Aggregate Model of Large Wind Parks for Power System Studies

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Degree project in

Aggregate Model of Large Wind Parks for Power System Studies

Fernando Sada

Stockholm, Sweden 2011

XR-EE-ES 2011:004 Electric Power Systems

Second Level

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Aggregate Model of Large Wind Parks for Power System Studies

FERNANDO J. SADA

Master’s Thesis at EPS

Kungliga Tekniska Högskolan (KTH) Stockholm, Sweden March 2011

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

©FERNANDO J. SADA, 2011 School of Electrical Engineering Kungliga Tekniska Högskolan SE-100 44 Stockholm

Sweden

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Abstract

This report describes the need for aggregation of wind farms due to the recent penetration of wind power generation in the power system and the methodology to simplify a distribution network consisting of a number of wind turbines equipped with induction or synchronous generators and MV lines. This methodology leads to an equivalent network which consists of an approximate equivalent wind turbine or groups of wind turbines and an approximate equivalent line or lines. The aim of the methodology is to reduce the complexity of the 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 dynamic analysis.

The validation of the methodology and models used are examined by ap- plying different layouts and considerations. The response of both detailed and aggregated models, under the same contingencies are compared. The influence of 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 to validate an aggregation methodology with DIgSilent PowerFactory Software.

The second part aims to verify a wind park aggregation considering the wake effect. In both cases the simulation time improvement is shown.

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Sammanfattning

Denna rapport visar behovet av sammanläggning av vindkraftverk på grund av den 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 ett ekvivalent nät som består av vindkraftverk eller grupper av vindkraftverk och en motsvarande 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 aggregerade modell jämförs. Hänsyn tas även till vindförhållandenas påverkan.

Projektet består av två huvuddelar. Den första delen validerar metodiken för sammanläggning av vinkraftparker med PowerFactory. Den andra delen försöker bekräfta effekterna av en vindkraftsparksammanläggning med hänsyn till "wake effect". 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 the beginning. Without their indirect support it would not have been possible to do this thesis.

I would like to sincerely acknowledge Katherine Elkington and Dirk Van Hertem for 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 Muhamad Reza and Kailash Srivastava for this opportunity of doing my Master Thesis in ABB (Västerås, Sweden) that provided great help regarding research methods and my first contact with the professional world. Additionally I thank to Antonis Marinopoulos, 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 during our stay in Västerås.

Thanks to all the people who accompanied me during this great adventure in Sweden 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 Sada Stockholm, Sweden March 2011

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Introduction

1.1 Purpose of the research

This project deals with the aggregation of a wind farm, by considering the equivalent of the connection lines of the turbines, and the equivalent power production of a wind farm. The proposal considers a general configuration of a wind farm layout. It also analyzes the effect on the aggregation when the wake effect is considered. The validation of the methodology is performed using the simulation package DIgSilent.

The two main objectives of this research are to simplify the models in order to carry 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 is to gather all information necessary to introduce the topic of the project and some important aspects of wind power generation. Chapters four and five present the models and simulations carried out. The results and their analysis are included in chapter six. Finally, the last chapter presents conclusions and future work of the research.

1.2 Wind Energy Development

During 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 generation in large scale networks. The recent penetration and the expected future increase of this type of technology leads to the study of different methodologies of aggregation of 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 1

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

Due to the development of wind power technologies it has been possible since the early 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 and nowadays the largest wind turbine built is the Enercon’s E-126 of 7 MW, which is a more sophisticated version of the E-112, formerly the world’s largest wind turbine of a 6 MW rated power [4].

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

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

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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 conventional plant [2].

