Aggregated Models

Aggregate Model of Large Wind Parks for PowerSystem Studies

FERNANDO J. SADA

Master’s Thesis at EPS

Kungliga Tekniska Högskolan (KTH) Stockholm, Sweden March 2011

iii

Aggregate model of large wind parks for power system studiesFERNANDO J. SADA

©FERNANDO J. SADA, 2011School of Electrical EngineeringKungliga Tekniska HögskolanSE-100 44 StockholmSweden

v

Abstract

This report describes the need for aggregation of wind farms due to the re-cent penetration of wind power generation in the power system and the method-ology to simplify a distribution network consisting of a number of wind tur-bines equipped with induction or synchronous generators and MV lines. Thismethodology leads to an equivalent network which consists of an approximateequivalent wind turbine or groups of wind turbines and an approximate equiv-alent line or lines. The aim of the methodology is to reduce the complexity ofthe system and also the simulation time.

Simulations are performed using a simulation software package PowerFac-tory supplied by DIgSilent, which is a tool for short term and long term dynamicanalysis.

The validation of the methodology and models used are examined by ap-plying different layouts and considerations. The response of both detailed andaggregated models, under the same contingencies are compared. The influenceof wind conditions such as wind speed and wind direction, is also considered.

The project consists of two main parts. The scope of the first part is tovalidate an aggregation methodology with DIgSilent PowerFactory Software.The second part aims to verify a wind park aggregation considering the wakeeffect. In both cases the simulation time improvement is shown.

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Sammanfattning

Denna rapport visar behovet av sammanläggning av vindkraftverk på grund avden ökande andelen vindkraft i elkraftsystemet. En metod för att förenkla ett dis-tributionsnät, som består av ett antal vindkraftverk med induktions- eller synkro-ngeneratorer och MV-ledningar, beskrivs i denna rapport. Denna metod ger ettekvivalent nät som består av vindkraftverk eller grupper av vindkraftverk och enmotsvarande kraftledningar. Resultatet är ett förslag som försöker minska kom-plexiteten i systemet och även minska simuleringstiden.

Simuleringen utförs med hjälp av ett simuleringspaket; DIgSilent-PowerFactory,som är ett verktyg för kortsiktiga och långsiktiga dynamiska analyser.

Valideringen av de använda metoderna och modeller sker utifrån tillämpning-sområde och hänsyn tas till olika utformningar. Både detaljerade och aggregerademodell jämförs. Hänsyn tas även till vindförhållandenas påverkan.

Projektet består av två huvuddelar. Den första delen validerar metodiken försammanläggning av vinkraftparker med PowerFactory. Den andra delen försökerbekräfta effekterna av en vindkraftsparksammanläggning med hänsyn till "wakeeffect". I båda fallen visas att tidskrävande steg kan effektiviseras.

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Acknowledgements

First I want to mention my family and friends, that were with me from thebeginning. Without their indirect support it would not have been possible to dothis thesis.

I would like to sincerely acknowledge Katherine Elkington and Dirk Van Hertemfor providing me this great opportunity for my project in KTH, Stockholm, Swe-den, and their help reviewing this thesis. I also want to especially thank MuhamadReza and Kailash Srivastava for this opportunity of doing my Master Thesis inABB (Västerås, Sweden) that provided great help regarding research methods andmy first contact with the professional world. Additionally I thank to AntonisMarinopoulos, who provided me necessary information, his help and patience.

To Álvaro Ruiz for being with me all this time and for all we have shared duringour stay in Västerås.

Thanks to all the people who accompanied me during this great adventure inSweden that started in 2009 and specially to my dear friend Sergio Romero.

My warm and sincere thanks to all. Tack så mycket. Muchas gracias.

Fernando SadaStockholm, SwedenMarch 2011

Contents

Contents xi

1 Introduction 11.1 Purpose of the research . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Wind Energy Development . . . . . . . . . . . . . . . . . . . . . . . 1

2 Wind Power Basics 72.1 Power Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Types of Wind Turbines . . . . . . . . . . . . . . . . . . . . . 92.2.2 Pitch Control in Wind Turbines . . . . . . . . . . . . . . . . 122.2.3 Electrical Considerations . . . . . . . . . . . . . . . . . . . . 13

3 Aggregation of a Large Wind Farm 153.1 Aggregation assumptions . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Aggregation of the distribution network . . . . . . . . . . . . . . . . 16

4 Models 194.1 DIgSilent Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1.1 DFIG Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.1.2 FCG Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.1.3 Scaling-up procedure of the models . . . . . . . . . . . . . . . 24

4.2 Wake Effect Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3 Description of Matlab Program . . . . . . . . . . . . . . . . . . . . . 31

5 Simulations carried out 375.1 First layout and scheme . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1.1 Original layout . . . . . . . . . . . . . . . . . . . . . . . . . . 385.2 Second layout and scheme . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2.1 Original layout . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2.2 Vertical incoming wind . . . . . . . . . . . . . . . . . . . . . 435.2.3 Horizontal incoming wind . . . . . . . . . . . . . . . . . . . . 435.2.4 45 Degrees incoming wind . . . . . . . . . . . . . . . . . . . . 45

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xii CONTENTS

6 Results and Analysis 496.1 First Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.1.1 DFIG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.1.2 FCG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.1.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6.2 Second Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.2.1 Vertical incoming wind verification . . . . . . . . . . . . . . . 656.2.2 Horizontal incoming wind verification . . . . . . . . . . . . . 656.2.3 45 Degrees incoming wind verification . . . . . . . . . . . . . 666.2.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.3 Other examples of the influence of wind direction and wake effect . . 686.3.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

7 Conclusions and Future Work 75

Bibliography 79

Chapter 1

Introduction

1.1 Purpose of the researchThis project deals with the aggregation of a wind farm, by considering the equivalentof the connection lines of the turbines, and the equivalent power production of awind farm. The proposal considers a general configuration of a wind farm layout. Italso analyzes the effect on the aggregation when the wake effect is considered. Thevalidation of the methodology is performed using the simulation package DIgSilent.

The two main objectives of this research are to simplify the models in order tocarry out different studies and to reduce the computation time of the simulations.

In the report there are seven chapters. The purpose of the first three chapters isto gather all information necessary to introduce the topic of the project and someimportant aspects of wind power generation. Chapters four and five present themodels and simulations carried out. The results and their analysis are included inchapter six. Finally, the last chapter presents conclusions and future work of theresearch.

1.2 Wind Energy DevelopmentDuring the recent years the amount of wind power installations has increased con-siderably and therefore it is necessary to study the impact of wind power generationin large scale networks. The recent penetration and the expected future increase ofthis type of technology leads to the study of different methodologies of aggregationof wind farms [1].

Wind power generation is a renewable energy source that has increased quickly.The leading companies have increased their turnover by 30-40 % per year in the

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2 CHAPTER 1. INTRODUCTION

Figure 1.1. Wind Power Capacity. 2000-2007

first years of this century [2]. Additionally the price of electricity is becoming lower,as more wind turbines are installed [2].

For instance, in figure 1.1, the installed wind power capacity since 2000 to 2007can be seen, and the forecast until the year 2012 in figure 1.2. Between 2000 and2007 the installed capacity grew 482%, from 14.604 MW in 2000 to 84.934 MW in2007. The data from figure 1.2 reveals that the industry will grow 215% between2007 and 2012, from 84.934 MW to 267.837 MW. The international wind industryhas compounded an annual growth rate of 28.6% [3].

Due to the development of wind power technologies it has been possible since theearly 1980s the size of the wind turbines to double approximately every four years.For the moment, it is easy to find wind turbines with a rated power of 5 MW andnowadays the largest wind turbine built is the Enercon’s E-126 of 7 MW, which is amore sophisticated version of the E-112, formerly the world’s largest wind turbineof a 6 MW rated power [4].

The more the control system of wind turbines are developed, the more effectiveand cheaper they become. Nowadays the profile of the rotor blades can extractmore power from the wind and also the power electronic equipments optimize thecapacity of the turbines.

In the early days of wind power development, turbines were installed isolatedfrom the grid, often next to a farm. After a few years they were installed in groupsof 3-5 turbines but since then they are grouped in wind farms of more than hundreds

1.2. WIND ENERGY DEVELOPMENT 3

Figure 1.2. Wind Power Capacity. Forecast 2007-2012

of turbines located on land or off-shore, with the same capacity of a conventionalplant [2].

Wind power generation is becoming more competitive than oil, gas, coal ornuclear power production plants. Because of this, mass production of turbineshas increased, as in the case of Germany, Denmark, UK, Spain or USA. Germanmanufacturers are now competing against the Danish ones. Spain has installedseveral thousand of megawatts in the last few years and in 2004, took the lead interms of more installed capacity in a year. The Chinese and Indian markets areexpanding as well. The off-shore technology is becoming more important, speciallyin Denmark, the Netherlands, UK and Sweden. The Danish government has decidedthat wind should produce at leat 50 % of the Danish electrical power by 2030. Windpower technology is becoming very important in many countries as it con be seenin figure 1.3. Figure 1.3 shows the top ten installed capacity in 2010, where China’sposition as a major player in the wind energy sector has been further underlinedwith a prediction of 20 GW annually by 2014. Also in USA the American WindEnergy Association has a plan of 20 % by 2030 as shown in figure 1.4.

