VECTOR CONTROL OF PMSG FOR GRID-CONNECTED WIND …

INSTITUTE OF ENERGY TECHNOLOGY

VECTOR CONTROL OF PMSG FORGRID-CONNECTED WIND TURBINE

APPLICATIONS

CONDUCTED BY GROUP WPS4−1050SPRING SEMESTER, 2009

Institute of Energy TechnologyPontoppidanstræde 101Phone number 96 35 92 40Fax 98 15 14 11http://www.iet.aau.dk/

Title: Vector control of PMSG for grid-connected wind turbine applicationsSemester: 4th Semester, Spring 2009Semester Theme: Master’s thesisProject period: 02.02.09 to 03.06.09ECTS: 30Project group: WPS4−1050Members:

Daryoush Mehrzad

Javier Luque

Marc Capella Cuenca

Supervisor: Mihai Ciobotaru / Florin Iov

Number of prints: 6Number of pages: 87Finished: 03.06.2009

Abstract:

Nowadays, wind energy is a promising alter-native to the traditional energy sources. Dueto the increasing wind power penetration, theimprovements of the control strategies becomea new challenge for the manufacturers in or-der to comply with the grid interconnection re-quirements. This project focuses on the con-trol of the grid side converter which let thefull controllability of the DC-link voltage andthe reactive power delivered to the grid. Syn-chronous and stationary reference frame con-trol strategies are implemented to control thepower converter. Modeling and simulation ofthe grid side of the wind turbine system areperformed. MATLAB/Simulink has been usedto implement the models. Different tests havebeen done in order to analyze the control sys-tem. In addition, a small scale version of thesystem has been implemented for the labora-tory. Two different control strategies are com-pared and the results are verified in the labora-tory.

By signing this document, each member of the group confirms that all participated in the projectwork 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 June2009. The project theme with the title "Vector control of PMSG for grid-connected wind turbineapplications" is the continuation of the 9th semester project which was proposed by SIEMENSWind Power. The motivation of choosing this project is the increasing wind energy penetrationinto 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 []L f i Filter inductance inverter side [H]R f i Filter resistance inverter side [ohm]L f g Filter inductance grid side [H]R f g Filter resistance grid side [ohm]C f 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 GeneratorDC Direct CurrentSV M Space Vector ModulationV SC Voltage Source ConverterAC Alternative CurrentIGBT Insulated Gate Bipolar TransistorPCC Point Common Couplingp.u. per unit valuePWM Pulse Width ModulationPI Proportional Integral controllerPID Proportional Integral Derivative controllerB2B Back to BackPS Phase shiftUHF Upper limit full loadULF Lower limit full loadPLL Phase Locked LoopPR Proportional ResonantDPGS Distributed Power Generation SystemsGUI Graphical User Interface

V

Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Project goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Project limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.5 Project outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 System description and implementation 52.1 Premise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Power converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Space Vector Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4 Grid Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.5 Wind turbine system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.6 Grid Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Control of the system 193.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Grid side converter control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Phase Locked Loop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.4 PI controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.5 PR controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.6 Tuning of the controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4 Simulation and analysis 394.1 Simulation and analysis of 2.4 MW model . . . . . . . . . . . . . . . . . . . . . 394.2 Analysis and comparison of 11 kW model . . . . . . . . . . . . . . . . . . . . . 60

5 Experimental setup 815.1 Setup description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.2 Study cases and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6 Conclusions 87

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

VII

CONTENTS

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

B Project proposal 97

VIII CONTENTS

1Introduction

In this chapter, the background gives to the reader a general vision of the project. The problemis defined, the goals are listed, project limitations are mentioned and finally the project outlinesummarizes 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 oiland global warming make the fossil fuels less and less attractive solutions. Wind power is a veryimportant renewable energy source. It is free and not polluter unlike the traditional fossil energysources. 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 drivetrain 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 thewind turbine manufactures are developing new larger wind turbines. The power of wind turbinesbuilt in 1980 was 50 kW and the rotor diameter was 15 m long. In 2003 they had the power of 5MW 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 canbe synchronous or asynchronous and finally the connection with the grid can be through a powerconverter or be directly connected. Different modes of operation can be used depending on thewind turbine configuration. They are classified in variable-speed and fixed-speed. For fixed-speedoperation, 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 directlyconnected 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 tothe grid by means of a power converter. It increases the cost of the whole system but allows fullcontrollability of the system. Among all these configurations, the trend is to use variable-speedwind turbines because they offer more efficiency and control flexibility which is becoming veryimportant to comply with the grid requirements.

Permanent Magnet Synchronous Generator, (PMSG), is an interesting solution which is based onvariable-speed operation. Since the speed of wind turbine is variable, the generator is controlledby 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 withoutgearbox. 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 converterand the grid side converter. The generator side converter is mainly used to control the speed ofthe generator in order to maximize the output power at low wind speeds. The grid side converteris 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 sideconverters. 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, thereforehaving an efficient and a reliable control system is very important. Modeling the power systemand performing the simulation helps to have a better understanding of the system. Furthermore inthis 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 PMSGand to maximize the obtained power. In this project, 10th semester, the focus is on the controlof the grid side converter, in order to control the power delivered to the grid and to comply withthe grid requirements. PMSG studied in the previous project works in variable speed range andit is connected to a full scale power converter. The power converter is controlled so that theoutput power is maximized and the power delivered to the grid complies with the interconnectionrequirements. Consequently it is clear the importance of an efficient control strategy. This is verymuch important especially in the case of wind power applications in which the wind varies quicklyand in an unpredictable way. With a full scale back-to-back power converter is possible to havethe generator running at any speed within some certain range and to have a fixed frequency on thegrid 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 comparisonbetween 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 componentsof the systems are implemented by MATLAB/Simulink software. Finally the the model is scaleddown for the laboratory tests.

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

The control system chapter describes the two main control strategies used in the project. Later themethod used to synchronize the grid voltage with the control is explained and tested. Finally, theprocedure 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 controlstrategies for a 11 kW model, ending with a table which shows which strategy suits better in eachstudy 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

2System description

and implementation

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 somegrid 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 sidecontrol by considering a constant value for the DC-link voltage. The scheme of the wind turbinesystem is shown in Fig. 2.1.

wind AC

DC

DC

PMSG

AC

Generator Side Converter

Grid Side Converter

PCCFilter Impedance

Transformer

Wind Turbine Generator Side Grid Side

Pitch Control Generator Side Control Grid Side Control

Grid

Voltage source

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 sidecontrol, has been treated. The DC-link voltage has been considered constant [13]. In the secondsemester the grid side control is treated.

2.2 Power converter

Nowadays the Back-to-Back (B2B) converter is widely used in wind turbine applications. TheB2B converter is composed by two identical Voltage Source Converters (VSC) and a capacitorwhich 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 generatoror to the grid. Therefore the VSC can work as a rectifier or as an inverter. At first step the AC isconverted to DC through the generator side converter. Next, the DC is converted to AC throughthe grid side converter. Therefore in this case the generator side converter works as a rectifier andthe grid side converter works as an inverter. The DC-link voltage must be higher than the peakmain voltage and it is regulated by controlling the power flow to the AC grid. In fact one important

5

2.2 Power converter

AC AC

Generator side converter

Grid side converter

C

+

-

V dc

AC ACDC DC

dc

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 forthe 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 converterhaving 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 andin the block state its value is 0. Based on the state of the switches, the VSC can assume eightdifferent configurations.

+

-

VDC

Generator side converter

A

BC

Grid side converter

ibic

DA DB DC Transformer

VON

iDC

ia

0

CDC

-DA -DB -DC

Filter impedance

Y Δ

N

Grid

ACV. source

Figure 2.3: Grid side VSC IGBTs.

Based on the equivalent circuit in Fig. 2.3, for a star connected transformer in the low voltageside, 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 2.5shows the relation between phase voltages and the DC-link voltage. vAN

vBN

vCN

= vDC

DA

DB

DC

(2.5)

where vAN , vBN and vCN are the average phase voltages and DA, DB and DC are the switches statusat each leg respectively. The voltage between the star connection point N and the neutral point 0is defined as in the following:

v0N =13

(vAN + vBN + vCN) =vDC

3(DA +DB +DC) (2.6)

Regarding the equations 2.1-2.3, the phase voltages can be written as follows [11]: vAN

vBN

vCN

=13

1 0 −1−1 1 00 −1 1

· vAB

vBC

vCA

(2.7)

The current iDC is expressed in function of phase currents:

iDC = (DAia +DBib +DCic) (2.8)

Regarding the simulations in MATLAB/Simulink, the model of the converter has been taken fromthe Wind Turbine Blockset in MATLAB/Simulink [9]. In Fig. 2.4 it can be seen the black box ofthe VSC with its inputs and outputs. In order to complete a back-to-back converter, two VSC areput 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

VSCabcv

abci

abcDDCi

DCv

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.