Wind power generation is becoming more competitive than oil, gas, coal or nuclear power production plants. Because of this, mass production of turbines has increased, as in the case of Germany, Denmark, UK, Spain or USA. German manufacturers are now competing against the Danish ones. Spain has installed several thousand of megawatts in the last few years and in 2004, took the lead in terms of more installed capacity in a year. The Chinese and Indian markets are expanding as well. The off-shore technology is becoming more important, specially in Denmark, the Netherlands, UK and Sweden. The Danish government has decided that wind should produce at leat 50 % of the Danish electrical power by 2030. Wind power technology is becoming very important in many countries as it con be seen in figure 1.3. Figure 1.3 shows the top ten installed capacity in 2010, where China’s position as a major player in the wind energy sector has been further underlined with a prediction of 20 GW annually by 2014. Also in USA the American Wind Energy 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 power production necessary and its influence in the grid, specially during a contingency.

A sample of interest in wind power technology and its role within the complex electrical 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 when a high level of wind power is introduced into the electrical network [5]. Some

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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

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1.2. WIND ENERGY DEVELOPMENT 5

countries have issued dedicated grid codes for connecting the wind turbines to the network. Generally European grid codes require that wind farms stay connected during a fault or a disturbance in the net [6]. The requirements deal also with frequency control, voltage stability, active and reactive power control and fault ride through 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, Ireland and Denmark. Moreover some countries such as Germany and Spain, want grid support during disturbances. Wind farms should be operated as a conventional power plant, providing a wide range of controlling and even taking part in the primary and secondary control. On many occasions, to discuss compliance with these requirements, simplified models of wind farms are needed in order to conduct such studies.

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

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

It is important to analyze the types of machines, such as the fixed speed machines (with an induction machine) or the variable speed models, like the doubly fed induction machines (more widely used) and the full converter synchronous machine. This project presents different simulations in order to compare the behavior of the detailed model of a wind farm and the aggregated model under the same contingencies [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 considered in order to model the aggregation of a large wind farm and take these into account in the dynamic analysis. The study must to consider aspects like possible scenarios according to wind direction and layouts, apart from the wake affect, the wind profile and different fault situations in the wind farm and network connection.

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Chapter 2

Wind Power Basics

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

2.1 Power Curves

The kinetic energy of a mass m, with a speed ν follows the expression:

E_k= 1

2mν² (2.1)

The power associated to the wind is:

P = ∂E_k

∂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 C_p: Cp= Pw

P_o = C_p(β, λ) (2.3)

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

λ = ω_turbR

ν (2.4)

where ω_turb is the angular speed of the rotor of the turbine, R is the radius of the blades and ν is the wind speed.

The mechanical power extracted is then:

P_mec= 1

2ρπR²C_p(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, C_p is the aerodynamic efficiency, 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 across the turbine blades. The power curves can be described in two manners. In a deterministic way or in a probabilistic one. The deterministic method approximates the output power with a single curve like in figure 2.1.

Four phases can be identified. The first one is when the ν < ν_c, and there is no generation. The non linear power production phase is when ν_c < ν < ν_r. After that and until ν_s the rated power production can be considered and when ν > ν_s there is no production either to protect the turbine.

The probabilistic production curve considers that the output power of a wind turbine exhibits a lot of variations when the power production of two identical turbines in the same conditions is measured. The probabilistic models incorporate these variations in order to be more appropriate. What they establish is that in the non linear phase when ν_c< ν < νr, the power production variable is a random characterized by a mean power and a standard deviation. An example of this can be seen in figure 2.2.

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

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2.2. WIND TURBINES 9

Figure 2.2. Probabilistic Power Curve

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

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

2.2 Wind Turbines

A 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 technologies have been developed over the last years [2].

2.2.1 Types of Wind Turbines

Wind 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 concepts and main characteristics is given below. These machines are the most widely used in the industry because of their advantages compared with the fixed speed wind

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turbines, such as better energy efficiency, less mechanical stress or the improvement output 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 generator must 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 machines are operated either at fixed speed or variable speed. As mentioned before, generators driven by fixed speed turbines can be directly connected to the grid. However, variable speed generators need a power electronic converter interface for interconnection 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 power generation because it allows operation at a constant AC voltage and frequency while the rotor speed varies with the wind speed. It requires an electronic converter that only carries a fraction of the power that comes out of the generator to the grid and thus reduces the power losses and the cost of the equipment compared to the full converter wind turbines, although the speed range is limited [14]. Figure 2.3 shows 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 order to connect it to the grid a step-up transformer may be used.

