PI PI

iq dq
vDC id − ωL
SVM PWM
id
ωL αβ
Q* 2 iq* vq*
PI vDC
3vd θ vDC
iq vq

PMSG

Figure 3.3: General structure for synchronous rotating reference frame control [2].

This is the classical control structure, it is also known as dq-control. It transforms the grid voltages
and currents from the abc to the dq reference frame. In this way the variables are transformed to
DC values which can be controlled more easely. This structure uses PI controllers since they have
good performance for controlling DC variables.

In the output of the current controllers, cross-coupling term and voltage feed-forward are added
to improve the response of the system. The resultant value is the voltage reference for the SVM
technique [2].

The structure of the stationary reference frame control is shown in Fig. 3.4.

In this second case, the voltages and currents are transformed from abc to αβ reference frame. In
this reference frame, the variables are sinusoidal instead of constant. Therefore, as the PI con-
trollers are not able to remove the steady-state error, PR controllers are used instead. With the PR

3. Control of the system 21

 3.2 Grid side converter control

va
θ vb
PLL
vc

vα αβ

vβ
abc

θ
Filter
θ
iα αβ
ia
ib
iβ ic
* abc
vDC id* iα*
PI dq PR

vDC iα vα*
SVM PWM

Q* 2 iq* iβ* vβ*

αβ PR
3vd vDC
vDC
θ iβ

PMSG

Figure 3.4: General structure for stationary reference frame control [2].

~
~ controllers the feed-forwardVis
w not needed [2].

ωm
w *
vsd
Wind Turbine Twt Speed controller
wt The implementation of the two control strategies have been done* in MATLAB/Simulink as the rest
isd vsq
of the models. The control has been modeled based on the theoretical explanation seen previously
in this section. The box which
isq contains the model is presented in Fig. 3.5. The subsystem of the
model is shown in Appendix A.5.

v DC
Twt ω wt
i ABC
Drive Train Model
Control model gate _ signals
Te ωm v ABC

Enable

Figure 3.5: Dq and αβ control models.

The model has as inputs, the voltage of the DC-link vDC , the grid currents iABC , the grid voltages
vABC and the enable signal. The output is the gate signals that will feed the power converter.

22 3. Control of the system

 3.3 Phase Locked Loop.

3.3 Phase Locked Loop.

Nowadays, Distributed Power Generation Systems (DPGS) have to synchronize the injected cur-
rent with utility voltage in order to comply with required grid codes [8]. There are many methods
used so far, zero-crossing method, filtering of grid voltages and finally, Phase Locked Loop (PLL)
method.

The criterion to chose a suitable method is based on the best response in front of grid disturbances,
for instance notches, harmonics and voltage drops [2].

PLL can be described basically as a device which is used to obtain the phase angle from the grid
voltages. PLL output signal tracks the input one. Therefore PLL provides the inverter with fre-
quency and phase angle. The purpose of that is to synchronize the inverter current angle with the
grid voltage angle in order to obtain a power factor as close to 1 as possible. In Fig. 3.6 the PLL
diagram is shown.

v*q = 0 ωgrid
PI

va vq ⎛ 1 ⎞ 1 θ
abc -
Kp⎜⎜1 + ⎟⎟
⎝ Ti s ⎠ s
vb

vc vd
dq

Figure 3.6: PLL diagram block.

The inputs of the PLL model are the grid phase voltages and the output is the tracked phase angle.
The Vq∗ component is nothing but symbolic, to make clear that the reference of q-axis voltage is
set to zero, which locks the grid voltage phase. PLL model is implemented in dq synchronous
reference frame which means that a Park transform from abc to dq reference frame is needed. The
Park transform requires the output angle in order to synchronize the dq reference frame. A PI is
used to control the system by reducing to zero the difference between the sinus of grid phase angle
(γ) and inverter phase angle θ based on equation 3.4. Therefore the value of Vq is equal to zero and
Vd is the positive voltage magnitude [10]. The magnitude of the controlled variable Vq determines
the phase difference between the grid voltage and the inverter phase angle. Hence the PI input is
Vq [19].

γ−θ ∼
= sin(γ − θ) = ∆θ (3.4)

This approximation made in the previous equation linearizes the function of the sinus and it is
reliable when γ and θ are almost equal. In other words, for small values of ∆θ.

3. Control of the system 23

3.3 Phase Locked Loop.

The transfer function of the PLL is of second order as shown in the following expression:

θinv Kp s + KTip
H(s) = = K (3.5)
γ s2 + Kp s + Tip
Some components have been set to tune the PI controller. The desired settling time is to be around
two periods of the grid frequency, 0.04s, and the damping ratio ξ= √12 .

To obtain the parameters of the PI a MATLAB/simulink model has been implemented to design
the PI as it is shown in Appendix A.4, which provides Kp and Ti in function of settling time and
damping ratio [17]. Finally, Kp and Ti are obtained, whose values are Kp = 230 and Ti = 0.008693.

To prove the reliability of the PLL some tests have been done by means of frequency and angle
shift steps in the applied voltage grid. The response of the PLL is checked in time domain.

The frequency of the grid is 50Hz and the voltage is changed at the time 0.1s from 50Hz to 51Hz
by a step. The test of the PLL focuses on two responses, the frequency and the tetha angle.

a
51.5
Frequency [Hz]

51

50.5

50

49.5
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
b
400

300
Angle [deg]

200

100

0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

c
1.5
Error of angle [deg]

0.5

-0.5
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Time [s]

Figure 3.7: Frequency and angle response for 1Hz frequency step.

The analyzed time frame is 0.2s. Fig. 3.7.a. shows the frequency step as well as the response
obtained by the PLL. It can be noticed that the transient time is 0.04s as it was set.

Fig. 3.7.b. shows the angle of the grid voltages γ and the θ angle provided by the PLL by cycles
from zero to 360 degrees. Both curves are almost overlapped due to the small difference between
both angles. Therefore Fig. 3.7.c. is attached to show the small error between both angles previ-
ously called ∆θ.

24 3. Control of the system

 3.4 PI controllers

a
400

300
Angle [deg]
200

100

0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
b
100
Error of angle [deg]

50

-50
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Time [s]

Figure 3.8: θ angle and ∆θ responses.

Fig. 3.8 is composed by two graphs. In Fig. 3.8.a. it can be seen the angle shift applied in the
voltage utility. At the time 0.11s, a 60 degrees step is shown as well as the θ angle tracking this
step.

Fig. 3.8.b. shows the error between both angles (∆θ). The shift angle starts from 60 degrees at the
time 0.11s and responds according to the settling time.

3.4 PI controllers
The PI (proportional-integral) algorithm computes and transmits a signal which is desired to be
controlled. The computed output signal o (t) from the PI depends on the parameters, which are the
proportional gain Kp , the integral time Ti and the error e (t). Fig 3.9 shows the general scheme of
the PI controller [14].

Signalreference e(t ) ⎛ 1 ⎞ o(t )

K p ⎜⎜1 + ⎟⎟
⎝ Ti s ⎠
PI
Signalreal

Figure 3.9: General scheme of the PI controller.

The proportional gain Kp makes a change to the output that is proportional to the current error
value. If the value of the proportional gain is too high, the system can become unstable. On the
other hand, a small value gives a small output response to a large input error making the controller
less sensitive. A pure proportional controller would not be able to drive the signal at its target
value. There would remain a steady state error usually called offset. In order to make the offset
zero, the integral term is needed.

3. Control of the system 25

3.5 PR controllers

The integral term contribution is proportional to the magnitude and the duration of the error. The
integral gives the accumulated offset which is then multiplied by the inverse of the integral time
and added to the controller output. The magnitude of the contribution of the integral term to
the overall control action is determined by the integral time Ti . The integral term accelerates the
response of the controller and eliminates the residual steady-state error that occurs with a pure
proportional controller. However, since the integral term is responding to accumulated errors from
the past, it can cause the present value to overshoot the reference value.

3.5 PR controllers

In the stationary reference frame control, the grid currents are transformed into αβ reference frame.
In this case the variables are sinusoidal, thus PI controller cannot be used due to the fact that they
are not able to track a sinusoidal reference without a steady state error. Therefore, another con-
troller must be used instead.

Proportional Resonant (PR) controllers has gained a large popularity for current regulation of the
grid-tied systems [2]. The general scheme of the PR controller is shown in Fig. 3.10.

PR

i* v*
Kp

i
Ki s
s2 + ω 2

Figure 3.10: Structure of the PR controller [2].

In the scheme shown in Fig. 3.10, ω is the resonance frequency of the controller, Kp and Ki are the
proportional gain and the integral gain respectively. This controller has a very high gain around
the resonance frequency which it eliminates the steady state error between the reference and the
measured signal. The width of the frequency band around the resonance point depends on the
integral gain value. A small value produce a very narrow band, whereas a large value produce a
wider band [2] [20]. The Bode plots of the resonant controller for different integral gains Ki and
ω set to 50Hz as shown in Fig. 3.11.

Harmonic compensation can also be easily implemented by adding to the PR controller several
generalized integrators tuned at the frequency of the harmonics which have to be compensated.
The transfer function of the harmonic compensator for the 3rd , 5th and 7th would be as follows
[20]:

s
Ghc = ∑ Kih (3.6)
h=3,5,7 s2 + (hω)2

26 3. Control of the system

 3.6 Tuning of the controllers
Bode Diagram
350

300
Ki=100
250

Magnitude (dB)
Ki=500
200 Ki=1500
Ki=3000
150

100

50

0
-270

-315
Phase (Deg)

-360

-405

-450
0 1 2 3
10 10 10 10
Frequency (Hz)

Figure 3.11: Bode plot of the PR controller.

3.6 Tuning of the controllers

In this section, the tunning and analysis of the controllers and the plants for the 2.4 MW and 11kW
are carried out.

3.6.1 2.4 MW model

In the dq-control scheme, the parameters of the three controllers have to be tuned in order to get a
good performance of the system. In this case, the current controllers are tuned based on the design
criterion called optimal modulus. The outer loop is tuned according to the design criterion called
symmetry optimum. After the tuning calculations, the Matlab Sisotool is used to test, verify and
adjust, if necessary, the values obtained in the analytical calculations.

D-axis control loop

The control loop system of d-axes is shown in Fig. 3.12, where two controllers are present. One
controller is for the outer loop which is the DC-link voltage loop and the other is for the inner
loop, which is the current loop. For the tuning of the PI, the compensation term and the voltage
feed-forward are considered as disturbances and are neglected. However, both terms will defi-
nitely improve the dynamic of the system when they are included after the tuning process.