The recent penetration of large wind farms makes the study of wind powerproduction necessary and its influence in the grid, specially during a contingency.

A sample of interest in wind power technology and its role within the complexelectrical network is the development of grid codes, implemented by many countries.The objective of grid codes is to achieve continuity and security of the supply whena high level of wind power is introduced into the electrical network [5]. Some

4 CHAPTER 1. INTRODUCTION

Figure 1.3. Top Ten Installed capacity in 2010

Figure 1.4. The American Wind Energy Association plan for 20% wind by 2030

1.2. WIND ENERGY DEVELOPMENT 5

countries have issued dedicated grid codes for connecting the wind turbines to thenetwork. Generally European grid codes require that wind farms stay connectedduring a fault or a disturbance in the net [6]. The requirements deal also withfrequency control, voltage stability, active and reactive power control and fault ridethrough capability [1]. In some cases they are related to some power controllability,power quality and ride-through capability, as it is the example of Germany, Irelandand Denmark. Moreover some countries such as Germany and Spain, want gridsupport during disturbances. Wind farms should be operated as a conventionalpower plant, providing a wide range of controlling and even taking part in theprimary and secondary control. On many occasions, to discuss compliance withthese requirements, simplified models of wind farms are needed in order to conductsuch studies.

Wind generators are smaller (800 kW-3 MW) than conventional power genera-tors but through grouping them, big wind farms are needed [7]. The idea of creatingan aggregate model of a wind farm is useful for system studies. The idea of theaggregation consist of simplifying the wind farm in one equivalent machine or ingroups of machines with similar characteristics apart from simplify the distributionnetwork of the entire layout. A common practice is to present a group of windturbines, for example in a number A, of P megawatts each as a generator size ofAP MW, with all the parameters of the aggregated model configured identicallyas the ones corresponding to the parameters of a single turbine that composes thedetail model [7].

Some of the advantages of an aggregation model and its development is thereduction of simulation duration, the reduction of the complexity of wind farmmodels and an accurate representation of dynamic behavior [8].

It is important to analyze the types of machines, such as the fixed speed ma-chines (with an induction machine) or the variable speed models, like the doublyfed induction machines (more widely used) and the full converter synchronous ma-chine. This project presents different simulations in order to compare the behaviorof the detailed model of a wind farm and the aggregated model under the samecontingencies [9].

Simulations have been performed using the simulation software package Power-Factory supplied by DIgSilent.

The idea of the research is to study the different factors that should be consideredin order to model the aggregation of a large wind farm and take these into accountin the dynamic analysis. The study must to consider aspects like possible scenariosaccording to wind direction and layouts, apart from the wake affect, the wind profileand different fault situations in the wind farm and network connection.

Chapter 2

Wind Power Basics

Wind is air in motion. Modern wind turbines turn the kinetic energy of the movingair into electric power and water pump and windmills turn kinetic energy intomechanical work.

2.1 Power CurvesThe kinetic energy of a mass m, with a speed ν follows the expression:

Ek = 12mν

2 (2.1)

The power associated to the wind is:

P = ∂Ek

∂t= 1

2∂m

∂tν2 = 1

2qν2 (q = ρAν) (2.2)

Only a fraction of the power can be extracted from the wind to the turbine.This is what is called the aerodynamic efficiency Cp:

Cp = Pw

Po= Cp(β, λ) (2.3)

where β is the pitch angle of the blades of the rotor and λ is the tip speed ratio:

λ = ωturbR

ν(2.4)

where ωturb is the angular speed of the rotor of the turbine, R is the radius of theblades and ν is the wind speed.

The mechanical power extracted is then:

Pmec = 12ρπR

2Cp(β, λ)ν3 (2.5)

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8 CHAPTER 2. WIND POWER BASICS

Figure 2.1. Deterministic Power Curve

where ρ is the air density, R is the radius of the blades, Cp is the aerodynamicefficiency, β is the pitch angle and λ is the tip speed ratio.

The power curve is the plot of the output power, against the wind speed acrossthe turbine blades. The power curves can be described in two manners. In adeterministic way or in a probabilistic one. The deterministic method approximatesthe output power with a single curve like in figure 2.1.

Four phases can be identified. The first one is when the ν < νc, and there isno generation. The non linear power production phase is when νc < ν < νr. Afterthat and until νs the rated power production can be considered and when ν > νs

there is no production either to protect the turbine.

The probabilistic production curve considers that the output power of a windturbine exhibits a lot of variations when the power production of two identicalturbines in the same conditions is measured. The probabilistic models incorporatethese variations in order to be more appropriate. What they establish is that inthe non linear phase when νc < ν < νr, the power production variable is a randomcharacterized by a mean power and a standard deviation. An example of this canbe seen in figure 2.2.

Some examples of Monte Carlo simulation based curves are given in [10].

2.2. WIND TURBINES 9

Figure 2.2. Probabilistic Power Curve

The power curves of the turbines are used in the aggregation methodology inorder to know the power provided by each turbine.

In this project the deterministic curves are used and no the probabilistic ones.

2.2 Wind TurbinesA wind turbine is a device that allows to convert the energy of the wind and trans-form it into mechanical power and then electrical power. Different types of tech-nologies have been developed over the last years [2].

2.2.1 Types of Wind TurbinesWind turbines can be classified in the following way:

1. Fixed Speed Wind Turbines

2. Variable Speed Wind Turbine

a) Doubly Fed Induction Generator (DFIG)b) Full Converter Generator (FCG)

This project deals with DFIG and FCG. A short description of their conceptsand main characteristics is given below. These machines are the most widely usedin the industry because of their advantages compared with the fixed speed wind


turbines, such as better energy efficiency, less mechanical stress or the improvementoutput power quality [11].

Fixed Speed Wind Turbines

The aggregation methodology described later is applicable to this machine as well.

When the turbine is directly connected to the grid the rotor and the generatormust rotate at a fixed speed in order to produce power at main frequency [2].

As mentioned before, in the project this machine is not considered.

Variable Speed Wind Turbines. DFIG

Most wind turbines are now equipped with induction generators. These machinesare operated either at fixed speed or variable speed. As mentioned before, genera-tors driven by fixed speed turbines can be directly connected to the grid. However,variable speed generators need a power electronic converter interface for intercon-nection to the grid. Compared to the fixed speed devices they have some advantages[12], [13].

• They have better energy capture than fixed speed generation.

• Possibility to store energy from sudden wind gusts in the rotor.

• Less stress in the gearbox and the generator.

• Control of reactive power injected to the grid.

• Acoustic noise reduction.

The DFIG (Doubly Fed Induction Generator) is widely used for wind powergeneration because it allows operation at a constant AC voltage and frequencywhile the rotor speed varies with the wind speed. It requires an electronic converterthat only carries a fraction of the power that comes out of the generator to the gridand thus reduces the power losses and the cost of the equipment compared to thefull converter wind turbines, although the speed range is limited [14]. Figure 2.3shows the general concept of DFIG.

The DFIG consists of an induction machine and a converter with two terminals.One connected to the grid and the other one to the rotor of the machine. In orderto connect it to the grid a step-up transformer may be used.


Figure 2.3. Doubly Fed Induction Generator

The power converters feeding the rotor winding is usually controlled in a current-regulated PWM type, thus the stator current can be adjusted in magnitude andangle. The DFIG is controlled in a rotating d-q reference frame, with the d-axisaligned with the stator flux vector [15]. A control loop is needed to be able tocontrol d- and q-axis currents by adjusting the pulse width-modulation indices andhence the AC-voltages of the rotor-side and grid-side converters [16]. The statoractive and reactive powers of DFIG are controlled by regulating the current andthe voltage in the rotor. Therefore the current and voltage of the rotor needs tobe decomposed into the components related to stator active and reactive power[15]. Thus d-components correspond to active and q-components correspond toreactive currents. The active output has to be limited to ensure that the PWMconverters are not thermally overloaded by the increased reactive current of thewind generator when supporting the grid voltage during low voltage conditions inthe network. At the grid-side converter, an outer control loop regulates the voltageof the intermediate DC circuit by adjusting the d-axis-current component. Thereactive current of the grid-side converter can be used for sharing reactive powerbetween the stator and the grid-side converter [16].

Variable Speed Wind Turbines. FCG

This kind of wind turbines deal with a synchronous machine, which has the abilityto produce reactive power and compared with induction machines, higher efficiency.