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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 and angle. The DFIG is controlled in a rotating d-q reference frame, with the d-axis aligned with the stator flux vector [15]. A control loop is needed to be able to control d- and q-axis currents by adjusting the pulse width-modulation indices and hence the AC-voltages of the rotor-side and grid-side converters [16]. The stator active and reactive powers of DFIG are controlled by regulating the current and the voltage in the rotor. Therefore the current and voltage of the rotor needs to be decomposed into the components related to stator active and reactive power [15]. Thus d-components correspond to active and q-components correspond to reactive currents. The active output has to be limited to ensure that the PWM converters are not thermally overloaded by the increased reactive current of the wind generator when supporting the grid voltage during low voltage conditions in the network. At the grid-side converter, an outer control loop regulates the voltage of the intermediate DC circuit by adjusting the d-axis-current component. The reactive current of the grid-side converter can be used for sharing reactive power between 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 ability to produce reactive power and compared with induction machines, higher efficiency.

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Figure 2.4. Full Converter Generator

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

The FCG allows a full range of variable wind speeds. It needs a back-to-back converter between the generator and the grid. It has a complete control of reactive power. 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 of the 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 case the speed is higher it would be necessary to limit the power transfer to the shaft in order to protect the system and avoid damaging in the wind turbine. Though, a power control in wind turbines is needed [19].

In the pitch control, the turbine’s electronics check the power output of the turbine several times per second. When the power output is too high, a signal is sent to the blade to turn around, to pitch slightly out of the wind, and then receive less 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 rotor turns.

The pitch mechanism normally uses hydraulics or electric stepper motors.

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

2.2.3 Electrical Considerations

The dynamic response of a wind turbine is characterized largely by an electronic converter between the output of the electric generator and the grid. A variety of alternative configurations can be conceived, regarding the type of converters and the electrical generator, each presenting advantages and disadvantages. The power electronics system is used to supply the generator with variable voltage amplitude and frequency. The controlled voltage frequency results in controlled rotating speed [11].

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

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Chapter 3

Aggregation of a Large Wind Farm

In large wind farms, many wind turbines feed power into the power grid at the point of common connection (PCC). The type of turbine, control algorithm, wind-speed fluctuation, and tower shadow affect the power fluctuations at each wind turbine.

The power measurement from a single wind turbine usually shows a large fluctuation of the output power. Because many turbines are connected, the power fluctuation from one turbine may cancel the power fluctuation of another, which smooths the power fluctuation of the overall wind farm. As technology progress, wind turbines become larger and fewer turbines are needed to deliver the same power. Thus the power fluctuation of an individual wind turbine will have a greater impact on the power network [20]. To study these aspects the use of aggregation models is required otherwise the computing time will be prohibitive. On the other hand when an aggregated model is used, the information related to individual turbines is lost. With an aggregation model only studies behind the point of connection of the aggregation can be performed because there is not access to interconnection between the turbines of the layout aggregated.

3.1 Aggregation assumptions

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

The following assumptions are made to closely represent a real wind farm without 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 on their 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 same number of wind turbines, it depends on the amount of turbines with the same characteristics, but finally the total amount of wind turbines in the wind farm representation should remain the same.

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

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

Seq =^XSi Ceq=^XCi Pm,eq =^XPm,i (3.1) where the subscript i represents the single turbine in the aggregation.

3.2 Aggregation of the distribution network

In order to make the aggregation model, it is necessary to develop an equivalent representation of the wind power plant considering the power losses and the voltage drop. Every different layout has a different impact on the line impedances to the grid interconnection bus. The idea is to calculate the equivalent characteristics of the lines according to the initial conditions and the configuration of the lines.