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


a two-dimensional α-β plane providing the duty cycles necessary for the control of the powerflow 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. Furthermoredoes not require separate modulators and calculation of zero-sequence signals as in third harmonicPWM 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 advantagecompared with when the phases are considered separately. The reference voltage vector is shownin the following equation:

V re f =23(α

0van +α1vbn +α

2vcn)

(2.9)

where α is - 12 +j 3

2 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 andDC explained previously. In Fig. 2.5 are depicted the six state voltage vectors with the neededswitching status to perform them. The areas between two state vectors are sectors, hence sixsectors are present. In this way the output voltage of the converter could be represented by anequivalent rotating vector V re f with a counter clockwise direction, whose angle is represented byθ [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 usedby the null voltage vectors. In sector 1 The pattern used is [0 0 0],[1 0 0], [1 1 0], [1 1 1] whichreduces the number of switching commutations in each transition. The time duration equation isshown as follows:



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

T0

2=

Tsw

2−T1−T2 (2.10)

This reference voltage vector can be considered constant, for each switching period, if there is ahigh switching frequency.

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

SVM

α*vβ

*v

DCv

abcS

0.8 0.81 0.82 0.83 0.840

0.10.20.30.40.50.60.70.80.9

1

Dut

y cy

cles

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.

PWMabcS abcH

0.6 0.602 0.604 0.606 0.608 0.61-1.5

-1

-0.5

0

0.5

1

1.5

Gat

e S

igna

l leg

A

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.


2.4 Grid Connection

2.4 Grid Connection

When a considerable part of the electrical power is coming from the wind turbines, the networkoperators will have many technical and economical problems to manage the system. Therefore itis clear that one of the important aspects of research must be concentrated on the grid interactionof the wind turbines. One of the main concerns of the network operators is the power qualitywhich depends on what kind of sources are connected to the grid. The wind energy has to begrid compatible, because in any power system the operator has to control the frequency and thevoltage. 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 startingfrom the grid side converter as shown in Fig. 2.9.

DC

AC

Grid Side Converter

PCCFilter

TransformerImpedance

Grid

Voltage source

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 thetransmission 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 whichtakes into account the losses of the inductance. The filter is shown in Fig. 2.10.

DC

AC

Grid Side Converter

PCC

Lf RfVPCC

Vf

If

Figure 2.10: The representation of the filter.

The phasorial equation is as the following:

Vf (t) = I f (t)( jωL f +R f ) (2.11)

In s-domain the following expression is valid:

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

The transfer function has the following expression:


2.4 Grid Connection

F(s) =1

(sL f +R f )(2.13)

LCL-filter

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

DC

AC

Grid Side Converter

PCC

Lfi Rfi

Rd

Cf

Lfg RfgVPCC

Vi

Ii Ig

Figure 2.11: LCL filter scheme.

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

Ii

(sL f i +R f i +Rd +

1sC f

)− Ig

(Rd +

1sC f

)= Vi (2.14)

Ig

(sL f g +R f g +Rd +

1sC f

)− Ii

(Rd +

1sC f

)= 0 (2.15)

The transfer function of the filter is obtained by operating with the equations 2.14 and 2.15 inorder to obtain H = out put

input = IgVi

. The resulting transfer function is as follows:

H =sRdC f +1

s3(L f gL f iC f

)+ s2

(L f gC f

(R f i +Rd

)+L f iC f

(R f g +Rd

))+ s(C f(R f gR f i +R f gRd +RdR 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 impedanceof the inductances becomes equal to the impedance of the capacitor. It can be calculated by usingthe following equation:

ωres =

√L f i +L f g

L f iL f gC f(2.17)

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). Theideal transformer has the following characteristics:

VL = jωLLIL + jωLmIH (2.18)


2.4 Grid Connection

VH = jωLHIH + jωLmIL (2.19)

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

k =VH

VL=

IL

IH=

NH

NL(2.20)

where NL and NH are the number of turns in the primary and secondary winding respectively. Amore detailed representation of the transformer is the equivalent circuit of the linear transformerwhich is shown in Fig. 2.12.

RL LL LH RH

RM LM

IL

VL VH

IH

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 thelow voltage side of the transformer. Fig. 2.13 shows the equivalent circuit of the linear transformerwhen the impedances of the high voltage side are brought on the low voltage side.

RL LL L’H R’H

RM LM

IL

VL VH

IH

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

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

R′H =RH

k2 (2.21)

L′H =LH

k2 (2.22)

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, thereare 4 different possibilities depending on if the connections are delta or star. Another importantfactor to consider is the phase shift that occurs in some of three-phase transformer connectionswhich consists of a phase shift between the primary and secondary line-to-line voltages [3].


2.4 Grid Connection

2.4.3 Grid

The grid can be presented with the Thevenin equivalent circuit. Each of the three phases can bepresented by the equivalent circuit shown in Fig. 2.14. The equivalent impedance (R-L) takes intoaccount 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:

Vg = RgIg +LgdIg

dt+VPCC (2.23)

where Vg is the grid voltage and Vpcc is the voltage of the PCC. When there is a connection to thegrid many considerations have to be taken. There are important factors regarding the control ofthe important values and the grid requirements that regulate the operations. The amount of windenergy 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 moredependent 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 WindTurbine Blockset in MATLAB/Simulink [9]. In Fig. 2.15 it can be seen the black box of the gridmodel with its inputs and outputs.

Grid model

Phase

fpccV

abcI

A

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 andIabc the grid current. The output Vpcc is the voltage of the PCC. The MATLAB/simulink modeland the mask of the grid model is represented in the appendix A.3.


2.5 Wind turbine system

2.5 Wind turbine system

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

Drive-train PMSG

VSC

GENERATOR SIDE

CONVERTER CONTROL

PITCHCONTROL

Wind Wind Turbine

wV

wtω

wVwtω

wtT

eP

mω

abcv

DCLink VSC

Filter

GRID

GRID SIDE CONVERTER

CONTROL

βabci

abch

DCi

DCv DCi

DCvabcv abci

abcv

abch

DCv abci abcvsdimω sqiwV~

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, designvoltages 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 rangewhere the wind turbine can operate. It can also be decided to set a down-regulation operation. Thefigure shows an example where it has been decided a 50% down-regulation. It means that undernormal operation the wind turbine will deliver 50% of the rated power. If the network operatorneeds more power due to a frequency drop, the wind turbine can deliver more power in order tostabilize the frequency of the grid. It will act in the opposite way if the frequency of the gridincreases. Dead-band is the frequency between 49.85 and 50.15 Hz.



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 theactive 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 inFig. 2.19. It is observed that a wind turbine will be working in normal operation when the valuesof frequency are between 47 and 53 Hz and the voltage values are between 95% and a bit above105%. If in some moment the frequency and voltage values change and go out of the abovementioned range, the wind turbine will be disconnected from electrical network after the timeindicated in Fig. 2.19.



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 outof the white area, although, there is a vertical lines area where it is possible to choose if it will beor 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 followingsituations 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 thelower-limit full-load.A wind turbine should have sufficient capacity to satisfy the mentioned requirements for the nextsequences:

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



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 normaloperation.

• Voltage quality

The limits of rapid voltage variations and long term flicker severity for different levels of voltagesare 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 factthat 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 requirementsaccording to danish grid codes have been included and they will be taken into consideration in thechapter 4. The following chapter will explain the grid side converter control.




3Control of the system

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

3.1 Introduction

The control system is an important issue for the wind turbine performance. It maximizes theextracted 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 areapplied in different parts of the wind turbine and they have different aims. The general controlscheme is shown in Fig. 3.1.

wind AC

DC

DC

PMSG

AC

Generator Side Converter

Grid Side Converter

Control Generator Side Control Grid Side

CONVERTER CONTROL

WIND TURBINE CONTROL

Power Control

*mω

mωβ

I IDCv

*GP *

DCv *GQ

PCCP PCCQ

PCCV

PCC

Pitch Control Speed Control VDC and Q Control

Filter

Figure 3.1: General control scheme [7].

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

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

19

3.2 Grid side converter control


There are different control strategies used to perform the control of the grid side converter. Theyall are focused on the same topics: the control of the DC-link voltage, active and reactive powerdelivered 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 areshown in Fig. 3.2. In this project the focus is on the synchronous and stationary reference framecontrol strategies.