Figure 2.4. Full Converter Generator

They usually use permanent magnets in the rotor, that improve the efficiency andreduce their dimensions [17].

The FCG allows a full range of variable wind speeds. It needs a back-to-backconverter between the generator and the grid. It has a complete control of reactivepower. The rotational speed of the turbine and generator shaft is completely inde-pendent of the grid frequency. This converter has to be rated at the full power ofthe generator [18].

The general concept of this type of wind turbines is shown in the figure 2.4.

2.2.2 Pitch Control in Wind Turbines

The maximum power output in wind turbines is normally around at 15 m/s. In casethe speed is higher it would be necessary to limit the power transfer to the shaftin order to protect the system and avoid damaging in the wind turbine. Though, apower control in wind turbines is needed [19].

In the pitch control, the turbine’s electronics check the power output of theturbine several times per second. When the power output is too high, a signal issent to the blade to turn around, to pitch slightly out of the wind, and then receiveless wind power. Each blade has to be able to turn around its longitudinal axis.During normal operation, the blades will pitch a fraction of degree while the rotorturns.

The pitch mechanism normally uses hydraulics or electric stepper motors.


The turbine models described later deal with pitch control because it is oneof the most widely used in the industry. Easy mounting and low maintenance costmake pitch control a good investment. When changing the references in the controlsduring the aggregation the kind of control should be considered. The aggregation isvalid for other types of power control, such as passive stall control and active stallcontrol.

2.2.3 Electrical ConsiderationsThe dynamic response of a wind turbine is characterized largely by an electronicconverter between the output of the electric generator and the grid. A variety ofalternative configurations can be conceived, regarding the type of converters andthe electrical generator, each presenting advantages and disadvantages. The powerelectronics system is used to supply the generator with variable voltage amplitudeand frequency. The controlled voltage frequency results in controlled rotating speed[11].

The objective generally is to maximize the produced active power and also de-crease the variability of the electromagnetic torque that results in the decrease ofthe mechanical stress. The increase of energy capture is achieved by operating themachine at rotating speed near the optimal Cp curve.

Chapter 3

Aggregation of a Large Wind Farm

In large wind farms, many wind turbines feed power into the power grid at the pointof common connection (PCC). The type of turbine, control algorithm, wind-speedfluctuation, and tower shadow affect the power fluctuations at each wind turbine.The power measurement from a single wind turbine usually shows a large fluctuationof the output power. Because many turbines are connected, the power fluctuationfrom one turbine may cancel the power fluctuation of another, which smooths thepower fluctuation of the overall wind farm. As technology progress, wind turbinesbecome larger and fewer turbines are needed to deliver the same power. Thusthe power fluctuation of an individual wind turbine will have a greater impact onthe power network [20]. To study these aspects the use of aggregation models isrequired otherwise the computing time will be prohibitive. On the other handwhen an aggregated model is used, the information related to individual turbinesis lost. With an aggregation model only studies behind the point of connection ofthe aggregation can be performed because there is not access to interconnectionbetween the turbines of the layout aggregated.

3.1 Aggregation assumptions

It is important to consider the influence of power wind plants in power systems. Inorder to analyze their behavior and influence it is convenient to create aggregatedmodels of wind farms that allow different analysis to carry out. A large wind farmcan have more than one hundred wind turbines, therefore not all the turbines canbe represented in detail because the computation time would be too long and alsobecause the increased possibility of making mistakes if every turbine is consideredwhen modeling the entire wind farm.

The following assumptions are made to closely represent a real wind farm with-out simulating each wind turbine [20].

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16 CHAPTER 3. AGGREGATION OF A LARGE WIND FARM

1. A large wind farm is divided into several groups of turbines, depending ontheir characteristics, the wind profile or the distribution of the layout.

2. For each group of wind turbines the wind speed is considered uniform.

3. The groups are arranged in sequence according to the wind speed they en-counter.

4. All the turbines are exposed to the same turbulence level.

5. It is not necessary that every group of wind turbines is composed of the samenumber of wind turbines, it depends on the amount of turbines with the samecharacteristics, but finally the total amount of wind turbines in the wind farmrepresentation should remain the same.

6. Not only the wind turbines, but also the distribution network in the windfarm should be aggregated. This means that the resulting line or lines shouldbe equivalent to the original ones. In order to do this the power losses andvoltage drop are considered.

On the whole, and in a simplified manner, in the equivalent aggregated modelthe idea is:

Seq =∑

Si Ceq =∑

Ci Pm,eq =∑

Pm,i (3.1)

where the subscript i represents the single turbine in the aggregation.

3.2 Aggregation of the distribution networkIn order to make the aggregation model, it is necessary to develop an equivalentrepresentation of the wind power plant considering the power losses and the voltagedrop. Every different layout has a different impact on the line impedances to thegrid interconnection bus. The idea is to calculate the equivalent characteristics ofthe lines according to the initial conditions and the configuration of the lines.

Two assumptions can be taken. Firstly, the current injections from all the windturbines have the same magnitude and angle and, secondly, the reactive powergenerated by the line capacitive shunts is based on the assumption that the voltageis 1 p.u.

Two types of layouts are examined. The first one, corresponding to just onerow, shows a daisy chain configuration and the second one, corresponding to theaggregation of a different number of rows, shows different branches connected tothe same node [21].

The derivation of all the formulas shown here, is explained in detail in [21].

3.2. AGGREGATION OF THE DISTRIBUTION NETWORK 17

Figure 3.1. Distribution network aggregation Case 1


When the distribution looks like the distribution in figure 3.1, the equivalentimpedance is:

Zt =∑n

m=1m2Zm

n2 (3.2)

where Zm is the impedance in branch m and n is the number of branches. For theshunt representation the equivalent susceptance is:

Bt =n∑

i=1Bi (3.3)

When the lines are in parallel, such as in figure 3.2, the formula for the equivalentresultant line of the aggregated model considering the same amount of losses of thelines of the detail model, is:

Zt =∑n

m=1 nm2Zm

(∑n

m=1 nm)2 (3.4)

where Zm is the impedance in branch m and nm is the number of wind turbines inthe branch m.

As in the previous case, the equivalent susceptance is described by equation 4.3.

18 CHAPTER 3. AGGREGATION OF A LARGE WIND FARM


Figure 3.4. Transformers aggregation

Other kinds of configuration such as the one in figure 3.3 can be found. Thenthe equivalent impedance is:

Zt =∑p

m=1 nm2Zmp +

∑sm=1 (

∑pm=1 nm)2

Zms

(∑p

m=1 nm)2 (3.5)

where Zmp is the impedance in each branch m , Zms is the impedance in betweenbranch m and branch m+ 1 and nm is the number of wind turbines in branch m.

The equivalent susceptance remain the same as in the previous cases; and it isdescribed in equation 4.3.

The expression of the transformer impedance shown in figure 3.4, is:

Z ′transf = Ztransf

nturbines(3.6)

where nturbines is the number of wind turbines aggregated in the model.

Chapter 4

Models

4.1 DIgSilent Models

4.1.1 DFIG Model

The DFIG model that DIgSilent provides is shown in figure 4.1.

It is a 2 MW rated power generator, with a wind speed of 18 m/s and a speed1.08 p.u. It uses a DFIG with a wound rotor induction generator and two IGBT-bases PWM converter, the one connected to the rotor is internally modeled inthe generator element and the stator one external. The stator winding is directlyconnected to the grid with a frequency of 50 Hz and a voltage of 3.3 kV. The nominalvoltage of the DC bus is 1.15 kV and the AC voltage at the exit of the converter is0.69 kV. At the point of common connection the short circuit power is 150 MVA.The setpoint of the reactive power is equal to zero.

The internal DIgSilent Language Simulation (DSL) blocks of the DFIG modelare shown in figure 4.2. The prime mover represents the conversion of the kineticenergy stored in the wind through the blades, into rotational energy at the generatorshaft. It includes the pitch control, the wind turbine and the shaft. The windturbine block needs as input the speed of the wind, the speed of the turbine andpitch angle. The blade angle control deals with the characteristics of the pitch anglecontrol, this control regulates the power generated varying the power coefficient Cp.The shaft model approximates the shaft by a two mass model.

In the control system that regulates the active and reactive power through therotor converter, the rotor current controller that establishes the reference of powerin the d-axis and q-axis can be found. This control system includes the maximumpower tracking (MPT), power and current measurements and PQ and current con-trol. First the rotor current measurement is needed, which measures and transformsthe currents into the stator flux oriented frame. With the PQ controller, the refer-ence currents can be calculated. The references for the grid-side converter can be

19

20 CHAPTER 4. MODELS

Figure 4.1. DFIG DIgSilent’s model

4.1. DIGSILENT MODELS 21

Figure 4.2. DSL Blocks DFIG DIgSilent’s model

obtained in a similar way. The maximum power tracking contains an equation anda look-up table in order to provide the maximum power tracking of the turbine.