Firstly, the inner current loop is considered. The following blocks are present in the current loop:
   
• PI controller with the following transfer function: GPI = Kp 1 + T1i s = Kp TiTs+1
is

• Sampling time Ts which frequency fs is 10kHz.

L
• Plant with Te = R

The inner loop block can be moved as shown in Fig. 3.13 [4].

3. Control of the system 27

3.6 Tuning of the controllers

*
vDC id* vd* id vDC
1 1
PI PI
Ls + R Cs
vDC id
Plant

1
Ts s + 1
Inner currrent loop Sampling

1
Ts s + 1
Outer DC-link voltage loop Sampling

Figure 3.12: Block diagram of d-axis control loop.

G1

id* vd* id
1 1
PI Ts s + 1
Ls + R Ts s + 1
id Plant Sampling

Figure 3.13: Block diagram of the current loop.

The G1 transfer function is:

Tic s + 1 R1 1
G1 = Kpc L (3.7)
Tic s R s + 1 Ts s + 1
The transfer function can be simplified as follows [4]:

Tic s + 1 1 Ke
G1 = Kpc (3.8)
Tic s T∑ 1 s + 1 Te s + 1
where Ke = R1 , Te = RL and T∑ 1 = Ts .
Based on the optimal modulus, the next relation is satisfied [4]:

Tic s + 1 1 Ke 1
Kpc = (3.9)
Tic s T∑ 1 s + 1 Te s + 1 2T∑ 1 s (T∑ 1 s + 1)
Therefore, by comparing the two sides of the equation 3.9, the proportional gain and the integral
time of the controller can be calculated with the following equations:

L
Tic = Te = (3.10)
R

28 3. Control of the system

 3.6 Tuning of the controllers

and
Te L
Kpc = = (3.11)
2T∑ 1 Ke 2T∑ 1
24.768e−6 24.768e−6
Using the values of each variable, yields Kpc = 2·0.1e−3 = 0.1238 and Tic = 0.8e−3 = 0.031.

Sisotool has been used to verify the performance of the current controller where these parameters
are used. Root locus, bode diagram and the step response are used to analyze the performance of
the controller. The root locus as well as the bode diagram are shown in Fig. 3.14.

Root Locus Editor for Open Loop 1 (OL1) Open-Loop Bode Editor for Open Loop 1 (OL1)
5000 60
0.86 0.76 0.64 0.5 0.34 0.16
0.94
40

0.985 20

4e+003
1.2e+003 1e+003 800 600 400 200
0 0

0.985 -20

0.94 -40

0.86 0.76 0.64 0.5 0.34 0.16

-5000 -60 G.M.: Inf
-10000 -8000 -6000 -4000 -2000 0 Freq: Inf
Stable loop
Bode Editor for Closed Loop 1 (CL1) -80
10
-90

-10

-20 -135
0

-45
P.M.: 65.5 deg
Freq: 724 Hz
-90 -180
0 1 2 3 4 0 1 2 3 4 5
10 10 10 10 10 10 10 10 10 10 10
Frequency (Hz) Frequency (Hz)

Figure 3.14: Root locus and bode diagrams of the current controller design.

The location of the poles gives a damping of 0.707 which is the standard value. The phase and
gain margin are 65.5 degrees and infinite respectively, thus the loop is stable. The step response is
shown in Fig. 3.15. The overshoot is 6.7% and the settling time is 0.746 ms.
Step Response
1.4
System: Closed Loop r to y
I/O: r to y
Peak amplitude: 1.07
1.2 Overshoot (%): 6.7
At time (sec): 0.000466

1
System: Closed Loop r to y
I/O: r to y
Settling Time (sec): 0.000746
0.8
Amplitude

0.6

0.4

0.2

0
0 0.2 0.4 0.6 0.8 1 1.2
Time (sec) -3
x 10

Figure 3.15: Step response of the current controller design.

Therefore Sisotool has verified the values obtained with the the analytical calculations.
Once the parameters of the controller have been found and verified in s-domain, the block diagram
has been changed to z-domain. The parameters of the controller have been readjusted using the

3. Control of the system 29

3.6 Tuning of the controllers

graphical tuning in Sisotool. The new value of the proportional gain is Kpc = 0.0602, the integral
time remains equal, thus Tic = 0.031. The root locus as well as the bode diagram are shown in Fig.
3.16.

Root Locus Editor for Open Loop 1 (OL1) Open-Loop Bode Editor for Open Loop 1 (OL1)
1 60
3e3 2.5e3 2e3
3.5e3 0.1
0.21.5e3 50
0.3
0.5 4e3 0.4 1e3
0.5 40
0.6
0.7
4.5e3 0.8 500 30
0.9
5e3
0 20
5e3
4.5e3 500
10
-0.5 4e3 1e3 0
3.5e3 1.5e3
-10
3e3 2.5e3 2e3
-1 G.M.: 12.3 dB
-1 -0.5 0 0.5 1 -20 Freq: 1.3e+003 Hz
Stable loop
Bode Editor for Closed Loop 1 (CL1) -30
10
-90

0 -135

-10 -180

-225
-20
0 -270

-90 -315

-180 -360 P.M.: 61.9 deg

Freq: 378 Hz
-270 -405
0 1 2 3 4 0 1 2 3 4
10 10 10 10 10 10 10 10 10 10
Frequency (Hz) Frequency (Hz)

Figure 3.16: Root locus and bode diagrams of the current controller design.

The location of the poles gives a damping of 0.707 which is the standard value. The phase and
gain margin are 61.9 degrees and 12.3dB respectively, thus the loop is stable also in z-domain.
The step response is shown in Fig. 3.17. The overshoot is 5.17% and the settling time is 1.19ms.

Step Response
1.4
System: Closed Loop r to y
I/O: r to y
Peak amplitude: 1.05
1.2
Overshoot (%): 5.17
At time (sec): 0.0008

1
System: Closed Loop r to y
I/O: r to y
Settling Time (sec): 0.00119
0.8
Amplitude

0.6

0.4

0.2

0
0 0.5 1 1.5 2 2.5
Time (sec) -3
x 10

Figure 3.17: Step response of the current controller design.

Once the controller values for the inner loop are found, the outer loop can be tuned. First the inner
closed loop transfer function is found [4]:

1 Ts s + 1
G= Ts s + 1 ≈ (3.12)
2T∑2 1 s2 + 2T∑ 1 s + 1 2T∑ 1 s + 1
After finding the values for the current loop, the block diagram is shown in Fig. 3.18.

30 3. Control of the system

 3.6 Tuning of the controllers

*
vDC id* Ts s + 1
id
1
vDC
PI
2T 1 s + 1 Cs
∑
vDC Current closed loop

1
Ts s + 1
Sampling

Figure 3.18: DC-link voltage loop block diagram.

The blocks can be moved as shown in Fig. 3.19.

G2

*
vDC id* Ts s + 1
id
1
vDC
1
PI Ts s + 1
2T 1s + 1 Cs Ts s + 1
∑
vDC Current closed loop Sampling

Figure 3.19: Equivalent DC-link voltage loop block diagram.

The G2 transfer function is:

Tiv s + 1 Ts s + 1 1 1
G2 = Kpv (3.13)
Tiv s 2T∑ 1 s + 1 Cs Ts s + 1
The transfer function can be simplified as follows [4]:

Tiv s + 1 1
G2 = Kpv (3.14)
Tiv s Cs (T∑ 2 s + 1)
where T∑ 2 = 2T∑ 1 + Ts − Ts .
Now, based on the symmetry optimum, the next relation is satisfied [4]:

Tiv s + 1 1 4T∑ 2 s + 1
Kpv = 2
(3.15)
Tiv s Cs (T∑ 2 s + 1) 8T∑ 2 s2 (T∑ 2 s + 1)
Therefore, by comparing the two sides of the equation 3.15, the proportional gain and the integral
time of the controller can be calculated with the following equations:

Tiv = 4T∑ 2 (3.16)

and
TivC C
Kpv = 2
= (3.17)
8T∑ 2 2T∑ 2
0.232
Using the values of each variable yields Kpv = 2·0.2e−3 = 580 and Tiv = 4 · 0.2e − 3 = 0.8e − 3.

As in the previous case, Sisotool has been used to verify the performance of the DC-link voltage
controller. The root locus as well as the bode diagram are shown in Fig. 3.20.

3. Control of the system 31

3.6 Tuning of the controllers

Root Locus Editor for Open Loop 1 (OL1) Open-Loop Bode Editor for Open Loop 1 (OL1)
6000 60
0.89 0.81 0.68 0.5 0.3
0.945
4000 40
0.976
20
2000
0.994
0
2e+003 1.5e+003 1e+003 500
0
-20
0.994
-2000
-40
0.976
-4000
-60
0.945
0.89 0.81 0.68 0.5 0.3
-6000 G.M.: -Inf dB
-15000 -10000 -5000 0 5000 -80 Freq: 0 Hz
Stable loop
Bode Editor for Closed Loop 1 (CL1) -100
20
-140
P.M.: 36.9 deg
0 Freq: 398 Hz

-20
-150
-40

-60 -160
90

0
-170

-90

-180 -180
1 2 3 4 5 1 2 3 4 5
10 10 10 10 10 10 10 10 10 10
Frequency (Hz) Frequency (Hz)

Figure 3.20: Root locus and bode diagrams of the DC-link voltage controller design.

The location of the poles gives a damping of 0.5 which is not a standard value. The position of the
zero has been moved in order to modify the root locus of the system and thus to obtain a better
damping. This has been carried out by using the graphical tuning in Sisotool. The new position
of the zero gives a value of the integral time Tiv = 0.025. The new root locus as well as the bode
diagram are shown in Fig. 3.21.

Root Locus Editor for Open Loop 1 (OL1) Open-Loop Bode Editor for Open Loop 1 (OL1)
3000 150
0.968 0.94 0.88 0.76 0.5
0.986
2000
0.994 100
1000
0.999

2e+003 1.5e+003 1e+003 500 50

0

0.999
-1000
0
0.994
-2000
0.986
0.968 0.94 0.88 0.76 0.5 -50
-3000 G.M.: -Inf dB
-15000 -10000 -5000 0 5000 Freq: 0 Hz
Stable loop
Bode Editor for Closed Loop 1 (CL1) -100
20
-90
P.M.: 64.5 deg
0 Freq: 362 Hz

-20

-40 -120

-60
90
-150
0

-90

-180 -180
0 1 2 3 4 5 -2 0 2 4 6
10 10 10 10 10 10 10 10 10 10 10
Frequency (Hz) Frequency (Hz)

Figure 3.21: Root locus and bode diagrams of the DC-link voltage controller design.