VECTOR CONTROL

SYNCHRONOUS REFERENCE FRAME CONTROL

STATIONARY REFERENCE FRAME CONTROL

NATURAL REFERENCE 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 gridcurrents and the outer loops control the DC-link voltage and the reactive power. The current loopsare responsible of the power quality, thus harmonic compensation can be added to the action ofthe current controllers to improve it. The outer loops regulate the power flow of the system bycontrolling 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 activeand reactive power in dq-reference frame assuming that the reference frame is oriented along thesupply voltage are [5]:

P =32

(vd id) (3.1)

Q =32

(vd iq) (3.2)

Equations 3.1 and 3.2 show how to control the active and reactive power. It can be seen thatby changing the d and q-components of the current, the active and reactive power are controlledrespectively. Basically, the aim of the control is to transfer all the active power produced bythe wind turbine to the grid and also to produce no reactive power so that unity power factor isobtained, unless the grid operator requires reactive power compensation. In order to transfer allthe active power generated by the wind turbine the DC-link voltage must remain constant. It canbe derived from the following equation [1]:

CdvDC

dt=

Pt

vDC−

Pg

vDC(3.3)

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-linkvoltage and all the power will be transferred to the grid.

20 3. Control of the system


The difference between the two control schemes is in the inner loops where they use differentreference frames to perform the current control. In the first case, the currents are controlled inthe synchronous rotating reference frame using PI controllers. In the second case the currents andvoltages 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.

PMSG

SVMLω−

*dv

*qv

PIPI

*di

*qi

θDCv

αβ

dq

PWM

*DCv

*Q

DCv

PLLθ

DCv

abc

dq

abc

dqθ

Lω

dv

qv

di

qi

PI

θ

av

bvcv

aibi

cidv

qv

qi

di

di

qidv3

2

Filter

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 voltagesand currents from the abc to the dq reference frame. In this way the variables are transformed toDC values which can be controlled more easely. This structure uses PI controllers since they havegood performance for controlling DC variables.

In the output of the current controllers, cross-coupling term and voltage feed-forward are addedto improve the response of the system. The resultant value is the voltage reference for the SVMtechnique [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. Inthis 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


PMSG

SVM

PRPI

*di

*qi

aibi

ci

DCv

PWM

*DCv

*Q

DCv

av

bvcv

PLLθ

DCv

θ

αv

βv

PR

*αv

*βv

θabc

αβ

abc

αβ

αi

βiθ

αβ

dq

*αi

*βi

αi

βi

dv32

Filter

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

controllers the feed-forward is not needed [2].

The implementation of the two control strategies have been done in MATLAB/Simulink as the restof the models. The control has been modeled based on the theoretical explanation seen previouslyin this section. The box which contains the model is presented in Fig. 3.5. The subsystem of themodel is shown in Appendix A.5.

Wind Turbine

wV~

wtω

β

wtT Speed controller

sdi

mω *sdv

sqi

wV~

*sqv

Drive Train ModelwtT

eT

wtω

mωControl model

ABCv

ABCisignalsgate _

Enable

DCv

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 voltagesvABC and the enable signal. The output is the gate signals that will feed the power converter.


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 methodsused 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 gridvoltages. 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 thegrid voltage angle in order to obtain a power factor as close to 1 as possible. In Fig. 3.6 the PLLdiagram is shown.

abc

dq

θ

dv

qvav

bv

cv

s1 θ

gridω

⎟⎟⎠

⎞⎜⎜⎝

⎛+

sTKp

i

11

PI

-

0* =qv

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 V ∗q component is nothing but symbolic, to make clear that the reference of q-axis voltage isset to zero, which locks the grid voltage phase. PLL model is implemented in dq synchronousreference frame which means that a Park transform from abc to dq reference frame is needed. ThePark transform requires the output angle in order to synchronize the dq reference frame. A PI isused 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 andVd is the positive voltage magnitude [10]. The magnitude of the controlled variable Vq determinesthe phase difference between the grid voltage and the inverter phase angle. Hence the PI input isVq [19].

γ−θ∼= sin(γ−θ) = ∆θ (3.4)

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



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

H(s) =θinv

γ=

Kps+ K pTi

s2 +Kps+ KpTi

(3.5)

Some components have been set to tune the PI controller. The desired settling time is to be aroundtwo periods of the grid frequency, 0.04s, and the damping ratio ξ= 1√

2.

To obtain the parameters of the PI a MATLAB/simulink model has been implemented to designthe PI as it is shown in Appendix A.4, which provides Kp and Ti in function of settling time anddamping 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 angleshift 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 51Hzby a step. The test of the PLL focuses on two responses, the frequency and the tetha angle.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.249.5

50

50.5

51

51.5a

Freq

uenc

y [H

z]

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

100

200

300

400b

Ang

le [d

eg]

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-0.5

0

0.5

1

1.5c

Erro

r of a

ngle

[deg

]

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 responseobtained 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 cyclesfrom zero to 360 degrees. Both curves are almost overlapped due to the small difference betweenboth angles. Therefore Fig. 3.7.c. is attached to show the small error between both angles previ-ously called ∆θ.


3.4 PI controllers

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

100

200

300

400a

Ang

le [d

eg]

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-50

0

50

100b

Erro

r of a

ngle

[deg

]

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 thevoltage utility. At the time 0.11s, a 60 degrees step is shown as well as the θ angle tracking thisstep.

Fig. 3.8.b. shows the error between both angles (∆θ). The shift angle starts from 60 degrees at thetime 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 becontrolled. The computed output signal o(t) from the PI depends on the parameters, which are theproportional gain Kp, the integral time Ti and the error e(t). Fig 3.9 shows the general scheme ofthe PI controller [14].

⎟⎟⎠

⎞⎜⎜⎝

⎛+

sTK

ip

11

PI

( )tereferenceSignal

realSignal

( )to

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 errorvalue. If the value of the proportional gain is too high, the system can become unstable. On theother hand, a small value gives a small output response to a large input error making the controllerless sensitive. A pure proportional controller would not be able to drive the signal at its targetvalue. There would remain a steady state error usually called offset. In order to make the offsetzero, the integral term is needed.


3.5 PR controllers

The integral term contribution is proportional to the magnitude and the duration of the error. Theintegral gives the accumulated offset which is then multiplied by the inverse of the integral timeand added to the controller output. The magnitude of the contribution of the integral term tothe overall control action is determined by the integral time Ti. The integral term accelerates theresponse of the controller and eliminates the residual steady-state error that occurs with a pureproportional controller. However, since the integral term is responding to accumulated errors fromthe 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 theyare 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 thegrid-tied systems [2]. The general scheme of the PR controller is shown in Fig. 3.10.

*v

i

*ipK

22 ω+ssKi

PR

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 theproportional gain and the integral gain respectively. This controller has a very high gain aroundthe resonance frequency which it eliminates the steady state error between the reference and themeasured signal. The width of the frequency band around the resonance point depends on theintegral gain value. A small value produce a very narrow band, whereas a large value produce awider band [2] [20]. The Bode plots of the resonant controller for different integral gains Ki andω set to 50Hz as shown in Fig. 3.11.

Harmonic compensation can also be easily implemented by adding to the PR controller severalgeneralized 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]:

Ghc = ∑h=3,5,7

Kihs

s2 +(hω)2 (3.6)


3.6 Tuning of the controllers

0

50

100

150

200

250

300

350

Mag

nitu

de (

dB)

100

101

102

103

-450

-405

-360

-315

-270P

hase

(D

eg)

Bode Diagram

Frequency (Hz)

Ki=100Ki=500Ki=1500Ki=3000

Figure 3.11: Bode plot of the PR controller.


In this section, the tunning and analysis of the controllers and the plants for the 2.4 MW and 11kWare 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 agood performance of the system. In this case, the current controllers are tuned based on the designcriterion called optimal modulus. The outer loop is tuned according to the design criterion calledsymmetry optimum. After the tuning calculations, the Matlab Sisotool is used to test, verify andadjust, 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. Onecontroller is for the outer loop which is the DC-link voltage loop and the other is for the innerloop, which is the current loop. For the tuning of the PI, the compensation term and the voltagefeed-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+ 1

Tis

)= Kp

(Tis+1

Tis

)• Sampling time Ts which frequency fs is 10kHz.

• Plant with Te = LR

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



*dv

PI*di

*DCv

DCv di

PIRLs +

1 di

Cs1 DCv

11+sTs

Sampling

Sampling

Plant

Inner currrent loop

Outer DC-link voltage loop

11+sTs

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

*dv*

di

di

PIRLs +

1 di

Plant

1+sTs1

1+sTs

Sampling

G1

Figure 3.13: Block diagram of the current loop.