The protection block deals with under/over voltages, under/over speeds and therotor over current, which is called crow bar protection.

4.1.2 FCG Model

The model of the FCG in DIgSilent is shown in figure 4.3. It is a permanentmagnet synchronous generator. The synchronous generator, the series reactor, thegenerator-side and grid-side converter (somehow ideals because not lead with no-load losses), the DC capacitors and the step-up transformers can be identified inthe figure. It can be appreciated as well a chopper which maintains the voltage inthe DC bus within a certain level.

The generator has a rated power of 1.5 MVA. The voltage in the medium voltage


Figure 4.3. FCG DIgSilent’s model


Figure 4.4. DSL Blocks FCG DIgSilent’s model

bus MV , just behind the transformer, is 20 kV, which is the bus used for theconnection of each turbine in the layout explained.

The main DSL blocks of the machine are shown in figure 4.4, that, as in theDFIG model, deals with a pitch control, the wind turbine, the shaft and speedmeasurement. The synchronous generator has a AVR to provide excitation currentto the rotor, modeling in this way the permanent magnet. Figure 4.5 corresponds tothe control of the PWM converters, either the generator-side converter and the grid-side converter. It consist of two measurement blocks, the protection, the maximumpower tracking blocks and the controllers for active and reactive power in the twoconverters.


Figure 4.5. DSL Blocks FCG DIgSilent’s model

4.1.3 Scaling-up procedure of the models

In order to scale-up the models, some considerations have been taken into account.The following procedure is used to aggregate the systems that appear throughoutthis report. To scale-up the models, the system components have to be scaled-up,and therefore some changes are necessary.

When an aggregation is performed, the new output of the reference in the newaggregated model is changed compared to the one single turbine model. On theother hand, some of the elements do not need to change. The voltage levels and thecharacteristics of the external grid remain the same.

The procedure is the same for any number of n parallel machines.

The first thing that needs to be changed is the active power supply of the model.Thus in the DFIG element or FCG element, the number of parallel machines has tobe specified. DIgSilent allows to type the parallel machines number. An example can


Figure 4.6. DIgSilent scaling-up. Parallel machines.

be seen in figure 4.6 where in the DFIG model interface of the generator the numberof parallel machines is typed. In the example the number of parallel machines is 12.

Most of the parameters of the control blocks operate in per unit and do not needto be changed, since all the input and output variables are in p.u. base. So eventhough the aggregated model is scaled-up n times all the control variables are in p.u.with reference to the new power rating. However there are some parameters thatare defined as absolute values and regard the measurement and protection blocks.In the DLS common model that is responsible for the Rotor Current Measurement,the rated apparent power parameter Srated has to be multiplied by the number ofparallel machines in order to give the correct measurement for the rotor side currentas shown in figure 4.7. In the PQ Measurement the power rating has to be multipliedby the number of machines aggregated to give the correct measurement since thepower at the PCC is n times larger as shown in figure 4.8. In the protection block


Figure 4.7. DIgSilent scaling-up. Rotor current measurement.

of the scaled-up DFIG model since n machines are considered instead of just one,the maximum rotor current before the crow bar is inserted will be n times higheras shown in figure 4.9.

Apart from the controls, some changes have to be made in other elements. Asthe reactive power compensation has to increase because of the new power supply,the capacity of the DC bus capacitor has to be increased the same factor. In thePWM converter and Series Reactor the reference of the power has to be changed.

In the series reactor, apart from the reference of the power, the value of thereactor’s impedance has to be changed. There are two ways to do this. Followingthe first way, the impedance is represented by a resistance R and a reactance Xin Ohm. As the p.u. values should remain the same but with the aggregation therated power is n times bigger, the impedance should be n times lower, so the valuesof R and X should be divided by n. The second way is easier as the impedance isrepresented in form of short-circuit voltage and copper losses. In this case only thecopper losses have to be multiply by n, leaving the short-circuit voltage the sameas it is in %.

Finally, for the case of the transformers, it would be possible to use one trans-former with a power rating n times higher, but if it is assumed that all the machineshave their own transformers and they are connected in parallel, then the numberof parallel transformers needs to be specified, following the same procedure as with


Figure 4.8. DIgSilent scaling-up. PQ measurement.

Figure 4.9. DIgSilent scaling-up. Protection block.


the DFIG or FCG element as shown in figure 4.6. As all the transformers are thesame, the maximal power that the transformers are able to give is the sum of all ofthem.

4.2 Wake Effect ModelWind turbines extract the energy from the wind, and the air mass leaving theturbine has less energy and by implication lower speed than it had before goingthrough the turbine. This phenomenon affects the output power of wind farms.Here it is presented the wake effect model used in this project. All the formulasshown is this section were provided by the corporate research center of ABB inU.S.A. (ABB-USCRC) [22].

The turbines located upstream in the wind direction modify the input wind ofthe turbines positioned downstream. This shadowing effect is what is called as wakeeffect [23], [24].

According to the classical theory, the drop of wind speed when it goes throughthe wind turbine is approximately 2/3 of the original wind speed. If it is consid-ered that the original wind speed is V0 then the speed after the wind turbine isV ′0 = 1/3 V0. Experimentally the speed V ′0 is determined with the thrust coefficientCT (V0) which depends on the original wind speed V0 and the type of wind turbine.Thus, the speed after the disturbance can be obtained as:

V ′0 = V0

√1 − CT (V0) (4.1)

According to the classical theory, the wake effect tunnel has a variable radiusRd that depends on the distance d between the first and the second turbine, theradius of the turbine situated upstream R and the entrainment constant K whichis a free parameter of the model. It can be described as:

Rd = R+Kd (4.2)

Based on the above assumptions, writing the equation of continuity for fluidsand solving the equation in order to get the value of the wind speed in the secondturbine. The expression of the basic wake effect of figure 4.10 is:

V1 = V0

[1 −

(R

Rd

)2 (1 −

√1 − CT (V0)

)](4.3)

This effect can be added within several wind turbines, depending on the numberof rows of the layout and the distances between them. A scheme can be seen infigure 4.11.

4.2. WAKE EFFECT MODEL 29

Figure 4.10. Wake Effect scheme [22].

Figure 4.11. Wake Effect scheme. Multiple shadowing [22].


Figure 4.12. Wake Effect scheme. Partial shadowing [22].

A general formula for this multiple wake effect is:

V1 = V0

[1 −

(1 −

√1 − CT (V0)

)(R

R+Kd

)2]

V2 = V0

[1 −

(1 −

(V1V0

)√1 − CT (V1)

)(R

R+Kd

)2]

...

Vn = V0

[1 −

(1 −

(Vn−1V0

)√1 − CT (Vn−1)

)(R

R+Kd

)2]

(4.4)

where V0 is the original wind speed and Vi is the speed of turbine number i if V1 isconsidered as the wind speed facing the first turbine affected by the wake effect.

Sometimes the wind direction is not completely facing the wind turbine, andthen a partial shadow effect can appear as it is shown in figure 4.12.

In this case, the modification of the wind speed downstream depends directlyon the affected area. When there is multiple partial shadowing from the upstreamturbines, using the law of momentum conservation, the average speed of the down-stream turbine can be computed from the following equation:

ViMod = Vi

1 −

√√√√∑j

βij

((R

R+Kd

)(1 −

√1 − CT (Vi)

))2 (4.5)

4.3. DESCRIPTION OF MATLAB PROGRAM 31

In the above equation, ViMod is the modified wind speed (after shadowing) andVi is the original wind speed at turbine i. The summation index j stands for allupstream turbines having partial shadows on turbine i and βij is the ratio of theeffective area of the upstream turbine A to the total area of the affected turbine(the circle with radius R) which is defined as:

βij = A

πR2 (4.6)

4.3 Description of Matlab Program

The program provided by the ABB-USCRC uses the methods explained in theprevious section 4.2 related to the wake effect and provides the coherent groupingof wind turbines as well as the reduced network of the wind farm. With this programan aggregation can be implemented with one machine or a group of machines basedon the incoming wind speed of the turbines or the power they are providing. Forexample, if a group of turbines are receiving the same wind speed they will beaggregated into one group. The range for the wind speed or power can be adjustedwith a tolerance.

It has a template dialog box that can be seen in figure 4.13.

