Lillgrund Wind Farm Modelling and Reactive Power Control

(1)

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

(2)

(3)

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.

(4)

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.

(5)

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

(11)

- 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.

(12)

- 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.

(13)

- 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.

(14)

- 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

(15)

- 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:

mF

U C E

DC

C 15.6

) 10 754 . 1 (

10 24 2 2

2 3

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.

(16)

- 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 abc

conv

abc V

dt LdI I R

V _{_}     (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.

(17)

- 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  = 2f [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:





























q d q

q conv

q

q d

d conv

d

V dt I

LdI I R V

dt I LdI I R V



_ _

(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.

q q AC DC DC

DC U I P k V I

P       (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

(18)

- 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):





















q d q conv q

q d conv d

V I U V

I U V



' '

_

_ (5)





















dt LdI I R U

q q q

d d d

' '

(6)

Thus by using the Laplace transform:

















) ( ) (

) ( '

) ( ) (

) ( '

s i s L R s U

q q

d

d (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 T L

L k

s with k T

s F

C i

C C p

C i C p C

1 1 1

1 1 )

(



(8)

(19)

- 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:



₁_C t_r₁_C ln(9). 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:

DC

 

EDC Plosses PAC

dt

P d   (9)

where:

DC DC

DC U I

P   is the DC power

2

2 1

DC

DC C U

E    is the energy stored in the DC-capacitor

losses

P are the losses in the converter

d q

AC V I

P    2

3 is the AC power

Neglecting the losses, a linearity between I_qand

 

W_C dt

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:

C R

E R

I U U P

virtual DC

virtual DC DC

DC

DC 

 









 ²

2

(10)

This resistor is calculated knowing the voltage and current values at the DC link. When the losses are neglected, the relation (9) becomes:



DC



q q

virtual

DC E V I

dt d C R

E   



 

2 3

2

(11)

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

C s R

V I (s)

(s) E F

q

q DC DC

 

 



2 2 3

1 (12a)

(20)

- 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 (s) E F

q DC loop

closed (12b)

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



₁_DC

 t

_r₁_DC

 ln( 9 )

. The PI controller is calculated according to:











 



 



 





 



2 2 1 3

1 )

(

1

1 1

1

C T R

V k

s with k T

s F

virtual DC

i

q DC DC

p

DC i DC p DC



(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:

q q

AC V I

P   

2

3

and Q_AC  V_q I_d 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).

(21)

- 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 required

d

V I Q



 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( _needed

q required

d I where

I      (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:

(22)

- 13 -

2 _ 2 2

_ 2

__conv _q _conv ( _q) _q _conv

d

desired V V X I V

U      (18)

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

X

I X U

V X

V

I_d _ref V^q ^q ^conv ^q ^desired ^q

2 2

_ _

) ( 



 

  (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

s f_s rad

C 1570.8 /

10 2

1   

 

 (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:

s

DC 157.08rad/

1 



(21)

(23)

- 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

(24)

- 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.

(25)

- 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:













r s

rl ls l

R R R

L L L

L (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):

r r

s j

e    (23)

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

dt

Ldi i jL R e

U_s  _s (  )_s  ^s (24)

(26)

- 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

(

s E s U

s I R

L j s s

G _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 T L

L k

s with k T

s F

C i

C C p

C i C p C

2 2 2

2 2

2

1 1 )

(



(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

(27)

- 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:

( )

j R

'

I

(

rotor

)

dt and d

stator I

R dt U

d _s

r r s r r s s r

s s s s s

s   





 

 



(27)



_s^s  L_mI_r^s L_sI_s^s and



_r^s L_mI_s^s L_r I_r^s (28) Combining these equations in a proper way leads to the following expression of the rotor flux:



s^s



s s m r s

r L I

L

L  





_



(29)

where:

s r

m L

L L  L 

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

(28)

- 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 sq

rd r m

c I I

L p L

T  _{_}_ _{_}_ ^_^

2

3    

 (30)

where:

_rd_{_}is the rotor flux in the “ρ” reference frame

 _

Isq 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 r

sd L

I



 

_ (31)

where:

ref

r is the desired flux

 _

Isd 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

(29)

- 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:



 





 

k T s

s F

i p



2 2 2

1 1 )

( with













b T J

J k

i p



 

2 2 2

(32)

where



 

2 2

) 9 ln(

tr

 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

1 Av

P wind

the in power available

power rotor

C_p ^rotor







(33)

where:

ρ is the air density A is the rotor blade area v is the wind speed

v R speed

wind

speed tip

blade  

 

 (34)

where:

(30)

- 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

opt v

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.

(31)

- 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

(32)

- 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

(33)

- 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 %.

Lillgrund Wind Farm Modelling and Reactive Power Control