The new location of the zeros and poles gives a damping of 0.707 which is the standard value. The
phase and gain margin are 64.5 degrees and infinite respectively, thus the loop is stable.

The step response is shown in Fig. 3.22. The overshoot is 5.88% and the settling time is 1.97ms.

32 3. Control of the system

 3.6 Tuning of the controllers

Step Response
1.4
System: Closed Loop r to y
I/O: r to y
Peak amplitude: 1.06
1.2 Overshoot (%): 5.88
At time (sec): 0.00128

1
System: Closed Loop r to y
I/O: r to y
Settling Time (sec): 0.00197
0.8

Amplitude
0.6

0.4

0.2

0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Time (sec) -3
x 10

Figure 3.22: Step response of the DC-link voltage controller design.

Therefore Sisotool has verified and improved the values obtained using the analytical calculations.

As in the previous case, the block diagram has been changed to z domain. The parameters of
the controller have been readjusted using the graphical tuning in Sisotool. The new value of the
proportional gain is Kpc = 379.5, the integral time remains equal, thus Tiv = 0.025. The root locus
as well as the bode diagram are shown in Fig. 3.23.

Root Locus Editor for Open Loop 1 (OL1) Open-Loop Bode Editor for Open Loop 1 (OL1)
1 120
3e3 2.5e3 2e3
3.5e3 0.1
0.21.5e3 100
0.3
0.5 4e3 0.4 1e3
0.5
0.6 80
0.7
4.5e3 0.8 500
0.9
60
5e3
0
5e3
40
4.5e3 500

-0.5 20
4e3 1e3

3.5e3 1.5e3 0
3e3 2.5e3 2e3
-1 G.M.: 15.6 dB
-1 -0.5 0 0.5 1 -20 Freq: 995 Hz
Stable loop
Bode Editor for Closed Loop 1 (CL1) -40
10
-90
0
-135
-10
-180
-20
-225
-30
90 -270

0
-315
-90
-360 P.M.: 61.5 deg
-180
Freq: 248 Hz
-270 -405
0 1 2 3 4 -2 0 2 4
10 10 10 10 10 10 10 10 10
Frequency (Hz) Frequency (Hz)

Figure 3.23: Root locus and bode diagrams of the DC-link voltage controller design.

The new location of the poles gives a damping of 0.707 which is the standard value. The phase
and gain margin are 61.5 degrees and 15.6dB respectively, thus the loop is stable also in z-domain.

The step response is shown in Fig. 3.24. The overshoot is 7.1% and the settling time is 6.31ms.

3. Control of the system 33

3.6 Tuning of the controllers

Step Response
1.4
System: Closed Loop r to y
I/O: r to y
Peak amplitude: 1.07
1.2 Overshoot (%): 7.1 System: Closed Loop r to y
At time (sec): 0.0015 I/O: r to y
Settling Time (sec): 0.00631

0.8

Amplitude
0.6

0.4

0.2

0
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
Time (sec)

Figure 3.24: Step response of the DC-link voltage controller design.

Q-axis control loop

The q-axis control loop is simpler than the d-axis control loop. It only has a current loop. As the
block diagram of the current controller is the same in both cases, the same values for the propor-
tional gain and integral time have been used.

The parameters for the current and DC-voltage controller have been found and analyzed using
analytical and graphical approaches. The final values used in the model are presented all together
as a brief in the Fig. 3.25.

Kp Ti
PI id 0.0602 0.031
PI iq 0.0602 0.031
PIVDC 379.5 0.025

Figure 3.25: PI parameters for the current and DC-voltage controllers.

3.6.2 11 kW model

Comparing this model to the previous one, there are two big differences: the power converter
model is fed with a switching signal instead of the average and in the plant an LCL filter is used
instead of an L filter. These differences affect to the tunning of the controllers and so they have to
be carefully analyzed. The LCL filter has a resonance frequency which can affect the performance
of the system. The bode plot of the plant including the grid impedance is shown in Fig. 3.26.

34 3. Control of the system

 3.6 Tuning of the controllers
Bode Diagram

50

Magnitude (dB)
-50
Magnitude (dB): 7.87
Frequency (kHz): 2.39
-100

-150
0

-45

-90

Phase (deg)
-135

-180

-225

-270
-1 0 1 2 3 4 5
10 10 10 10 10 10 10
Frequency (Hz)

Figure 3.26: Bode plot of the LCL plant.

It can be seen that for this plant the resonance frequency is placed in 2.39kHz. Therefore the
switching frequency must be two times bigger according to the Shannon limit.

Before selecting the switching frequency, the tunning of the controllers have to be done. The same
procedure as for the 2.4 MW model has been used. For the inner current loop the first obtained
values for the proportional gain and the integral time are Kpc = 17.75 and Tic = 0.047. The value
of the integral time has been decreased to Tic = 0.01, in order to improve the dynamics of the
system. Fig. 3.27 shows the different root locus of the system for different values of switching
frequency.

5kHz 6kHz 7kHz

8kHz 9kHz 10kHz

Figure 3.27: Root locus of the system for different switching frequencies.

From the table, 7kHz has been chosen as the switching frequency of the model. The higher and

3. Control of the system 35

3.6 Tuning of the controllers

lower frequencies does not allow to tune the system in order to get a good performance.

The root locus of the system and the bode diagram are shown in Fig. 3.28. The phase and gain
margin are 59.7 and 7.66 degrees respectively, thus the loop is stable. The poles have been adjusted
in order to get a damping of 0.707. The new value for the proportional gain is Kpc = 17.35.

Root Locus Editor for Open Loop 1 (OL1) Open-Loop Bode Editor for Open Loop 1 (OL1)
1
1.75e3
2.1e3 1.4e3 60
0.8 2.45e3 1.05e3
40
0.6
2.8e3 700

0.4 20

3.15e3 350
0.2 0 G.M.: 7.66 dB
Freq: 1.17e+003 Hz
3.5e3 Stable loop
0
3.5e3 -20
0.9 0
-0.2
3.15e3 0.8 350 -90
0.7
-0.4 0.6 -180
0.5
2.8e3 0.4 700 -270
-0.6 0.3 -360
0.2
2.45e3 1.05e3
0.1 -450
-0.8
2.1e3 1.4e3 -540 P.M.: 59.7 deg
1.75e3 Freq: 397 Hz
-1 -630
-1 -0.5 0 0.5 1 -2 0 2 4
10 10 10 10
Real Axis Frequency (Hz)

Figure 3.28: Root locus and bode diagrams of the current controller design.

The step response of the system is shown in Fig. 3.29.

Step Response
1.4 System: Closed Loop r to y
I/O: r to y
Peak amplitude: 1.11
Overshoot (%): 11.3
1.2 At time (sec): 0.000714

1
System: Closed Loop r to y
I/O: r to y
0.8 Settling Time (sec): 0.00174
Amplitude

0.6

0.4

0.2

0
0 0.5 1 1.5 2 2.5 3 3.5
Time (sec) -3
x 10

Figure 3.29: Step response of the current controller design.

For the outer DC-link voltage loop the values of the proportional gain and the integral time are
Kpv = 1.17 and Tiv = 0.02. After adjusting the Kpv = 1.01 in order to get a damping of 0.707, the
root locus and the bode plots of the system are shown in Fig. 3.30.

36 3. Control of the system

 3.6 Tuning of the controllers

Root Locus Editor for Open Loop 1 (OL1) Open-Loop Bode Editor for Open Loop 1 (OL1)
1 120
1.75e3
2.1e3 1.4e3
100
0.8 2.45e3 1.05e3
80
0.6
2.8e3 700 60

0.4 40
3.15e3 350 20
0.2 G.M.: 7.59 dB
0 Freq: 1.16e+003 Hz
3.5e3 Stable loop
0
3.5e3 -20
0.9 -90
-0.2
3.15e3 0.8 350 -180
0.7
-0.4 0.6
-270
0.5
2.8e3 0.4 700 -360
-0.6 0.3
0.2 -450
-0.8 2.45e3 1.05e3
0.1
-540 P.M.: 58.3 deg
2.1e3 1.4e3
1.75e3 Freq: 400 Hz
-1 -630
-1 -0.5 0 0.5 1 -2 0 2 4
10 10 10 10
Real Axis Frequency (Hz)

Figure 3.30: Root locus and bode diagrams of the DC-link voltage controller design.

The phase and gain margin are 58.3 and 7.59 degrees respectively, thus the loop is stable. The step
response of the system is shown in Fig. 3.31.
Step Response
1.4 System: Closed Loop r to y
I/O: r to y
Peak amplitude: 1.14
Overshoot (%): 13.5
1.2 At time (sec): 0.000714 System: Closed Loop r to y
I/O: r to y
Settling Time (sec): 0.00244

0.8
Amplitude

0.6

0.4

0.2

0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Time (sec) -3
x 10

Figure 3.31: Step response of the DC-link voltage controller design.

The final values used in the model are presented all together as a brief in the Fig. 3.32.

Kp Ti Ki
PI id 17.35 0.01 --
PI iq 17.35 0.01 --
PRα 17.35 -- 1735
PRβ 17.35 -- 1735
PIVDC 1.01 0.02 --

Figure 3.32: PI an PR parameters for the current and DC-voltage controllers.

Through this chapter the grid side control has been explained as well as the methods used to tune
the controllers. In the next chapter different study cases have been carried out, in order to analyse
the performance of the system.

3. Control of the system 37

3.6 Tuning of the controllers

38 3. Control of the system

 Simulation and analysis

In this chapter the response of the system will be analyzed for the 2.4 MW model. For this purpose
4
different study cases have been performed. In addition a scale down of the model has been pre-
pared for an 11 kW system. In this case it has been decided to make the comparison between dq
and αβ strategies.

4.1 Simulation and analysis of 2.4 MW model

The study cases of this section will be focused on power flow, variations in grid voltage and
some grid fault studies. The response of the system will be analyzed and discussed taking into
consideration Danish grid codes mentioned in refsec:gridrequirements.

4.1.1 Power flow analysis

A. Active power steps with reactive power reference set to zero

First simulation is performed for a number of wind speed steps. From the project of last semester
the generator side control model has been used to obtain the DC-link current which corresponds
to different wind speeds in steady state. Therefore these different currents are the inputs in this
study case. The purpose of the Fig. 4.1 is to show the response of active and reactive power flow
during this simulation.

a
0.7
Active power [p.u.]

0.6

0.5

0.4

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

b
0.1
Reactive power [p.u.]

