wind farm modelling

Kungliga Tekniska Högskolan

Lillgrund Wind Farm Modelling and Reactive Power Control

Isabelle Boulanger

Master Thesis

Stockholm 2009

Electrical Machines and Power Electronics, Power Systems

Royal Institute of Technology

SWEDEN


Abstract

The installation of wind power plant has significantly increased since several years due to the recent

necessity of creating renewable and clean energy sources. Before the accomplishment of a wind power

project many pre-studies are required in order to verify the possibility of integrating a wind power

plant in the electrical network. The creation of models in different software and their simulation can

bring the insurance of a secure operation that meets the numerous requirements imposed by the

electrical system.

Hence, this Master thesis work consists in the creation of a wind turbine model. This model represents

the turbines installed at Lillgrund wind farm, the biggest wind power plant in Sweden. The objectives

of this project are to first develop an accurate model of the wind turbines installed at Lillgrund wind

farm and further to use it in different kinds of simulations. Those simulations test the wind turbine

operating according to different control modes. Also, a power quality analysis is carried out studying

in particular two power quality phenomena, namely, the response to voltage sags and the harmonic

distortion.

The model is created in the software PSCAD that enables the dynamic and static simulations of

electromagnetic and electromechanical systems. The model of the wind turbine contains the electrical

machine, the power electronics (converters), and the controls of the wind turbine. Especially, three

different control modes, e.g., voltage control, reactive power control and power factor control, are

implemented, tested and compared. The model is tested according to different cases of voltage sag and

the study verifies the fault-ride through capability of the turbine. Moreover, a harmonics analysis is

done. Eventually the work concludes about two power quality parameters.

Index Terms: Wind Power, Power Electronics, Induction Machine, Controls (Voltage Control, Active

and Reactive Power Control, Current Control, DC Voltage Control), Voltage Source Converter (VSC),

Power Quality, Voltage Sags, Harmonics, and Grid Code.


Acknowledgements

This Master thesis was done at Vattenfall Research and Development AB and approved by the

Division of Power Systems and the Division of Electrical Machines and Power Electronics belonging

to the School of Electrical Engineering at KTH. Both divisions are engaged in this project since it

treats different aspects within the whole electrical engineering area. The work was funded by

Vattenfall Vindkraft.

My supervisors at KTH were Dr. Valerijs Knazkins and Professor Hans-Peter Nee and Dr. Fredrik

Carlsson at Vattenfall Research and Development AB. My examiner at KTH was Assistant Professor

Mehrdad Ghandhari.

I would like to thank some persons that played an important role during the 20 weeks of my Master

thesis work.

I express my gratitude to Dr. Fredrik Carlsson, Dr. Valerijs Knazkins, and Professor Hans-Peter Nee

for their help and guidance during the whole project. Thank to Mehrdad Ghandhari for accepting being

my examiner for this Master thesis.

I am indebted to Evabritt, Urban Axelsson and Daniel Salomonsson for their help and support.

I absolutely want to thank Lovisa Stenberg and Laura Bergholz for being helpful, attentive and who

always encouraged me. Especially I am very grateful to Lovisa Stenberg with whom I was sharing

more than a room during these 20 weeks and who facilitated so much my integration in VRD.

I want to thank my parents for teaching me perseverance and rewards of work and also for

encouraging me despite the 2000 km distance between us.

Finally I am thankful to Benjamin Boullanger who never gave up encouraging me and helping me. For

the productive discussions we had and his relevant suggestions and advices.


Table of Contents Page

1 Introduction 1

1.1 Background and prior studies 1

1.2 Lillgrund wind farm 2

1.3 Purpose 3

1.4 Report outline 4

2 Control theory 5

2.1 The control system of the wind turbine 5

2.2 Determination of the DC capacitor 5

2.3 Grid side control 7

2.3.1 The system 7

2.3.2 The inner current controller 9

2.3.3 The DC voltage controller 10

2.3.4 Three different control modes on turbine level and park pilot 11

2.3.5 Problems raised by the close bandwidth of the imbricate loops 13

2.4 Generator side control 15

2.4.1 Introduction to vector control 15

2.4.2 The induction generator 16

2.4.3 Current controller 16

2.4.4 Flux estimation for rotor flux orientation 17

2.4.5 Speed controller 19

2.4.6 Optimal speed control system 20

2.5 Siemens control system 21

3 Introduction to power quality analysis 22

3.1 Introduction to power quality – Grid Code 22

3.2 Voltage sags 23

3.2.1 Definition 23

3.2.2 Studied case 24

3.3 Harmonics 25

3.3.1 Measurements of harmonics 25

3.3.2 Induction machine harmonics 26

3.3.3 Power electronics harmonics 26

3.3.4 Transformer harmonics 27

4 Modelling and implementation in PSCAD 28

4.1 Wind turbine 28

4.1.1 Wind source 28


4.1.2 Wind turbine 28

4.1.3 Governor 29

4.2 Induction generator 29

4.3 Voltage source converter 30

4.3.1 One module 30

4.3.2 The PWM inverter filter 31

4.4 Control system 31

4.4.1 Grid side control 32

4.4.2 Generator side converter 32

4.4.3 Pitch control in PSCAD 34

4.5 DC-link chopper 34

5 Simulation in PSCAD and analysis of results 35

5.1 Simulation on PSCAD – Introduction 35

5.2 Reactive Power Control and Voltage Control Modes 35

5.3 Results for one turbine – Compliance with IEC 61400-21 36

5.3.1 Voltage sags study 36

5.3.2 Harmonics analysis 39

5.4 Results concerning the voltage sag study for one or several turbines connected to

the grid 40

5.4.1 Impact on the different voltages of the system 42

5.4.2 Impact on the wind turbine current 46

5.5 Results concerning the harmonics study for one or several turbines connected to

the grid 47

5.6 Comparative analysis between two control modes 49

5.7 Comparison with the Siemens’ study 50

5.7.1 Harmonics study 50

5.7.2 Dynamic simulation study 51

5.8 Island Operation 53

6 Conclusions 55

7 Improvements and future works 56

References 58

Appendices 60

Simulations 65

SIMULATION A: Control mode test on the grid-side inverter connected to the grid 66

SIMULATION B: Test of the generator-side system 71

SIMULATION C: Test turbine with connexion IEC 73


List of symbols

Symbol Quantity Unit

Vtri PWM triangular signal V

fs switching/triangular frequency Hz

Vcontrol PWM control/modulation signal V

f1 modulating frequency Hz

ma amplitude modulation ratio -

mf frequency modulation ratio -

--------------------------------------------------------------------------------------------------------

C DC-link capacitance F

UDC DC-link voltage V

IDC DC-link current A

EDC energy stored in the DC-link capacitor J

PDC DC power W

--------------------------------------------------------------------------------------------------------

Vabc 0.69/33 kV transformer input voltage V

Iabc converter output current A

Vabc_conv converter output voltage V

PAC AC active power W

QAC AC reactive power VAr

Vd,q Park coordinates of Vabc V

Vd,q_conv Park coordinates of Vabc_conv V

Id,q Park coordinates of Iabc A

R PWM filter resistance Ω

L PWM filter inductance H

X reactance corresponding to L (X = ω.L) Ω

Ω angular frequency rad/s

αβ axes defining the reference frame -

dq axes defining the Park reference frame -

θ Park transformation angle rad

k Park transformation coefficient -

α1C bandwidth of a closed loop system rad/s

kp,1C proportional gain of the first current controller Ω

Ti,1C time constant of the first current controller s

tr,1C rise time corresponding to α s

--------------------------------------------------------------------------------------------------------

Plosses losses in the converter W

Rvirtual virtual resistance in DC voltage control Ω

α1DC bandwidth of a closed loop system rad/s

kp,1DC proportional gain of the DC voltage controller Ω

Ti,1DC time constant of the DC voltage controller s


tr,1DC rise time corresponding to α s

--------------------------------------------------------------------------------------------------------

Us induction machine (IM) voltage V

Es IM internal voltage V

Is IM stator current A

ωm mechanical angular speed of the IM rad/s

ωr electrical angular speed of the IM rad/s

ψs rotor flux Wb

ψr stator flux Wb

Rs stator resistance Ω

Rr rotor resistance Ω

Lm magnetising inductance H

Lr rotor inductance H

Lls stator leakage inductance H

Llr rotor leakage inductance H

--------------------------------------------------------------------------------------------------------

ρ Park transformation angle for flux oriented frame rad

Lσ leakage inductance H

cT constant factor of the speed controller Nm/A

α2C bandwidth of a closed loop system rad/s

kp,2C proportional gain of the second current controller Ω

Ti,2C time constant of the second current controller s

tr,2C rise time corresponding to α s

--------------------------------------------------------------------------------------------------------

T torque N.m

J inertia of the IM kg.m2

b damping constant of the IM Nm/s

α2ω bandwidth of the closed loop system rad/s

kp,2ω proportional gain of the speed controller Ω

Ti,2ω time constant of the speed controller s

tr,2ω rise time corresponding to α s

--------------------------------------------------------------------------------------------------------

cos(φ) power factor -

H magnetic field intensity A/m

s Laplace symbol 1/s


Abbreviations

AC Alternating Current

abc Three phase coordinates system

DC Direct Current

dq Park equivalent coordinates system

d-axis direct axis in the Park representation

q-axis quadrature axis in the Park representation

DSO Distribution System Operator

EMTDC ElectroMagnetic Transient including DC

FFT Fast Fourier Transform

FRT Fault Ride Through

IEC International Electrotechnical Commission

IGBT Insulated Gate Bipolar Transistor

IHD Individual Harmonic Distortion

IM Induction Machine

IMC Internal Model Control (method)

LVRT Low Voltage Ride Through

mmf MagnetoMotive Force

PCC Point of Common Coupling

PE Power Electronics

PI Proportional Integral

PLL Phase Locked Loop

PSCAD Power System Computer Aided Science

pu per unit

PWM Pulse Width Modulation

RMS Root Mean Square

THD Total Harmonic Distortion

TSO Transmission System Operator

VPC Vattenfall Power Consultant

VRD Vattenfall R&D

VSC Voltage Source Converter


- 1 -

1 Introduction

1.1 Background and prior studies

Issues concerning electricity and energy generation have increased considerably over the last few

decades. There exist many different ways of producing electrical energy. However, with the current

concern about pollution, planet safety and oil reserve, the use of renewable energy sources has become

much more systematic. Research and development in renewable energies such as wind power have

increased since several decades. The wind power penetration is growing constantly over the world and

especially the wind power production is increasing in Sweden [24][25].

The wind appears to be a perpetual source of power that can be used efficiently thanks to the

development of new technologies. The wind industry meets different issues such as grid compatibility,

acoustic performance, aerodynamic efficiency, visual impact, and wind farm location. All these issues

constitute the main research and challenge of the wind industry these days. Important projects such as

the Lillgrund wind farm are built up to give birth to a modern, reliable and clean source of energy.

The Lillgrund wind farm is the most important offshore wind power plant installed in Sweden with a

total capacity of 110 MW, corresponding to 48 turbines. This large project sparked the interest of

Vindforsk which decided to support a study principally by creating a PSCAD model of the farm.

Vindforsk is a 3 years co-sponsored Swedish research program in the domain of wind power. The

model of the wind farm was developed by VPC (Vattenfall Power Consultant) and studied especially

the cables, transformers, breakers, and the grid. However the turbine power generation is represented

by an AC current source connected to the turbine transformer, which is relatively simplistic.

This model has been used to simulate some overvoltage cases, caused in particular by breaker

switching . Siemens Erlangen has also performed different system studies for Lillgrund, which did not

match exactly with the one of Vindforsk [26].

The objective of this project is to get a more elaborated representation of the turbine power generation.

In the former model, the simple current source is not representative of the realistic turbine operation

but the modelling of cables and transformers are good. Therefore, the Lillgrung wind farm model from

VPC does not represent the wind turbine influence. The current project deals with the building of a

turbine, which contains the electrical machine, the power electronics, and the control system of the

turbine. With such a realistic model, some further simulations can be completed and compared with

the former model. Vattenfall Vindkraft is the investigator and also funded the present project.

Thanks to the help of different tools, it is now possible to develop models and to simulate more or less

accurately the real system of wind power. Now that the penetration of wind power is growing in the

power system, the modelling of wind farms and wind turbines is more and more needed. The power

system analysis is now often performed by means of different simulation tools.

The modelling of the wind farm is performed in PSCAD/EMTDC [1]. PSCAD (Power System

Computer Aided Design) is a graphical interface using the software EMTDC (ElectroMagnetic

Transient including DC) that allows electromagnetic transients and electromechanical dynamic


- 2 -

analysis [2]. The version used in this project is PSCAD 4.2.2 Professional. The software enables the

creation of block diagram models and the simulation of them.

PSCAD/EMTDC allows the construction of models containing power electronics, machines, cables,

transformers and breakers but also signal control process. PSCAD was chosen by Vattenfall to

develop a model because it is suitable for steady state and transients simulation among others. Indeed

a power quality study with analysis of voltage sags and harmonics will be carried out. Moreover,

Vattenfall may start a two years project aiming at measuring and analysing the electrical transients and

power quality parameters at Lillgrund wind farm. This study will try to correlate and compare the

measurements with the simulation results from different models such as the one built in this Master

thesis work.

1.2 Lillgrund wind farm

Figure 1: Lillgrund site

The Lillgrund offshore wind farm is situated 7 km south of the Öresund Bridge that connects

Copenhagen in Denmark and Malmö in Sweden (Figure 1). The Lillgrund offshore wind farm consists

of 48 wind turbines of type Siemens 2.3 MW Mk II. The wind farm plant includes:

An EON’s 138 kV substation located at Bunkeflo near Malmö

A 138 kV land and sea cable lines

An offshore substation containing the main transformer 138/33 kV

The 33 kV internal grid (Figure 2)

48 wind turbines in total

The layout of the farm is seen on the Figure 2 and shows 5 feeders connected to the offshore

substation each containing 9 or 10 turbines.


- 3 -

Figure 2: Layout of the 33kV internal grid

Each 2.3MW wind turbine is then constituted as seen in Figure 3:

3-blades rotor

Gear box

Induction generator

4 quadrant Voltage Source Converter (VSC or full-power converter)

0.69/33kV transformer

Figure 3: Electrical system of one 2.3 MW turbine

1.3 Purpose

The aim of this project is to first develop an accurate model of one wind turbine. This model includes

the induction generator, the power electronics, the turbine’s transformer, the filter situated at the VSC

output, and the control system of the turbine. Further some power quality parameters, such as the

turbine’s response to a voltage sag and the harmonics analysis, will be investigated for one, two and

three turbines. Finally, a conclusion about the relevancy and the suitability of the model will be drawn.