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

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

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

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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 equivalent impedance is:

Zt= Pn

m=1m²Zm

n² (3.2)

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

B_t=

n

X

i=1

B_i (3.3)

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

Z_t= Pn

m=1n_m²Z_m

(^Pⁿ_m=1nm)² (3.4)

where Z_m is the impedance in branch m and n_m is the number of wind turbines in the branch m.

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

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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. Then the equivalent impedance is:

Z_t= Pp

m=1nm2Zmp+^P^s_m=1(^P^p_m=1nm)²Zms

(^P^p_m=1n_m)² (3.5)

where Z_mp is the impedance in each branch m , Z_ms is the impedance in between branch m and branch m + 1 and n_m is the number of wind turbines in branch m.

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

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

Z_transf⁰ = Z_transf

n_turbines (3.6)

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

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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 speed 1.08 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 in the generator element and the stator one external. The stator winding is directly connected to the grid with a frequency of 50 Hz and a voltage of 3.3 kV. The nominal voltage of the DC bus is 1.15 kV and the AC voltage at the exit of the converter is 0.69 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 model are shown in figure 4.2. The prime mover represents the conversion of the kinetic energy stored in the wind through the blades, into rotational energy at the generator shaft. It includes the pitch control, the wind turbine and the shaft. The wind turbine block needs as input the speed of the wind, the speed of the turbine and pitch angle. The blade angle control deals with the characteristics of the pitch angle control, 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 the rotor converter, the rotor current controller that establishes the reference of power in the d-axis and q-axis can be found. This control system includes the maximum power tracking (MPT), power and current measurements and PQ and current control. First the rotor current measurement is needed, which measures and transforms the currents into the stator flux oriented frame. With the PQ controller, the reference currents can be calculated. The references for the grid-side converter can be

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20 CHAPTER 4. MODELS

Figure 4.1. DFIG DIgSilent’s model

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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 and a 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 the rotor 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 permanent magnet synchronous generator. The synchronous generator, the series reactor, the generator-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 in the figure. It can be appreciated as well a chopper which maintains the voltage in the DC bus within a certain level.

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

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Figure 4.3. FCG DIgSilent’s model

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Figure 4.4. DSL Blocks FCG DIgSilent’s model

bus M V , just behind the transformer, is 20 kV, which is the bus used for the connection of each turbine in the layout explained.

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

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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 throughout this 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 new aggregated model is changed compared to the one single turbine model. On the other hand, some of the elements do not need to change. The voltage levels and the characteristics 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 to be specified. DIgSilent allows to type the parallel machines number. An example can

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Figure 4.6. DIgSilent scaling-up. Parallel machines.

be seen in figure 4.6 where in the DFIG model interface of the generator the number of 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 need to be changed, since all the input and output variables are in p.u. base. So even though 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 that are 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 of parallel machines in order to give the correct measurement for the rotor side current as shown in figure 4.7. In the PQ Measurement the power rating has to be multiplied by the number of machines aggregated to give the correct measurement since the power at the PCC is n times larger as shown in figure 4.8. In the protection block

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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 higher as shown in figure 4.9.

Apart from the controls, some changes have to be made in other elements. As the 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 the PWM 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 the reactor’s impedance has to be changed. There are two ways to do this. Following the first way, the impedance is represented by a resistance R and a reactance X in Ohm. As the p.u. values should remain the same but with the aggregation the rated power is n times bigger, the impedance should be n times lower, so the values of R and X should be divided by n. The second way is easier as the impedance is represented in form of short-circuit voltage and copper losses. In this case only the copper losses have to be multiply by n, leaving the short-circuit voltage the same as 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 machines have their own transformers and they are connected in parallel, then the number of parallel transformers needs to be specified, following the same procedure as with

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Figure 4.8. DIgSilent scaling-up. PQ measurement.

Figure 4.9. DIgSilent scaling-up. Protection block.