The G1 transfer function is:

G1 = KpcTics+1

Tics

1R

LR s+1

1Tss+1

(3.7)

The transfer function can be simplified as follows [4]:

G1 = KpcTics+1

Tics1

T∑1s+1Ke

Tes+1(3.8)

where Ke = 1R , Te = L

R and T∑1 = Ts.Based on the optimal modulus, the next relation is satisfied [4]:

KpcTics+1

Tics1

T∑1s+1Ke

Tes+1=

12T∑1s(T∑1s+1)

(3.9)

Therefore, by comparing the two sides of the equation 3.9, the proportional gain and the integraltime of the controller can be calculated with the following equations:

Tic = Te =LR

(3.10)



andKpc =

Te

2T∑1Ke=

L2T∑1

(3.11)

Using the values of each variable, yields Kpc = 24.768e−62·0.1e−3 = 0.1238 and Tic = 24.768e−6

0.8e−3 = 0.031.

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

100

101

102

103

104

-90

-45

0

Frequency (Hz)

-20

-10

0

10Bode Editor for Closed Loop 1 (CL1)

100

101

102

103

104

105

-180

-135

-90

P.M.: 65.5 degFreq: 724 Hz

Frequency (Hz)

-80

-60

-40

-20

0

20

40

60

G.M.: InfFreq: InfStable loop

Open-Loop Bode Editor for Open Loop 1 (OL1)

-10000 -8000 -6000 -4000 -2000 0-5000

0

50000.160.340.50.640.760.86

0.94

0.985

0.160.340.50.640.760.86

0.94

0.985

2004006008001e+0031.2e+0034e+003

Root Locus Editor for Open Loop 1 (OL1)

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 andgain margin are 65.5 degrees and infinite respectively, thus the loop is stable. The step response isshown in Fig. 3.15. The overshoot is 6.7% and the settling time is 0.746 ms.

Step Response

Time (sec)

Am

plitu

de

0 0.2 0.4 0.6 0.8 1 1.2

x 10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4System: Closed Loop r to yI/O: r to yPeak amplitude: 1.07Overshoot (%): 6.7At time (sec): 0.000466

System: Closed Loop r to yI/O: r to ySettling Time (sec): 0.000746

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 diagramhas 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 = 0.0602, the integraltime remains equal, thus Tic = 0.031. The root locus as well as the bode diagram are shown in Fig.3.16.

100

101

102

103

104

-270

-180

-90

0

Frequency (Hz)

-20

-10

0


100

101

102

103

104

-405

-360

-315

-270

-225

-180

-135

-90


Frequency (Hz)

-30

-20

-10

0

10

20

30

40

50

60

G.M.: 12.3 dBFreq: 1.3e+003 HzStable loop


-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

500

1e3

1.5e32e32.5e33e3

3.5e3

4e3

4.5e3

5e3

500

1e3

1.5e32e32.5e33e3

3.5e3

4e3

4.5e3

5e3

0.10.2

0.30.40.50.60.70.80.9



The location of the poles gives a damping of 0.707 which is the standard value. The phase andgain 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

Time (sec)

Am

plitu

de

0 0.5 1 1.5 2 2.5

x 10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4


System: Closed Loop r to yI/O: r to yPeak amplitude: 1.05Overshoot (%): 5.17At time (sec): 0.0008


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

G =1

2T 2∑1s2 +2T∑1s+1

Tss+1≈ Tss+12T∑1s+1

(3.12)

After finding the values for the current loop, the block diagram is shown in Fig. 3.18.



PI*di

*DCv

DCv12

1

1 +∑

+sT

sTsdi

Cs1 DCv

11+sTs

Sampling

Current closed loop

Figure 3.18: DC-link voltage loop block diagram.

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

PI*di

*DCv

DCv12

1

1 +∑

+sT

sTsdi

Cs1 DCv

11+sTs

Current closed loop

1+sTs

Sampling

G2

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

The G2 transfer function is:

G2 = KpvTivs+1

TivsTss+1

2T∑1s+11

Cs1

Tss+1(3.13)

The transfer function can be simplified as follows [4]:

G2 = KpvTivs+1

Tivs1

Cs(T∑2s+1)(3.14)

where T∑2 = 2T∑1 +Ts−Ts.Now, based on the symmetry optimum, the next relation is satisfied [4]:

KpvTivs+1

Tivs1

Cs(T∑2s+1)=

4T∑2s+18T 2

∑2s2 (T∑2s+1)(3.15)

Therefore, by comparing the two sides of the equation 3.15, the proportional gain and the integraltime of the controller can be calculated with the following equations:

Tiv = 4T∑2 (3.16)

andKpv =

TivC8T 2

∑2=

C2T∑2

(3.17)

Using the values of each variable yields Kpv = 0.2322·0.2e−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 voltagecontroller. The root locus as well as the bode diagram are shown in Fig. 3.20.



101

102

103

104

105

-180

-90

0

90

Frequency (Hz)

-60

-40

-20

0


101

102

103

104

105

-180

-170

-160

-150

-140P.M.: 36.9 degFreq: 398 Hz

Frequency (Hz)

-100

-80

-60

-40

-20

0

20

40

60

G.M.: -Inf dBFreq: 0 HzStable loop


-15000 -10000 -5000 0 5000-6000

-4000

-2000

0

2000

4000

60000.30.50.680.810.89

0.945

0.976

0.994

0.30.50.680.810.890.945

0.976

0.994

5001e+0031.5e+0032e+003


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 thezero has been moved in order to modify the root locus of the system and thus to obtain a betterdamping. This has been carried out by using the graphical tuning in Sisotool. The new positionof the zero gives a value of the integral time Tiv = 0.025. The new root locus as well as the bodediagram are shown in Fig. 3.21.

100

101

102

103

104

105

-180

-90

0

90

Frequency (Hz)

-60

-40

-20

0


10-2

100

102

104

106

-180

-150

-120

-90P.M.: 64.5 degFreq: 362 Hz

Frequency (Hz)

-100

-50

0

50

100

150

G.M.: -Inf dBFreq: 0 HzStable loop


-15000 -10000 -5000 0 5000-3000

-2000

-1000

0

1000

2000

30000.50.760.880.940.968

0.986

0.994

0.999

0.50.760.880.940.9680.986

0.994

0.999

5001e+0031.5e+0032e+003



The new location of the zeros and poles gives a damping of 0.707 which is the standard value. Thephase 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.



Step Response

Time (sec)

Am

plitu

de

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4


System: Closed Loop r to yI/O: r to yPeak amplitude: 1.06Overshoot (%): 5.88At time (sec): 0.00128

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 ofthe controller have been readjusted using the graphical tuning in Sisotool. The new value of theproportional gain is Kpc = 379.5, the integral time remains equal, thus Tiv = 0.025. The root locusas well as the bode diagram are shown in Fig. 3.23.

100

101

102

103

104

-270

-180

-90

0

90

Frequency (Hz)

-30

-20

-10

0


10-2

100

102

104

-405

-360

-315

-270

-225

-180

-135

-90


Frequency (Hz)

-40

-20

0

20

40

60

80

100

120

G.M.: 15.6 dBFreq: 995 HzStable loop


-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

500

1e3

1.5e32e32.5e33e3

3.5e3

4e3

4.5e3

5e3

500

1e3

1.5e32e32.5e33e3

3.5e3

4e3

4.5e3

5e3

0.10.2

0.30.40.50.60.70.80.9



The new location of the poles gives a damping of 0.707 which is the standard value. The phaseand 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.



Step Response

Time (sec)

Am

plitu

de

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

0.2

0.4

0.6

0.8

1

1.2

1.4System: Closed Loop r to yI/O: r to yPeak amplitude: 1.07Overshoot (%): 7.1At time (sec): 0.0015



Q-axis control loop

The q-axis control loop is simpler than the d-axis control loop. It only has a current loop. As theblock 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 usinganalytical and graphical approaches. The final values used in the model are presented all togetheras a brief in the Fig. 3.25.

pK iT

idPI 0.0602 0.031

iqPI 0.0602 0.031

DCVPI 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 convertermodel is fed with a switching signal instead of the average and in the plant an LCL filter is usedinstead of an L filter. These differences affect to the tunning of the controllers and so they have tobe carefully analyzed. The LCL filter has a resonance frequency which can affect the performanceof the system. The bode plot of the plant including the grid impedance is shown in Fig. 3.26.



Bode Diagram

Frequency (Hz)10

-110

010

110

210

310

410

5-270

-225

-180

-135

-90

-45

0

Pha

se (

deg)

-150

-100

-50

0

50

Mag

nitu

de (

dB)

Magnitude (dB): 7.87Frequency (kHz): 2.39

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 theswitching 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 sameprocedure as for the 2.4 MW model has been used. For the inner current loop the first obtainedvalues for the proportional gain and the integral time are Kpc = 17.75 and Tic = 0.047. The valueof the integral time has been decreased to Tic = 0.01, in order to improve the dynamics of thesystem. Fig. 3.27 shows the different root locus of the system for different values of switchingfrequency.

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



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 gainmargin are 59.7 and 7.66 degrees respectively, thus the loop is stable. The poles have been adjustedin order to get a damping of 0.707. The new value for the proportional gain is Kpc = 17.35.