- 4 -

1.4 Report outline

Part 1 introduces the project by describing the context of the studied system, by explaining the main

goal, and by giving an overview of the work.

Part 2 gives details about the theoretical study concerning the whole control system of the new wind

turbine model.

Part 3 brings forth some informations about power quality and especially the parameters that will be

further studied.

Part 4 presents the model created in PSCAD.

Finally Part 5 shows some simulation results that follows from the new model and analyses it.


- 5 -

2 Control theory

2.1 The control system of the wind turbine

The wind turbine generator is an induction machine that is used as a variable speed machine thanks to

the use of a full-power converter. The control system is based on two voltage source converters (VSC)

as shown in Figure 3. The DC-link between the two converters consists of an energy storage device

(capacitor); the choice of the capacitor is exposed in Section 2.2. One of the converters is connected to

the turbine’s 0.69/33 kV transformer and controls the DC-link voltage across the capacitor as well as

the active and reactive power flowing from the generator to the grid. The control of the DC-voltage

and the control of the power flow are related and consist in one control (Section 2.3.3). It also permits

a three-mode control, detailed in Section 2.3.4. From now on, this converter is referred to as the grid-

side converter or inverter and the second one is referred to as the generator-side converter. The

generator-side converter is connected to the generator and is used to control the speed and the

electrical torque of the generator (Section 2.4). Upstream, a pitch control system governs the

mechanical torque of the turbine. The vector control of induction machine turned out to be one of the

most common and effective methods for ac-machines nowadays and especially for induction

machines. This warrants the use of the vector control in this project. Since Vattenfall has no hint from

Siemens, the control system supplier, it is assumed without any certainties that Siemens might use the

vector control method.

In total there are six controllers, displayed in Table 1, that compose the control system. In the table the

controllers are ordered from the inner to the outer controller in the imbricate loop control system.

Table 1: List of the different controllers that compose the system

Grid-Side Generator-Side

Current controller: PI Current controller: PI

DC-voltage controller including

active power control: PI Speed and Torque controller: PI

Reactive power, power factor and

voltage control Pitch control (governor PSCAD)

2.2 Determination of the DC capacitor

The DC-link capacitor for such a system has a time constant of about 5 to 10 ms [17]. Given the

impossibility to access the data of the Siemens’ control, the following model is used to guess a

valuable value for the capacitor.

The cost of dc capacitor is relative to the cost of the voltage source converter (2.4 MW) that the

capacitor is connected to. That is about 3.7 pu / (Energy Base). The power base in this case is 2.4

MVA. The energy base is 2.4 MJ that is the VSC power during 1 second. Therefore, the cost is 3.7 pu


- 6 -

/2.4 MJ. Assume the cost of the VSC is 1 per unit. For a capacitor with a voltage rating equal to 1.754

kV and a time constant of 10 ms, the energy stored in the capacitor to get full power is 24 kJ. From

these one can estimate the cost of the capacitor at 0.037 per unit that is 3.7 % of the whole VSC cost.

The capacitance of the capacitor is then calculated:

mFU

EC

DC

C 6.15)10754.1(

10242223

3

2

(1)

The cost figure is applicable to high power VSCs. This model is valid for high capacity converter [18].

A film capacitor of this size is generally made of several units in parallel. Typical units are found on

the Internet web sites of different manufacturers.

There are two different solutions to install the capacitor devise. Either it is composed by many small

capacitors or by a few large capacitors in parallel. An example is drawn by examining the products of

one manufacturer [19]. This manufacturer proposes a large choice of high power capacitor for power

electronics.

Table 2 shows different possibilities to design the DC-link capacitor. Vn corresponds to the maximum

operating peak voltage for which the capacitor has been designed for continuous operation.

Table 2: List of possible capacitor devices for the DC-link

Capacitance

[uF] Vn [V]

Number of

devices

Total weight

[kg]

825 2000 20 210

1980 2000 8 152

1980 2000 8 168

3960 2000 4 144

3970 2000 4 142

8000 2000 2 120

8160 2000 2 117

The more devices, the heavier the capacitor is. Also, many small devices mean that more space is

needed. The weight and size may be a factor to choose the design of the capacitor since the turbine

must tolerate a certain maximum weight.

However if one capacitor should fail, it is more ingenious to have small devices so that it is easier and

cheaper to replace it. The case number 2 with 8 units of 1980 μF each seems to be a good compromise.

A lot of other aspects as electrical and thermal characteristics and mechanical design of the devices are

of interest for the user but are not part of the present study.


- 7 -

2.3 Grid side control

2.3.1 The system

The purpose of the grid-side control is to regulate the DC voltage of the DC-link situated between the

two converters. It also maintains the power balance between the DC-link and the AC side of the

converter. The control strategy is studied in [2]. Also, the grid-side converter is equipped with a three-

mode controller, which makes it possible for the grid-owner to choose either the reactive power

control at the point of common coupling (PCC) or the power factor control at the PCC or the grid-side

converter output voltage control.

The controller of the grid-side converter is represented in Figure 4. The VSCs are constituted by six

diodes and six IGBTs (isolated gate bipolar transistor) commanded by a PWM control (pulse width

modulation).

Figure 4: Control model of the grid side converter

The equation connecting the converter AC voltage and the grid-side voltage is:

abc

abc

abcconvabc Vdt

dILIRV _ (2)

where Vabc, Iabc and Vabc_conv represent the grid-side voltages, the grid currents and the converter output

voltages. R and L are the three-phase resistance and inductance between the converter and the

transformer. The PWM filter of the grid-side converter, which consists of R and L, is studied later in

4.3.2.


- 8 -

In order to compute the VSC controller, it is more convenient to work in the dq- reference frame

which is rotating at the grid speed = 2f [rad/s]. The transformation from the initial to the rotating

reference frame is known as Park’s transformation and the rotating reference frame referred to as

Park’s reference frame (or dq-reference frame). The angle θ (Figure 5) is the transformation angle for

the Park transformation. The αβ- axis represents the initial reference frame corresponding to the three-

phase vectors where Va is aligned on the α- axis. The choice is made to align the grid side voltage Vabc

on the q-axis of the Park’s reference frame. This implies Vd = 0 and will simplify the equations.

Figure 5 shows the old reference frame and the new reference frame in dq-coordinates defined by the

grid-side voltage, which is aligned on the q-axis.

Figure 5: The initial reference frame and the dq-coordinates

Then equation (2) in the dq- reference frame becomes:

qd

q

qconvq

qd

dconvd

VIdt

dILIRV

Idt

dILIRV

_

_

(3)

The power balance between the AC and DC side of the converter can be written in equation (4) and

allows the control of the flowing power.

qqACDCDCDC IVkPIUP (4)

The factor k depends on the dq-transformation used and is equal to k = 3/2 in our case. It means that

the Park’s transformation is amplitude invariant. k is determined by the abc to dq transformation made

by the software PSCAD thanks to the block:

Figure 6: abc to dq transformation function on PSCAD


- 9 -

The power control of a PWM converter is here achieved by using an inner current controller. To make

it simple, the chosen controller is a proportional integral (PI) controller. It is calculated in details in

Subsection 2.3.2. A PI controller is sufficient for this control since the grid-side electrical system is a

first order with complex values. The DC voltage controller, which allows reasonable constant value of

the voltage, is developed in Subsection 2.3.3.

2.3.2 The inner current controller

Figure 7: Block diagram representing the current control system

The inner current controller is obtained from equation (3):

qdqconvq

qdconvd

VIUV

IUV

'

'

_

_ (5)

dt

dILIRU

dt

dILIRU

q

qq

ddd

'

'

(6)

Thus by using the Laplace transform:

)()()('

)()()('

sisLRsU

sisLRsU

qq

dd (7)

And then, according to the block diagram in Figure 7 and the internal model control (IMC) design

method [4], the coefficients of the PI controller are calculated. The results give the proportional gain

and integral time constant of the PI function:

R

LT

Lk

withsT

ksFCi

CCp

Ci

CpC

1

11

1

11

11)(

(8)


- 10 -

1C corresponds to the bandwidth of the closed loop system and is linked to the rise time of the closed

loop system by the relation: )9ln(11 CrC t . This relation is valuable for a first order system as has

been designed in our case [5].

2.3.3 The DC voltage controller

It is necessary to control the DC-link voltage in order to ensure proper operation of the converters and

thus of the whole wind turbine. Further, the grid-side VSC is used as the interface to the AC grid-side

system and it allows the power balance between DC-side and grid-side.

The control strategy used to regulate the DC link voltage is a simple PI controller, which regulates the

energy stored in the DC side capacitor. This model is largely inspired by [4]. The power balance can

be written as:

AClossesDCDC PPEdt

dP (9)

where:

DCDCDC IUP is the DC power

2

2

1DCDC UCE is the energy stored in the DC-capacitor

lossesP are the losses in the converter

dqAC IVP 2

3 is the AC power

Neglecting the losses, a linearity between qI and CWdt

d is implied by the equation (9). The power

flowing from the DC side is modelled as the power from a virtual resistor Rvirtual, which gives:

CR

E

R

UIUP

virtual

DC

virtual

DC

DCDCDC

22

(10)

This resistor is calculated knowing the voltage and current values at the DC link. When the losses are

neglected, the relation (9) becomes:

qqDC

virtual

DC IVEdt

d

CR

E

2

32 (11)

The Laplace transform leads to a transfer function defined by the following relation:

CRs

V

(s)I

E(s)F

q

q

DCDC

2

2

3

1 (12a)


- 11 -

A PI controller is designed using the IMC design method to get a closed-loop transfer function of

order 1 in the following form:

s(s)

I

E(s)F

q

DCloopclosed (12b)

1DC corresponds to the bandwidth of the closed loop system and is related to the rise time of this first

order system by: )9ln(11 DCrDC t . The PI controller is calculated according to:

2

2

31

1)(

1

1

1

1

11

CRT

V

k

withsT

ksF

virtual

DCi

q

DC

DCp

DCi

DCpDC

(13)

2.3.4 Three different control modes on turbine level and park pilot

The grid-side converter allows the choice of three different control modes. Thanks to the use of the

vector control method the reactive power, the power factor or the voltage can be regulated. The

network owner requires the reactive power export to be zero at the point of common coupling (PCC)

that corresponds to a unity power factor [6]. The voltage control aims at controlling the inverter output

voltage amplitude. It is possible to switch from one control mode to another during operation.

In fact, the voltage control mode is not implemented at Lillgrund. The only requirement is the unity

power factor at Bunkeflo [6].

2.3.4.1 Reactive power control

As seen on Figure 4, the q-axis reference current is the output of the DC-voltage controller. Here, the

d-axis current is used to control the reactive power, the power factor or the voltage. The expressions

for the active and reactive power in the dq-reference frame are:

qqAC IVP 2

3 and dqAC IVQ

2

3 (14)

Thus, the d-axis current determines which quantity of reactive power is transmitted to the grid.

Depending on which quantity of reactive power is needed at the PCC, a certain quantity of d-current is

injected into the system. Figure 8 shows the vector representation of the system when the d-axis

current is zero, i.e. no reactive power is flowing through the grid (the PWM filter resistance R is

neglected).


- 12 -

Figure 8: Vector representation of the system when Id=0, that is Q=0

If the reactive power needed is Qneeded, then the required current that must be injected becomes:

q

needed

requiredd

V

QI

2

3 (15)

2.3.4.2 Power factor control

The power factor control is close to the reactive power control since, from (14):

q

d

AC

AC

I

I

P

Q)tan( (16)

If the power factor needed is cos(φneeded), then the required current that must be injected becomes:

))(arccos(cos)tan( neededqrequiredd whereII (17)

2.3.4.3 Voltage control

The aim of the voltage control is to regulate the voltage amplitude at a specific point in the wind farm,

by adjusting the d-axis current to output reactive power. For instance, the desired voltage amplitude

for the inverter output could either be the amplitude at the 0.69/33 kV transformer (node A between

the transformer and the PWM filter) or at the offshore substation. Obviously, a new interaction

between the turbines might appear when the voltage is controlled at the offshore substation. This will

be discussed further in Chapter 5.

The desired voltage amplitude is measured and is equal to Udesired. This means that the inverter output

amplitude has the form:


- 13 -

2

_

22

_

2

_ )( convqqconvqconvddesired VIXVVU (18)

From that, the required d-axis current is deduced:

X

IXUV

X

VVI

qdesiredqconvqq

refd

22

_

_

)(

(19)

Figure 9: Vector representation of the system when the voltage control mode is active

Figure 9 shows the process of the voltage control mode. Injecting some Id current in the system lowers

the voltage amplitude of the inverter output. Meanwhile, the q-current Iq is maintained (the resistance

R of the PWM filter is neglected).

2.3.5 Problems raised by the close bandwidth of the imbricate loops

The bandwidth must be appropriate for the different imbricate loops of the control system. In order to

get a good operation of the system, the current loop bandwidth should be at least 10 times narrower

than the switching angular speed of the PWM [17] that is

sradf s

C /8.157010

21

(20)

Then, the DC voltage controller should also be 10 times slower than the current controller in order to

insure some good dynamic of the control system:

sradDC /08.1571 (21)


- 14 -

However, the DC voltage loop controls the voltage across the DC capacitor. The latter one has been

chosen taking into account principally the price of this capacitor as seen previously in Section 2.2.

This led us to the choice of a capacitor with a time constant of 10 ms. The DC voltage controller must

be faster than the capacitor that is a bandwidth greater than 628 rad/s.

All these conditions can obviously not be fulfilled simultaneously. A compromise must be found. This

is achieved by trying several bandwidths for the closed loop controllers during the simulation. The

final bandwidth for the current controller and the DC-voltage controller are respectively equal to

1570.8 rad/s and 157 rad/s.

To conclude with this DC side control system, the final representation of the control is drawn on

Figure 10. A phase locked loop (PLL) is used to compute the angle θ (Figure 5

), which allows the abc to dq and dq to abc transformation. This PLL is a PSCAD library component

and it generates a ramp signal that varies between 0 and 2π, locked in phase with the first input signal.

Figure 10: Detailed scheme of the Grid Side VSC Control


- 15 -

2.4 Generator side control

2.4.1 Introduction to vector control

In order to control the speed and the torque of an induction machine (IM) tools such as vector control

and speed regulation are needed. The following section aims at implementing a vector control for the

induction generator. The vector control is one of the most common and effective modern methods

used in the control of ac-machines. The induction machine will be forced to behave dynamically as the

DC-machine thanks to the use of a feedback control. The machine is fed from the VSC, thus the

frequency of the input signal can change. The frequency of the stator must not be seen as constant.