0.05

-0.05

-0.1
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.1: Active power steps and reactive power set to zero.

Fig. 4.1 is composed by two graphs. Fig 4.1.a. shows the active power delivered to the grid. At
the time 0.7s the power step corresponds to a wind step from 10m/s to 11m/s, later at the second
0.9 there is another negative step to 10m/s of wind speed. Finally, the steps are opposite and they

39
4.1 Simulation and analysis of 2.4 MW model

go back to the initial value.

In this simulation the reactive power reference is set to zero. In every step, it can be observed that
small bumps of reactive power are almost negligible compared to the rated power as shown in Fig.
4.1.b. The reactive power transient is positive or negative, when active power step is upward or
downward respectively, that means delivering or absorbing reactive power from the grid. To check
if the system is really working and delivering power to the grid the Fig. 4.2 shows the DC-link
voltage transient.

1.02
DC link voltage [p.u.]

reference
1.01 measured

0.99

0.98
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.2: DC-link voltage.

Fig. 4.2 shows at the time 0.7s and 1.3s two positive bumps of the voltage in the DC-link, which
return after a transient to the reference value. According to the equation 3.3, when the difference
between input power and output power in DC-link is positive, the current coming from the recti-
fier is bigger than the current going to the inverter. Therefore all the exceeding current is flowing
through the capacitor, thus the capacitor is charging. When the inverter current reaches the rectifier
current, the voltage goes back to the reference value.

In the case of negative steps of active power at second 0.9 and 1.1 the response is opposite. The
difference between both currents are negative and the capacitor supplies the needed current. There-
fore it discharges itself, the voltage in the DC-link drops until the control makes both currents
equal.

0.7
DC-link currents [p.u.]

0.65 rectifier
inverter
0.6
0.55
0.5
0.45
0.4
0.35
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.3: DC-link currents.

Fig 4.3 shows both currents, rectifier inverter side where it can be seen the transient response of
the control system.
The importance of this graph is in the relation between active and reactive with d and q-axis cur-
rents respectively. Fig 4.4.a. depicts the d-axis current reference and measured, and the second
graph shows q-axis current reference and measured. The relation between active power and d-axis

40 4. Simulation and analysis

 4.1 Simulation and analysis of 2.4 MW model

a
0.7

D-axis current [p.u.]

reference
0.6 measured

0.5

0.4

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
b
0.1
Q-axis current [p.u.]

reference
0.05 measured

-0.05

-0.1
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.4: D and q-axis currents reference and measured from active power steps.

current is clear in Fig 4.4.a. as well as the relation between reactive power and q-axis current as
shown in the Fig 4.4.b.

a
Voltage at the PCC [p.u.]

1.02

1.01

0.99

0.98
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

b
1
Grid currents [p.u.]

0.5

-0.5

-1
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.5: Voltage of the PCC and grid current.

Fig 4.5 shows the voltage of the PCC and grid currents. In Fig 4.5.a. it can be noticed that the
voltage of the PCC above one, which means that power is being delivered to the grid. Finally, in
Fig 4.5.b. shows the grid currents with smalls variations according to the power steps.

In this study case it can be verified one of the grid requirements which focuses on the relation
between active and reactive power flow. It can be seen in Fig. 4.1 that the system keeps reactive
power under grid requirement limitations 10% for rated value of active power as it was shown in

4. Simulation and analysis 41

4.1 Simulation and analysis of 2.4 MW model

Fig. 2.18. Besides, it is worth of remark that the variation of the applied voltage at the PCC does
not reach 0.5% which is under limits of grid requirement shown in Fig. 2.19.

B. Reactive power steps with active power reference set to 0.9 of the rated value

In this simulation active power is set to 0.9 of the rated value. The control in this case will be
focused on changes of ±20% of reactive power by keeping constant the active power.

a
1
Active power [p.u.]

0.9
0.8
0.7
0.6
0.5
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

b
0.4
Reactive power [p.u.]

0.2

-0.2

-0.4
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.6: Reactive power steps and active power set to 0.9 of the rated value.

Fig. 4.6.a. shows the active power. Fig. 4.6.b. shows the reference reactive steps which are applied
to the current controllers. The 0.9 of the rated power is not reached due to the small power losses.
As it was explained in the previous subsection, DC-link voltage response helps to verify the power
flow.

1.01
DC link voltage [p.u.]

reference

1.005 measured

0.995

0.99
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.7: DC-link voltage.

Fig. 4.7 shows the DC-link voltage response and its reference. It can be seen that the curves are
overlapped and there are no significant bumps.

42 4. Simulation and analysis

 4.1 Simulation and analysis of 2.4 MW model

a
1

D-axis current [p.u.]

0.9
0.8
reference

0.7 measured

0.6
0.5
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
b
0.4
Q-axis current [p.u.]

0.2

0
reference
-0.2
measured

-0.4
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.8: D-axis currents and q-axis currents reference and measured.

Fig. 4.8.a. shows the reference and the measured d-axis currents. Fig. 4.8.b. shows the response
of the system in q-axis. Next the voltages of the PCC and grid are shown in Fig. 4.9.

a
Voltage at the PCC [p.u.]

1.1

1.05

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

b
1.1
Grid currents [p.u.]

0.9

0.8
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.9: Voltage of the PCC and grid currents.

Fig. 4.9.a. shows the voltages of the PCC where it can be seen the changes at the times 0.7, 0.9,
1.1 and 1.3 seconds, where the magnitude of the voltage rises when reactive power is applied. Fig.
4.9.b. depicts the grid currents which rise when is applied an either positive or negative reactive
power.

For this analysis it is known that Danish grid requirements do not allow more than 10% of reactive
power flow. however this simulation pursuits the limits of nowadays wind turbines reactive power

4. Simulation and analysis 43

4.1 Simulation and analysis of 2.4 MW model

flow. It is noticeable that the voltage of the PCC is on the limits between normal operation and
disconection.

4.1.2 Voltage excursion

One common case is having voltage excursions in the grid voltage as shown in Fig. 4.10. The
voltage in this case is varying between 110% and 90% of the rated value. The variation in the
voltage grid causes istantaneus variation of the voltage drop between the grid voltage and the
converter voltage and conseguently in the grid current.
Amplitude of the Grid voltage [p.u.]

1.15
1.1
1.05
1
0.95
0.9
0.85
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.10: Amplitude of the grid voltage.

Instantaneous variation of the grid voltage causes an initial variation of the power, which can be
seen in Fig. 4.11. For example when the voltage increases there is a sudden increase in the power
which will be brought back to the original value thanks to the action of the control system. It can
be also be noticed that the reactive power is able to go back to the reference value which in this
case is zero.

a
1.3
Active power [p.u.]

1.1

0.9

0.7

0.5
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

b
0.1
Reactive power [p.u.]

0.05

-0.05

-0.1
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.11: Active and reactive power.

In Fig. 4.12 the DC-link voltage is shown. Because of the sudden variation of the voltage, the
power varies as well which makes the currents of the DC-link unbalanced. This causes the charge

44 4. Simulation and analysis

 4.1 Simulation and analysis of 2.4 MW model

or the discharge of the capacitor in the DC-link and therefore the variation of the DC-link voltage.
It is possible to see in the graph that for example when the voltage rises, the power rises as well
which causes the DC current of the inverter to increase. This means that the capacitor of the
DC-link is discharging and therefore the DC-link voltage decreases.

1.01
DC-link voltage [p.u.]

reference
measured
1.005

0.995

0.99
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.12: DC-link voltage.

In Fig. 4.13 the dq currents are shown. The variation in the dq reference currents are made in a
way to bring back the power and voltage to the desired values.

a
1,3
D-axis current [p.u.]

reference
measured
1,1

0,9

0,7
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

b
0.1
Q-axis current [p.u.]

reference
measured
0.05

-0.05

-0.1
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.13: Dq currents.

In Fig. 4.14 the PCC voltage and the grid currents are shown. It is possible to see that for example
when the grid voltage increases, the grid current decreases. This can be explained by the fact that
the power flowing to the grid is constant. When the grid voltage decreases the output voltage of
the converter decreases in order to bring back the current to the desired value.

4. Simulation and analysis 45

4.1 Simulation and analysis of 2.4 MW model

Voltage of the PCC [p.u.]

1

0.5

-0.5

-1
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
b
1
Grid current [p.u.]

0.5

-0.5

-1
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.14: PCC voltage and grid current.

According to the grid requirements, when the frequency is 50Hz and the voltage varies between
110% and 90% of the rated value, The system can remain connected for one minute as shown in
Fig. 2.19. Therefore ít can be seen that in this study case the system is complying with this grid
requirement. It can be observed that the values of the active and reactive powers are within the
accepted range according to the grid requirement shown in Fig. 2.18.

4.1.3 Frequency excursion

Through this section the response of the system will be analyzed in the case of grid frequency
changes, by keeping the active power at 0.9 of its rated value and reactive power to zero. Grid
voltage frequency varies ±3Hz of its rated value considering that each step lasts 200ms as shown
in Fig. 4.15.
Grid voltage frequency [Hz]

55
54
53
52
51
50
49
48
47
46
45
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.15: Grid frenquency steps.

Power flow response is shown in Fig. 4.16.

46 4. Simulation and analysis

 4.1 Simulation and analysis of 2.4 MW model

a
1

Active power [p.u.]

0.95

0.9

0.85

0.8
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

b
0.2
Reactive power [p.u.]

0.1

-0.1

-0.2
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.16: Active and reactive power flow.

Fig. 4.16.a. shows the active power. As it was said before the 0.9 of rated value is not reached
due to the filter losses. Fig. 4.16.b. shows the reactive power where it can be noticed that is more
sensible than the active power. This is because the reactive power is related with q-axis current
control as shown in Fig 4.18.

Fig. 4.17 shows the DC-link voltage response.

1.01
DC link voltage [p.u.]

1.005 reference
measured

0.995

0.99
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.17: DC-link voltage.

In can be noticed that the voltage bumps are negligible compared to the rated value. Fig. 4.18
shows the reference and measured dq currents.

4. Simulation and analysis 47

4.1 Simulation and analysis of 2.4 MW model

a
1

D-axis current [p.u.]

reference
measured
0.95

0.9

0.85

0.8
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

b
0.1
Q-axis current [p.u.]

reference
measured
0.05

-0.05

-0.1
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.18: Reference and measured dq.

In this case q-axis current is more sensible than d-axis current. It can be seen that after a short
transient both currents go back to the reference values. In this simulation there are not big changes
in the dq currents as they are below 1%. Finally, the PCC voltage and the grid currents are shown
in Fig. 4.19.

a
Voltage at the PCC [p.u.]