10-2

100

102

104

-630

-540

-450

-360

-270

-180

-90

0


Frequency (Hz)

-20

0

20

40

60



-1 -0.5 0 0.5 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

350

700

1.05e3

1.4e31.75e3

2.1e3

2.45e3

2.8e3

3.15e3

3.5e3

350

700

1.05e3

1.4e31.75e3

2.1e3

2.45e3

2.8e3

3.15e3

3.5e3

0.10.20.30.40.50.60.70.80.9


Real Axis


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

Step Response

Time (sec)

Am

plitu

de

0 0.5 1 1.5 2 2.5 3 3.5

x 10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4 System: Closed Loop r to yI/O: r to yPeak amplitude: 1.11Overshoot (%): 11.3At time (sec): 0.000714



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



10-2

100

102

104

-630

-540

-450

-360

-270

-180

-90


Frequency (Hz)

-20

0

20

40

60

80

100

120



-1 -0.5 0 0.5 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

350

700

1.05e3

1.4e31.75e3

2.1e3

2.45e3

2.8e3

3.15e3

3.5e3

350

700

1.05e3

1.4e31.75e3

2.1e3

2.45e3

2.8e3

3.15e3

3.5e3

0.10.20.30.40.50.60.70.80.9


Real Axis


The phase and gain margin are 58.3 and 7.59 degrees respectively, thus the loop is stable. The stepresponse of the system is shown in Fig. 3.31.

Step Response

Time (sec)

Am

plitu

de

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4 System: Closed Loop r to yI/O: r to yPeak amplitude: 1.14Overshoot (%): 13.5At time (sec): 0.000714 System: Closed Loop r to y

I/O: r to ySettling Time (sec): 0.00244


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

pK iT iK

idPI 17.35 0.01 --

iqPI 17.35 0.01 --

αPR 17.35 -- 1735

βPR 17.35 -- 1735

DCVPI 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 tunethe controllers. In the next chapter different study cases have been carried out, in order to analysethe performance of the system.




4Simulation and analysis

In this chapter the response of the system will be analyzed for the 2.4 MW model. For this purposedifferent 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 dqand 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 andsome grid fault studies. The response of the system will be analyzed and discussed taking intoconsideration 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 semesterthe generator side control model has been used to obtain the DC-link current which correspondsto different wind speeds in steady state. Therefore these different currents are the inputs in thisstudy case. The purpose of the Fig. 4.1 is to show the response of active and reactive power flowduring this simulation.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0.4

0.5

0.6

0.7a

Act

ive

pow

er [p

.u.]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.1

-0.05

0

0.05

0.1b

Rea

ctiv

e po

wer

[p.u

.]

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. Atthe time 0.7s the power step corresponds to a wind step from 10m/s to 11m/s, later at the second0.9 there is another negative step to 10m/s of wind speed. Finally, the steps are opposite and they

39


go back to the initial value.

In this simulation the reactive power reference is set to zero. In every step, it can be observed thatsmall 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 ordownward respectively, that means delivering or absorbing reactive power from the grid. To checkif the system is really working and delivering power to the grid the Fig. 4.2 shows the DC-linkvoltage transient.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.98

0.99

1

1.01

1.02

DC

link

vol

tage

[p.u

.]

referencemeasured

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, whichreturn after a transient to the reference value. According to the equation 3.3, when the differencebetween 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 flowingthrough the capacitor, thus the capacitor is charging. When the inverter current reaches the rectifiercurrent, 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. Thedifference 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 currentsequal.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.350.4

0.450.5

0.550.6

0.650.7

DC

-link

cur

rent

s [p

.u.]

Time [s]

rectifierinverter

Figure 4.3: DC-link currents.

Fig 4.3 shows both currents, rectifier inverter side where it can be seen the transient response ofthe 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 secondgraph shows q-axis current reference and measured. The relation between active power and d-axis

40 4. Simulation and analysis


0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0.4

0.5

0.6

0.7a

D-a

xis

curre

nt [p

.u.]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.1

-0.05

0

0.05

0.1b

Q-a

xis

curre

nt [p

.u.]

Time [s]

referencemeasured

referencemeasured

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 asshown in the Fig 4.4.b.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.98

0.99

1

1.01

1.02a

Vol

tage

at t

he P

CC

[p.u

.]

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

-0.5

0

0.5

1b

Grid

cur

rent

s [p

.u.]

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 thevoltage of the PCC above one, which means that power is being delivered to the grid. Finally, inFig 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 relationbetween active and reactive power flow. It can be seen in Fig. 4.1 that the system keeps reactivepower under grid requirement limitations 10% for rated value of active power as it was shown in

4. Simulation and analysis 41


Fig. 2.18. Besides, it is worth of remark that the variation of the applied voltage at the PCC doesnot 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 befocused on changes of ±20% of reactive power by keeping constant the active power.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.5

0.6

0.7

0.8

0.9

1a

Act

ive

pow

er [p

.u.]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.4

-0.2

0

0.2

0.4b

Rea

ctiv

e po

wer

[p.u

.]

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 appliedto 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 powerflow.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.99

0.995

1

1.005

1.01

DC

link

vol

tage

[p.u

.]

reference

measured


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



0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.5

0.6

0.7

0.8

0.9

1a

D-a

xis

curre

nt [p

.u.]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.4

-0.2

0

0.2

0.4b

Q-a

xis

curre

nt [p

.u.]

Time [s]

referencemeasured

referencemeasured

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 responseof the system in q-axis. Next the voltages of the PCC and grid are shown in Fig. 4.9.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

1

1.05

1.1a

Vol

tage

at t

he P

CC

[p.u

.]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.8

0.9

1

1.1b

Grid

cur

rent

s [p

.u.]

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 reactivepower.

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



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

4.1.2 Voltage excursion

One common case is having voltage excursions in the grid voltage as shown in Fig. 4.10. Thevoltage in this case is varying between 110% and 90% of the rated value. The variation in thevoltage grid causes istantaneus variation of the voltage drop between the grid voltage and theconverter voltage and conseguently in the grid current.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.85

0.9

0.95

1

1.05

1.1

1.15

Am

plitu

de o

f the

Grid

vol

tage

[p.u

.]

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 beseen in Fig. 4.11. For example when the voltage increases there is a sudden increase in the powerwhich will be brought back to the original value thanks to the action of the control system. It canbe also be noticed that the reactive power is able to go back to the reference value which in thiscase is zero.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.5

0.7

0.9

1.1

1.3a

Act

ive

pow

er [p

.u.]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.1

-0.05

0

0.05

0.1b

Rea

ctiv

e po

wer

[p.u

.]

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, thepower varies as well which makes the currents of the DC-link unbalanced. This causes the charge



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 wellwhich causes the DC current of the inverter to increase. This means that the capacitor of theDC-link is discharging and therefore the DC-link voltage decreases.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.99

0.995

1

1.005

1.01

DC

-link

vol

tage

[p.u

.]

referencemeasured


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

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50,7

0,9

1,1

1,3a

D-a

xis

curr

ent [

p.u.

]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.1

-0.05

0

0.05

0.1b

Q-a

xis

curr

ent [

p.u.

]

Time [s]

referencemeasured

referencemeasured

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 examplewhen the grid voltage increases, the grid current decreases. This can be explained by the fact thatthe power flowing to the grid is constant. When the grid voltage decreases the output voltage ofthe converter decreases in order to bring back the current to the desired value.



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

-0.5

0

0.5

1

a

Vol

tage

of t

he P

CC

[p.u

.]

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

-0.5

0

0.5

1

b

Grid

cur

rent

[p.u

.]

Time [s]

Figure 4.14: PCC voltage and grid current.

According to the grid requirements, when the frequency is 50Hz and the voltage varies between110% and 90% of the rated value, The system can remain connected for one minute as shown inFig. 2.19. Therefore ít can be seen that in this study case the system is complying with this gridrequirement. It can be observed that the values of the active and reactive powers are within theaccepted 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 frequencychanges, by keeping the active power at 0.9 of its rated value and reactive power to zero. Gridvoltage frequency varies ±3Hz of its rated value considering that each step lasts 200ms as shownin Fig. 4.15.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.54546474849505152535455

Grid

vol

tage

freq

uenc

y [H

z]

Time [s]

Figure 4.15: Grid frenquency steps.

Power flow response is shown in Fig. 4.16.



0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.8

0.85

0.9

0.95

1a

Act

ive

pow

er [p

.u.]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.2

-0.1

0

0.1

0.2b

Rea

ctiv

e po

wer

[p.u

.]

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 reacheddue to the filter losses. Fig. 4.16.b. shows the reactive power where it can be noticed that is moresensible than the active power. This is because the reactive power is related with q-axis currentcontrol as shown in Fig 4.18.