Furthermore, the different values of current, voltage and flux are ac-values in the induction machine.

Consequently, the rotating reference frame is needed to get DC-values under steady state.

The knowledge of the parameters of the IM is needed. During the description of the vector control,

several reference frames (stator reference frame, synchronous reference frame and field oriented

reference frame) are used. A current controller and a speed regulation system are built. Both

controllers use PI-controllers, which is suitable since the systems are defined only by first order

equations.

Figure 11: Scheme of the generator-side VSC control system

All this part is almost exclusively inspired by [5]. The control system is drawn on Figure 11.


- 16 -

2.4.2 The induction generator

Figure 12 depicts the equivalent circuit of the induction machine. Unlike the traditional model of the

IM, this dynamic model from [5] is even correct during transients; it is not limited to steady-state

cases.

Figure 12: Dynamic equivalent circuit for the induction machine

The parameters of the machine are deduced from the no-load and rotor-blocked tests performed by the

manufacturer (Appendix 4). This model is used later to determine part of the control system and some

simplifying assumptions will be made (see next section 2.4.3).

2.4.3 Current controller

Assumption:

The induction machine, as a three-phase device, can be represented according to the Figure 13.

Because of the very fast dynamic of the magnetizing current, the magnetizing inductance is

disregarded and in our case:

rs

rllsl

RRR

LLLL (22)

The voltage Us is the rectifier voltage vector, es the voltage is the internal voltage of the machine, φr is

the rotor flux and ωr is the rotor electrical speed. They are linked by equation (23):

rrs je (23)

The differential equation governing the system is in the synchronous reference frame:

dt

diLijLReU s

sss )( (24)


- 17 -

Figure 13: Load/Generator model

By dropping the equation in the d- and q-axis, one gets two interacting systems that leads to the cross

coupling between the d- and q-axis currents (as for the grid-side controller in Subsection 2.3.2).

The current-controller system is represented on Figure 14 where G2C(s) represents the machine and

F(s) the controller.

)()(

)(

)(

1)(2

sEsU

sI

RLjssG C

(25)

Figure 14: Current controller loop

The IMC method is used to design a PI controller and make the closed loop system responding as a

first order system.

R

LT

Lk

withsT

ksFCi

CCp

Ci

CpC

2

22

2

22

11)(

(26)

This controller has the same shape as the one defined in Subsection 2.3.2 for the grid side control.

2.4.4 Flux estimation for rotor flux orientation

That step makes the necessary calculations that will allow working in the new coordinates system. The

new frame is the so-called “field-oriented reference frame”. It is more natural and also simpler to use

this one instead of the synchronous reference frame since the field-oriented reference frame rotates

synchronously during steady state operation. On the contrary, the synchronous reference frame


- 18 -

depends on the stator frequency that can be affected by transients. The new frame is field-oriented,

that is the d-axis is aligned with the rotor flux.

Consequently, one needs to know the rotor flux. Since there is no cheap and reliable way to measure

the rotor flux, it will be estimated. The estimation can be made according to different methods

described in [5]. However, given that the rotor will not operate at low speeds (not under 40%); one

decides to estimate the flux by using the “Voltage Model”. Indeed, at low speed the voltage drop due

to the stator resistance cannot be neglected anymore and the model would not be valid. The induction

machine can be described by the following differential equations linking the rotor and stator flux ψ,

currents I and voltages U:

)(')( rotorIRjdt

dandstatorIRU

dt

d s

rr

s

rr

s

rs

ss

s

s

s

s

(27)

s

rr

s

sm

s

r

s

ss

s

rm

s

s ILILandILIL (28)

Combining these equations in a proper way leads to the following expression of the rotor flux:

s

s

s

s

m

rs

r ILL

L (29)

where:

s

r

m LL

LL

2

represents an equivalent inductance

That corresponds to the voltage model for rotor flux estimation. All these equations are written in the

synchronous rotating reference frame denoted by the superscript “s” and rotating with the stator

currents. The subscripts “s” and “r” means respectively the stator and rotor values.

Figure 15: Stator reference frame and rotor flux reference frame


- 19 -

Figure 15 shows the old reference frame and the new reference frame in dq-coordinates defined by the

rotor flux φr, which is aligned on the d-axis. The transformation from the initial to the rotating

reference frame use Park’s transformation and the new dq-reference frame corresponds to the field-

oriented reference frame. The angle ρ is the transformation angle that allows working in the field-

oriented reference frame. The αβ-axis represents the initial reference frame corresponding to the

synchronous reference frame.

Knowing the rotor flux, it is from now on possible to work with the flux coordinates that will be

denoted by a subscript “ρ”. Figure 15 illustrates the transformation from the stator reference frame to

the field-oriented reference frame. The new rotating reference frame “flux-oriented” will be used to

determine the speed controller.

2.4.5 Speed controller

In the flux-oriented reference frame, the relation between the electrical torque T and the current I is:

T

sq

sqrd

r

m

c

II

L

LpT

_

__2

3 (30)

where:

_rd is the rotor flux in the “ρ” reference frame

_sqI is the d-axis current in the “ρ” reference frame

p is the number of pole pair of the IM

cT defines a variable that will be used later

The speed controller will force the machine to turn at a certain reference speed by providing a

reference value to the torque that is for the q-axis current. The reference q-axis current input in the

current controller is the output of the speed controller.

In the flux-oriented reference frame, the relation (31) defines the reference d-axis current input in the

current controller:

m

ref

rsd

LI

_ (31)

where: ref

r is the desired flux

_sdI is the q-axis current in the “ρ” reference frame

Figure 16 shows the block diagram of the speed control loop including the controller and the system. It

describes the mechanical relation between the speed and the torques (load torque TL and electrical


- 20 -

torque Te). The factor cT is defined by the equation (30) and describes the relation between the

electrical torque and the q-axis current.

Figure 16: Speed control loop

Again, the PI control is determined by using the IMC method and its expression is found as:

sTksF

i

p

2

22

11)( with

b

JT

Jk

i

p

2

22

(32)

where

2

2

)9ln(

rt is the bandwidth of the closed loop system, b is the coefficient corresponding to

the frictions and J is the inertia of the induction machine.

The choice of the bandwidth is also critical for the speed controller; a too high bandwidth could lead to

very high current peaks when a change in the speed occurs [5]. It will be discussed further in section

4.4.2.

2.4.6 Optimal speed control system

Equations (33) and (34) defines the power coefficient Cp and the tip speed ratio λ.

3.

2

1vA

P

windtheinpoweravailable

powerrotorC rotor

p

(33)

where:

ρ is the air density

A is the rotor blade area

v is the wind speed

v

R

speedwind

speedtipblade

(34)

where:


- 21 -

R is the rotor radius

ω is the angular speed of the rotor

Figure 17: Power coefficient versus tip speed ratio [22]

To increase the aerodynamic efficiency of the wind turbine, it is possible to control the mechanical

torque in order to get the optimal speed operation. The power coefficient Cp of the wind turbine

depends on the tip ratio λ as illustrated on the Figure 17. The maximum power coefficient corresponds

to a certain tip speed ratio λopt from which an optimum speed can be deduced according to equation

(35). From this, a reference value for the speed is input in the speed controller defined in section

2.4.5.

R

vopt

opt

(35)

The speed tracking for optimum efficiency is a practical tool and several strategies exist. The

knowledge of the power coefficient versus the tip speed ratio is needed to employ this method. The

turbine manufacturer Siemens can provide it. However, it is not implemented in the PSCAD model

since it is not defined in the project initial purpose.

2.5 Siemens control system

Siemens is the provider of the control system of the turbines and the offshore substation of Lillgrund

wind farm. Vattenfall did not succeed in obtaining any information from Siemens concerning the

control system of Lillgrund. Therefore, the whole project is based on some assumptions of what

Siemens might use as control. In particular, the most common methods for controlling such a wind

farm are used in this project. For example, the vector control of the induction machine, and the whole

grid-side converter control correspond to common tools for such a system. The only known

information about the wind farm control is the unity power factor at the PCC (Bunkeflo) and that the

grid codes are fulfilled.


- 22 -

3 Introduction to power quality analysis

3.1 Introduction to power quality – Grid Code

Nowadays with the increasing penetration of wind power generation in the power system, the

necessity of defining the so-called grid code appeared. This code corresponds to technical

requirements insuring a secure and safe operation of the electrical system. Especially, it defines in

which extent and under which conditions a wind power plant can be connected to the network and

power quality requirements has to be satisfied. Indeed, the transmission system operator (TSO) and the

distribution system operator (DSO) must deliver high quality energy to the consumer.

Thus the connection of Lillgrund wind farm, being the biggest wind power production in Sweden, has

raised the interest of studying the power quality carefully. A two years project will be launch by

Vattenfall aiming at a power quality and transient measurements study which will lead to a secure and

high performance operation of Lillgrund offshore wind farm [7].

The electrical system must fulfil the grid codes and some specific devices are installed as for example

the PWM filter studied previously. The power quality concerns several phenomena as listed in Table 3

below. In general, power quality concerns any possible divergence of the voltage from the ideal

sinusoidal waveform, with constant and unique frequency, constant amplitude, and power factor. This

work focuses on the study of harmonics and voltage sags (see Section 1.3).

Table 3: Power quality variation categories

Example of power

quality category Symptom Main cause

Flicker Voltage fluctuation Large fluctuating load

Voltage sags and swells

rms voltage reduction or

increase during a certain

duration

Faulted power line,

starting of large load

Harmonics Distortion in the current or

voltage waveform Non linear load

Undervoltage and

Overvoltage

rms voltage reduction or

increase for more than 1

minute

Motor starting, load

variations, load dropping

Interruption Total loss of electric power

during a certain duration

System protection,

maintenance

Transient Voltage Sudden increase in the

voltage during a short time

Switching (load, capacitor,

line), lightning


- 23 -

Besides the grid codes, there exists some voltage tolerance for information technology (IT) equipment

and control systems [26]. The ITI curves represent the AC voltage envelope that can be tolerated by

most of the IT equipment and control systems [28].

A Danish project, dealing with the power quality study of wind farms, was carried out lately.

Vattenfall participated to this Master thesis work, which deeply investigates the measurement methods

for harmonics and flicker [9].

The IEC standard 61400-21 stipulates the methods to assess and measure the power quality parameters

of grid-connected wind turbines [12]. In the simulation part of the project, an attempt is made to

measure two power quality parameters (response to a voltage sag and harmonics study) according to

this standard (see Section 5.3). Obviously, if the results obtained during simulations are within the

limits; the conclusion will be drawn that the system has good power quality reliability.

3.2 Voltage sags

One requirement of the grid-code is the fault ride-through (FRT) capability and also low-voltage ride

through (LVRT) capability. It means that the wind turbine or the wind park must endure voltage sags

without disconnecting from the grid. The LVRT is a more recent concept. The LVRT is a type of FRT

where the voltage reduction that the system must handle is limited. Indeed, the most common voltage

sags present between 70 and 90 % remaining voltage (see Figure 18 in Subsection 3.2.2).

3.2.1 Definition

A voltage sag is a reduction down to 90-10% of the RMS voltage magnitude during a period from half

a cycle (10 ms at 50 Hz) to one minute [16]. The voltage sag mainly origins from motor starting,

transformer energizing, and faults [19]. The latter provokes the most important damage and for this

reason, the study principally focuses on this type of fault. The different types of voltage sags are

summarized in Table 4.

Table 4: Voltage sag - origins and characteristics

Origin Characteristics Impact on 3 phases

Motor Starting

Sudden drop in the voltage and

progressive recovery Balanced

Transformer Energizing

Sudden drop in the voltage and

progressive recovery Unbalanced

Fault

Usually constant voltage sag with

immediate recovery (can contain

different stages if several events

happens)

Depends on the type of fault


- 24 -

The duration of the sag that origins from failures, is the time it takes for the protections to disconnect

the faulted power line that is the fault clearing time. Mostly it takes 100 ms. There are different types

of voltage sags depending on the nature of the short circuit, which provoked it. That can be line-to-

line, line-to-ground or two or three phases.

The effects of voltage sag are stated in [11] as well as some solution to ride-through voltage sags. An

induction machine may trip and disconnect under voltage sag, there are also impacts on wind turbines,

line-connected synchronous machine and DC-link voltage stability.

3.2.2 Studied case

The model has not been implemented for asymmetrical cases. The simulation of asymmetrical cases

would need some further considerations (positive and negative sequences modelling) and

consequently a more complex model. Thus, symmetrical fault will be considered more carefully.

Voltage sag ride through is one of the requirements of the grid code for a wind power plant. The wind

power plant must remain connected to the grid when a voltage sag occurs that is when a fault happens

in a power line.

Figure 18: Voltage sags recorded during March-August 1999 at SSAB Oxelösund AB, Sweden

Figure 18 shows the 6 months measurements results of voltage sags at SSAB Oxelösund [10]. Most of

the voltage sags have a short duration of 100-150 ms and a magnitude of 70-90 %.


- 25 -

Thus the project essentially focuses on symmetrical voltage sags on the magnitude range of 70-90 %

and a duration of 100 ms. Furthermore, such a voltage sag can be simply simulated on the software.

3.3 Harmonics

Every integrable function and among it every periodical function sT(t) can be factorized according to

the Fourier analysis (equation (36)). The signal is then composed by a fundamental component and

several harmonic components. Each is characterized by amplitude and a frequency. The harmonics

frequencies are multiple of the fundamental frequency. A perfect sinusoidal signal contains only the

fundamental component.

20

)()()..sin()..cos()(n

nfDC

n

nn tstsstnbtnats (36)

where:

DCs is the DC component of the signal

)(ts f is the fundamental component of the signal, frequency f0 = 50 Hz

)(tsn is the harmonic of order n, frequency fn = n. f0

The presence of harmonics in a signal provokes the distortion of the signal. In this project, harmonics

are due to the switching power electronics devices and the variable speed induction machine among

others.

Among voltage and current harmonics, the later has the most important impact in the power

installations. The consequences of harmonics are significant on the distribution network since the

transformers, the cables and the overhead lines bear it. Partly because transformers must endure more

than under good conditions, they are oversized by 40% rated power to handle that. Moreover,

harmonics current provokes overheating of the transformers that is losses. That also reduces the

lifetime of the transformer. All these facts lead to non-negligible costs. Presence of harmonics in the

power system raises costs and must be limited. Some codes and regulations exist that defines the

maximum tolerable harmonic quantity. For wind power generation these limitations are defined in the

grid-code. Harmonics causes and effects are studied in [13] and [14].