1.01

1.005

0.995

0.99
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
b
0.9
Grid currents [p.u.]

0.895

0.89

0.885

0.88
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.19: Voltage of the PCC and grid current.

It can be observed that during the simulation, the PCC voltage is larger than the grid voltage when
the active power is being delivered to the grid. Thus, it is worth to remark that the voltage of
PCC has fluctuations which produces the transients in the grid currents. It is necessary to zoom
in to realize the grid current transients. Another important point is that in spite of the fact that the
frequency excursions of 3Hz are significants, the reactive power flow does not reach the limits of

48 4. Simulation and analysis

 4.1 Simulation and analysis of 2.4 MW model

grid requirements. The voltage of the PCC is within the acceptable range of the grid requirement.

4.1.4 Phase jumps

The purpose of this simulation is to see the behavior of the system when the voltage angle of the
grid is shifted. This study case is performed with some steps in the grid voltage angle, as shown
in Fig. 4.20, when the system is delivering 0.9 of rated active power and zero reactive power is set
to zero.

80
Grid voltage angle [Deg]

60
40
20
0
-20
-40
-60
-80
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.20: Phase angle of grid voltage.

Fig. 4.21 shows the active and reactive power flow. In Fig. 4.21.a. it can be seen that the active
power flow decreases when the change in the phase angle of the voltage is applied. This is because
the active power is related to the d-axis current and voltage reference, which is shown in Fig. 4.23.

a
1.5
Active power [p.u.]

1.2
0.9
0.6
0.3
0
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

b
1.5
Reactive power [p.u.]

1
0.5
0
-0.5
-1
-1.5
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.21: Active and reactive power flow.

Fig. 4.21.b. shows that the reactive power flow reaches the reference value of zero after the
transients. Due to the relation between reactive power and phase angle, these transients have
abrupt starts. Therefore, depending on the sign of this shifted angle, the peak of power will be
negative or positive. The response of the DC-link voltage is shown in Fig. 4.22.

4. Simulation and analysis 49

4.1 Simulation and analysis of 2.4 MW model

1.1

DC link voltage [p.u.]

1.05 reference
measured

0.95

0.9
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.22: DC-link voltage.

The graph shows how the DC-link voltage arrives at steady state after a small transient, whose
maximum peak for each angle variation is below 1% of the rated value. Fig. 4.23 shows the dq
currents of the grid.

a
1.6
D-axis current [p.u.]

reference
1.4
measured

1.2

0.8
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
b
0.4
Q-axis current [p.u.]

0.2 reference
measured

-0.2

-0.4
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.23: Reference and measured dq currents.

Fig. 4.23.a. shows reference and measured d-axis current where it can be seen that after a small
transient they become overlapped. It can be noticed that during the transient, the maximum value
is below 20% of the rated value. Fig. 4.23.b. shows the reference and measured of the q-axis
current. Fig. 4.24 shows the PCC voltage and the grid current.

50 4. Simulation and analysis

 4.1 Simulation and analysis of 2.4 MW model

a b c d

Voltage at the PCC [p.u.]

1.5 1.5 1.5 1.5
1 1 1 1
0.5 0.5 0.5 0.5
0 0 0 0
-0.5 -0.5 -0.5 -0.5
-1 -1 -1 -1
-1.5 -1.5 -1.5 -1.5
0.68 0.7 0.72 0.88 0.9 0.92 1.08 1.1 1.12 1.28 1.3 1.32
Time [s] Time [s] Time [s] Time [s]

e f g h
1.5 1.5 1.5 1.5
Grid currents [p.u.]

1 1 1 1
0.5 0.5 0.5 0.5
0 0 0 0
-0.5 -0.5 -0.5 -0.5
-1 -1 -1 -1
-1.5 -1.5 -1.5 -1.5
0.68 0.7 0.72 0.88 0.9 0.92 1.08 1.1 1.12 1.28 1.3 1.32
Time [s] Time [s] Time [s] Time [s]

Figure 4.24: Voltages of the PCC and the grid currents.

4.1.5 Unbalanced
Another situation could be the case of an unbalanced three-phase sinusoidal waveform in the grid
voltage. In a balanced sinusoidal supply system the three line-neutral voltages are equal in magni-
tude and are phase displaced from each other by 120 degrees. A system is called unbalanced when
there is a difference between the voltage magnitudes and/or when there is phase shift different than
120 degrees. In this study case the unbalanced percentage is chosen to be 3%. In other words the
amplitude of one phase is 3% more than the other two, as shown in Fig. 4.25.

Voltage unbalance is considered as a power quality problem of significant importance. The volt-
ages can become unbalanced when there are unequal impedances and unequal distribution of
single-phase loads [6].

1.2
Grid voltage [p.u.]

1
0.8
0.6
0.4
0.2
0
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.25: Unbalanced grid voltage.

In Fig. 4.26 the active and reactive power are shown. Here as in all other graphs of this study case,
the situation is the same. The values fluctuate around the desired value. The same situation can be
seen for dq currents as shown in Fig. 4.28.

4. Simulation and analysis 51

4.1 Simulation and analysis of 2.4 MW model

a
1.3

Active power [p.u.]

1.1

0.9

0.7

0.5
0.5 0.51 0.52 0.53 0.54 0.55 0.56
b
0.4
Reactive power [p.u.]

0.2

-0.1

-0.4
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.26: Active and reactive power.

Fig. 4.27 shows the DC-link voltage. It can be noticed that there are small fluctuations over the
reference value. These small fluctuations can be seen in all the graphs presented here for this study
case. They are caused by the dq transformation.

1.01
DC-link voltage [p.u.]

reference
measured
1.005

0.995

0.99
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.27: DC-link voltage.

The dq currents are shown in Fig. 4.28. We can see that the currents are slightly oscillating around
the reference value.

52 4. Simulation and analysis

 4.1 Simulation and analysis of 2.4 MW model

a
1.3

d-axis current [p.u.]

reference
1.1 measured

0.9

0.8

0.6
0.5 0.51 0.52 0.53 0.54 0.55 0.56

b
0.1
q-axis current [p.u.]

reference
0.05
measured

-0.02

-0.04
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.28: Dq currents.

In Fig. 4.29 it is possible to see the grid current. Where one of the phases has a bigger amplitude
compare to the other two.

1
0.9
Grid current [p.u.]

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.29: Grid current.

4. Simulation and analysis 53

4.1 Simulation and analysis of 2.4 MW model

4.1.6 Short-circuit
Electrical systems are susceptible to short circuits and to the abnormal current levels they create.
These currents can produce considerable thermal and mechanical stresses in electrical distribution
equipment. Therefore, it is important to protect people and equipment by calculating short-circuit
currents during system upgrade and design. Because these calculations are life-safety related,
they’re mandated by 110.9 of the NEC, which states:

“Equipment intended to interrupt current at fault levels shall have an interrupting rating sufficient
for the nominal circuit voltage and the current that is available at the line terminals of the equip-
ment. Equipment intended to interrupt current at other than fault levels shall have an interrupting
rating at nominal circuit voltage sufficient for the current that must be interrupted.”

When you apply these requirements to a circuit breaker, you must calculate the maximum 3-phase
fault current the breaker will be required to interrupt. This current can be defined as the short-
circuit current available at the terminals of the protective device [18].

A. Three-phase short-circuit

A three-phase short-circuit can be considered as a balanced load, which means it is possible to use
a single-phase circuit to analyze the fault. In this study case a three-phase short-circuit occurs at
second 0.5 and it last for 150 ms.

a
Grid voltage [p.u.]

-1

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

b
Grid current [p.u.]

-1

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

Time [s]

Figure 4.30: Voltages and currents of the PCC.

In Fig. 4.30 the voltage and current of the PCC are shown. The value of the short-circuit resistance
is chosen so that the voltage drop will be equal to 90% of the rated value which can be seen in Fig.
4.30.a. After the short-circuit the grid voltage has a short transient, where the value is temporarily
higher than the rated value, before going back to the rated value. This temporarily raise does not
happend if the system is connected to a stronger grid with a higher short-circuit power. The grid
current is kept at the same value thanks to the control system which acts on the power references.

54 4. Simulation and analysis

 4.1 Simulation and analysis of 2.4 MW model

a
2

Active power [p.u.]

1

-1
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

b
2
Reactive power [p.u.]

1.5
1
0.5
0
-0.5
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
Time [s]

Figure 4.31: Active and reactive power.

In Fig. 4.31 the active and the reactive power are shown. It is possible to see the action of the
control system. At second 0.5, when the fault happens, the active power reference is set to zero,
because otherwise considering the small value of the voltage the current would be extremely high.
In the same moment the reactive power reference is set to maximum. This is required by the grid
and helps to maintain the voltage.

1.1
DC-link voltage [p.u.]

reference
1.05 measured

0.95

0.9
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

Figure 4.32: DC-link voltage.

In Fig. 4.32 The DC-link voltage is shown. It can be noticed that when the short-circuit occurs
there is a temporary drop in the DC-link voltage. At the end of the short-circuit the DC-link volt-
age rises temporarily before reaching the reference value.

In Fig. 4.33 dq currents are shown. After the short-circuit, the d-axis component of the current
goes to zero as the active power reference is set to zero. In the same moment the q-axis component
of the current rises since the reactive power is set to maximum.

According to the grid requirements, when the voltage drops to less than 2% of the rated value,
within the first 10 seconds "may be disconnected" and after that "shall disconnected" as shown in

4. Simulation and analysis 55

4.1 Simulation and analysis of 2.4 MW model

a
1

d-axis current [p.u.]

0.5
reference
0 measured

-0.5

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

b
1
q-axis current [p.u.]

0.5
reference
0 measured

-0.5

-1
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
Time [s]

Figure 4.33: Dq currents.

Fig. 2.20. Therefore in this situation for the first 10 seconds it can be choose to keep the wind
turbine connected to grid.

B. Two-phase short-circuit

In this study case a two-phase short-circuit occurs in second 0.5 and it lasts 150 ms. In Fig. 4.34
the voltage and currents of the PCC are shown. In the two phases affected by the short-circuit the
voltage drops to half of the original value as shown in Fig. 4.34.a.

a
Grid voltage [p.u.]

-1

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

b
2
Grid current [p.u.]

-1

-2
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
Time [s]

Figure 4.34: Voltage and currents of the PCC.