The inputs of the program are seen on the left hand side of the dialog box andcan be edited according to the specific requirements. All the parts of the interfaceare identified with numbers in figure 4.13. The turbine characteristic curves can bevisualized and edited if needed. On the left hand side the input data appears: theinitial wind speed, wind direction and turbine characteristics (nr.1), the number ofrows and number of turbines per row (nr.3) and internal network data (nr.4). Alsotwo graphics illustrating two input curves are shown (nr.5), i.e. the speed vs thrustcoefficient graph (that has its maximum when the wind is 4 m/s and it goes until0.005 when the wind is 25 m/s) and the power curve of the wind turbines used. Thegrouping of the turbines depends on the tolerance specified (nr.2). The programallows to regulate the tolerance according to the wind speed or the power of eachturbine. In this particular case the speed tolerance was specified (tol: 0.1 m/s).The smaller the tolerance is, the more groups will appear, and the bigger it is, thefewer groups will be made. In the figure four groups can be identified. On the righthand side the results of the simulation are obtained. There are four graphs on theright side (nr.6). The up-left figure corresponds to the figure with the speed vs thenumber of the wind turbine, the power of each wind turbine can be seen in the up-right graph and also the grouping of the turbines depending on their characteristicswith different colors in the down-left graph. In the upper right table of the interface,the characteristics of the equivalent lines after the aggregation are shown (nr.7).


Figure

4.13.Matlab

programinterface.


The wake coefficient graph requires special attention because it gives informationabout which is the most favorable orientation of the layout or the worst case, interms of output power of the wind farm. It is situated in the lower right corner ofthe interface. The wake coefficient is the ratio between the provided power of a windturbine in a specific situation considering the wake effect and the rated power. Itvaries from 0 to 1. The graph shows how the wake effect coefficient varies respectingthe angle of the incoming wind. The program only shows a range of the angle ofthe incoming wind between 0 degrees and 90 degrees with respect to the horizontal.

Mainly the program takes into account the input wind speed and direction,and with the wake effect equations described before it calculates the input windspeed and thus power production for each turbine of the layout. If it detects thatthere are several turbines with the same input values, it creates different groupsand calculates the characteristics of the aggregation of these groups. Each group isshown with a different color.

The program allows to deal with a layout with the configuration shown in fig-ure 4.14, consisting on several rows of turbines connected in parallel. In figure 4.14the turbines are numered from 1 to 30.

The way the equivalent impedance is calculated for each group is the following.For example, if the wind is coming from the left hand side of the layout exposedbefore, then the turbines 1-7-13-19 and 25 represent a group with an input windspeed of the 100%. The second row would have less wind speed input and the samewith the rest of the rows of the layout according the wind direction. In order tocalculate the equivalent impedance of the first group the rest of wind turbines aredeleted and then the aggregation takes the form of the diagram in figure 4.15, whichis one of the aggregation cases shown in section 3.2.

The same procedure is followed for the rest of the groups.

The equivalent impedance calculation may be the aggregation of one row. Thisis the case if the wind is coming vertically from the bottom. In that case thefirst group will be formed by the turbines 1-2-3-4-5 and 6 and thus the equivalentprocedure is like in figure 4.16.

The same procedure is performed with the rest of the groups.

Both procedures described can be combined, if the wind direction is not hori-zontal or vertical, if it is coming with a specific angle with respect to the horizontal,45 degrees with the respect to the horizontal for instance. Figure 4.17 shows theaggregation of a group of wind turbines receiving the same wind speed when the


Figure 4.14. Matlab program layout configuration with 30 turbines


Figure 4.15. Matlab program aggregation procedure Case 1




wind comes with 45 degrees.

Chapter 5

Simulations carried out

Figure 5.1 shows a general wind farm configuration [25] and this is the one consideredin all the simulations of this project. It consists of a local grid with a number ofwind turbines distributed in rows and connected radially, a collecting point wherethe voltage is adapted to a correct value for transmission, a transmission system anda wind farm interface to the PCC that adjust the voltage, frequency and reactivepower. This configuration is one of the most used and that is the reason why thisproject deals with this kind of layouts.

The following figures show different examples that follow this configuration. Theconfiguration is applicable to AC systems such as in figure 5.2, AC/DC wind farmsor DC transmission systems such as in figure 5.3 and figure 5.4.

5.1 First layout and schemeThe purpose of this section is to gather all information necessary to simulate anaggregation model of a large wind farm and validate an aggregation method using

Figure 5.1. General Wind Farm Layout.

37

38 CHAPTER 5. SIMULATIONS CARRIED OUT

Figure 5.2. Electrical System for AC Wind Farms.

Figure 5.3. Electrical System for AC/DC Wind Farms.

Figure 5.4. Electrical System for DC Wind Farms.

DIgSilent PowerFactory. The behavior of a detailed layout of a wind farm and itsaggregation model, during a fault, at the PCC are described. The scope of theresearch is to compare both models and analyze whether the aggregated modelcorresponds correctly to the detailed one and if it can be used for future powersystem studies. It is assumed that all the turbines are the same and they behave inthe same manner having the same wind speed input.

5.1.1 Original layout

The model shown in figure 5.5, was taken as a base [26]. The aggregation in this re-port is based on the following model. It consists of a wind farm with eleven differentrows of wind turbines, with twelve turbines each. The distance between each windturbine in one row is 500 m and the separation between each row is 700 m. Fromeach row to the PCC the distance is 4 km. Each line has the same characteristics,apart from the length. The characteristics of the lines are in table 5.1.

5.1. FIRST LAYOUT AND SCHEME 39

Figure 5.5. Distribution Network for the DFIG model

Table 5.1. Network Parameters

R1(Ω/km) R0 (Ω/km) X1(Ω/km)0.1153 0.413 0.32987

X0 (Ω/km) B1 (s/km) B0 (s/km)1.04301 3.55e-6 1.5739e-6

Depending on the machine used, and due to the different voltage characteristics,the voltages in the lines and at the PCC vary. For instance, in the case of DFIG,the resulting layout can be seen in figure 5.5 with a PCC voltage if 30 kV, but in thecase of the FCG the model suffers some modifications in the voltages of the busesas it can be seen in figure 5.6 when the PCC voltage is 20 kV.

First it is created and validated the aggregation model of just one row as it canbe seen in figure 5.7 and then, once it is completed, create the aggregation modelof the whole system considering each row as its aggregation. The process of theaggregation of the resulting parallel wind turbines can be seen in figure 5.8.

As well as creating the layout, some elements need to be scaled-up as well as itwas described in section 4.1.3.


Figure 5.6. Distribution Network for the FCG model

Figure 5.7. Aggregation of one row

5.2. SECOND LAYOUT AND SCHEME 41

Figure 5.8. Aggregation of the total number of rows

Before the implementation of the aggregated model, is necessary to start withthe non-aggregated model. The model of the wind farm must be copied severaltimes, and it is also necessary to take into account the block diagram. Each newelement has to be connected to the correct bus and select the right reference of thecontrols.

5.2 Second layout and schemeThe purpose of this section is to gather all information necessary to describe theverification of PowerFactory v.14 DIgSilent’s wind turbine models against the ag-gregated model. They are used to create aggregation models of large scale windfarms suitable for power system dynamic and transient stability studies. For theaggregation now, each wind turbine provides different amount of power. To do this,the wake effect is taken into account in order to calculate the wind power productionof each wind turbine on the whole wind farm.

Many theoretical studies and programs take the dynamic characteristics of thecontrol loops and wind variations into consideration. The purpose of this projectis to verify, in this case with DIgSilent, the validity of this results and the correctbehavior of the designed models.

Here the handling of the aggregation of a wind farm is described, dealing with


Figure 5.9. Power Curve of the DFIG turbines.

the results of the equivalent connection lines, and the equivalent power productionof the wind turbines that the Matlab program provided by ABB-USCRC calculatesas explained in section 4.3.

5.2.1 Original layout

Figure 4.14, shown in section 4.3, showed the layout of the wind farm that theMatlab program deals with. It consists of five rows with six wind turbines each,a total of thirty turbines. All the turbines are numbered. The distances from therows to the PCC varies depending on the row. The distance between the rows is700 m and in between two turbines in the same row is 500 m.

In this particular case all the turbines are considered the same, with the samecharacteristics and same rated power. All of them are DFIG wind turbines with arated power of 1.5 MW each and the voltage at the PCC bus is 25 kV. Figure 5.9shows the power curve obtained from the default DFIG model in DIgSilent. Theoutput power of every single wind turbine in the detailed model must be modifiedto carry out the analysis.

The cable characteristics are shown in table 5.2


Table 5.2. Network Parameters

R1(Ω/km) R0 (Ω/km) L1(H/km)0.1153 0.413 0,00105

L0 (H/km) C1 (µF/km) C0 (µF/km)0,00332 0,01133 0,00501

5.2.2 Vertical incoming wind

In order to validate the aggregation considering the wake effect, three scenarios areunder study. The first of them is when the wind comes vertically with respect thelayout.

The first thing to do is to check the results that the Matlab program providesfor this specific configuration. A vertical incoming from the wind refers to the windwhich comes from the bottom of the layout so the row of the turbines 1-2-3-4-5 and6 is the first facing the wind.

In figure 5.10 the interface of the program for this specific configuration can beseen. It can be seen that turbines 1-2-3-4-5 and 6 receive the same wind speed andrepresent group 1. Group 2 consists of the next six turbines. Group 3 the othernext six turbines and group 4 consists of the last twelve turbines of the layout.