3.3.1 Measurements of harmonics

Several ways exists to depict the harmonics impact and importance on a signal. The Fast Fourier

Transform (FFT) is a powerful algorithm that decomposes a signal into its different harmonic

components. The on-line frequency scanner of the PSCAD’s master library uses the FFT algorithm to

measure the amplitude and phase of a signal harmonics (till a certain order n). This tool is used in the

harmonic measurement part of the project. Also a common tool remains the individual harmonic

distortion (IHD) and the total harmonic distortion (THD) defined by equations (37) and (38). These

two quantities represent the part of harmonics contained in a periodical signal compared to its

fundamental part.


- 26 -

The current and voltage harmonic measurements are made at the output of the 0.69/33 kV transformer

that is at the output of the turbine.

T

f

T

n

n

dttsT

dttsT

IHD

0

2

0

2

)(1

)(1

(37)

T

f

n

T

n

dttsT

dttsT

THD

0

2

20

2

)(1

)(1

(38)

3.3.2 Induction machine harmonics

In a real induction machine several types of harmonics exists as space and time harmonics. Times

harmonics are mainly due to the presence of harmonics in the supplying source, but can also be a

consequence of space harmonics. Space harmonics are due to the winding distribution in the stator. In

reality it is not perfectly sinusoidal. The slots in the stator may also influence the magnetomotive force

(mmf). Mostly when studying an induction machine, these harmonics are neglected since the mmf is

supposed to be perfectly sinusoidal.

3.3.3 Power electronics harmonics

A PWM signal is defined by its amplitude and frequency modulation ratio that are respectively:

triangle

control

a

V

Vm

^

^

(39)

1f

fm s

f (40)

where:

controlV^

is the peak amplitude of the control signal that oscillates at the frequency of the line 50 Hz.

triangleV^

is the peak value of the triangle signal which has a high frequency (2.5 kHz for the grid-side

converter).

From [15], the harmonics in the inverter output voltage waveform are centred on the switching

frequency fs and its multiples. The harmonic orders are: kmin f (i and k integers). The

harmonics only exist when i is even and k is odd, or vice versa. The amplitude of the harmonic

depends on the amplitude modulation ratio ma and an example is shown in the following table.


- 27 -

Table 5: Harmonics in the voltage for a large mf [15]

order n fn (Hz) Amplitude for ma=0.6

1 50 0.6

fm 2500 1.006

2fm 2400/2600 0.131

4fm 2300/2700

12 fm 4950/5050 0.37

32 fm 4850/5150 0.071

52 fm 4750/5250

…

fm3 7500 0.083

23 fm 7400/7600 0.203

43 fm 7300/7700 0.047

…

14 fm 9950/10050 0.008

34 fm 9850/10150 0.132

…

As seen previously, a PWM filter is installed behind the inverter to comply with the grid code. This

powerful filter removes the harmonics of high order (Appendix 3).

3.3.4 Transformer harmonics

The magnetic material that composes the transformer is almost linear when operating under low value

of magnetic field intensity H. Nevertheless, when working in the saturation zone of the material, i.e.

under high H, the transformer is not linear and it induces harmonics.


- 28 -

4 Modelling and implementation in PSCAD

4.1 Wind turbine

4.1.1 Wind source

VwES

Wind SourceMean

Figure 19: PSCAD wind source component

This component simulates the wind speed available for the turbine. It can be a simple constant wind

speed source. It allows the simulation of gusts, ramp and noise in the wind speed.

4.1.2 Wind turbine

Figure 20: PSCAD wind turbine component

This model simulates a wind turbine when entering the wind speed and the mechanical speed of the

electrical generator connected to it. The angle beta is the angle of the pitch that can be controlled by a

governor (see section 4.1.3 and simulation B in the appendices).

The parameters defining the model are:

-The machine rated power: 2.7 MVA

-The machine rated speed: 162.42 rad/s

-The rotor radius: 46.5 m

-The rotor blade area: 6800 m2

-The air density: 1.225 kg/m3

-The gearbox ratio and its efficiency 97 %

Finally, the user chooses a mode “MOD2” that corresponds to a horizontal axis turbine with 3 blades.

The wind turbine component gives the torque and the power produced.


- 29 -

4.1.3 Governor

Wind TurbineGovernor

Beta

PgMOD 2 Type

Figure 21: PSCAD wind governor – pitch control component

The governor needs the mechanical power produced by the generator “Pg” in order to compute the

pitch angle “Beta”. The dynamic pitch control means that the blades can turn around their longitudinal

axis. A power reference of the regulation system is given and according to that reference, the system

turns the blades in order to regulate the output power.

4.2 Induction generator

Squirrel cage induction generator is a good solution in the field of wind power generation since it

appears to be robust, cheap compared with other solution and it needs less maintenance.

The model used first in PSCAD is shown on the following figure. It can be either speed or torque

controlled. The starting of the machine is made with speed control and then a control signal permit to

switch to the torque control mode. When the machine is torque controlled, the speed is calculated

based on the machine inertia, the damping factor among others.

A

C

I MB

W

S

T

Figure 22: PSCAD induction machine

The motor has a nominal power of 2.7 MVA. In the reality the stator windings are Delta-connected,

but in PSCAD the IM model is Y-connected.

Delta Connection:

kVU

kAI

LL

LL

75.0

07.2

Y Connection:

kVU

kAI

LL

LL

75.03

195.1


- 30 -

Figure 23: Delta and Star Connexion

The typical data generation model in PSCAD defines the machine thanks to the nominal voltage,

power and current. The others parameters are calculated by the software. However, to create the vector

control of the machine, these parameters are needed. In consequence, the parameters of the machines

are determined thanks to the rotor-locked and the no-load tests simulated in PSCAD (see Appendix 4).

4.3 Voltage source converter

The full-power converter used in the turbine is constituted by a parallel connection of six IGBT-

modules: three for the generator-side converter (fs = 1250 Hz) and three for the grid-side inverter (fs =

2500 Hz). It is manufactured by Alstom and represents an essential part of the turbine since it allows

the main control of the wind farm that is the reactive power control [6].

4.3.1 One module

One module of the VSC is constituted by a diode and an IGBT (Figure 24). The latter is commanded

by the PWM signal. This PWM signal is calculated by the controllers defined in the Chapter 2.

2

I I

Figure 24: PSCAD module of the VSC composed by a diode and an IGBT in parallel

The configuration of the IGBT and diode is studied in order to get a model matching with the reality.

The main parameters are the on-resistance, the off-resistance and the forward voltage drop. All these

parameters will affect the converter losses. Indeed the losses in the power electronics switch

corresponds to (the off- losses are neglected):

conductionswitchingswitchlosses PPP _ (41)

2

0_ )( rmsONaverageOFFONsswitchlosses IRIVEEfP (42)


- 31 -

tcondcondrms

tcondcondaverage

dttIT

I

dttIT

I

)(1

)(1

2

(43)

where:

switchlossesP _ are the total losses in the devices [W]

switchingP are the losses due to switching [W]

conductionP are the conduction losses [W]

ONE is the turn-on switching energy [J]

OFFE is the turn-off switching energy [J]

0V is the forward voltage drop [V]

ONR is the conduction resistance [Ω]

sf is the switching frequency [Hz]

4.3.2 The PWM inverter filter

In order to satisfy the grid code and to decrease the harmonics caused by the PWM inverter (2,5 kHz),

a PWM filter is installed between the 0.69/33 kV transformer and the inverter.

Figure 25: PWM filter installed at the output of the grid-side converter

There are several ways to construct such a filter. However one easy way is to use a RL series filter.

The model used comes from [8] and it is represented on Figure 25. A frequency analysis of this filter

is made in the Appendix 3 and shows the efficiency of the RL series filter.

Nevertheless a RL filter is a simple filter and does not represent the most powerful filter. In [4] a more

complex and powerful filter is developed that could be adapted to the wind turbine model in an

eventual future work.

4.4 Control system

The control system in PSCAD could be implemented in two different ways: by writing a FORTRAN

code which describes the systems thanks to equations or by using the graphical interface and the

library pre-defined functions. The second has been chosen for a question of simplicity and rapidity as

well as for a friendly use of the software (the author was not familiar with the FORTRAN language).


- 32 -

Coding the whole system in FORTRAN may have led to a more accurate and quicker model but

would also consist of a heavy code.

4.4.1 Grid side control

Figure 26 shows the grid-side system. A DC-current source is connected in parallel to the DC-

capacitor and to the grid-side converter, which is connected to the PWM filter.

2

I

PWM1 PWM2 PWM3

PWM1inv PWM2inv PWM3inv

Uab_conv

I

Po

we

r

AB

PQ

0.007406[ohm]

2.3574e-4 [H] V

A

A

B

C

SYSTEM

2

I I

I2

I

2

I

2

I

2

I

I

II

VA

Vdcc

15

60

7 [u

F]

V

A

Grid-Side

Converter

PWM filter : R and LCurrent source + DC-link Capacitor

measurements

NODE A

Q

Figure 26: Grid-Side Converter System

The grid-side converter is controlled as described in Section 2.3. A switch has been installed which

allows the choice between constant reactive power, power factor control, and constant power factor

control. Depending on the chosen control, the d-axis reference current is computed and input to the

control system (see Subsection 2.3.4). Appendix 1 contains the PSCAD schemes of the control system

and Figure A 1 in SIMULATION A shows the PSCAD scheme that allows the different control

modes.

4.4.2 Generator side converter

As explained in Section 4.2 the IM data generation is made by PSCAD. Some of the parameters of the

IM are calculated thanks to the results of several tests (see section 2.4.2 and Appendix 4).

Nevertheless, the inertia J and the damping constant b of the IM remain unknown. These two

parameters are the key for the speed loop controller since they allow computing the PI controller time

constant and gain. That fact made the implementation of the speed loop control complicated and long.

Moreover the bandwidth must be chosen with care in order not to reach high peak currents whe a

speed change occurs (see Subsection 2.4.5). Thanks to perseverance and some simulation tests, the PI

controller is finally tuned correctly.


- 33 -

Figure 27 shows the IM connected to the generator-side controller and to a DC-voltage source that was

used to tune the control of the generator-side converter. The control scheme appears in Appendix 2.

Figure 28 shows the wind turbine which blade pitch is controlled by the wind governor, and the wind

source that input the wind speed to the turbine. The mechanical torque produced by the turbine is input

to the IM. This one obviously operates with the torque control mode (see Section 4.2).

TIME

Rated speed

in pu

Vdcc

StoT

R=

0

Switch to Torque

input at 0.1 Second

V

A1

I M

W

S

TABB Gene

TS

1.034

V

A

measuremen...

2

I

Uab_gene

I

A

B

C

I

I2

I

2

I

2

I

2

I

I

I I

2

I

PWM1_rec

PWM1inv_rec

PWM2_rec

PWM2inv_rec

PWM3_rec

PWM3inv_rec

Generator-Side Converter + DC voltage

source

Figure 27: Generator-side system – IM and converter

MinD

E

TS

A

B

Ctrl

Ctrl = 1

999.0

Sample & Hold Tm

when switched from

constant Speed to

constant Torque

StoT *-1

VwES

Wind Source

GustMean

Ramp

TmVw

Beta

W P

Wind TurbineMOD 2 Type

Wind TurbineGovernor

Beta

PgMOD 2 Type

Es

Wg

*100

N

D

N/D

2.0pole pairs

Main ...

30

0

Es

5

GR

Vw

Cut-in/out

speed

limits

3.07

TIME

A

B

Ctrl

Ctrl = 0

CNT

Pi *

Pg

1.034

A

B

Ctrl

Ctrl = 1

CNT

*-1

Initial Pitch angle and the Power

reference (demand) are inputs to

this module.

For this example :

w=13.5 m/s

Initial pitch angle =3.07 deg

Power demand = 2.3 MWSignal CNT enables the

pitch angle dynamics at t=1s

A 4 Pole Machine

Mechanical speed =

W(pu)*2*pi*f/(pole

paris)

GR - Gear Ratio

Es - External signal for wind

speed

Main ...

400

0

GR

100

When w>13.5 m/s, for a demand of

Power demand = 2.3 MW

Then, the blades has to pitch in

order to produce a maximum of 2.3

MW

P_demand

Main ...

2.3

0

P_demand

2.3

MW

1.0P_init

Figure 28: Generator-side system – Wind source and pitch control


- 34 -

4.4.3 Pitch control in PSCAD

The wind turbine governor component regulates the pitch angle β of the blades. The governor

compares the power reference that corresponds to the power that we want to output from the turbine

and the current power output of the induction generator. Then, according to certain characteristic

defined on the FORTRAN code, the pitch angle is calculated to produce the desired power.

4.5 DC-link chopper

In parallel to the DC-link capacitor, a chopper resistance is installed. It permits to waste the excess of

energy produced during fault in order to comply with the current limits of the different components of

the system. During voltage sags for example, the current transmitted becomes higher, which can cause

the damage of some components if it is not limited. Thanks to the DC-chopper, there will be less

abrupt changes in the power output from the induction generator. Another solution would be to reduce

the induction generator output power thanks to a control. However it depends on how the IM responds

to a sudden voltage variation. The DC chopper appears to be a robust and reliable solution that is easy

to implement both in the software model and the reality. It remains one of the most common

contemporary solutions.

In our project, the VSCs (voltage source converters) are water cooled and not so compact. The IGBT

can approximately handle currents up to 1.5 or even 2 pu during a short time of a few hundred

milliseconds. For the same duration, diodes handle currents up to 7 pu [8].

It is chosen that the breaker in series with the chopper resistance closes when the DC-link voltage

exceed 1.08 pu. However this maximum value must be inferior to the voltage ripple across the

capacitor. Thus, the ripple in the DC-link voltage was first measured: UDC varies between +/- 1.94 %

of its reference value. To ensure safe operation of the turbine, the control of the breaker is separated

from the main control of the turbine.


- 35 -

5 Simulation in PSCAD and analysis of results

5.1 Simulation on PSCAD – Introduction

One of the biggest issues in the simulation of such a project is the runtime settings that play a decisive

role in the results computed by the software. The runtime, the solution time step and also the channel

plot step are parameters that must be chosen with care in order to obtain coherent and correct results.

With the introduction of very fast switching power electronics components (2500 and 1250 Hz), the

solution time step should be at the most 1 μs [8]; unless the calculations will accumulate errors that

lead to incorrect and illogical results.