Fig. 4.17 shows the DC-link voltage response.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.99

0.995

1

1.005

1.01

DC

link

vol

tage

[p.u

.]

referencemeasured


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



0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.8

0.85

0.9

0.95

1a

D-a

xis

curre

nt [p

.u.]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.1

-0.05

0

0.05

0.1b

Q-a

xis

curre

nt [p

.u.]

Time [s]

referencemeasured

referencemeasured

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 shorttransient both currents go back to the reference values. In this simulation there are not big changesin the dq currents as they are below 1%. Finally, the PCC voltage and the grid currents are shownin Fig. 4.19.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.99

0.995

1

1.005

1.01a

Vol

tage

at t

he P

CC

[p.u

.]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.88

0.885

0.89

0.895

0.9b

Grid

cur

rent

s [p

.u.]

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 whenthe active power is being delivered to the grid. Thus, it is worth to remark that the voltage ofPCC has fluctuations which produces the transients in the grid currents. It is necessary to zoomin to realize the grid current transients. Another important point is that in spite of the fact that thefrequency excursions of 3Hz are significants, the reactive power flow does not reach the limits of



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 thegrid is shifted. This study case is performed with some steps in the grid voltage angle, as shownin Fig. 4.20, when the system is delivering 0.9 of rated active power and zero reactive power is setto zero.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-80-60-40-20

020406080

Grid

vol

tage

ang

le [D

eg]

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 activepower flow decreases when the change in the phase angle of the voltage is applied. This is becausethe active power is related to the d-axis current and voltage reference, which is shown in Fig. 4.23.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50

0.3

0.6

0.9

1.2

1.5a

Act

ive

pow

er [p

.u.]

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

-1-0.5

00.5

11.5

b

Rea

ctiv

e po

wer

[p.u

.]

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 thetransients. Due to the relation between reactive power and phase angle, these transients haveabrupt starts. Therefore, depending on the sign of this shifted angle, the peak of power will benegative or positive. The response of the DC-link voltage is shown in Fig. 4.22.



0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.9

0.95

1

1.05

1.1

DC

link

vol

tage

[p.u

.]

referencemeasured


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

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.8

1

1.2

1.4

1.6a

D-a

xis

curre

nt [p

.u.]

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.4

-0.2

0

0.2

0.4b

Q-a

xis

curre

nt [p

.u.]

Time [s]

referencemeasured

referencemeasured

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 smalltransient they become overlapped. It can be noticed that during the transient, the maximum valueis below 20% of the rated value. Fig. 4.23.b. shows the reference and measured of the q-axiscurrent. Fig. 4.24 shows the PCC voltage and the grid current.



0.68 0.7 0.72-1.5

-1-0.5

00.5

11.5

a

Vol

tage

at t

he P

CC

[p.u

.]Time [s]

0.88 0.9 0.92-1.5

-1-0.5

00.5

11.5

b

Time [s]1.08 1.1 1.12

-1.5-1

-0.50

0.51

1.5c

Time [s]1.28 1.3 1.32

-1.5-1

-0.50

0.51

1.5d

Time [s]

0.68 0.7 0.72-1.5

-1-0.5

00.5

11.5

e

Grid

cur

rent

s [p

.u.]

Time [s]0.88 0.9 0.92

-1.5-1

-0.50

0.51

1.5f

Time [s]1.08 1.1 1.12

-1.5-1

-0.50

0.51

1.5g

Time [s]1.28 1.3 1.32

-1.5-1

-0.50

0.51

1.5h

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 gridvoltage. 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 whenthere is a difference between the voltage magnitudes and/or when there is phase shift different than120 degrees. In this study case the unbalanced percentage is chosen to be 3%. In other words theamplitude 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 ofsingle-phase loads [6].

0.5 0.51 0.52 0.53 0.54 0.55 0.560

0.2

0.4

0.6

0.8

1

1.2

Grid

vol

tage

[p.u

.]

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 beseen for dq currents as shown in Fig. 4.28.



0.5 0.51 0.52 0.53 0.54 0.55 0.560.5

0.7

0.9

1.1

1.3a

Act

ive

pow

er [p

.u.]

0.5 0.51 0.52 0.53 0.54 0.55 0.56-0.4

-0.1

0

0.2

0.4b

Rea

ctiv

e po

wer

[p.u

.]

Time [s]


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

0.5 0.51 0.52 0.53 0.54 0.55 0.560.99

0.995

1

1.005

1.01

DC

-link

vol

tage

[p.u

.]

Time [s]

referencemeasured


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



0.5 0.51 0.52 0.53 0.54 0.55 0.560.6

0.8

0.9

1.1

1.3a

d-ax

is c

urre

nt [p

.u.]

0.5 0.51 0.52 0.53 0.54 0.55 0.56-0.04

-0.02

0

0.05

0.1b

q-ax

is c

urre

nt [p

.u.]

Time [s]

referencemeasured

referencemeasured


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

0.5 0.51 0.52 0.53 0.54 0.55 0.560

0.10.20.30.40.50.60.70.80.9

1

Grid

cur

rent

[p.u

.]

Time [s]

Figure 4.29: Grid current.



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 distributionequipment. Therefore, it is important to protect people and equipment by calculating short-circuitcurrents 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 sufficientfor 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 interruptingrating 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-phasefault 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 usea single-phase circuit to analyze the fault. In this study case a three-phase short-circuit occurs atsecond 0.5 and it last for 150 ms.

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

-1

0

1

a

Grid

vol

tage

[p.u

.]

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

-1

0

1

b

Grid

cur

rent

[p.u

.]

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 resistanceis 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 temporarilyhigher than the rated value, before going back to the rated value. This temporarily raise does nothappend if the system is connected to a stronger grid with a higher short-circuit power. The gridcurrent is kept at the same value thanks to the control system which acts on the power references.



0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-1

0

1

2a

Act

ive

pow

er [p

.u.]

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-0.5

0

0.5

1

1.5

2b

Rea

ctiv

e po

wer

[p.u

.]

Time [s]


In Fig. 4.31 the active and the reactive power are shown. It is possible to see the action of thecontrol 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 gridand helps to maintain the voltage.

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.80.9

0.95

1

1.05

1.1

DC

-link

vol

tage

[p.u

.]

referencemeasured


In Fig. 4.32 The DC-link voltage is shown. It can be noticed that when the short-circuit occursthere 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 currentgoes to zero as the active power reference is set to zero. In the same moment the q-axis componentof 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



0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

-0.5

0

0.5

1a

d-ax

is c

urre

nt [p

.u.]

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-1

-0.5

0

0.5

1b

q-ax

is c

urre

nt [p

.u.]

Time [s]

referencemeasured

referencemeasured


Fig. 2.20. Therefore in this situation for the first 10 seconds it can be choose to keep the windturbine 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. 4.34the voltage and currents of the PCC are shown. In the two phases affected by the short-circuit thevoltage drops to half of the original value as shown in Fig. 4.34.a.

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

-1

0

1

a

Grid

vol

tage

[p.u

.]

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-2

-1

0

1

2b

Grid

cur

rent

[p.u

.]

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



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

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-1

-0.5

0

0.5

1a

Act

ive

pow

er [p

.u.]

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-1

-0.5

0

0.5

1b

Rea

ctiv

e po

wer

[p.u

.]

Time [s]


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.

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.80.9

0.95

1

1.05

1.1

DC

-link

vol

tage

[p.u

.]

referencemeasured





0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

-1

-0.5

0

0.5

1

a

d-ax

is c

urre

nt [p

.u.]

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-1

-0.5

0

0.5

1

b

q-ax

is c

urre

nt [p

.u.]

Time [s]

referencemeasured

referencemeasured


The voltage drop of the two phases affected by the fault, in this case, is around 50% of the ratedvalue. 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 currentof the PCC are shown. It can be seen that one phase of the grid voltage drops to 10% of the initialvalue. The current rises to almost three times of the rated value.

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

-1

0

1

a

Grid

vol

tage

[p.u

.]

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-4

-2

0

2

4b

Grid

cur

rent

[p.u

.]

Time [s]

Figure 4.38: Voltage and currents of the PCC.



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

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-1.5

-1-0.5

00.5

11.5

aA

ctiv

e po

wer

[p.u

.]

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-1.5

-1-0.5

00.5

11.5

b

Rea

ctiv

e po

wer

[p.u

.]

Time [s]


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

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.80.9

0.95

1

1.05

1.1

DC

-link

vol

tage

[p.u

.]

referencemeasured




4.2 Analysis and comparison of 11 kW model

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

-0.5

0

0.5

1a

d-ax

is c

urre

nt [p

.u.]

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-1

-0.5

0

0.5

1b

q-ax

is c

urre

nt [p

.u.]