The input wind speed is 14 m/s. This speed was chosen because it is the firstspeed which provides the rated power as can be seen in the power curve. Theprogram identifies four groups of turbines with similar characteristics. Thus in theaggregation model four turbines will appear. For each group the equivalent line wascalculated as explained in section 3.2. The equivalent layout is shown in figure 5.11.

In order to be able to compare the behavior of the aggregation model obtainedand the real one, without any aggregation, the original model should be taken firstand the parameters of the power provided for each wind turbine according the wakeeffect consideration specified. Each turbine of the first group provides 1.425 MW,each turbine of the second group provides 1.036 MW, in the third group they provide0.826 MW each and in the fourth group each turbine provide 0.598 MW. Afterwards,the aggregated model can be implemented by altering the control loops and thescaling up of each turbine of the aggregation. The aggregation model in DIgSilentis shown in figure 5.12.

5.2.3 Horizontal incoming wind

The incoming wind speed is 14 m/s and it comes horizontally from the left handside of the layout proposed.


Figure 5.10. Matlab Program interface. Vertical incoming wind

Figure 5.11. Vertical incoming wind aggregation layout


Figure 5.12. Vertical incoming wind aggregation. DIgSilent

The results of the Matlab program can be seen in figure 5.13 and the equivalentlayout in figure 5.14.

In the original model the turbines of the first group have to provide 1.425 MWeach, 0.949 MW each turbine in the second group, 0.596 MW each in the thirdgroup and 0.36 MW each turbine in the fourth group.

The procedure to scale-up the models is exactly the same as the one used forthe last case.

5.2.4 45 Degrees incoming windAs it was done in the last two cases, the results shown by the Matlab programwhen the wind speed is 14 m/s and it is coming with 45 degrees with respect to thehorizontal can be appreciated in figure 5.15.

To modify the original model just should be considered that the turbines in thefirst group have to provide 1.425 MW each and in the second group they have toprovide 1.3046 MW each. After the implementation of the aggregation model thencomparison of both system can be done.


Figure 5.13. Matlab Program interface. Horizontal incoming wind

Figure 5.14. Horizontal incoming wind aggregation layout


Figure 5.15. Matlab Program interface. 45 degrees incoming wind

Figure 5.16. 45 degrees incoming wind aggregation layout

Chapter 6

Results and Analysis

6.1 First Layout

6.1.1 DFIG

Here the aggregation and the results of the first aggregation done with the DFIGmodel is shown, the one corresponding to the scaling-up of the twelve wind turbinesthat are in the same row. The layout of the model presented is shown in figure 6.1.Here only the interconnection between the different buses of the turbines is shown.The turbines are in different diagrams but then the bus of connection was copiedand pasted again in other diagram to simplify and make easier the visualizationof the total connection. In figure 6.1 the connection of one turbine to another(represented by their MV buses) and finally to the grid can be seen. To createthe non-aggregated model some references of some elements of the control haveto be modified according to the turbine they refer. Thus the reference has to bechanged in the generator block, the power measurement, voltage measurement, thePWM converters, current measurement in the grid-side converter, PLL-1 (phasemeasurement device at node U11 ) and in the DC voltage measurement. After this,in order to scale-up the model, it is necessary to change some internal parametersas explained in section 4.1.3.

The arrow indicates the aggregation of the layout after the scaling-up.

After one row aggregation, the results for the load flow of the non-aggregatedmodel and the ones for the aggregated model are shown in table 6.1.

The behavior of both systems after a 3-phase fault at the PCC (BB in thegraph), with a clearing time of 100 ms looks like in figure 6.2. Sbase=24 MVA, andVbase and Ibase are according the rated values at the PCC. The simulation times areshown in table 6.2.

49

50 CHAPTER 6. RESULTS AND ANALYSIS

Figure 6.1. Aggregation of one row. DFIG model.

6.1. FIRST LAYOUT 51

Table 6.1. Load Flow Results. DFIG Model.

BB Voltage (kV) Active Power Reactive Powerto the Grid (MW) to the Grid(MVAr)

Non-Aggregated 30 25.62 -0.52Aggregated 30 25.62 -0.52

Table 6.2. Simulation times. DFIG Model.

Simulation time Detailed Model 53 sSimulation time Aggregated Model 6 s

Figure 6.2. RMS Simulation after a 3-phase fault. DFIG Row Aggrega-tion. Detailed model (red). Aggregated model (blue). Upper-left)Injected ActivePower. Upper-right)Injected Reactive Power. Lower-left)Voltage at PCC. Lower-right)Current at PCC.

Now the whole aggregation is considered. Every row was substituted by its ownaggregation and it is used to scale-up the entire system. The process is shown infigure 6.3.

The results of the load flow of both systems are shown in table 6.3.


Figure 6.3. Aggregation of the whole system. DFIG model.


Table 6.3. Load Flow Results. DFIG Model.

PCC Voltage (kV) Active Power Reactive Powerto the Grid (MW) to the Grid(MVAr)


Table 6.4. Simulation times. DFIG Model.


Figure 6.4. RMS Simulation after a 3-phase fault. DFIG Total Aggrega-tion. Detailed model (red). Aggregated model (blue). Upper-left)Injected ActivePower. Upper-right)Injected Reactive Power. Lower-left)Voltage at PCC. Lower-right)Current at PCC.

Their behavior after a 3-phase fault with a clearing time of 100 ms are in fig-ure 6.4. Sbase=264 MVA, and Vbase and Ibase are according the rated values at thePCC. The simulation times are shown in table 6.4.


Table 6.5. Load Flow Results. FCG Model.

MV Voltage (kV) Active Power Reactive Powerto the Grid (MW) to the Grid(MVAr)


Table 6.6. Simulation times. FCG Model.


6.1.2 FCG

Before starting with the aggregation model it is necessary to create the non-aggregatedone. It is not enough just copying and pasting the model of the turbines that DIgSi-lent has, but it is necessary also to refer the controls according with the turbinewe are dealing with. Thus in the PWM composite model, it is needed to changethe reference of the PWM grid-side and PWM generator-side and also change themeasurement point in the PLL-1 (phase measurement device at node LV ), mea-surement DC voltage, PQ measurement gen, PQ measurement grid, PLL-R (phasemeasurement device at node Rec Gen), AC gen voltage, AC grid voltage and theDC valve of the chopper. After this, in order to scale-up the model, as it was donein the DFIG model, it is necessary to change some internal parameters.

Both models are shown in figure 6.5.

After one row aggregation, the results for the load flow of the non-aggregatedmodel and the ones for the aggregated model are shown in table 6.5.

After a 3-phase fault at the PCC, with a clearing time of 100 ms, the behaviorin both systems can be seen in figure 6.6. Sbase=18 MVA, and Vbase and Ibase

are according the rated values at the PCC. The simulation times can be seen intable 6.6.

For the whole aggregation the models are shown in figure 6.7. The load flowresults for both models can be seen in table 6.7.

Their behavior after a 3-phase fault with a clearing time of 100 ms is in figure 6.8.Sbase=198 MVA, and Vbase and Ibase are according the rated values at the PCC.The simulation times are shown in table 6.8.


Figure 6.5. Aggregation of one row. FCG model.


Figure 6.6. RMS Simulation after a 3-phase fault. FCG Row Aggregation. Detailedmodel (red). Aggregated model (blue). Upper-left)Injected Active Power. Upper-right)Injected Reactive Power. Lower-left)Voltage at PCC. Lower-right)Current atPCC.

Table 6.7. Load Flow Results. FCG Model.

MV Voltage (kV) Active Power Reactive Powerto the Grid (MW) to the Grid(MVAr)


Table 6.8. Simulation times. FCG Model.



Figure 6.7. Aggregation of the whole system. FCG model.


Figure 6.8. RMS Simulation after a 3-phase fault. FCG Total Aggregation. Detailedmodel (red). Aggregated model (blue). Upper-left)Injected Active Power. Upper-right)Injected Reactive Power. Lower-left)Voltage at PCC. Lower-right)Current atPCC.

6.1.3 Analysis

In the case of the DFIG it can be seen how the aggregated model is very similarto the non-aggregated one. Actually the load flow looks approximately the same inboth cases and the response under the disturbance is exactly the same. It can beconcluded that the validity of the aggregation is demonstrated.

In figure 6.9 the relative errors and the mean square errors of the DFIG aggre-gation can be seen during the pre-fault, the fault and the post-fault. It can be seenthat the magnitude of the errors are very small.

The FCG aggregation was also verified. From figure 6.10 it can be seen thatthe errors between the detailed model and the aggregated one are very small. Thenumbers their self are not very important, because they depend on the step timesize of the recorded data, but the magnitude of the values is worth noting.