However, it appears that a solution time step of 1 μs conducts to false computations of the model. It

induces a very high amount of losses in the system. The switching frequency of the PWM inverter

(2500 Hz) corresponds to a 400 μs period, thus the solution time step must be very short. Furthermore,

all the calculations induced by the control system increase the total amount of errors. In fact, the

control system uses block components defined in the master library of PSCAD and the whole

connected system is then encoded in FORTRAN language to make the calculations. The control

system being complex and weighty brings error accumulation in the system that provokes a huge

amount of losses. An example of some aberration that can happen when the time step is not adapted is

quoted in Table 6.

Table 6: Example of the aberration caused by a wrong solution time step

Solution time step (μs) Losses in the converter (%)

10 120

1 45

0.1 18

0.05 9

Then the problem raised by having a very short solution time step is that the sample density and the

storage needs become very high. This can provoke instability when solving the system. Moreover, the

simulation time increases when decreasing the solution time step especially for a so complex system.

The simulation can be very long depending on which runtime parameters are chosen.

Concerning the channel plot step, an inappropriate one may also be the cause of some errors in the

practical results. Indeed, if it is not short enough, the observed curves may be distorted. The channel

plot step must remain consistent especially with the different frequencies of the system.

5.2 Reactive Power Control and Voltage Control Modes

From now on, only two control modes are considered and tested: reactive power and voltage control.

Indeed, the power factor control mode uses the same principle as the reactive power control mode.

Furthermore, it gives the same results since unity power factor at Bunkeflo corresponds to zero

reactive power at the same node.


- 36 -

It is chosen that the voltage level of the grid-side converter is regulated compared to the offshore

substation voltage level. The offshore substation connects every wind turbines through five feeders.

The simulations using the voltage control mode and the reactive power control mode give

coherent results. These are detailed and compared in SIMULATION C in the appendices. The

simulation tests the turbine both during normal condition and when a voltage sag (50%

remaining voltage during 500 ms) occurs.

5.3 Results for one turbine – Compliance with IEC 61400-21

5.3.1 Voltage sags study

Reference [12] specifies the conditions under which the turbine must be tested for a voltage sag event

as well as the measurement settings. The test is made for a non-connected turbine and it checks the

wind turbine response to voltage sags. Four different tests are made on the turbine, that are 50%

symmetrical three-phase and two-phase voltage sags with a duration of 500 ms and 20% symmetrical

three-phase and two-phase voltage sags with a duration of 200 ms (see Figure 30). The simulation of

the voltage drop is made according to [12] that is according to Figure 29.

Figure 29: System for testing wind turbine under voltage sag

These four tests are made on the new model with the voltage control mode or the reactive power

control mode active. Moreover, the former model (current source + transformer) is also tested. This

leads to some comparative analysis between the two modes of control and the former model of turbine

that is not equipped with control.

The new model with power factor control is not tested since it is quite the same principle of control as

for the reactive power control. Indeed, instead of measuring the reactive power to deduce the Id current

necessary to compensate it, the power factor is measured and then the Id current is deduced

(Subsection 2.3.4).


- 37 -

Symmetrical three-phase fault Asymmetrical two-phase fault

50 %

remaining

voltage

Main : Graphs

0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 1.300 ...

...

...

-30

-20

-10

0

10

20

30

y

Ea

Main : Graphs

0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 1.300 ...

...

...

-30

-20

-10

0

10

20

30

y

Ea

20 %

remaining

voltage

Main : Graphs

0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 1.300 ...

...

...

-30

-20

-10

0

10

20

30

y

Ea

Main : Graphs

0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 1.300 ...

...

...

-30

-20

-10

0

10

20

30

y

Ea

Figure 30: Type of fault applied to the voltage at node A

In each case, the turbine rides through the voltage sag. However, the consequences of the fault are

more or less significants depending on the voltage sag type. With the reactive power control active, the

reactive power is adjusted to zero at node A (Figure 29) whereas it is not when the voltage control

mode is active.

Symmetrical voltage sag with 20% remaining voltage represents the worst case. Some severe changes

and peaks in the DC-link voltage, the speed of the IM and the output voltage and current of the

turbines occur right after the fault is cleared. The limits for current and voltage defined by the hard

limiters and the chopper are reached. The chopper operates almost during the entire sag.

For voltage sags with 50% remaining voltage, either two- or three-phase fault, the amplitude of the

DC-link voltage does not exceed 1.05 pu. For voltage sags with 20% remaining voltage, either two- or

three-phase fault, the amplitude of the DC-link voltage does not exceed 1.1 pu (see Figure 31).The

chopper resistance is only used when the sag is more severe that is 20% remaining voltage in this case.

Concerning the negative overflow, it can reach some high values especially in the case of the 20%

three-phase voltage sag.

Also the voltage control implies an important variation of the reactive power right after the voltage sag

due to the brutal change in the voltage. Because of that, it will be essential to verify if the grid owner

will accept this transfer of reactive power when the turbine is connected to the grid. However since it

is a large and short variation (about 100 ms) that should not be a problem.

During two-phase voltage sag the turbine rides through. Though an amplified oscillating phenomenon

appears. The reactive power oscillates with large amplitude during the sag. Consequently, the Id

current shows also some oscillations during the sag. This phenomenon is due to the fact that the fault


- 38 -

is not symmetrical. As explained previously in Section 3.2.2, it is also important to remind that the

control system has not been designed for asymmetrical cases.

Figure 31: Maximum and minimum peak values reached by the DC-link voltage UDC at the

beginning and right after the voltage sag

In general it is seen that the impact of the voltage sag is more important when the voltage control

mode is active than when the reactive power control mode is active. The peak values reached by the

DC-link voltage (see Figure 31) are larger with the voltage control mode. This result was expected.

The voltage regulation depends on the voltage at the node where the sag is applied. When the sag

happens, it implies an abrupt change in the rms voltage, which reflects in the regulation of the voltage.

Impact of a sag on the turbine current

two control modes - IEC connection

0

0,5

1

1,5

2

2,5

0 20 40 60 80 100 120

remaining voltage during the sag [%]

pe

ak

cu

rre

nt

at

the

ou

tpu

t

of

the

tu

rbin

e [

pu

]

reactive powercontrol

voltage control

Former model

Figure 32: Peak current caused by a three-phase voltage sag at the output of the turbine


- 39 -

The most noticeable fact from Figure 32 is that the former wind turbine model withstands a very low

variation of the current due to the voltage sag compared to the new model equipped either with voltage

or reactive power control. It was observed previously that the peak currents due to a voltage sag are

more severe in the reality than the one simulated with the former model of VPC (Vattenfall Power

Consultant) [23]. The former turbine model from VPC is composed of an ideal current source and a

transformer.

The impacts of the voltage sags are different for the two control modes of the new model. The turbine

operating with voltage control has to face higher peak current. The current peak is roughly

proportional to the voltage change, especially when the reactive power control is active. But for the

voltage control, beyond a 50% remaining voltage sag the peak currents rises. Furthermore, beyond a

certain amplitude of the voltage sag, the limits imposed by the DC-chopper and the current hard-

limiters are reached and the curves of Figure 32 become flat.

With the IEC standard connection (Figure 29) the reactive power at the node A is about zero.

Consequently the d-axis current injected by the wind turbine is also close to zero. However, it will not

be the case in the next section where the wind turbine is connected to the grid through different cables

and transformer. Thus, the d-axis current injected will be quite high and the wind turbine will output a

higher current during normal conditions (no sag). It is thus expected that the red curve in Figure 32

will be translated upward.

5.3.2 Harmonics analysis

The harmonic measurement described in the IEC 61400-21 is tedious because it is long and heavy.

Current harmonics, interharmonics and high frequency harmonics are considered. Furthermore, the

measurements are made for 11 sets of operation (active power bins). Consequently and because of the

long simulation time implied, the measurements of harmonics will not be carried out according to the

IEC 61400-21.

However, the harmonics are calculated thanks to the software Matlab that use the fast Fourier

transform (FFT). Matlab computes the discrete Fourier transform of a discrete signal output from the

PSCAD simulations. The following table shows the results obtained in the scope of the IEC61400-21

connection defined previously. The harmonics are measured in the output voltage and current of the

grid-side converter.

Table 7: Harmonic content of the grid-side converter output current and voltage

order n fn (Hz) Amplitude

Measured Ivsc (pu)

Amplitude

Measured Evsc (pu)

1 50 1 1

Harmonics due to PWM

fm 2500 0 0.01

2fm 2400/2600 0.015 0.03

4fm 2300/2700 ~ 0 0.01


- 40 -

… …. ~ 0

12 fm 4950/5050 0.02 0.06

32 fm 4850/5150 ~ 0 0.02

52 fm 4750/5250 ~ 0 0.01

… … ~ 0

fm3 7500 0 ~ 0

23 fm 7400/7600 0.006 0.03

43 fm 7300/7700 0.006 0.01

…

14 fm 9950/10050 ~ 0 0.02

34 fm 9850/10150 ~ 0 ~ 0

…

Other order

112.5 0.03 0

215 0.02 0

13 f 150 0.01 0.01

15 f 250 0.02 0.005

17 f 350 0.01 0.02

The orders of the PWM harmonics correspond to the one in Section 3.3 Table 5 and some other

harmonic orders are observed. The third, fifth and seventh harmonics especially appear in the

converter output voltage and current. However, neither the current nor the voltage contains harmonics

with an amplitude superior to 6%. Compared to the values quoted in the Table 5 the harmonics content

is very low which partly proves the efficiency of the PWM filter.

5.4 Results concerning the voltage sag study for one or several turbines

connected to the grid

Figure 33: Connection of the turbine to the grid via cables and offshore substation transformer


- 41 -

As stipulated in Section 3.2.2, the simulation test is a 75% symmetrical three-phase voltage sag during

100 ms. The wind speed is constant, equal to 13.5 m/s to get the maximum power output from the

wind turbine. Also, to observe the response of the turbine facing a larger disturbance, it was decided

that a simulation test with 25% symmetrical three-phase voltage sag during 100 ms would be studied.

The wind turbine is tested according to Figure 33 in this section.

Main : Graphs

0.900 0.950 1.000 1.050 1.100 1.150 1.200 ...

...

...

-200

-150

-100

-50

0

50

100

150

200

y

Bunkeflo Voltage

Figure 34: Voltage sag at Bunkeflo: 75%

remaining voltage during 100 ms

Main : Graphs

0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 ...

...

...

-200

-150

-100

-50

0

50

100

150

200

y

Bunkeflo Voltage

Figure 35: Voltage sag at Bunkeflo: 25%

remaining voltage during 100 ms

The simulation time of two turbines connected to the grid is almost equal to twice the simulation time

for one turbine. The turbine model is heavy and induces a lot of calculations. Many signals are

registered, plotted and then analyzed. This provokes a quite long simulation time. Moreover the time

step has to be short to obtain a plausible and more accurate response as explained in Section 5.1.

During the simulations, the time step is not so short because it could then increase the simulation time

a lot. The solution time step is 0.5 μs that induces losses in the converter (see Section 5.1). So one

turbine output about 1.2 MW of active power and output different amount of reactive power

depending on the control mode active. It output almost 2 MVAr when the reactive power control is

active, which thus means that the wind turbine runs at about 2.3 MVA.

At the end of the voltage sag, some disturbance in the Bunkeflo voltage occurs (see Figure 34 and

Figure 35). Figure 36 zooms on this phenomenon, which appears to be some kind of resonance in the

Bunkeflo voltage. The oscillations starts when the phase voltage reaches zero and disappear after 150

ms. The resonance might come from a resonant circuit formed by the capacitance (cable) and

inductance (grid) of the upstream circuit.

Main : Graphs

1.090 1.100 1.110 1.120 1.130 ...

...

...

-200

-150

-100

-50

0

50

100

150

200

y

Bunkeflo Voltage

Figure 36: Zoom on the oscillation occurring after the fault is cleared


- 42 -

5.4.1 Impact on the different voltages of the system

The two following figures show the results obtained when simulating two different voltage sags, with

two different control modes and with one, two turbines and three turbines.

Voltage Sag 100 ms 75 % remaining voltage

-15

-10

-5

0

5

10

1 2 3 4 5 6

Control Mode & Number of Turbine running

Ma

xim

a a

nd

Min

ima in U

DC

cau

sed

by

th

e v

olt

age

sa

g [

%]

Turbine 1

Turbine 2

Turbine 3

Voltage Control Reactive Pow er

Figure 37: Results for two control modes and one, two or several turbines – 75 % voltage sag

Voltage Sag 100 ms 25 % remaining voltage

-20

-15

-10

-5

0

5

10

1 2 3 4 5 6

Control Mode & Number of Turbines

Maxim

a a

nd

Min

ima i

n U

DC

cau

sed

by t

he v

olt

ag

e s

ag

[%]

Turbine 1

Turbine 2

Turbine 3

Figure 38: Results for two control modes and one, two or several turbines – 25 % voltage sag

The same conclusion as in Section 5.3 cannot be drawn by analyzing Figure 37 and Figure 38. The

impact on the DC-link voltage appears to be larger in the case when the reactive power control mode

is active. In this case, the turbine is connected to the grid (Figure 33) and partly compensates the

amount of reactive power at Bunkeflo. This generates larger currents and can explain a larger impact


- 43 -

on the whole turbine electrical system than in the case of the IEC connection where quite no reactive

power is transferred from the turbine (see Figure 42).

The general tendency consists in a decrease of the peaks in the DC-link voltage when more turbines

are operating. The voltage sag effect is damped when more turbines are running. One can expect that a

whole feeder of nine turbines could handle the same voltage sag more easily.

The following figures (Figure 39 to Figure 41) show the rms voltages in per unit at different nodes in

the system, namely at the PCC (Bunkeflo), at the offshore substation and at the wind turbine output

(output of the turbine transformer) for two control modes when a 100 ms voltage sag with 25%

remaining voltage occurs.

As stated previously, the voltage level of the grid-side converter output (behind the wind turbine

transformer) is regulated according to the offshore substation level. The three following figures

illustrate the voltage regulation (blue curves); the regulated and reference voltages are close by 0.5%.

In the case of reactive power control, the wind turbine voltage level differs from the substation voltage

level by about 4%. The voltage control mode is therefore quite efficient according to the results

obtained during the simulation.

The number of turbine operating does not affect the voltage control at each turbine output; the turbine

voltage it differs from the offshore substation voltage by maximum 0.5 % in each case (one, two or

three turbines running). However, a small difference appears at the moment when the voltage sag

occurs. With three turbines running, a peak is observed at the time of the sag and during the voltage

sag, the voltage regulation is less fast and accurate when two or three turbines are running.