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

4.2 Wake Effect Model

Wind turbines extract the energy from the wind, and the air mass leaving the turbine has less energy and by implication lower speed than it had before going through 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 formulas shown is this section were provided by the corporate research center of ABB in U.S.A. (ABB-USCRC) [22].

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

According to the classical theory, the drop of wind speed when it goes through the 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 is V₀⁰ = 1/3 V₀. Experimentally the speed V₀⁰is determined with the thrust coefficient CT(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:

V₀⁰ = V₀ q

1 − C_T(V₀) (4.1)

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

R_d= R + Kd (4.2)

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

V₁= V₀

"

1 −

R Rd

2

1 −^q1 − C_T(V₀)

#

(4.3) This effect can be added within several wind turbines, depending on the number of rows of the layout and the distances between them. A scheme can be seen in figure 4.11.

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4.2. WAKE EFFECT MODEL 29

Figure 4.10. Wake Effect scheme [22].

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

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

A general formula for this multiple wake effect is:

V₁ = V₀

"

1 −

q

1 − C_T(V₀)

R R + Kd

2#

V₂ = V₀

"

1 −

V₁ V0

q

1 − C_T(V₁)

R R + Kd

2#

...

Vn = V0

"

1 −

Vn−1

V₀

q

1 − C_T(V_n−1)

R R + Kd

2#

(4.4)

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

Sometimes the wind direction is not completely facing the wind turbine, and then 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 directly on the affected area. When there is multiple partial shadowing from the upstream turbines, using the law of momentum conservation, the average speed of the downstream turbine can be computed from the following equation:

V_{iM od} = V_i



1 − v u u t

X

j

β_ij

R R + Kd

1 −

q

1 − C_T(V_i)

2

 (4.5)

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4.3. DESCRIPTION OF MATLAB PROGRAM 31

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

β_ij = A

πR² (4.6)

4.3 Description of Matlab Program

The program provided by the ABB-USCRC uses the methods explained in the previous section 4.2 related to the wake effect and provides the coherent grouping of wind turbines as well as the reduced network of the wind farm. With this program an aggregation can be implemented with one machine or a group of machines based on the incoming wind speed of the turbines or the power they are providing. For example, if a group of turbines are receiving the same wind speed they will be aggregated into one group. The range for the wind speed or power can be adjusted with 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 and can be edited according to the specific requirements. All the parts of the interface are identified with numbers in figure 4.13. The turbine characteristic curves can be visualized and edited if needed. On the left hand side the input data appears: the initial wind speed, wind direction and turbine characteristics (nr.1), the number of rows and number of turbines per row (nr.3) and internal network data (nr.4). Also two graphics illustrating two input curves are shown (nr.5), i.e. the speed vs thrust coefficient graph (that has its maximum when the wind is 4 m/s and it goes until 0.005 when the wind is 25 m/s) and the power curve of the wind turbines used. The grouping of the turbines depends on the tolerance specified (nr.2). The program allows to regulate the tolerance according to the wind speed or the power of each turbine. 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, the fewer groups will be made. In the figure four groups can be identified. On the right hand side the results of the simulation are obtained. There are four graphs on the right side (nr.6). The up-left figure corresponds to the figure with the speed vs the number 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 characteristics with 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).

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Figure4.13.Matlabprograminterface.

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The wake coefficient graph requires special attention because it gives information about which is the most favorable orientation of the layout or the worst case, in terms of output power of the wind farm. It is situated in the lower right corner of the interface. The wake coefficient is the ratio between the provided power of a wind turbine in a specific situation considering the wake effect and the rated power. It varies from 0 to 1. The graph shows how the wake effect coefficient varies respecting the angle of the incoming wind. The program only shows a range of the angle of the 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 wind speed and thus power production for each turbine of the layout. If it detects that there are several turbines with the same input values, it creates different groups and calculates the characteristics of the aggregation of these groups. Each group is shown with a different color.