In relation to the FCG, in the case of the aggregation of only one row, it can


Figure 6.9. Relative and Mean Square Errors of the DFIG aggregation

Figure 6.10. Relative and Mean Square Errors of the FCG aggregation


Figure 6.11. FCG aggregation responses. Detailed model (red). Aggregated model(blue)

be seen that the aggregation fits the requirements of the aggregation because theresults finally remain the same in steady state. As can be seen in figure 6.11, thebehavior of the curves of the aggregated model is a little bit delayed with respectto the non-aggregated. In the four graphs the delay is the same: 76 ms, as can beseen in the figure 6.11. Considering this delay, the aim is then try to find the originof the delay. Whether it is something resulting from the aggregation methodologyor instead it is from the model used itself.

The DSL block of the generator is in figure 6.12. It is important to note that apermanent magnet synchronous generator is used. A permanent magnet motor doesnot have a field winding on the stator frame, instead relying on permanent magnetsto provide the magnetic field against which the rotor field interacts to producetorque. It does not use an excitation current or voltage, because the magnetic fieldis provided by the magnet. It can be observed in figure 6.12 that from the generatorblock the excitation current is measured. The reason for this is that the GeneratorElmSym block is a standard block which we have no access, and then a control iscreated in order to establish a constant excitation voltage. The aim is to simulatethe permanent magnet. The control, which is shown in figure 6.13, tries to keep the


Figure 6.12. DSL Block FCG model

voltage constant.

Analyzing the behavior of this excitation currents, it can be compared, in p.u.the curves of the aggregated model and the detailed model as can be seen in fig-ure 6.14.There is a delay in the responses of the excitation currents as well. Once thefault is cleared after 100 ms a delay exists in the the aggregated model respectingthe turbines of the detailed model, and it is the same delay observed in the graphicsbefore (76 ms). This could be the reason of the displacement of the original curves.This is not a problem of the aggregation methodology, but from the model and howit works. There is no access to the generator block and it cannot be seen how thiscurrent is obtained. In a synchronous machine the power factor can be controlledwith the excitation current, any disturbance in this current will affect the powerbehavior of the machine, as reflected in the graphs.

In order to complete this rationing, the responses of the active power and theexcitation currents when only two machines in parallel are aggregated can be seenin figure 6.15. It appears a delay in the responses of the active power of 8 ms and italso appears in the responses of the excitation currents. It may be then a problemin the model used. When two parallel machines are aggregated the delay is lowerthan when the whole layout of 132 turbines is aggregated, then it can be commentedthat when the aggregation handles more power, the delay is greater.


Figure 6.13. AVR Control

In table 6.9 it can be seen the errors of the original aggregation of one rowand the same results but with the second time series shifted to the right as muchas observed time lag. Therefore it is shown that the errors after the fault in thesecond case are less and may be due to the time lag and not to the aggregationmethodology.

It can be assumed that the aggregation fits. The behavior of both remain thesame in steady state.

In both cases, with the DFIG and FCG, the aggregation model works and ap-proximates correctly the behavior of the whole system, as well as the network ag-gregation.

In table 6.10 the mean square errors of both aggregations can be seen. Fromthe results it can be concluded that the aggregation of one row, turbines in series,leads to grater errors than the aggregation of parallel machines, although in bothcases are considerably small. This is consequence of the assumptions of the networkaggregation. One of the assumptions was that the voltage was in all the connectionpoints equal to 1 p.u. This is not exactly true when the layout deals with turbines


Figure 6.14. Excitation currents. Detailed model (blue). Aggregated model (red).

Figure 6.15. Aggregation two parallel machines. Left: Active power responses. De-tailed model (red). Aggregation model (blue). Right: Excitation currents responses.Detailed model (green & blue). Aggregated model (red).


Table 6.9. Mean Square Errors with time lag and without time lag.

Mean Square Errors (%) With time lag Without time lag

Active PowerPre-Fault 3.8e-1 3.8e-1Fault 2.6e-3 2.6e-3

Post-Fault 6.7 1.4

Reactive PowerPre-Fault 1.2e-2 1.2e-2Fault 1.0e-3 1.0e-3

Post-Fault 15.6 10.5

VoltagePre-Fault 6.0e-4 6.0e-4Fault 5.7e-5 5.7e-5

Post-Fault 5.2e-1 3.1e-1

CurrentPre-Fault 3.3e-1 3.3e-1Fault 2.5e-3 2.5e-3

Post-Fault 4.9 2.3

Table 6.10. Mean Square Errors.

DFIG FCGMean Square Errors (%) Row Agg Total Agg Row Agg Total Agg

Active PowerPre-Fault 1.8e-3 5.4e-4 3.8e-1 3.1e-4Fault 2.0e-4 4.9e-5 2.6e-3 2.2e-5

Post-Fault 2.6e-1 8.9e-4 6.7 6.2

Reactive PowerPre-Fault 2.4e-1 5.7e-3 1.2e-2 6.9e-4Fault 2.4e-2 5.7e-4 1.1e-3 4.9e-5

Post-Fault 2.4 1.6e-2 15.6 10.1

VoltagePre-Fault 8.4e-5 0.0 6.1e-4 0.0Fault 8.6e-6 1.4e-4 5.7e-5 0.0

Post-Fault 1.1e-2 1.7e-5 5.2e-1 1.1e-1

CurrentPre-Fault 1.7e-3 5.8e-4 3.3e-1 0.0Fault 5.8e-4 8.9e-4 2.4e-3 1.1e-5

Post-Fault 8.9e-2 8.4e-4 4.8 4.2

connected in series, due to the voltage drops that occur in the lines that connectthe turbines. The requirement is satisfied if the machines are connected in parallel,as the case of the final aggregation of the rows.

The simulation times of the aggregated model are around five to nine times lowerthan in the detailed model as seen in table 6.2, table 6.4, table 6.6 and table 6.8.

6.2. SECOND LAYOUT 65

Table 6.11. Load Flow Results. Vertical Incoming Wind.



Table 6.12. Simulation times. Vertical Incoming Wind.

Simulation time Detailed Model 1 min 18 sSimulation time Aggregated Model 7 s

Table 6.13. Load Flow Results. Horizontal Incoming Wind.



6.2 Second Layout

6.2.1 Vertical incoming wind verification

The results of the load flow in the original model and the aggregated one when thewind is coming vertically from the bottom are shown in table 6.11.

After a 3-phase fault at the PCC with a clearing time of 150 ms the behaviorof both systems are shown in the figure 6.16. Sbase=26.9 MVA, and Vbase andIbase are according the rated values at the PCC. The simulation times are shown intable 6.12.

6.2.2 Horizontal incoming wind verification

The results of the load flow in the original model and the aggregated one when thewind is coming horizontally from the left hand side are can be seen in table 6.13.

After a 3-phase fault at the PCC with a clearing time of 150 ms the behaviorof both systems are shown in the figure 6.17. Sbase=18,45 MVA, and Vbase andIbase are according the rated values at the PCC. The simulation times are shown intable 6.14.


Figure 6.16. RMS Simulation after a 3-phase fault. Vertical Incoming Wind.Detailed model (red). Aggregated model (blue). Upper-left)Injected ActivePower. Upper-right)Injected Reactive Power. Lower-left)Voltage at PCC. Lower-right)Current at PCC.

Table 6.14. Simulation times. Horizontal Incoming Wind.


Table 6.15. Load Flow Results. 45 Degrees Incoming Wind.



6.2.3 45 Degrees incoming wind verification

The results of the load flow in the original model and the aggregated one when thewind is coming with 45 degrees are shown in table 6.15.

After a 3-phase fault at the PCC with a clearing time of 150 ms the behavior

6.2. SECOND LAYOUT 67

Figure 6.17. RMS Simulation after a 3-phase fault. Horizontal IncomingWind. Detailed model (red). Aggregated model (blue). Upper-left)Injected ActivePower. Upper-right)Injected Reactive Power. Lower-left)Voltage at PCC. Lower-right)Current at PCC.

Table 6.16. Simulation times. 45 Degrees Incoming Wind.


of both systems are shown in the figure 6.18. Sbase=41.67 MVA, and Vbase andIbase are according the rated values at the PCC. The simulation times of thesesimulations are shown in table 6.16.

6.2.4 AnalysisWith the results shown in section 6.2.1, section 6.2.2 and section 6.2.3, it can beconcluded that the aggregation methodology that the Matlab program considersis valid. The assumptions taken by the program for the equivalency of the linesseem to be right when considering different output power of the turbines based onthe wake effect. With the use of the DIgSilent’s models it was checked that the


Figure 6.18. RMS Simulation after a 3-phase fault. 45 Degrees IncomingWind. Detailed model (red). Aggregated model (blue). Upper-left)Injected ActivePower. Upper-right)Injected Reactive Power. Lower-left)Voltage at PCC. Lower-right)Current at PCC

aggregation was correct. In the three cases the load flow looks very similar or evenidentical. And after the three-phase fault the behavior is completely overlapped,which means that the behavior of the detailed model and the aggregated one is verysimilar. The aim of the aggregation was reached.