Figure 39: Voltage response at different nodes for one turbine for different control modes


- 44 -

Figure 40: Voltage response at different nodes for two turbines for different control modes

Figure 41: Voltage response at different nodes for three turbines for different control modes

For each case (one, two or three turbines running) the voltage response is the same for each turbine.

This result is expected since the control implemented in the PSCAD model is exactly the same for

every turbine.

It would be interesting to simulate one feeder containing ten wind turbines and even more in order to

observe an eventual interaction between the wind turbines when the voltage control mode is active. In

fact, the voltage control is regulated according to the reference voltage at the offshore substation that

connects the five feeders together (description in Section 1.2). This might imply an interaction

between the turbines operating with voltage control.

The following figure (Figure 42) shows the reactive power measured at Bunkeflo (PCC) for one, two

or three turbines withstanding a 100 ms 25 % remaining voltage sag. On the right figure, the voltage

control is active and on the left figure the reactive power control is active. It is observed that one

turbine output about 1.8 MVAr of reactive power at the maximum when the reactive power control is


- 45 -

active. We can guess that with a fourth wind turbine the whole reactive power at Bunkeflo would be

compensated. On the contrary, the reactive power at Bunkeflo remains high when the voltage control

is active. During the voltage sag, the reactive power at Bunkeflo drops due to the decrease of the rms

voltage.

Figure 42: Reactive power measured at Bunkeflo in the cases of one, two, and three turbines

operating and withstanding a 100 ms 25% remaining voltage

Figure 43 shows the generator electrical speed for one wind turbine with two control modes

withstanding a 100 ms 25 % remaining voltage sag. The speed variation due to the voltage sag is at the

most 0.5%. Also when the reactive power control is active, the speed suffers the impact of the voltage

sag faster than when the voltage is controlled. Moreover the peaks values of the speed right after the

voltage sag are higher with the reactive power control. The impact is more important on the speed

when the reactive power is controlled.

Figure 43: IM electrical speed for two control modes


- 46 -

The same comments can be formulated for the rotor flux shown in Figure 44 and Figure 45. The later

shows the rotor flux angle that varies between -π and π. The influence of the sag is not obvious on this

figure but it is in the left side figure. It represents the dq-axis rotor flux. The q-axis rotor flux is zero

since the field oriented reference frame is used (see Section 2.4). The d-axis withstands the voltage sag

quite well. Its oscillations amplitude decreases but some noise appears in it. After the voltage sag, the

oscillations show greater amplitude, that are then damped with the time.

Figure 44: dq-axis flux angle for two control

modes

Figure 45: rotor flux angle for two control

mode

The impact of the voltage sag on the induction machine is thus of no consequences. The effects are far

from large and are damped quite immediately. The induction machine is protected by the VSCs

control system.

5.4.2 Impact on the wind turbine current

Figure 46 shows the results expected in Section 5.3.1.

The former wind turbine model from VPC (current source + transformer) is not realistic; there

is quite no impact of the voltage sag on the turbine output current.

Since the reactive power at Bunkeflo is high due to the cables in particular, the wind turbine

injects quite a high amount of reactive power to the grid in order to compensate it (about 1.8

MVAr). It means that the d-axis current injected is high. Thus the wind turbine operates with

larger currents than when the voltage control mode is active. The wind turbine output almost 1

pu during normal conditions (no voltage sag) when the reactive power is controlled although it

output 0.6 pu when the voltage is controlled (See Figure 46).


- 47 -

Therefore the impact of a voltage sag on the turbine output current is less significant when the

voltage control mode is active

The overcurrents increase with the amplitude of the voltage sag for the new wind turbine

model.

Beyond certain remaining amplitude of the sag, the overcurrents keep the same value (for the

red curve): the limits imposed by the currents hard limiters that are the maximum allowed

values are reached.

The maximum overcurrents are about 2 pu that is acceptable during a few hundred ms as

stated in 4.5

Impact of a voltage sag on the turbine current for two

control modes

Connection to the grid

0

0,5

1

1,5

2

2,5

0 20 40 60 80 100 120

remaining voltage during the voltage sag [%]

pe

ak

cu

rre

nt

at

the

ou

tpu

t o

f

the

tu

rbin

e [

pu

] voltage control

former model

Reactive power control

Figure 46: Peak current caused by a three-phase voltage sag at the output of the turbine

5.5 Results concerning the harmonics study for one or several turbines connected

to the grid

The Matlab program (in Appendix 5) gives the following results concerning the harmonics content of

the current measured at the offshore substation. The computation of the FFT in Matlab is made on a

finite interval and that can might affect the accuracy of the results.


- 48 -

Table 8: Amplitude of harmonics in the offshore substation current for one, two or three

turbines operating

order n fn (Hz) Amplitude (pu)

1 turbine

Amplitude (pu)

2 turbines

Amplitude (pu)

3 turbines

1 50 1 1 1

Harmonics

due to PWM

fm 2500 ~ 0 ~ 0 0

2fm 2400/2600 0.02 0.02 ~ 0

4fm 2300/2700 0.01 ~ 0.005 0

… ….

12 fm 4950/5050 0.04 0.05 0.04

32 fm 4850/5150 ~ 0 ~ 0 0

52 fm 4750/5250 0.005 ~ 0.005 0

… …

fm3 7500 ~ 0 ~ 0 0

23 fm 7400/7600 0.02 0.03 ~ 0

43 fm 7300/7700 0.01 0.02 0

…

14 fm 9950/10050 0.015 ~ 0 0

34 fm 9850/10150 ~ 0 ~ 0 0

Other order 112.5 0.03 0.03 0.01

215 0.03 0.03 0.03

15 f 250 0.02 0.01 ~ 0.008

17 f 350 0.01 ~ 0.005 ~ 0.005

Harmonic Analysis of the turbine output current

0

0,01

0,02

0,03

0,04

0,05

0,06

112.

525

0

2500

2300

/270

0

4850

/515

0

7500

7300

/770

0

9850

/101

50

frequency [Hz]

Am

plit

ud

e o

f th

e h

arm

onic

[pu]

1 turbine

2 turbines

3 turbines

Figure 47: Amplitude of harmonics in the offshore substation current for one, two or three

turbines operating


- 49 -

Table 9: Amplitude of harmonics in the offshore substation voltage for one, two or three

turbines operating

order n fn (Hz) Amplitude (pu)

1 turbine

Amplitude (pu)

2 turbines

Amplitude (pu)

3 turbines

1 50 1

Harmonics

due to PWM

fm 2500 0 0 0

2fm 2400/2600 ~ 0 ~ 0 ~ 0

4fm 2300/2700 ~ 0 ~ 0 ~ 0

… ….

12 fm 4950/5050 ~ 0 0.01 0.03

32 fm 4850/5150 ~ 0 ~ 0 ~ 0

52 fm 4750/5250 ~ 0 ~ 0 ~ 0

… …

fm3 7500 0 0 0

23 fm 7400/7600 ~ 0 0.01 0.015

43 fm 7300/7700 ~ 0 ~ 0.005 ~ 0

…

14 fm 9950/10050 ~ 0 ~ 0 ~ 0

34 fm 9850/10150 ~ 0 ~ 0 ~ 0

…

Other order 112.5 - - 0.03

215 - - 0.01

15 f 250 - - 0.01

17 f 350 - - ~ 0

The harmonics content for current and voltage is the same as in the previous section (Section 5.3.2 in

Table 7). With one two or three turbines, the harmonics content changes. Either some harmonics are

cancelled or reduced; some others do not change and some increases. With several turbines operating,

the harmonics can be added to each other or cancel each other. This clearly appears on Figure 47.

5.6 Comparative analysis between two control modes

From the previous results in Section 5.3, 5.4, and 5.5 some conclusions comparing the two control

modes studied can already be done.

Table 10 summarizes the results obtained from the simulations of the new wind turbine model. It

concerns the characteristics of each control mode and the short power quality analysis (response to a

voltage sag and harmonics study).

From the electrical network point of view the reactive power control mode is more advantageous

because it allows fulfilling the requirement of zero reactive power at Bunkeflo. This is also wanted by


- 50 -

the wind farm owner, that has to meet the requirement. However, it induces higher currents which also

means that the wind turbine run at higher apparent power. So the wind turbine is fully used unlike with

the voltage control mode. The high overcurrents are a drawback for the turbine manufacturer that must

invest in adapted equipment. Therefore, for the turbine manufacturer the voltage control is profitable.

Moreover, the voltage is maintained stable at the turbines output. One other advantage is that the

impact of voltage sags on the internal DC-link voltage is less important with the voltage control mode

(for voltage sag with remaining amplitude superior to 30% of the initial voltage).

The harmonics content of currents and voltage does not depends on the control mode and we know

that the requirements concerning the harmonic distortion are fulfilled at Lillgrund.

Table 10: Comparative analysis between reactive power and voltage control

Reactive power

control Voltage control

Constant and stable value for the voltage

even during events - +

Reactive power compensation + -

Impact of a sag on the turbine output

current

+ -

Impact of a sag on the DC-link voltage

Depends on the type of

fault

Depends on the type of

fault

Harmonics = =

In Table 10, + corresponds to positive and – to negative points.

5.7 Comparison with the Siemens’ study

This section compares the results obtained by Siemens and summarized in [6] with the one obtained

during the simulations of the new model. The results might differ because of different causes:

The control system is built with no hint from Siemens, the control system supplier.

The simulation on a software always induces errors, e.g. the losses explained in Section 5.1.

We are not sure that the measurements are carried out in the same way.

5.7.1 Harmonics study

Table 11 compares the harmonics results obtained in this study and the results from Siemens study. A

quite important difference is observed that could mainly comes from the two following facts.


- 51 -

For one turbine, the harmonic content of the current mainly depends on the PWM filter

installed at the output of the inverter. Siemens stipulates that the IHD (individual harmonic

distortion) of the current varies within the range indicated in Table 11 depending on the filter

concept. The filter adopted in the PSCAD model was described and justified in section 4.3.2

and Appendix 3. However, it was seen that a more adapted filter (from [4]) could be studied in

the new turbine model to improve its efficiency (Section 4.3.2).

In the case of the entire wind farm, the phenomenon of random mitigation occurs. That

induces the cancellation or the decrease of many harmonics in the current. This was shown in

the previous Section 5.5 when comparing the harmonic content of one, two or three turbines

connected to the main grid. In the Siemens study, control mitigation is implemented. By the

mean of probabilistic methods, it decreases considerably the quantity of harmonics by

cancellation. The random mitigation is more significant for many turbines. However, the

results of the random mitigation cannot be observed in the present case since the 48 wind

turbines are not simulated.

Table 11: Comparison of the THD and IHD from Siemens and from simulating the new model

THD (%) IHD (%)

Siemens PSCAD Model Siemens PSCAD Model

One

turbine Unknown THD < 3 0.125 < IHD < 0.5 IHD < 2

PCC at

Bunkeflo THD < 0.9 THD < 4.5 (3 turbines) IHD < 0.025 IHD < 2 (3 turbines)

In Table 11, the last row shows the IHD (individual harmonic distortion) and THD (total harmonic

distortion) for 48 wind turbines in the case of Siemens study but only of 3 turbines in the case of the

new model. This must be taken into consideration when reading the table.

5.7.2 Dynamic simulation study

Siemens carried out a study to check some dynamic response of the wind farm.

Siemens:

For a voltage sag defined by the TSO and occurring at the PCC, the wind turbines rides through. The

voltage sag curve is defined by Svenska Kraftnät and is shown on Figure 48. Figure 48 corresponds to

the most severe voltage sag that might happen at PCC and that is one of the requirements of the grid

code. The wind farm or wind turbine must withstand it [21].

New model simulation:

The simulation of similar voltage sag is made on PSCAD with a duration of 250 ms and no remaining

voltage. The turbine rides through this sag.


- 52 -

Figure 48: Ride-through requirement for Svenska Kraftnät grid code [21]

Siemens:

When the voltage sag occurs at the PCC, the voltage drop at the output of the wind turbine is limited

to 0.3 pu by the FRT system. Maximum reactive power is brought in to the grid.

New model simulation:

The next three tests shows that the voltage drop at the output of the wind turbine is limited to 0.15 pu

by the FRT system for the present model (see Figure 49 and Table 12). This limit is induced by the

current limits. The maximum reactive power is also brought in to the grid when the reactive power

control is active.

The voltage sags tests are 250 ms voltage sags with 75% (green curves), 25% (red curves) and 0%

(blue curves) remaining voltage (Figure 49).

Figure 49: Rms voltages at the output of the turbines and at Bunkeflo during different voltage

sag occurring at the PCC (Bunkeflo) for two control modes (reactive power on the left and

voltage on the right)


- 53 -

Table 12: Remaining voltage level at the turbine output foe three types of voltage sag

Duration of the sag [ms] 100 100 250

Remaining voltage during the voltage sag at

Bunkeflo [pu] 0.75 0.25 0

Remaining voltage during the voltage sag at the

output of the turbine [pu] 0.71 ~0.25 ~0.15

Figure 50 shows the reactive power at Bunkeflo for these three different voltage sags. When running

one turbine with reactive power control, the maximum possible reactive power is transmitted in to the

grid during normal condition (Figure 50 before the sag happens). Nevertheless, only one turbine

cannot compensate the whole reactive power induced at Bunkeflo. With voltage control there is no

reactive power compensation. However, the turbine voltage level is regulated (see Figure 50, graph on

the right).

Figure 50: Bunkeflo reactive power during different voltage sags occurring at the PCC

(Bunkeflo) for two control modes (reactive power on the left and voltage on the right)

5.8 Island Operation

It might happen in the future that wind power plant becomes disconnected from the grid but must still

supply some loads. This might only be possible if the wind park is able to operate within a certain

range of frequencies and voltage level when disconnected from the grid. Indeed, the customers

supplied by the wind power plant still need the same quality of energy. If the requirements are not

respected, the wind power plant must also disconnect from the remaining loads.

This part concerns the island operation of the wind turbine or farm. What are the consequences of the

disconnection of the turbine from the grid? How the present model of turbine handles this event? The

island operation has no time limit. However, 1 s of island operation is sufficient to draw some

conclusions. The connection of the wind turbine is the same as described in Figure 33.


- 54 -

The three following figures (Figure 48 to Figure 50) illustrate the response of the turbine when it is

disconnected from the grid at t = 1 s. Particularly, the frequency and the voltage at the offshore

substation are observed. The wind turbine could not be connected to a load to supply it energy.

The frequency decreases and varies between 0.65 and 0.8 pu with the reactive power control

mode. With the voltage control mode, it first drops and then stabilizes at a constant value of

0.88 pu which is quite good but not high enough to satisfy the TSO requirements.