Time [s]

referencemeasured

referencemeasured


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 ratedvalue, within the first 10 seconds "may be disconnected" and after that "shall disconnected" asshown in Fig. 2.20. Therefore in this situation for the first 10 seconds it can be choose to keep thewind turbine connected to grid.


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

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

22

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 tableFig. 4.43.



4.2.1 Study cases

A. Power flow active steps and reactive power set to zeroB. Power flow reactive steps and active power set to 0.9 of rated valueC. Voltage excursionD. UnbalancedE. Voltage phase angle steps for active power set to 0.9 of rated valueF. 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 zeroB. αβ Power flow reactive steps and active power set to 0.9 of rated valueC. αβ Voltage excursionD. αβ UnbalancedE. αβ Voltage phase angle steps for active power set to 0.9 of rated valueF. 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 zeroB. Dq Power flow reactive steps and active power set to 0.9 of rated valueC. Dq Voltage excursionD. Dq UnbalancedE. Dq Voltage phase angle steps for active power set to 0.9 of rated valueF. 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 tozero value. The active power starts at 60% of the rated value, later it rises to 90% and at the end itgoes down to 40%.

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50

0.2

0.4

0.6

0.8

1

Act

ive

pow

er in

puts

[p.u

.]

Time [s]

Figure 4.44: Active power steps applied to the system.



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 beapplied. The active power flow is set to 90% of the rated value.

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.4-0.3-0.2-0.1

00.10.20.30.4

Rea

ctiv

e po

wer

inpu

ts [p

.u.]

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. Thevoltage in this case is varying between ±10% of the rated value.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.85

0.9

0.95

1

1.05

1.1

1.15

Grid

vol

tage

am

plitu

de [p

.u.]

Time [s]

Figure 4.46: Voltage excursion.

D. Unbalanced

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

0.5 0.51 0.52 0.53 0.54 0.55 0.560

0.2

0.4

0.6

0.8

11.1

Grid

vol

tage

[p.u

.]

Time [s]

Figure 4.47: Unbalanced grid voltage.



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, afew steps in the voltage phase angle are applied. These steps are 60 degrees positive and negativerespectively.

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-80-60-40-20

020406080

Grid

vol

tage

ang

le [D

eg]

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 frequencyvariations the system is delivering 90% of the rated value.

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.54546474849505152535455

Grid

vol

tage

freq

uenc

y [H

z]

Time [s]

Figure 4.49: Frequency steps of the grid voltage.



4.2.2 αβ and dq control simulation results

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

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50

0.20.40.60.8

11.21.4

Act

ive

pow

er [p

.u.]

Time [s]

referencemeasured

Figure 4.50: Active power flow.

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

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured

Figure 4.51: Reactive power flow.

0.6 0.7 0.8 0.9 1 1.1-1.25

-1-0.75-0.5

-0.250

0.250.5

0.751

1.25

Vol

tage

at t

he P

CC

[p.u

.]

Time [s]

Figure 4.52: Voltage of the PCC.



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

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Grid

cur

rent

s [p

.u.]

Time [s]

Figure 4.53: Grid currents.

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.99

0.995

1

1.005

1.01

DC

link

vol

tage

[p.u

.]

Time [s]

referencemeasured


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

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50

0.25

0.5

0.75

1

1.25

1.5

Act

ive

pow

er [p

.u.]

referencemeasured


0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.4-0.3-0.2-0.1

00.10.20.30.4

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured




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

-1

-0.5

0

0.5

1

1.5

Vol

tage

at t

he P

CC

[p.u

.]


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

-0.75

-0.25

0.25

0.75

1.25

Grid

cur

rent

s [p

.u.]


0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.99

0.995

1

1.005

1.01

DC

link

vol

tage

[p.u

.]

referencemeasured


C. αβ voltage excursion

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.5

0.7

0.9

1.1

1.3

Act

ive

pow

er [p

.u.]

Time [s]

referencemeasured

Figure 4.60: Active power.



0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.4

-0.2

0

0.2

0.4

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured

Figure 4.61: Reactive power.

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

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

Vol

tage

of t

he P

CC

[p.u

.]

Time [s]


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

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Grid

cur

rent

s [p

.u.]

Time [s]


0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.97

0.98

0.99

1

1.01

1.02

1.03

DC

-link

vol

tage

[p.u

.]

Time [s]

referencemeasured




D. αβ unbalanced voltage

0.5 0.51 0.52 0.53 0.54 0.55 0.560.5

0.7

0.9

1.1

1.3

Act

ive

pow

er [p

.u.]

Time [s]

referencemeasured


0.5 0.51 0.52 0.53 0.54 0.55 0.56-0.4

-0.2

0

0.2

0.4

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured


0.5 0.51 0.52 0.53 0.54 0.55 0.560

0.10.20.30.40.50.60.70.80.9

11.11.2

Vol

tage

of t

he P

CC

[p.u

.]

Time [s]


0.5 0.51 0.52 0.53 0.54 0.55 0.560

0.2

0.4

0.6

0.8

1

1.2

Grid

cur

rent

s [p

.u.]

Time [s]




0.5 0.51 0.52 0.53 0.54 0.55 0.560.99

0.995

1

1.005

1.01

DC

-link

vol

tage

[p.u

.]

Time [s]

referencemeasured


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

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

-1.5-1

-0.50

0.51

1.52

2.53

Act

ive

pow

er [p

.u.]

referencemeasured


0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-2.5

-2-1.5

-1-0.5

00.5

11.5

22.5

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured


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

-1.5-1

-0.50

0.51

1.52

Vol

tage

at t

he P

CC

[p.u

.]

Figure 4.72: Voltage at the PCC.



0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

-3

-2

-1

0

1

2

3

Grid

cur

rent

s [p

.u.]


0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.60.70.80.9

11.11.21.31.4

DC

link

vol

tage

[p.u

.]

referencemeasured


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

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.5

0.7

0.9

1.1

1.3

Act

ive

pow

er [p

.u.]

referencemeasured


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

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured




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

-1-0.75-0.5

-0.250

0.250.5

0.751

1.25

Vol

tage

at t

he P

CC

[p.u

.]


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

-0.75-0.5

-0.250

0.250.5

0.751

Grid

cur

rent

s [p

.u.]


0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.98

0.99

1

1.01

1.02

DC

link

vol

tage

[p.u

.]

referencemeasured


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

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50

0.20.40.60.8

11.21.4

Act

ive

pow

er [p

.u.]

referencemeasured




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

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured


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

-1.5-1

-0.50

0.51

1.52

Vol

tage

at t

he P

CC

[p.u

.]


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

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Grid

cur

rent

s [p

.u.]


0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.99

0.995

1

1.005

1.01

DC

link

vol

tage

[p.u

.]

referencemeasured




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

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50

0.25

0.5

0.75

1

1.25

1.5

Act

ive

pow

er [p

.u.]

referencemeasured


0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.4-0.3-0.2-0.1

00.10.20.30.4

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured


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

-1

-0.5

0

0.5

1

1.5

Vol

tage

at t

he P

CC

[p.u

.]


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

-0.75

-0.25

0.25

0.75

1.25

Grid

cur

rent

s [p

.u.]




0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.99

0.995

1

1.005

1.01

DC

link

vol

tage

[p.u

.]

referencemeasured


C. Dq voltage excursion

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.5

0.7

0.9

1.1

1.3

Act

ive

pow

er [p

.u.]

Time [s]

referencemeasured


0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.4

-0.2

0

0.2

0.4

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured


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

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

Vol

tage

of t

he P

CC

[p.u

.]

Time [s]




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

-0.5

0

0.5

1

Grid

cur

rent

s [p

.u.]

Time [s]


0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.97

0.98

0.99

1

1.01

1.02

1.03

DC

-link

vol

tage

[p.u

.]

Time [s]

referencemeasured


E. Dq unbalanced voltage

0.5 0.51 0.52 0.53 0.54 0.55 0.560.5

0.7

0.9

1.1

1.3

Act

ive

pow

er [p

.u.]

Time [s]

referencemeasured


0.5 0.51 0.52 0.53 0.54 0.55 0.56-0.4

-0.2

0

0.2

0.4

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured




0.5 0.51 0.52 0.53 0.54 0.55 0.560

0.2

0.4

0.6

0.8

1

1.2

Vol

tage

of t

he P

CC

[p.u

.]

Time [s]


0.5 0.51 0.52 0.53 0.54 0.55 0.560

0.2

0.4

0.6

0.8

1

1.2

Grid

cur

rent

s [p

.u.]

Time [s]


0.5 0.51 0.52 0.53 0.54 0.55 0.560.99

0.995

1

1.005

1.01

DC

-link

vol

tage

[p.u

.]