It can be seen again in figure 6.19 that the magnitude of the errors of the 45degrees incoming wind aggregation are small.

The simulation times of the aggregated model are around ten to fourteen timeslower than in the detailed model as seen in table 6.12, table 6.14 and table 6.16.

6.3 Other examples of the influence of wind direction andwake effect

The influence of wind direction and wake effect on the aggregation is evident. Tocomplete the results of section 6.2, some examples will be shown with the Matlab

6.3. OTHER EXAMPLES OF THE INFLUENCE OF WIND DIRECTION AND WAKEEFFECT 69

Figure 6.19. Relative and Mean Square Errors of the 45 Degrees Incoming WindAggregation.

program to illustrate how the aggregation model is not always the same and itdepends on different factors, as the initial incoming wind speed, the original layout,the direction of the incoming wind or the wake effect.

To illustrate these examples it was considered a 10 m/s incoming wind speed.The layout consists of five rows with six turbines each. The distance between eachturbine is 500 m and the distance between each row is 700 m. A speed toleranceof 0.1 m/s and a maximum of five groups were taken as grouping criterion. All theturbines have the same characteristics.

In the results it can be seen how the supplied power and also the aggregationvaries according to the wake coefficient graph. This graph is shown in the lowerright corner of the Matlab’s program interface.

Figure 6.20 is the result of the aggregation when the wind is coming horizontallyfrom the right with a wind speed of 10 m/s, there is not any variation in the layoutdistances and also the wake effect is considered. This situation is shown in order tocompare it with the other cases explained below.

Figure 6.21 shows what would happen if no wake effect is considered.

Figure 6.22 shows what would happen if the wake effect is considered but with


Figure 6.20. Matlab interface. Horizontal incoming wind.

Figure 6.21. Matlab interface. Thrust coefficient equal to zero.


Figure 6.22. Matlab interface. Variation in the layout.

a variation on the layout distances, if the layout is modified. In this particular casevery long distances were introduced. Instead of 500 m and 700 m for the distancesbetween the turbines and the lines as it was mentioned before, 5000 m and 7000 mare considered.

In order to analyze the influence of wind direction, different wind angles ori-entation of the incoming wind were introduced. By increasing the incoming windangle with 5 degrees and starting from the situation shown in figure 6.20 with zerodegrees, many results can be extracted, but here only the most favorable and theworst case from the output power point of view, are shown in figure 6.23.

6.3.1 Analysis

From the results shown in section 6.2 can be concluded that the aggregation of aspecific wind farm is influenced by many different factors. Mainly it is affected bythe wind direction and the wake effect.

Figure 6.21 shows how if any wake effect is considered then the aggregation withone equivalent machine is very easy because it is considered that all the turbinesare receiving the same wind speed. It is like in the case of section 6.1 where all theturbines are the same and all of them are providing the power corresponding to this


Figure 6.23. Left: Worst case (Zero degrees incoming wind - 14.24 MW) Right:Most favorable case (15 degrees incoming wind - 33 MW)

specific wind speed. According to the power curve each turbine is providing 80% ofits rated power when the wind speed is 10 m/s. In figure 6.21 it can be seen thatall the turbines are facing the same wind speed and they represent one group.

In figure 6.22, how the configuration of the layout also influences in the aggre-gation can be seen. In this case the wake effect has some affect, but as the layoutwas modified spreading out the turbines, it has less effect as can be seen in thewake coefficient vs wind direction graph. The incoming wind in figure 6.20 andfigure 6.22 is the same, but the output power is considerable different; 14.24 MWinstead of 32.8 MW. Also the configuration of the aggregated model is not the same;four groups in figure 6.20 and two groups in figure 6.22.

Depending on wind direction and according to the wake effect equations, anumber of wind turbines or another will be affected. The greater the number ofwind turbines is affected, the lower the output power is. With this kind of studycan be found which is the most favorable and the worst case of wind direction fromthe output power point of view for this specific layout. The most favorable case iswhen the wind is coming with 15 degrees with respect to the horizontal. In thiscase the output power is 33 MW, there is a total wake effect coefficient of 0.92 p.u.and the aggregation model is composed of three groups of turbines as the right sidepicture of figure 6.23 shows.


The worst case is when it is coming horizontally, zero degrees with respectto the horizontal. In that case the output power is 14.24 MW, there is a totalwake coefficient of 0.4 p.u. and there are four groups in the aggregation model asfigure 6.23 shows. This kind of study can be very useful in order to maximize theoutput power of a wind farm knowing the space available to build up the wind farmand the layout we want to deal with. For instance for the layout treated in theexample it would be nice to match the main wind direction of the area with themost favorable one. The main wind direction is the one that will give the necessaryinformation to create the aggregation model. These studies can be useful as well tohave different aggregation models depending on the season of the year or even thetime of the day when the main wind direction can be considered different.

Chapter 7

Conclusions and Future Work

This report describes a method to implement an aggregated model of a wind farm.The aim of the project is to apply the methodology to specific models provided bythe electrical software DIgSilent PowerFactory and analyze its limitations.

The main conclusion of the research is that for both cases, the DFIG and FCGmodels, the aggregation model developed works and approximates correctly the be-havior of the whole system. In the case of the network aggregation, the calculationsallow computation of equivalent collector system according to the size and config-uration of the distribution. The aggregation provides a good approximation of thewind farm performance in order to use it for interconnection studies. Very largeand diverse power plants can be represented aggregating the whole wind farm by asmall number of wind turbines with similar attributes.

Every different layout has a different impact on the line impedances and thenetwork aggregation formulas apply to different cases such as the aggregation ofturbines in daisy chain configuration or turbines connected in parallel. The methoddoes not incorporate the Qmax and Qmin capability, which is an important aspectof wind power plants.

From the results it can be seen that the aggregation errors are significantly smalland it is not relevant to analyze the values. It is worth noting to comment thatthe aggregation of turbines in one row leads to greater mean square errors thanthe aggregation of parallel machines connected to the PCC. This is consequence ofassuming that the voltage is 1 p.u. at all the connection points of the wind farm,although this assumption is not completely true in the case in which the turbinesare connected in series in one row.

The time delays in the FCG results are consequence of the model itself. Itseems as if it is a consequence of the stator excitation current which should remainat a constant value given the characteristics of the permanent magnet synchronous

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76 CHAPTER 7. CONCLUSIONS AND FUTURE WORK

machine. The purpose of the aggregation of observing the same the behavior of thedetailed model and the aggregated model before and after the transient, is reachedand the equivalence of the model is satisfactory.

From the second layout and scheme proposed in the project it can be concludedthat the Matlab program calculates the aggregation correctly. The assumptionsmade by the program for the equivalency of the lines considering the wake effect,are correct and provide a good enough approximation of the wind farm accordingto the behavior of both systems, the detailed and the aggregated one, and also theerrors observed.

The aggregation depends always on the initial wind speed and the wind direction.

There are some situations when a detailed model is required. One of thesecases is when the fault is applied at any point of the internal interconnection ofthe wind farm, inside the system under study. The simplified model is only validwhen the case of study considers a fault or disturbance from the PCC to the grid.When applied to interconnection studies between different wind farms, it is usuallyenough to model the wind farms which are not the subject of the assessment usingan aggregated model and the wind farm which is under study with a detailed model.

As mentioned before, the aggregation depends on the incoming wind and thereis a direct relation between the wind speed and the aggregated model implementedfor this wind speed. Therefore the more the wind speed varies from its mean value,the less accuracy the model has.

In all the cases the efficiency with regard to calculation time was shown. It canbe concluded that the objective of the research of reducing the computation timein the simulations was also achieved.

Future Work

For future work it would be interesting to simulate different wind turbines availablenow in the market with the proposed methods and models.

These results could be easily extended to other cases. For example, if in one windfarm we are dealing with different types of wind turbines, then the procedure is thesame. The number of groups is determined by the different types of turbines and thewake effect considerations. Going deeper in this way, future work can be to analyzehow the existence of different manufactures of the same wind turbine can affect,for example if in a certain wind farm all the turbines are DFIG but coming fromdifferent manufacturers. It would be interesting to develop a model able to aggregate

77

the mechanical parameters and also the controls of different manufacturers into onesingle machine and analyze how realistic the response is.

It would be interesting as well to try to develop aggregation models for otherkind of layouts.

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[11] F.D. Kanellos, S.A. Papathanassiou & N.D. Hatziargyriou, "Dynamic analysisof a Variable Speed Wind Turbine equipped with a Voltage Source AC/DC/ACConverter Interface and a Reactive Current Control loop", Electrotecnical Con-ference, 2000. MELECON 2000. 10th Mediterranean, Volume 3, Athens, 2000.

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