The rms voltage oscillates largely (between 0.6 and 1.3 pu) with the reactive power control.

No stability is reached. With the voltage control, the voltage level reaches a stable value of

about 0.5 pu.

However the signal is not sinusoidal at all. It contains a large amount of harmonics.

The island operation does not fulfil the necessary requirements concerning the voltage quality in order

to supply a potential customer.

Figure 51: Voltage at the offshore

substation

Figure 52: rms voltage at the offshore

substation

Figure 53: Island operation at t = 1 s – Impact on the frequency


- 55 -

6 Conclusions

The master thesis work gives an overview of one possible control system for a wind turbine installed

at Lillgrund wind farm. The corresponding model has been implemented in PSCAD in order to

simulate and verify the operation of such a turbine. Reactive power control is installed at Lillgrund

wind farm and is implemented in the PSCAD model. Moreover, a voltage control has also been

implemented in the project in order to compare the results for different control modes of the turbine.

The results show that the requirements concerning the reactive power are fulfilled. That is the power

factor at the PCC at Bunkeflo is maintained at the unity or the reactive power at zero. Four turbines are

necessary to manage it that is to compensate the reactive power created by the cables in particular.

Only one turbine can produce a limited amount of reactive power because of its electrical design.

The comparison between the reactive power control and the voltage control leads to the conclusion

that the impact of voltage sags on the turbine differ a little. The peak currents reached by the turbine

bearing voltage sags are larger in the case when the turbine is reactive power controlled. This is partly

due to the fact that the reactive power control induces higher current even during normal conditions of

operation. The comparison between the two control modes is summarized in Table 10 in Section 5.6.

The new model implemented in PSCAD is closer to the reality since it includes almost all the

components and controls of the turbine. Also, the simulations give coherent results that approach the

reality. Especially, it was seen that the former turbine model (current source + transformer) does not

show large overcurrents when a voltage sag occurs although it happens in the real case. Also, the

harmonics study of the former wind turbine model is obviously not representative of the real case

since nor power electronics neither generator are implemented in the model.

The power quality study of the model shows first of all that the wind turbine rides through voltage

sags independently of its amplitude and duration. Secondly the harmonics content of the output

currents and voltages changes with the number of turbines. The main advantage is the harmonics

cancellation that results from this random mitigation.


- 56 -

7 Improvements and future works

Improvements for the model:

The data generation for the induction machine is the typical method defined on PSCAD. It is also

possible to use the explicit method, which would give an IM model close to the real machine. This

explicit method needs the knowledge of the machine parameters and also a good understanding of the

machine theory and model of PSCAD.

The model has not been equipped by some protections. A study could be carried out in order to

include protective equipment in the model.

Optimal speed control system could be implemented to increase the efficiency of the turbine (see

Section 2.4.6).

To make the model less heavy, it could be possible to encode some of the control in FORTRAN that

could decrease the simulation time and in the same time the errors.

Field weakening control could be implemented in the PSCAD model to allow the induction machine

operating at low torque. At low torque, the variable speed induction generator runs at higher speed and

the power is kept approximately constant. This is done by reducing the flux (“flux weakening”) which

is controlled by the d-axis current Isd control the flux (equation 31). A reduced flux corresponds to an

increased speed since the inverter voltage is kept constant (equation 23). However this possibility

would not increase the efficiency of the wind turbine significantly since the power from the low wind

speed is low.

Future works:

First of all, the results obtained with this new model developed by PSCAD might be compared with

some measurements. So far, no measurements allowing a potential comparison were available at

Lillgrund. However, some on-coming project might lead to the achievement of such a comparison and

a verification of the present model.

The simulation of the whole farm equipped with the new turbine model could lead to some possible

studies. However, the simulation time of this would become huge (more than a day, maybe one week).

The suggestion of using wind farm for power quality improvement might lead to a possible future

project applicable in the national grid (proposal by F. Carlsson).

The model developed in the project might also be used to simulate another wind farm. The future

project of a 23 wind turbines power plant at Hjuleberg could be simulated. However, the present

model should be simplified or reduced in order to simulate the 23 turbines. One possible simplification


- 57 -

would be to represents the part upstream the capacitor by a controllable current source. Then the

reactive power control is still possible and the size of the model is almost divided by two. Another

possibility would be to encode some of the control in FORTRAN so that the model is less heavy and

more accurate.


- 58 -

References

[1] PSCAD/EMTDC, Manitoba HVDC Research Centre, https://pscad.com/index.cfm

[2] T. Lund, J. Eek, S. Uski, A. Perdana, “Dynamic Fault Simulation of Wind Turbines

using Commercial Simulation Tools ” 5th International Workshop on Large-Scale

Integration of Wind Power and Transmission Networks for Offshore Wind Farms,

pages 238-246, Glasgow, April 2005.

[3] M. Molina, B. Naess, W. Gullvik, T. Undeland, “Control of Wind Turbine with

Induction Generators interfaced to the Grid with Power Electronics Converters”

Presented at the International Power Electronics Conference IPEC 05, Niigata, Japan.

[4] H. Xie, “Voltage Source Converter with Energy Storage Capability”. KTH,

Stockholm, Sweden. Licentiate Thesis in Power Electronics. 2006.

[5] ”Electrical Machines and Drives”. KTH Electrical Machines and Power Electronics.

Stockholm, 2008.

[6] Å. Larsson “Lillgrund Wind Power Plant – Documentation of electrical system”,

April 2008, Vattenfall Power Consultant AB.

[7] F Carlsson, U Axelsson, M. Lindgren, H. K. Nielsen ”Assignment Specification for

Simulation Studies and Measurements of Electrical Transients and Power Quality

Parameters at Lillgrund Wind Power Farm”, October 2008, Vattenfall Research and

Development AB.

[8] Private communication with D. Salomonsson, Vattenfall research and development

AB, 2008-2009.

[9] B. B. Garzon, “Power quality of wind farm – Validation of standard methods for

assessing flicker and harmonics” Technical University of Denmark DTU,

Copenhagen, Denmark. Master thesis. July 2008.

[10] F. Carlsson “On impact and Ride Through of Voltage Sags Exposing Line-Operated

AC-Machines and Metal Processes”. KTH Electrical Engineering, Stockholm,

Sweden. Doctoral Thesis. 2003.

[11] K. Pietiläinen “Voltage Sag Ride-Through of AC drives: Control and Analysis”. KTH

Electrical Engineering, Stockholm, Sweden. Doctoral Thesis. 2005.

[12] IEC 61400-21 “Wind Turbines – Part 21: Measurement and assessment of power

quality characteristics of grid connected wind turbines”

[13] F. Carlsson, A. Badano “Elektronisk last - Omvärldsanalys”, Elforsk rapport 08:51,

June 2008, Elforsk.

[14] ”Harmonics – Causes and Effects” Power Quality Application Guide,

http://www.copperinfo.co.uk/power-quality/downloads/pqug/31-causes-and-

effects.pdf

[15] N. Mohan, T M. Undeland, W P. Robbins “Power Electronics – Converters,

Applications, and Design”, third edition, John Wiley & Sons. USA. 2003.

http://www.copperinfo.co.uk/power-quality/downloads/pqug/31-causes-and-effects.pdf

http://www.copperinfo.co.uk/power-quality/downloads/pqug/31-causes-and-effects.pdf


- 59 -

[16] IEEE recommended Practice for Monitoring Electrical Power Quality, IEEE

Std.1159-1995, New-York, IEEE, 1995.

[17] Private communication with H-P. Nee, KTH Electrical Engineering, division Power

Electronics and Electrical Machines, 2008-2009.

[18] Private communication with H. Xie, KTH Electrical Engineering, division Power

Electronics and Electrical Machines, 2008-2009.

[19] M.H.J. Bollen “Voltage Sags in Three-Phase Systems”, IEEE Power Engineering

Review. Volume 21, September 2001.

[20] AVX Corporation, Kyocera group company, http://www.avx.com

[21] Ackermann, Thomas (editor) (2005). Wind Power in Power Systems. Chichester,

West Sussex: John Wiley & Sons, Ltd.

[22] R. Pena, R. Cardenas, R. Blasco, G. Asher, J. Clare, “A Cage Induction Generator

Using Back to Back PWM Converters for Variable Speed Grid Connected Wind

Energy System” the 27th

Annual Conference of the IEEE Industrial Electronics

Society, 2001.

[23] Private communication with U. Axelsson, Vattenfall Research and Development AB,

2008-2009.

[24] F. Carlsson, V. Neimane, “A massive introduction of wind power - changed market

conditions? ”, Elforsk report 08:41 June 2008.

[25] Energimyndigheten: “Nytt planeringsmål för vinkraften år 2020”. ER 2008:45, ISSN

1403-1892. 2007.

[26] “Syftet med förstudiens simuleringar”

[27] Angelo Baggini, "Handbook of Power Quality", John Wiley & Sons, 2008

[28] “ITI (CBEMA) Curves Application Note” Technical Committee 3 (TC3) of the

Information Technology Industry Council (ITI, formerly known as the Computer &

Business Equipment Manufacturers Association). http://www.itic.org/

http://www.avx.com/

http://www.itic.org/


- 60 -

Appendices

Appendix 1: Grid-side control system - PSCAD model

PWM3

PWM3inv

PWM1

PWM2

PWM1inv

PWM2inv

PWMfs

ua_ctrl

ub_ctrl

uc_ctrl

pwm1

pwm1_in

pwm2

pwm2_in

pwm3

pwm3_in

2500.0fs [Hz]

VSC_Controller

ua_ctrl ub_ctrl uc_ctrl

Vdc_mea

I_line

U_net

Vdc_ref

Q_neededctrl U_desired cosphi_needed

TIME*

1.7537

Vdcc

U_net

I_line

ctrl

Appendix 2: Generator side-control - PSCAD model I_gene

PWM1inv_rec

PWM2_rec

PWM3_rec

PWM2inv_rec

PWM3inv_rec

PWM1_rec

1250.0fs [Hz]

Rotor Flux Estimator

I_gene

V_gene

rho

Current Controller

I_gene

rho

ua_ctrl

ub_ctrl

uc_ctrl

id_ref iq_ref

Wg

Speed Controller

Wg_ref

Wg

Iq_ref

V_gene

0.918665

1.034

PWMfs

ua_ctrl

ub_ctrl

uc_ctrl

pwm1

pwm1_in

pwm2

pwm2_in

pwm3

pwm3_in


- 61 -

Appendix 3: PWM filter frequency analysis

Figure x in the report shows the PWM filter installed at the output of the grid-side converter. The

transfer function F(s) linking the current through the filter I and the voltage across it Vconv is expressed

as:

sLRsV

sIsF

conv

1

)(

)()( (43)

Written in the normalized way:

c

conv j

K

sV

sIsF

1)(

)()( (44)

The constant R

K1

represents the gain of the low pass-filter and HzL

Rf c

c 522

is the

cut-off frequency of the filter, which is the frequency, corresponding to the point at which the filter

attenuates the signal by 3dB.

Figure 54 shows the bode diagram of the filter transfer function and proves the efficiency of the filter.

The filter attenuates the frequency above 1000 Hz by more than 45dB that is the amplitude is

attenuated by more than 99 %.

Figure 54: Bode diagram of the PWM filter transfer function


- 62 -

Appendix 4: Rotor-locked test and no-load test for the induction machine (IM)

By simulating the PSCAD IM model, the induction machine parameters can be identified.

Figure 55: Equivalent circuit of the IM

The parameters of the IM shown on Figure 55are:

Rs the stator resistance

Lls the stator leakage inductance

Llr the rotor leakage inductance

Lm the magnetizing inductance

Rr’ the rotor resistance

(s is the slip)

The active power of the IM is

)cos(3 ss IUP (45)

The no-load test is simulated by setting the input value of the electrical torque equal to zero, which

signify no load torque. The slip is very close to zero, which means a very high equivalent resistance on

the rotor side. Thus, the equivalent resistance is:

s

s

lsmseqI

UXXjRZ

30 (46)

)cos(3

s

s

sI

UR (47)

)sin(3

s

s

lsmI

UXX (48)

The rotor-blocked test is imitated by inputting the nominal current but reduced voltage. The IM is

used under speed control mode with the speed equal to zero, that is the rotor does not move. The

magnetizing reactance is much bigger than the other impedance, thus it is approximated as an open

circuit. Consequently the equivalent impedance is:


- 63 -

s

s

lrlsrseqI

UXXjRRZ

3'0 (49)

)cos(3

'

s

s

rsI

URR (50)

)sin(3

s

s

lrlsI

UXX (51)

The IM parameters are deduced as follows.

0726.0

8164.0

0352.0'

0507.0

lsls

m

r

s

XX

X

R

R

(52)

Appendix 5: Matlab code used to compute the harmonics of a signal saved from PSCAD in a

data file

%----------------------------------------------------------------------

% COMPUTATION OF THE HARMONICS

% The data are loaded from PSCAD and the function FFT is used on

% matlab to compute and observ the harmonics.

%----------------------------------------------------------------------

clear all;

format long;

%----------------------------------------------------------------------

%Parameters

ts = 5e-5; % [s] channel plot step

fs = 1/ts;

t0 = 0.8; % [s] initial time

tf = 1; % [s] end time

T = [t0 : ts : tf]; % calculation period

L0 = t0/ts + 1;

LF = tf/ts + 1;

L = L0-LF;

%----------------------------------------------------------------------

%Loading the data from a data file

load channels_01.dat; % load the file containing the data of

load channels_02.dat; % PSCAD channels output

load channels_04.dat;


- 64 -

%----------------------------------------------------------------------

%Plot the curves that we want the FFT

n = 10; % column n in the data file corresponding to the current

values

X1 = channels_01 (:,n); % Vector of which the FFT will be computed

figure (1)

plot (T,X1(L0:LF))

title('Current at node A - IA')

xlabel('time s')

ylabel('amplitude kA')

%----------------------------------------------------------------------

%Calculate the FFT

NFFT = 2^nextpow2(L); % returns the first NFFT such that 2^NFFT >= abs(L)

Y1 = fft(X1(L0:LF),NFFT)/L; % calculate the FFT of the vector X1

f = fs/2*linspace(0,1,NFFT/2);

figure (4)

plot(f,2*abs(Y1(1:NFFT/2))); % plot the single sided amplitude spectrum of the signal

title('Spectrum of IA and Ivsc')

xlabel('Frequency (Hz)')

ylabel('|IA(f)|')


- 65 -

Simulations

SIMULATION A: Control mode test on the grid-side inverter connected to the grid.