In Fig. 4.35 the active and the reactive power are shown. The active power goes to zero as required

56 4. Simulation and analysis

 4.1 Simulation and analysis of 2.4 MW model

by the control system and the reactive power to its maximum.

a
1
Active power [p.u.]
0.5

-0.5

-1
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

b
1
Reactive power [p.u.]

0.5

-0.5

-1
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
Time [s]

Figure 4.35: Active and reactive power.

In Fig. 4.36 The DC-link voltage is shown. It can be noticed that when the short-circuit occurs,
the DC-link voltage decreases slightly and then reaches the reference value.

1.1
DC-link voltage [p.u.]

reference
1.05 measured

0.95

0.9
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

Figure 4.36: DC-link voltage.

In Fig. 4.37 dq currents are shown. After the short-circuit, the d-axis component of the current
goes to zero as the active power reference is set to zero. In the same moment the q-axis component
of the current rises since the reactive power is set to maximum.

4. Simulation and analysis 57

4.1 Simulation and analysis of 2.4 MW model

a
1

d-axis current [p.u.]

reference
measured
0.5
0
-0.5
-1
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
b
1
q-axis current [p.u.]

0.5 reference
measured
0

-0.5

-1
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
Time [s]

Figure 4.37: Dq currents.

The voltage drop of the two phases affected by the fault, in this case, is around 50% of the rated
value. Therefore according to the grid requirements, Fig. 2.20, during this fault the wind turbine
"shall remain connected".

C. One-phase short-circuit

In this study case the short-circuit occurs in one of the phases. In Fig. 4.38 the voltage and current
of the PCC are shown. It can be seen that one phase of the grid voltage drops to 10% of the initial
value. The current rises to almost three times of the rated value.

a
Grid voltage [p.u.]

-1

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

b
4
Grid current [p.u.]

-2

-4
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
Time [s]

Figure 4.38: Voltage and currents of the PCC.

58 4. Simulation and analysis

 4.1 Simulation and analysis of 2.4 MW model

In Fig. 4.39 the active and reactive powers are shown where it is possible to see the action of the
control system. After the fault the active power reference is set to zero. In the same moment the
reactive power reference is set to maximum.

a
1.5
Active power [p.u.]

1
0.5
0
-0.5
-1
-1.5
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
b
1.5
Reactive power [p.u.]

1
0.5
0
-0.5
-1
-1.5
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
Time [s]

Figure 4.39: Active and reactive power.

In Fig. 4.40 the DC-link voltage is shown. It can be noticed that when the short-circuit occurs the
DC-link voltage decreases slightly and then reaches the reference value.

1.1
DC-link voltage [p.u.]

1.05 reference
measured

0.95

0.9
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

Figure 4.40: DC-link voltage.

In Fig. 4.41 dq currents are shown. After the short-circuit, the d-axis component of the current
goes to zero as the active power reference is set to zero. In the same moment the q-axis component
of the current rises since the reactive power is set to maximum.

4. Simulation and analysis 59

4.2 Analysis and comparison of 11 kW model

a
1

d-axis current [p.u.]

0.5

0 reference
measured
-0.5

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

b
1
q-axis current [p.u.]

0.5
reference
measured
0

-0.5

-1
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
Time [s]

Figure 4.41: Dq currents.

The voltage drop of the phase affected by the fault, in this case, is around 90% of the rated value.
Therefore according to the grid requirements, when the voltage drops to less than 20% of the rated
value, within the first 10 seconds "may be disconnected" and after that "shall disconnected" as
shown in Fig. 2.20. Therefore in this situation for the first 10 seconds it can be choose to keep the
wind turbine connected to grid.

4.2 Analysis and comparison of 11 kW model

In this section the model has been scaled down in order to control a 11kW system. The control
has been carried out in αβ and dq reference frame. The procedure is to analyze the system under
different grid conditions in both types of control strategies and to compare the results at the end
of the subsection. The comparison is made for active and reactive power flow, voltage of the
PCC, grid currents and the DC-link voltage responses. The rated values of the main variables are
presented in Fig. 4.42.

Parameters Units Value

Rated active power Prat. [kW] 11
Grid voltage (peak value) Vgrid. [V] 230· 2
Grid currents (peak value) Igrid. [A] 16,43· 2
DC-link voltage VDC. [V] 650

Figure 4.42: Main parameters of the system.

The summary of the study cases as well as the obtained results are presented in the following table
Fig. 4.43.

60 4. Simulation and analysis

 4.2 Analysis and comparison of 11 kW model

4.2.1 Study cases

A. Power flow active steps and reactive power set to zero
B. Power flow reactive steps and active power set to 0.9 of rated value
C. Voltage excursion
D. Unbalanced
E. Voltage phase angle steps for active power set to 0.9 of rated value
F. Voltage frequency steps for active power set to 0.9 of rated value

4.2.2 Simulation results

A. αβ Power flow active steps and reactive power set to zero
B. αβ Power flow reactive steps and active power set to 0.9 of rated value
C. αβ Voltage excursion
D. αβ Unbalanced
E. αβ Voltage phase angle steps for active power set to 0.9 of rated value
F. αβ Voltage frequency steps for active power set to 0.9 of rated value

A. Dq Power flow active steps and reactive power set to zero

B. Dq Power flow reactive steps and active power set to 0.9 of rated value
C. Dq Voltage excursion
D. Dq Unbalanced
E. Dq Voltage phase angle steps for active power set to 0.9 of rated value
F. Dq Voltage frequency steps for active power set to 0.9 of rated value

Figure 4.43: Index of the simulation and results.

4.2.1 αβ and dq control study cases

A. Active power flow steps and reactive power set to zero

This analysis is performed for a number of active power excursions by setting reactive power to
zero value. The active power starts at 60% of the rated value, later it rises to 90% and at the end it
goes down to 40%.
Active power inputs [p.u.]

1
0.8
0.6
0.4
0.2
0
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.44: Active power steps applied to the system.

4. Simulation and analysis 61

4.2 Analysis and comparison of 11 kW model

B. Reactive power flow steps and active power set to 0.9 of rated value

In this analysis positive and negative reactive power steps of 20% of the rated value, will be
applied. The active power flow is set to 90% of the rated value.

Reactive power inputs [p.u.]

0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.45: Reactive power steps applied to the system.

C. Voltage excursion

In this analysis voltage excursions in the grid voltage are considered as shown in Fig. 4.46. The
voltage in this case is varying between ±10% of the rated value.
Grid voltage amplitude [p.u.]

1.15
1.1
1.05
1
0.95
0.9
0.85
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.46: Voltage excursion.

D. Unbalanced

In this study case the grid voltage is an unbalanced three-phase sinusoidal waveform, where one
of the phases is 3% bigger in amplitude as shown in Fig. 4.47.

1.1
1
Grid voltage [p.u.]

0.8
0.6
0.4
0.2
0
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.47: Unbalanced grid voltage.

62 4. Simulation and analysis

 4.2 Analysis and comparison of 11 kW model

E. Voltage phase angle steps for active power set to 0.9 of rated value

This study case considers that the system is delivering 90% of the rated active power. Besides, a
few steps in the voltage phase angle are applied. These steps are 60 degrees positive and negative
respectively.

80
Grid voltage angle [Deg] 60
40
20
0
-20
-40
-60
-80
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.48: Voltage phase angle.

F. Voltage frequency steps for active power set to 0.9 of rated value

Frequency excursions of ±3Hz are taken into consideration in this analysis. During the frequency
variations the system is delivering 90% of the rated value.
Grid voltage frequency [Hz]

55
54
53
52
51
50
49
48
47
46
45
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.49: Frequency steps of the grid voltage.

4. Simulation and analysis 63

4.2 Analysis and comparison of 11 kW model

4.2.2 αβ and dq control simulation results

A. αβ active power flow steps and reactive power set to zero

1.4
reference
1.2
Active power [p.u.]

measured
1
0.8
0.6
0.4
0.2
0
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.50: Active power flow.

1
Reactive power [p.u.]

0.8 reference
0.6 measured
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.51: Reactive power flow.

1.25
Voltage at the PCC [p.u.]

1
0.75
0.5
0.25
0
-0.25
-0.5
-0.75
-1
-1.25
0.6 0.7 0.8 0.9 1 1.1
Time [s]

Figure 4.52: Voltage of the PCC.

64 4. Simulation and analysis

 4.2 Analysis and comparison of 11 kW model

1
0.8

Grid currents [p.u.]

0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.53: Grid currents.

1.01
DC link voltage [p.u.]

reference
measured
1.005

0.995

0.99
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.54: DC-link voltage.

B. αβ reactive power flow steps and active power set to 0.9 of rated value

1.5
reference
1.25 measured
Active power [p.u.]

1
0.75
0.5
0.25
0
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.55: Active power flow.

0.4
Reactive power [p.u.]

reference
0.3
measured
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.56: Reactive power flow.

4. Simulation and analysis 65

4.2 Analysis and comparison of 11 kW model

1.5

Voltage at the PCC [p.u.]

1
0.5
0
-0.5
-1
-1.5
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.57: Voltage of the PCC.

1.25
Grid currents [p.u.]

0.75

0.25

-0.25

-0.75

-1.25
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.58: Grid currents.

1.01
reference
DC link voltage [p.u.]

1.005 measured

0.995

0.99
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.59: DC-link voltage.

C. αβ voltage excursion

1.3
reference
Active power [p.u.]

1.1 measured

0.9

0.7

0.5
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.60: Active power.

66 4. Simulation and analysis

 4.2 Analysis and comparison of 11 kW model

0.4

Reactive power [p.u.]

reference
0.2 measured

-0.2

-0.4
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.61: Reactive power.

1.2
Voltage of the PCC [p.u.]

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.62: Voltage of the PCC.

1
0.8
Grid currents [p.u.]

0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.63: Grid current.

1.03
DC-link voltage [p.u.]

1.02 reference
measured
1.01
1
0.99
0.98
0.97
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.64: DC-link voltage.

4. Simulation and analysis 67

4.2 Analysis and comparison of 11 kW model

D. αβ unbalanced voltage

1.3
reference
Active power [p.u.] 1.1 measured

0.9

0.7

0.5
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.65: Active power.

0.4
Reactive power [p.u.]

reference
0.2 measured

-0.2

-0.4
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.66: Reactive power.

1.2
Voltage of the PCC [p.u.]

1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.67: Voltage of the PCC.

1.2
Grid currents [p.u.]

1
0.8
0.6
0.4
0.2
0
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.68: Grid current.

68 4. Simulation and analysis

 4.2 Analysis and comparison of 11 kW model

1.01

DC-link voltage [p.u.]

reference
1.005 measured

0.995

0.99
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.69: DC-link voltage.