The program allows to deal with a layout with the configuration shown in figure 4.14, consisting on several rows of turbines connected in parallel. In figure 4.14 the 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 exposed before, then the turbines 1-7-13-19 and 25 represent a group with an input wind speed of the 100%. The second row would have less wind speed input and the same with the rest of the rows of the layout according the wind direction. In order to calculate the equivalent impedance of the first group the rest of wind turbines are deleted and then the aggregation takes the form of the diagram in figure 4.15, which is 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. This is the case if the wind is coming vertically from the bottom. In that case the first group will be formed by the turbines 1-2-3-4-5 and 6 and thus the equivalent procedure 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 horizontal 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 the aggregation of a group of wind turbines receiving the same wind speed when the

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Figure 4.14. Matlab program layout configuration with 30 turbines

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Figure 4.15. Matlab program aggregation procedure Case 1

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wind comes with 45 degrees.

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Chapter 5

Simulations carried out

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

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

5.1 First layout and scheme

The purpose of this section is to gather all information necessary to simulate an aggregation model of a large wind farm and validate an aggregation method using

Figure 5.1. General Wind Farm Layout.

37

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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 its aggregation model, during a fault, at the PCC are described. The scope of the research is to compare both models and analyze whether the aggregated model corresponds correctly to the detailed one and if it can be used for future power system studies. It is assumed that all the turbines are the same and they behave in the 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 report is based on the following model. It consists of a wind farm with eleven different rows of wind turbines, with twelve turbines each. The distance between each wind turbine in one row is 500 m and the separation between each row is 700 m. From each 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.

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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 the case of the FCG the model suffers some modifications in the voltages of the buses as 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 can be seen in figure 5.7 and then, once it is completed, create the aggregation model of the whole system considering each row as its aggregation. The process of the aggregation 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 it was described in section 4.1.3.

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Figure 5.6. Distribution Network for the FCG model

Figure 5.7. Aggregation of one row

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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 with the non-aggregated model. The model of the wind farm must be copied several times, and it is also necessary to take into account the block diagram. Each new element has to be connected to the correct bus and select the right reference of the controls.

5.2 Second layout and scheme

The purpose of this section is to gather all information necessary to describe the verification of PowerFactory v.14 DIgSilent’s wind turbine models against the aggregated model. They are used to create aggregation models of large scale wind farms suitable for power system dynamic and transient stability studies. For the aggregation 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 production of each wind turbine on the whole wind farm.

Many theoretical studies and programs take the dynamic characteristics of the control loops and wind variations into consideration. The purpose of this project is to verify, in this case with DIgSilent, the validity of this results and the correct behavior of the designed models.

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

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Figure 5.9. Power Curve of the DFIG turbines.

the results of the equivalent connection lines, and the equivalent power production of the wind turbines that the Matlab program provided by ABB-USCRC calculates as 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 the Matlab 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 the rows to the PCC varies depending on the row. The distance between the rows is 700 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 same characteristics and same rated power. All of them are DFIG wind turbines with a rated power of 1.5 MW each and the voltage at the PCC bus is 25 kV. Figure 5.9 shows the power curve obtained from the default DFIG model in DIgSilent. The output power of every single wind turbine in the detailed model must be modified to carry out the analysis.

The cable characteristics are shown in table 5.2

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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 are under study. The first of them is when the wind comes vertically with respect the layout.

The first thing to do is to check the results that the Matlab program provides for this specific configuration. A vertical incoming from the wind refers to the wind which comes from the bottom of the layout so the row of the turbines 1-2-3-4-5 and 6 is the first facing the wind.

In figure 5.10 the interface of the program for this specific configuration can be seen. It can be seen that turbines 1-2-3-4-5 and 6 receive the same wind speed and represent group 1. Group 2 consists of the next six turbines. Group 3 the other next 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 first speed which provides the rated power as can be seen in the power curve. The program identifies four groups of turbines with similar characteristics. Thus in the aggregation model four turbines will appear. For each group the equivalent line was calculated 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 obtained and the real one, without any aggregation, the original model should be taken first and the parameters of the power provided for each wind turbine according the wake effect 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 provide 0.826 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 the scaling up of each turbine of the aggregation. The aggregation model in DIgSilent is 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 hand side of the layout proposed.