SIMULATION B: Test of the Generator-Side system

SIMULATION C: Test new model with IEC-connexion

SIMULATION D: Comparison of the control modes for different amplitude of the sag


- 66 -

SIMULATION A: Control mode test on the grid-side inverter connected to the grid

Here, the voltage control and the reactive power control mode are tested on a simulation. The power

factor control mode is not tested since it is very similar to the reactive power mode. The voltage

control maintains the voltage amplitude of the inverter output at the offshore sub-station level. The

reactive power is controlled to be zero at Bunkeflo.

The turbine operate at 2,25 MW power and the reactive power depends on the control modes but the

maximum amount that can be produced or consumed is 0,5 MVAr (S=2,3 MVA).

The table above describes the different stages of a simulation made on the grid side converter system

connected to the grid via the two transformers and two different cables.

Time period (s) Main control

signal Control mode Control place Event

Phase 1 0 - 0.5 4 No control Substation -

Phase 2 0.5 – 1 1 Reactive

power Bunkeflo -

Phase 3 1 – 1.5 3 Voltage Substation -

Phase 4 1.5 – 1.6 3 Voltage Substation Voltage sag

in the grid

Table A 1: Description of the Simulations Stages

A control interface of PSCAD is used to make the choice of the control mode. The value of the control

can change during the simulation (see Figure A 1).

Choice of Control

Control

Choice of The COntrol Mode :

1 Reactive POwer

2 Power Factor

3 Voltage

4 Default Mode (no Id injected)

Measurement needed :

Reactive Power at Bunkeflo

Power Factor at Bunkeflo

Voltage at the offshore substation

(low voltage)

E_offsub_rms

Qbunk

ctrl_choice

phibunk

Pbunk

ctrl_choice

*0.8165

Main : Controls

4

3

2

1

Choice Control Mode

4

Figure A 1: Control Implementation in the Model – Possibility to Switch during the Simulation


- 67 -

The voltage sag that occurs at 1,5 s at Bunkeflo has duration of 100 ms and the remaining voltage is

75% of the normal voltage (Figure A 2).

Main : Graphs

1.400 1.450 1.500 1.550 1.600 1.650 1.700 ...

...

...

-200

-150

-100

-50

0

50

100

150

200

y

Bunkeflo Voltage

Figure A 2: Voltage sag in Bunkeflo: 75 % remaining voltage, duration = 200 ms

First no control is active. By default, it means that no d-axis current is injected. That also means that

the reactive power injected by the turbine is zero.

At the second stage, the control is switched on reactive power control mode. The device is supposed to

supply a certain amount of reactive power, which will partly compensate the reactive power at

Bunkeflo. The objective is that the whole wind farm compensate the reactive power at Bunkeflo in

order to get no reactive power at that node. Indeed, it is required to have a unity power factor at

Bunkeflo that is no reactive power. However, it is not possible with only one turbine. So a d-axis

current is estimated and then injected to remedy the reactive power; the maximum possible reactive

power is injected by the turbine (Q = 0,5 MVAr). It is seen on Figure A 3 that 0,6 kA are supplied

during this second step. However, it only allows to decrease the reactive power at Bunkeflo by 0,5

MVAr (Figure A 4). Only one device cannot handle the whole compensation of the Bunkeflo reactive

power.

VSC_Controller : Graphs

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...

...

...

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

y

Iq_net Id_net Iq_ref Id_ref

Figure A 3: dq-axis current at the converter output¨


- 68 -

Main : Graphs

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 ...

...

...

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

y

Bunkeflo reactive pow er

Main : Graphs

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...

...

...

-0.70

-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

y

turbine reactive pow er

Figure A 4: Bunkeflo and turbine output reactive power

During the two last stages, the voltage control mode is active. As it is seen on the Figure A 5, the

voltage amplitude is maintained to the desired level, which is the amplitude of the substation voltage

(readjusted to the 0,69 kV base voltage on this side of the transformer). It is especially well shown

during the voltage sag event.


0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...

...

...

0.20

0.40

0.60

0.80

1.00

1.20

1.40

y

Amplitude output converter voltage Amplitude desired

Figure A 5: Converter output voltage amplitude and the desired amplitude for voltage control

During the whole simulation the DC-link voltage is regulated at the required level and reasonably

constant value, even during the voltage sag (Figure A 6). This allows good operation of the turbine.

Main : Graphs

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...

...

...

1.660

1.680

1.700

1.720

1.740

1.760

1.780

1.800

y (

kV

)

Vdcc

Figure A 6: DC-link voltage UDC


- 69 -

Main : Graphs

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...

...

...

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

y

Ia_conv

Figure A 7: Output current of the converter

Main : Graphs

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 ...

...

...

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

y

Ua_conv

Figure A 8: Ouput voltage of the converter

Figure A 7 and Figure A 8 show the current and voltage at the output of the converter. The voltage is

observed and the current variation commented previously can also be seen.

Main : Graphs

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...

...

...

0.750

0.800

0.850

0.900

0.950

1.000

1.050

y

Turbine Voltage [pu] Offshore Substation Voltage [pu]

Figure A 9: Amplitude if the voltage in per unit at the output of the converter and at the

offshore substation

Figure A 9 shows the amplitude of the voltages at the offshore substation and at the output of the

converter. From t = 1 s, the voltage control mode is activated and the two voltage amplitudes

corresponds. In the contrary during the two first stages, the two voltage amplitudes are different by 5

and 4 % respectively.

Main : Graphs

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...

...

...

-0.150

-0.100

-0.050

0.000

0.050

0.100

0.150

y

I offshore substation

Figure A 10: Current at the offshore substation


- 70 -

During the stage 2, some d-axis current is injected to compensate the reactive power at Bunkeflo.

Consequently, there is an increase of the current amplitude as seen in Figure A 10. Also, during the

voltage sag the amplitude of the current increases due to two reasons. First, during the sag, the voltage

decreases; some q-axis current is injected to maintain the power balance. Secondly, some d-axis

current is injected to maintain the voltage level of the converter output.

Conclusion:

The simulation was carried out with a time step of 0,5 us. This time step is a good compromise since

then the simulation last only a few minutes and the losses induced by the calculation are not so

important (12 %).

The dq-axis currents are limited by a hard limiter that keeps them within a certain range of value (+/- 2

pu). Indeed, the material must be protected from overcurrents.

The reactive power at the PCC (point of common coupling, Bunkeflo) is high (7.5 MVar) because of

the cables. When using the reactive power control mode, the d-axis current Id that would theoretically

compensate this reactive power at Bunkeflo is unfeasible, so compensation is not achievable with one

turbine. However, the hard limiter limits the current. Because of that, the reactive power at Bunkeflo is

only partially compensated. To compensate the reactive power induced by the source and cables, at

least 15 wind turbines are necessary (with this set of operation).

If we assume that there is no limits for the currents, then the d-axis current Id would reach a high value

in order to compensate the reactive power. Nevertheless, it would imply a decrease of the active power

transmitted from the converter as it is shown on Figure A 11 and equation (14).

Figure A 11: Park representation of the voltages and current at the converter output

One possibility is to set the different controls at different nodes. For example, the voltage can be

regulated to follow any voltage of the system. For example the reference voltage could be the voltage

at the output of the 0.69/33 kV transformer.

For the farm or for a radian, we can expect some interactions between the turbines if the voltage

controller reference is the offshore substation voltage. However if the voltage controller reference

were the output of each 0.69/33 kV transformers, then these would disappear.


- 71 -

SIMULATION B: Test of the generator-side system

The system is composed of the wind source, the wind turbine, the pitch governor, the IM and the

inverter. Also it includes the control system of the machine described in section 2.4. The system

PSCAD scheme consists in Figure 11 in section 2.4.1.

The test is a simulation during a runtime of 75 s with the occurrence of several events described in

Table B 1.

Table B 1: Description of the simulation stages

Time Event

Step 1 0.1 s Switch the generator from speed control to torque

control mode

Step 2 1 s Switch ON the Pitch control

Step 3 25 s 3 gusts with a period of 0.2 s and an amplitude of

2 m/s

Step 4 35 – 45 s Wind ramp during 10 s

The IM is started in speed control mode, which means that the speed reference is imposed. After the

initial transients, it operates in torque control mode and the input torque of the IM is the output torque

of the wind turbine component.

At t = 1 s, the pitch control is activated. The governor regulates the pitch angle by knowing the power

demand (set to 2.3 MW) and the generator active power. Normally it takes more than 100 s for the

pitch to reach its steady state value under good conditions (wind speed constant).

When the gusts occurs at t = 25 s, a zoom on the pitch angle shows that it is recalculated. Also, the

impact on the torque and the speed of the IM is seen on Figure B 1 and Figure B 4.

When the wind speed ramp occurs at t = 35 s, the pitch angle is regulated. As soon as the wind speed

increase, the pitch angle starts increasing. Since the power demand remains 2.3 MW, but the wind

increases, the blades must pitch to control the output power produced by the generator.

Speed_Controller : Graphs

0 20 40 60 ...

...

...

1.100

1.120

1.140

1.160

1.180

1.200

1.220

1.240

y

Wg

Figure B 1: IM mechanical speed in pu


- 72 -

Main : Graphs

0 10 20 30 40 50 60 70 80 ...

...

...

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0 y

Beta

13.50

13.75

14.00

14.25

14.50

14.75

15.00

15.25

15.50

y

w ind speed

Figure B 2: Pitch Angle of the Blades and Wind Speed

The dynamic of the mechanical system induced by the pitch control is very slow. However the

solution time step must be kept short because of the power electronics of the VSC. Thus, the

simulations time increases.

Main : Graphs

0 10 20 30 40 50 60 70 ...

...

...

1.60

1.80

2.00

2.20

2.40

2.60

2.80

y (

MW

)

P_gene P_turbine [MW]

Figure B 3: Generator Electrical Power and

Turbine Mechanical Power

Main : Graphs

0 10 20 30 40 50 60 70 ...

...

...

-1.20

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

y

Tel mechanical torque machine

Figure B 4: Electrical Torque of the Machine

and Mechanical Torque

The mechanical torque of the IM and the turbine torque are the same since the IM operates at torque

control mode. Thus, the input of the IM is the mechanical torque that corresponds to the turbine

torque.


- 73 -

SIMULATION C: Test turbine with connexion IEC

This appendix shows the results obtained for different tests made on one turbine connected according

to Figure 29 in 5.3.1 and Figure C 1 below. It details the section 5.3.1 that only gives a summary of the

whole simulation results.

At t = 1 s, the 500 ms voltage sag is applied at the output of the transformer thanks to the short-circuit

emulator (Figure C 1). The voltage supports a three-phase symmetrical voltage sag with 50%

remaining amplitude.

0.1[ohm]fV

R=0

50.0

0.5

[oh

m]

2.0

[nF

]

2.0

[nF

]

2.0

[nF

]

A

B

C

A

B

C

#2 #1

33 [kV]

0.69 [kV]

2.55 [MVA]

umec

V

A

Fault

TimedFaultLogic

Fa

ult

Fa

ult

Fa

ult

0.1

[o

hm

]

26.94U [kV]

Ek

0.1

[o

hm

]

0.1

[o

hm

]

50 % R = 0.1 ohm

20 % R = 0.4 ohm

Figure C 1: Connexion of one turbine to test it according the IEC standard

C1 - Comparison of the reactive power flowing for different cases

The four following figures show the reactive power measured at the node where the sag occurs for the

former model and the new model with different control mode active.

Main : Graphs

0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 ...

...

...

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

y

Qa

Figure C 2: Former model of the wind

turbine – No control

Main : Graphs

1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 ...

...

...

-0.250

-0.200

-0.150

-0.100

-0.050

0.000

0.050

y

Qa

Figure C 3: New Model – No control active

(no Id is injected)


- 74 -

Main : Graphs

0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 ...

...

...

-0.150

-0.100

-0.050

0.000

0.050

0.100

0.150

0.200

y

Qa

Figure C 4: New model – Reactive Power

Control Mode active

Main : Graphs

0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 ...

...

...

-1.40

-1.20

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

y

Qa

Figure C 5: New Model – Voltage Control

Mode active

The former turbine model is an ideal current source connected to the 0.69/33 kV transformer.

The reactive power is not regulated and oscillates around its average value. The sag induces a

small change in the reactive power flowing. This is due to the change in the rms voltage level

at the output of the turbine and the impedances of the circuit.

When there is no d-axis current injected, it means that the reactive power at the output of the

converter is zero (equation (14)). It also means that the reactive power at the output of the

transformer is not exactly zero (Figure C 3). During the sag, a small decrease of the reactive

power is seen.

The reactive power controller is quite efficient and regulates the reactive power to zero at the

output of the turbine. When the voltage sag occurs, it takes 150 ms for the reactive power to be

cancelled. The control is fast.

The voltage control mode is also efficient since the voltage level at the output of the grid-side

converter follows the desired voltage (defined in equation (18)). Figure C 6 shows it.


0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 ...

...

...

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

y

U_conv_module U_desired

Figure C 6: Output Voltage at the output of the converter and desired voltage

The injection of d-axis current at the output of the grid-side converter is the mean for both reactive

power and voltage control. The dq-axis currents are analysed for each mode in the following section.


- 75 -

C2- Comparison of the dq-axis current for each control mode

The three following figures illustrate the dq-axis current of the grid-side converter output before,

during and after the voltage sag.


0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...

...

...

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

y

Iq_net Iq_ref Id_net Id_ref

Figure C 7: New Model – No control active (no Id is injected)


0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 ...

...

...

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

y


Figure C 8: New model – Reactive Power

Control Mode active


0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 ...

...

...

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

y


Figure C 9: New Model – Voltage Control

Mode active

q-axis current analysis

In the case observed on Figure C 7, the reference of the d-axis current is zero, no control is active (Id =

0 constitute the default mode). During the voltage sag, the q-axis current is increased. Indeed, the

control has been designed to control the power balance between the DC- and AC- side of the

controller. During the voltage sag, the voltage decreases by 25 % in this case. Thus, the DC-link

voltage controller output a q-axis reference current higher in order to maintain the relation defined by

equation (9). For any control mode, the q-axis current has the same shape during the sag (see also

Figure C 9 and Figure C 9).

d-axis current analysis

When the reactive power mode is active, some d-axis current is injected as well to regulate the

quantity of reactive power. During the voltage sag, the reactive power change since the voltage

amplitude changes. Thus some d-axis current is injected to cancel this reactive power (see Figure C 9).

When the voltage control mode is active, some d-axis current is injected in order to regulate the

amplitude of the converter output voltage. This is especially obvious during the sag (see Figure C 9)

since the converter voltage amplitude must decrease by 25 %.

wind farm modelling

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