E. αβ voltage phase angle steps for active power set to 0.9 of rated value

3
2.5
Active power [p.u.]

2
1.5
1
0.5
0
-0.5
-1 reference
-1.5 measured
-2
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.70: Active power flow.

2.5
Reactive power [p.u.]

2 reference
1.5 measured
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.71: Reactive power flow.

2
Voltage at the PCC [p.u.]

1.5
1
0.5
0
-0.5
-1
-1.5
-2
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.72: Voltage at the PCC.

4. Simulation and analysis 69

4.2 Analysis and comparison of 11 kW model

3
2

Grid currents [p.u.]

1
0
-1
-2
-3
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.73: Grid currents.

1.4
1.3
DC link voltage [p.u.]

reference
1.2 measured

1.1
1
0.9
0.8
0.7
0.6
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.74: DC-link voltage.

F. αβ voltage frequency steps for active power set to 0.9 of rated value

1.3
reference
measured
Active power [p.u.]

1.1

0.9

0.7

0.5
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.75: Active power flow.

1
Reactive power [p.u.]

0.8 reference
0.6 measured
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.76: Reactive power flow.

70 4. Simulation and analysis

 4.2 Analysis and comparison of 11 kW model

1.25

Voltage at the PCC [p.u.]

1
0.75
0.5
0.25
0
-0.25
-0.5
-0.75
-1
-1.25
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.77: Voltage at the PCC.

1
0.75
Grid currents [p.u.]

0.5
0.25
0
-0.25
-0.5
-0.75
-1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.78: Grid currents.

1.02
reference
DC link voltage [p.u.]

measured
1.01

0.99

0.98
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.79: DC-link voltage.

A. Dq active power flow steps and reactive power set to zero

1.4
1.2
Active power [p.u.]

reference
1 measured

0.8
0.6
0.4
0.2
0
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.80: Active power flow.

4. Simulation and analysis 71

4.2 Analysis and comparison of 11 kW model

Reactive power [p.u.]

0.8 reference
0.6 measured
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.81: Reactive power flow.

2
Voltage at the PCC [p.u.]

1.5
1
0.5
0
-0.5
-1
-1.5
-2
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.82: Voltage of the PCC.

1
0.8
Grid currents [p.u.]

0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.83: Grid currents.

1.01
DC link voltage [p.u.]

reference
1.005 measured

0.995

0.99
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.84: DC-link voltage.

72 4. Simulation and analysis

 4.2 Analysis and comparison of 11 kW model

B. Dq reactive power flow steps and active power set to 0.9 of rated value

1.5
reference
1.25 measured

Active power [p.u.]

1
0.75
0.5
0.25
0
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.85: Active power flow.

0.4
Reactive power [p.u.]

0.3 reference
measured
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.86: Reactive power flow.

1.5
Voltage at the PCC [p.u.]

1
0.5
0
-0.5
-1
-1.5
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.87: Voltage of the PCC.

1.25
Grid currents [p.u.]

0.75

0.25

-0.25

-0.75

-1.25
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.88: Grid currents.

4. Simulation and analysis 73

4.2 Analysis and comparison of 11 kW model

1.01
reference

DC link voltage [p.u.]

measured
1.005

0.995

0.99
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.89: DC-link voltage.

C. Dq voltage excursion

1.3
reference
Active power [p.u.]

1.1 measured

0.9

0.7

0.5
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.90: Active power.

0.4
Reactive power [p.u.]

reference
0.2 measured

-0.2

-0.4
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.91: Reactive power.

1.2
Voltage of the PCC [p.u.]

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.92: Voltage of the PCC.

74 4. Simulation and analysis

 4.2 Analysis and comparison of 11 kW model

Grid currents [p.u.]

0.5

-0.5

-1
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.93: Grid current.

1.03
DC-link voltage [p.u.]

1.02 reference
measured
1.01
1
0.99
0.98
0.97
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.94: DC-link voltage.

E. Dq unbalanced voltage

1.3
reference
Active power [p.u.]

1.1 measured

0.9

0.7

0.5
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.95: Active power.

0.4
Reactive power [p.u.]

reference
0.2 measured

-0.2

-0.4
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.96: Reactive power.

4. Simulation and analysis 75

4.2 Analysis and comparison of 11 kW model

1.2

Voltage of the PCC [p.u.]

1
0.8
0.6
0.4
0.2
0
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.97: Voltage of the PCC.

1.2
Grid currents [p.u.]

1
0.8
0.6
0.4
0.2
0
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.98: Grid current.

1.01
DC-link voltage [p.u.]

reference
1.005 measured

0.995

0.99
0.5 0.51 0.52 0.53 0.54 0.55 0.56
Time [s]

Figure 4.99: DC-link voltage.

E. Dq voltage phase angle steps for active power set to 0.9 of rated value

3
reference
2.5 measured
Active power [p.u.]

2
1.5
1
0.5
0
-0.5
-1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.100: Active power flow.

76 4. Simulation and analysis

 4.2 Analysis and comparison of 11 kW model

2.5

Reactive power [p.u.]

2
1.5
1
0.5
0
-0.5
-1 reference
-1.5 measured
-2
-2.5
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.101: Reactive power flow.

1.5
Voltage at the PCC [p.u.]

1
0.5
0
-0.5
-1
-1.5
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.102: Voltage at the PCC.

3
2
Grid currents [p.u.]

1
0
-1
-2
-3
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.103: Grid currents.

1.05
DC link voltage [p.u.]

1.025

reference
0.975 measured

0.95
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.104: DC-link voltage.

4. Simulation and analysis 77

4.2 Analysis and comparison of 11 kW model

F. Dq voltage frequency steps for active power set to 0.9 of rated value

1.3

Active power [p.u.]

reference
1.1 measured

0.9

0.7

0.5
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.105: Active power flow.

1
Reactive power [p.u.]

0.8 reference
0.6 measured
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Time [s]

Figure 4.106: Reactive power steps.

1.25
Voltage at the PCC [p.u.]

1
0.75
0.5
0.25
0
-0.25
-0.5
-0.75
-1
-1.25
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.107: Voltage at the PCC.

1
0.75
Grid currents [p.u.]

0.5
0.25
0
-0.25
-0.5
-0.75
-1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.108: Grid currents.

78 4. Simulation and analysis

 4.2 Analysis and comparison of 11 kW model

1.02

DC link voltage [p.u.]

1.01 reference
measured

0.99

0.98
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 4.109: DC-link voltage.

4.2.3 General comparison between αβ and dq

In the previous subsection the simulation results of the study cases have been presented graphi-
cally. In this section the comparison between the results obtained for αβ and dq control strategies
is shown in Fig. 4.110.

CONTROL STRATEGY
αβ dq
STUDY CASES P and Q V and I at PCC DC-link voltage P and Q V and I at PCC DC-link voltage

Active power steps, Reactive power 0

Reactive power steps, Active power 0,9 Pn

Voltage excursion

Volage unbalanced

Voltage phase jumps

Voltage frequency excursion

Very good performace

Acceptabe performance
Bad performance

Figure 4.110: Comparison table for dq and αβ.

It can be observed that the performance of both strategies is very good for most of the study cases.
However, the results of voltage phase angle shift and voltage frequency excursions cases are poor,
being poorer in αβ than in dq.

The simulations and analysis for the 2.4 MW model under different voltage disturbances, power
flow fluctuations and faults in the grid have been carried out, taking into consideration the grid
requirements. The comparison between αβ and dq has been performed. Next chapter will show
the laboratory tests and its results compared with the model.

4. Simulation and analysis 79

4.2 Analysis and comparison of 11 kW model

80 4. Simulation and analysis

 Experimental setup
5
In this chapter, the experimental setup used in the laboratory is presented and the main components
are described. Next, αβ and dq control strategies are implemented. Finally the results obtained
for the active power flow study case are shown.

5.1 Setup description

The setup used in the laboratory to carry out the experimental tests is presented in Fig. 5.1. It
emulates the grid side connection of the wind turbine system. The system contains a DC voltage
supply, a power inverter, a LC filter, a three-phase transformer, the grid, the dSPACE system and
the PC computer.

4 3

5
6

7
2

Figure 5.1: Laboratory setup components: 1:PC computer, 2:dSPACE Hardware, 3:LC filter,
4:Power Inverter, 5:Main supply, 6:DC voltage connection, 7:three-phase trans-
former.

The power inverter is controlled by a Graphical User Interface (GUI) from the PC computer
through the dSPACE system. The dSPACE system sends the needed pulses to the converter gates
in order to generate the active and reactive power set in the control system. It is composed by
the software, the expansion box which contains the main boards as the processor and I/O boards
and finally the panels with BNC connectors to read and send the signal from the computer to the
system and vice versa.

The setup structure is shown in Fig. 5.2.

81
5.1 Setup description

AC grid

Power Inverter
LC filter
Transformer
DC supply

I/O panel

PC computer
dSPACE
Expansion Box

Figure 5.2: structure of the laboratory setup.

The GUI used to control the system is shown in Fig. 5.3.

Figure 5.3: dSPACE graphical user interface.  

Basically, from the GUI, it is possible to enable and disable the converter, to set the active and
reactive power and to modify the parameters of the controller during the tests. Furthermore the
main variables of the system are shown by means of different graphs. Behind the GUI both control
strategies (dq and αβ) are implemented. The results of the laboratory tests are analyzed and
compared with the results obtained in the previous chapter for the power flow study case.

82 5. Experimental setup
 5.2 Study cases and results

5.2 Study cases and results

In this section the load flow study case that was analyzed in the section 4.2, is carried out in the
laboratory for both control strategies.

5.2.1 αβ active power flow steps and reactive power set to zero

reference
1.2
measured
Active power [p.u.]

1
0.8
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1 1.2
Time [s]

Figure 5.4: Active power.

0.5
0.4 reference
Reactive power [p.u.]

0.3 measured
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
0 0.2 0.4 0.6 0.8 1
Time [s]

Figure 5.5: Reactive power

1.5

1
Grid voltages [p.u.]

0.5

-0.5

-1

-1.5
0.4 0.41 0.42 0.43 0.44 0.45 0.46
Time [s]

Figure 5.6: Grid voltages.

5. Experimental setup 83
5.2 Study cases and results

1
0.8

Grid currents [p.u.]

0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0 0.2 0.4 0.6 0.8 1
Time [s]

Figure 5.7: Grid currents.

1 alpha-ref.
Alpha-beta currents [p.u.]

0.8 alpha-meas.
0.6 beta-ref.
0.4 beta-meas.
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.4 0.41 0.42 0.43 0.44 0.45 0.46
Time [s]

Figure 5.8: αβ currents of the grid.