Time [s]

referencemeasured


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

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

-0.50

0.51

1.52

2.53

Act

ive

pow

er [p

.u.]

referencemeasured




0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-2.5

-2-1.5

-1-0.5

00.5

11.5

22.5

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured


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

-1

-0.5

0

0.5

1

1.5

Vol

tage

at t

he P

CC

[p.u

.]


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

-2

-1

0

1

2

3

Grid

cur

rent

s [p

.u.]


0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.95

0.975

1

1.025

1.05

DC

link

vol

tage

[p.u

.]

referencemeasured




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

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.5

0.7

0.9

1.1

1.3

Act

ive

pow

er [p

.u.]

referencemeasured


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

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured

Figure 4.106: Reactive power steps.

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

-1-0.75-0.5

-0.250

0.250.5

0.751

1.25

Vol

tage

at t

he P

CC

[p.u

.]


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

-0.75-0.5

-0.250

0.250.5

0.751

Grid

cur

rent

s [p

.u.]




0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.98

0.99

1

1.01

1.02

DC

link

vol

tage

[p.u

.]

referencemeasured


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 strategiesis shown in Fig. 4.110.

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

αβ dqCONTROL STRATEGY

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, powerflow fluctuations and faults in the grid have been carried out, taking into consideration the gridrequirements. The comparison between αβ and dq has been performed. Next chapter will showthe laboratory tests and its results compared with the model.




5Experimental setup

In this chapter, the experimental setup used in the laboratory is presented and the main componentsare described. Next, αβ and dq control strategies are implemented. Finally the results obtainedfor 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. Itemulates the grid side connection of the wind turbine system. The system contains a DC voltagesupply, a power inverter, a LC filter, a three-phase transformer, the grid, the dSPACE system andthe PC computer.

4 3

56

72

1

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 computerthrough the dSPACE system. The dSPACE system sends the needed pulses to the converter gatesin order to generate the active and reactive power set in the control system. It is composed bythe software, the expansion box which contains the main boards as the processor and I/O boardsand finally the panels with BNC connectors to read and send the signal from the computer to thesystem and vice versa.

The setup structure is shown in Fig. 5.2.

81

5.1 Setup description

dSPACE Expansion Box

PC computer

DC supply

Power InverterLC filter

AC grid

Transformer

I/O panel

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 andreactive power and to modify the parameters of the controller during the tests. Furthermore themain variables of the system are shown by means of different graphs. Behind the GUI both controlstrategies (dq and αβ) are implemented. The results of the laboratory tests are analyzed andcompared with the results obtained in the previous chapter for the power flow study case.

82 5. Experimental setup

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 thelaboratory for both control strategies.

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

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2

Act

ive

pow

er [p

.u.]

Time [s]

referencemeasured


0 0.2 0.4 0.6 0.8 1-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured

Figure 5.5: Reactive power

0.4 0.41 0.42 0.43 0.44 0.45 0.46-1.5

-1

-0.5

0

0.5

1

1.5

Grid

vol

tage

s [p

.u.]

Time [s]

Figure 5.6: Grid voltages.

5. Experimental setup 83


0 0.2 0.4 0.6 0.8 1

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Grid

cur

rent

s [p

.u.]

Time [s]


0.4 0.41 0.42 0.43 0.44 0.45 0.46

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Alp

ha-b

eta

curre

nts

[p.u

.]

Time [s]

alpha-ref.alpha-meas.beta-ref.beta-meas.

Figure 5.8: αβ currents of the grid.

0.4 0.41 0.42 0.43 0.44 0.45 0.46

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Pha

se-A

vol

tage

& c

urre

nt [p

.u.]

Time [s]

voltagecurrent

Figure 5.9: Voltage and current of phase A.



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

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2A

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured


0 0.2 0.4 0.6 0.8 1 1.2-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

Rea

ctiv

e po

wer

[p.u

.]

Time [s]

referencemeasured


0.4 0.42 0.44 0.46 0.48 0.5-1.5

-1

-0.5

0

0.5

1

1.5

Grid

vol

tage

s [p

.u.]

Time [s]

Figure 5.12: Grid voltages.

5. Experimental setup 85


0 0.2 0.4 0.6 0.8 1 1.2-1.2

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

Grid

cur

rent

s [p

.u.]

Time [s]


0 0.2 0.4 0.6 0.8 1-1.2

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

Dq

curre

nts

[p.u

.]

Time [s]

d-axis ref.d-axis meas.q-axis ref.q-axis meas.

Figure 5.14: Dq currents of the grid.

0.4 0.41 0.42 0.43 0.44 0.45 0.46

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Pha

se-A

vol

tage

& c

urre

nt [p

.u

Time [s]

voltagecurrent

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 obtainedin the simulations. This confirms the expected performance of the grid side wind turbine system.


6Conclusions

Summary

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 systemconnected 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 thereforegood skills about MATLAB/Simulink and modeling was required.

Power systems connected to the grid have to comply with the grid requirements. In the case ofthe wind turbines, considering that the amount of wind energy penetrating to the grid is increasingconsiderably, it is very important to develop reliable and quality control systems. In this projectDanish 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 studycases under various grid conditions have been performed. By analyzing the results it is possible toconclude that the main objective of the project has been reached. In fact thought the simulations itis 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. Consideringthat 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 beenperformed on this model and different study cases have been analyzed. The reason for makingthe simulation on a small-scale system was to be able to verify the results with experimental testsin the laboratory. By comparing the results of the two control strategies it has been possible toobserve 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 andhave a better understanding of the systems. For this purpose, it was necessary to acquire goodknowledge 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

[1] A. Abedini and A. Nasiri, “Pmsg wind turbine performance analysis during short circuitfaults,” IEEE Canada Electrical Power Conference, pp. 160–165, 2007.

[2] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, “Overview of control and gridsynchronization for distributed power generation systems,” IEEE Transactions on IndustrialElectronics, 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 DesSystèmes. Editura Tehnica, 1997, no. ISBN: 973-31-2103-7.

[5] M. Chinchilla, S. Arnaltes, and J. Burgos, “Control of permanent-magnet generators appliedto variable-speed wind-energy systems connected to the grid,” IEEE Transactions on energyconversion, 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 powermanagment in future electricity network,” Tech. Rep., 2007.

[9] F. Iov, A. D. Hansen, P. Sørensen, and F. Blaabjerg, Wind Turbine Blockset inMatlab/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 pitchwind 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 turbineapplications,” 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 forwind,” 2007.

88

BIBLIOGRAPHY

[16] V. H. Prasad, “Analysis and comparison of space vector modulation schemes for three-legand 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,” PowerElectronics 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 failuredetection operating in stand-alone and grid connected mode,” IEEE Transactions on PowerElectronics, vol. 19, 2004.

[20] A. V. Timbus, M. Ciobotaru, R. Teodorescu, and F. Blaabjerg., “Adaptive resonantcontroller for grid-connected converters in distributed power generation systems,” IEEEXplore, pp. 1601–1606, 2006.

BIBLIOGRAPHY 89

AMatlab models

A.1 Voltage Source Converter model

Output voltage

Commutation functions

DC-link voltage

vABC2

idc1

MatrixGain

u*K

DC_link current

u(1)+u(2)+u(3)iABC3

vdc2

gate _signals1

90

A.2 Space Vector Modulation model

A.2 Space Vector Modulation model

duty_ABC1

pulse dropping

duty _ABC duty _abc

Weight

Weight

If

u1

u2

if (..)

elseIf (..)

elseIf (..)

elseIf (..)

vdc

vqref

vdref

vq

vd

vq

vd

vq

vd

vq

vd

vq

vd

Avoid saturation

AvoidSaturation

4th quadrant

elseif { }vd

vqduty _ABC

3rd quadrant

elseif { }vd

vqduty _ABC

2nd quadrant

elseif { }vd

vqduty _ABC

1st quadrant

if { }vd

vqduty _ABC

Vdc2

vAlpha /Beta _ref1

vdc

vdref

A. Matlab models 91

A.3 Grid model

A.3 Grid model

vpcc1

Short -circuit path

Vpcc Isc

Local Load

vpcc iload

HarmonicVoltage Source

ampl

freq

phase

vRST

Ground

Grid Impedance

IRST

Isc

Iload

VgSCval

iRST4

phase3fq

2|A|1

92 A. Matlab models

A.4 PLL tuning model

A.4 PLL tuning model

Output1

2.3

psi

Tset

9.2

u(1)^2

K Ts

z-1

Input1

Kp

Ti

A. Matlab models 93

A.5 dq and αβ control models


94 A. Matlab models


A. Matlab models 95

A.6 Complete model

A.6 Complete model

96 A. Matlab models

BProject proposal

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

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Documents

VECTOR CONTROL OF PMSG FOR GRID-CONNECTED WIND …