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Figure 5.10. Matlab Program interface. Vertical incoming wind

Figure 5.11. Vertical incoming wind aggregation layout

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Figure 5.12. Vertical incoming wind aggregation. DIgSilent

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

In the original model the turbines of the first group have to provide 1.425 MW each, 0.949 MW each turbine in the second group, 0.596 MW each in the third group 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 for the last case.

5.2.4 45 Degrees incoming wind

As it was done in the last two cases, the results shown by the Matlab program when the wind speed is 14 m/s and it is coming with 45 degrees with respect to the horizontal can be appreciated in figure 5.15.

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

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Figure 5.13. Matlab Program interface. Horizontal incoming wind

Figure 5.14. Horizontal incoming wind aggregation layout

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Figure 5.15. Matlab Program interface. 45 degrees incoming wind

Figure 5.16. 45 degrees incoming wind aggregation layout

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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 DFIG model is shown, the one corresponding to the scaling-up of the twelve wind turbines that 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 copied and pasted again in other diagram to simplify and make easier the visualization of 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 create the non-aggregated model some references of some elements of the control have to be modified according to the turbine they refer. Thus the reference has to be changed in the generator block, the power measurement, voltage measurement, the PWM converters, current measurement in the grid-side converter, PLL-1 (phase measurement 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 parameters as 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-aggregated model 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 the graph), with a clearing time of 100 ms looks like in figure 6.2. S_base=24 MVA, and V_base and I_base are according the rated values at the PCC. The simulation times are shown in table 6.2.

49

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50 CHAPTER 6. RESULTS AND ANALYSIS

Figure 6.1. Aggregation of one row. DFIG model.

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6.1. FIRST LAYOUT 51

Table 6.1. Load Flow Results. DFIG Model.

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

Non-Aggregated 30 25.62 -0.52

Aggregated 30 25.62 -0.52

Table 6.2. Simulation times. DFIG Model.

Simulation time Detailed Model 53 s Simulation 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 Active Power. 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 own aggregation and it is used to scale-up the entire system. The process is shown in figure 6.3.

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

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52 CHAPTER 6. RESULTS AND ANALYSIS

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

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6.1. FIRST LAYOUT 53

Table 6.3. Load Flow Results. DFIG Model.

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

Non-Aggregated 30 278.23 -15.83

Aggregated 30 278.23 -16.19

Table 6.4. Simulation times. DFIG Model.

Simulation time Detailed Model 48 s Simulation time Aggregated Model 6 s

Figure 6.4. RMS Simulation after a 3-phase fault. DFIG Total Aggrega- tion. Detailed model (red). Aggregated model (blue). Upper-left)Injected Active Power. 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. S_base=264 MVA, and V_base and I_base are according the rated values at the PCC. The simulation times are shown in table 6.4.

Aggregate Model of Large Wind Parks for Power System Studies

Aggregate Model of Large Wind Parks for Power System Studies

Fernando Sada

Aggregate Model of Large Wind Parks for Power System Studies

Acknowledgements

Contents

Chapter 1

Introduction

1.1 Purpose of the research

1.2 Wind Energy Development

Chapter 2

Wind Power Basics

2.1 Power Curves

2.2 Wind Turbines

Chapter 3

Aggregation of a Large Wind Farm

3.1 Aggregation assumptions

3.2 Aggregation of the distribution network

Chapter 4

Models

4.1 DIgSilent Models

4.2 Wake Effect Model

4.3 Description of Matlab Program

Chapter 5

Simulations carried out

5.1 First layout and scheme

5.2 Second layout and scheme

Chapter 6

Results and Analysis

6.1 First Layout