Phase-A voltage & current [p.u.]

1 voltage
0.8 current
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.4 0.41 0.42 0.43 0.44 0.45 0.46
Time [s]

Figure 5.9: Voltage and current of phase A.

84 5. Experimental setup
 5.2 Study cases and results

5.2.2 Dq active power flow steps and reactive power set to zero

reference
1.2
Active power [p.u.] measured
1
0.8
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1 1.2
Time [s]

Figure 5.10: Active power.

0.5
0.4 reference
Reactive power [p.u.]

0.3 measured
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
0 0.2 0.4 0.6 0.8 1 1.2
Time [s]

Figure 5.11: Reactive power.

1.5

1
Grid voltages [p.u.]

0.5

-0.5

-1

-1.5
0.4 0.42 0.44 0.46 0.48 0.5
Time [s]

Figure 5.12: Grid voltages.

5. Experimental setup 85
5.2 Study cases and results

1.2
1
0.8

Grid currents [p.u.]

0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
0 0.2 0.4 0.6 0.8 1 1.2
Time [s]

Figure 5.13: Grid currents.

1.2
1 d-axis ref.
0.8 d-axis meas.
Dq currents [p.u.]

0.6 q-axis ref.

0.4 q-axis meas.
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
0 0.2 0.4 0.6 0.8 1
Time [s]

Figure 5.14: Dq currents of the grid.

Phase-A voltage & current [p.u

1 voltage
0.8 current
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0.4 0.41 0.42 0.43 0.44 0.45 0.46
Time [s]

Figure 5.15: Voltage and current of phase A.

As it can be seen in the previous graphs, the laboratory results are very close to the results obtained
in the simulations. This confirms the expected performance of the grid side wind turbine system.

86 5. Experimental setup
Summary
Conclusions
6
It is possible to state that the main objectives of the project have been achieved. The main objec-
tive was to implement the control system of the grid side converter for a large wind turbine system
connected to the grid. Therefore good knowledge about control systems has been necessary. Be-
sides, to perform the simulations, the models of the components have been prepared and therefore
good skills about MATLAB/Simulink and modeling was required.

Power systems connected to the grid have to comply with the grid requirements. In the case of
the wind turbines, considering that the amount of wind energy penetrating to the grid is increasing
considerably, it is very important to develop reliable and quality control systems. In this project
Danish grid codes have been taken into consideration.

The control strategy used to control the wind turbine model of 2.4 MW is dq reference frame strat-
egy. The control system has been implemented and in order to analyze the results, different study
cases under various grid conditions have been performed. By analyzing the results it is possible to
conclude that the main objective of the project has been reached. In fact thought the simulations it
is possible to see that the system responds well and fast in front of different conditions.

In addition it has been decided to compare two different control strategies, αβ and dq. Considering
that αβ uses PR controllers and dq PI controllers, it is interesting to compare this two methods.
For this purpose a small-scale model of 11 kW has been implemented. Simulations have been
performed on this model and different study cases have been analyzed. The reason for making
the simulation on a small-scale system was to be able to verify the results with experimental tests
in the laboratory. By comparing the results of the two control strategies it has been possible to
observe that both of them have good performances and they are quite similar.

The laboratory tests are very important. In this way it is possible to verify the results of the simu-
lations. Besides that, the experimental work is useful to familiarize with the real components and
have a better understanding of the systems. For this purpose, it was necessary to acquire good
knowledge about the components of the setup, specially dSPACE.

Future work
• Different control strategies could be studied to improve the performance of the system as a
future work.
• The complete wind turbine system, containing the generator side and the grid side of the
system can be studied and analyzed more in detail.
• The laboratory work could be done also for the generator side control and for the complete
wind turbine system.

87
Bibliography

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faults,” IEEE Canada Electrical Power Conference, pp. 160–165, 2007.

[2] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, “Overview of control and grid
synchronization for distributed power generation systems,” IEEE Transactions on Industrial
Electronics, vol. 53, pp. 1398–1409, 2006.

[3] A. Carlsson, “The back to back converter,” May 1998.

[4] E. Ceanga, C. Nichita, L. Protin, and N. A. Cutululis, Théorie De La Commande Des

Systèmes. Editura Tehnica, 1997, no. ISBN: 973-31-2103-7.

[5] M. Chinchilla, S. Arnaltes, and J. Burgos, “Control of permanent-magnet generators applied

to variable-speed wind-energy systems connected to the grid,” IEEE Transactions on energy
conversion, vol. 21, p. 6, 2006.

[6] V. Gosbell, S. Perera, and V. Smith, Voltage Unbalance, October 2002.

[7] F. Iov, “Wind turbine system technology,” Lecture at AAU, 2008.

[8] F. Iov and F. Blaabjerg, “Advanced power converters for universal and flexible power
managment in future electricity network,” Tech. Rep., 2007.

[9] F. Iov, A. D. Hansen, P. Sørensen, and F. Blaabjerg, Wind Turbine Blockset in

Matlab/Simulink: General Overview and Description of the Models. Aalborg University,
2004, no. ISBN 87-89179-46-3.

[10] V. Kaura and V. Blasko, “Operation of a phase locked loop system under utility conditions,”
IEEE Transactions on Industry Applications, vol. 33, 1997.

[11] M. P. Kazmierkowski, R. Krishnan, and F. Blaabjerg, Control in Power Electronics.

Academic Press, 2002, no. ISBN 0-12-402772-5.

[12] A. R. Massimo Valentini, Thordur Ofeigsson, “Control of a variable speed variable pitch
wind turbine with full scale power converter,” Tech. Rep., 17. December 2007.

[13] D. Mehrzad, J. Luque, and M. capella Cuenca, “Vector control of pmsg for wind turbine
applications,” Tech. Rep., 2008.

[14] K. Ogata, Modern Control Engineering. Tom Robbins, 2002, no. ISBN: 0-13-043245-8.

[15] A. Petersson, “Analysis, modeling and control of doubly-fed induction generators for
wind,” 2007.

88
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[16] V. H. Prasad, “Analysis and comparison of space vector modulation schemes for three-leg
and four-leg voltage source inverters,” 9th Semester Report, Institute of Energy Technology,
Aalborg University, May 15, 1997.

[17] M. L. R. Teodorescu and P. Rodríguez, “Linearized small signal pll model,” Power
Electronics for Renewable Energy Systems Course, Institute of Energy Technology,
Aalborg University, May 13-15, 2008.

[18] R. Roeper, Short-circuit currents in three-phase systems. Siemens, John Wiley & Sons,
1985, no. ISBN 0-471-90707-3.

[19] R. Teodorescu and F. Blaabjerg, “Flexible control of small wind turbine with grid failure
detection operating in stand-alone and grid connected mode,” IEEE Transactions on Power
Electronics, vol. 19, 2004.

[20] A. V. Timbus, M. Ciobotaru, R. Teodorescu, and F. Blaabjerg., “Adaptive resonant

controller for grid-connected converters in distributed power generation systems,” IEEE
Xplore, pp. 1601–1606, 2006.

BIBLIOGRAPHY 89
 Matlab models
A
A.1 Voltage Source Converter model

3
iABC
u(1)+u(2)+u(3) 1
idc
DC_link current

1 u*K
gate _signals
Matrix
Commutation functions 2
Gain
vABC
2
Output voltage
vdc
DC-link voltage

90
 A.2 Space Vector Modulation model

A.2 Space Vector Modulation model

vdref
Avoid
Weight
1 Saturation
vdref
vAlpha /Beta _ref
vqref
Weight Avoid saturation

2 vdc
vdc
Vdc

if (..)

vd vd if { }
duty _ABC
vd u1
vq vq
1st quadrant
elseIf (..)

vd vd elseif { }
duty _ABC
vq vq
2nd quadrant
elseIf (..) duty _ABC duty _abc 1
duty _ABC
vd vd elseif { } pulse dropping
duty _ABC
vq u2
vq vq
3rd quadrant
elseIf (..)

vd vd elseif { }
duty _ABC
If vq vq

4th quadrant

A. Matlab models 91
A.3 Grid model

A.3 Grid model

1 ampl
|A|
2 freq vRST 1
fq vpcc
3 phase
phase
Harmonic
Voltage Source

4 IRST
iRST

Vpcc Isc

Short -circuit path SCval Isc Vg

Ground

vpcc iload Iload

Local Load
Grid Impedance

92 A. Matlab models
 A.4 PLL tuning model

A.4 PLL tuning model

9.2

Kp
Tset
1 1
Input Output
K Ts
psi u(1)^2 z-1
Ti

2.3

A. Matlab models 93
A.5 dq and αβ control models

A.5 dq and αβ control models

94 A. Matlab models
 A.5 dq and αβ control models

A. Matlab models 95
A.6 Complete model

A.6 Complete model

96 A. Matlab models
 Project proposal
B
Siemens Wind Power A/S 22-08-2008

Vector control of PMSG for wind turbine applications

Background:
The generator of a wind turbine is usually connected to the main shaft via a step down
gearbox. It would however be advantageous to omit the gearbox and connect the
generator directly to the main shaft. Depending on the generator design, this can result
in a wind turbine which has e.g. an increased efficiency, increased reliability and is more
cost-effective. The permanent magnet synchronous generator (PMSG) is regarded as a
realistic solution for a direct drive generator for variable speed wind turbines.

In order to obtain full control possibilities and in order to minimize the generator size, a
full scale 4Q frequency converter can be applied between the generator and the grid.
The converter can e.g. consist of two Voltage Source Inverters (VSI) connected back to
back and with an intermediate DC link. The generator torque and the generator terminal
voltage can be controlled by the generator side VSI. The DC link voltage and the
reactive power/grid voltage can be controlled by the grid side VSI. At nominal power, the
speed of the generator can be controlled by pitching the blades.

Objectives:
It is the objective of the project to design, analyze and optimize controllers for the
converter for a 2 - 3 MW non-salient pole PMSG. The controllers shall be based on
vector control theory and shall be able to operate independently of each other. The
controllers shall be well damped and have a fast response time in the whole operation
area both during normal operation and during grid faults. The controllers shall be
designed and analyzed using Matlab/Simulink.

Contents:
- Modeling of drive train, PMSG, converter, filter and grid
- Design and optimization of torque and voltage/flux vector controllers for the
generator side VSI
- Design and optimization of DC link and reactive power vector controllers for the
grid side VSI.
- Simulation of controller performance during normal operation and during grid
faults

Suggested by:
Erik Grøndahl, Siemens Wind Power A/S

97