## Analysis of the dynamic impact

## of large wind parks in power

## systems

## Analysis of the dynamic impact

## of large wind parks in power

## systems

### Foreword

The inclusion of a large amount wind turbines in the power system affects the stability properties of the power system. During Vindforsk II a PhD-project was therefore started to develop models and analytical methods which can be used to better evaluate the dynamic behaviour of a power system with large scale wind power expansions.

During Vindforsk III this project has further continued with studies of how control of the turbines can be designed such that the turbines can contribute to damping of power system instabilities.

The work has led to several papers and a PhD-thesis by Katherine Elkington. A new method for controlling wind parks is presented, and a method for coordinating the control of multiple parks distributed throughout a power system is derived. It is also demonstrated that wind turbines with so called Double fed Induction Generators ,DFIGs, can be used for damping oscillations. This report is a “popular” version of the main results of the Vindforsk III V-311, Analysis of the dynamic impact of large wind parks in power systems. The project was carried out by Katherine Elkington under the supervision of Mehrdad Ghandhari at the Royal Institute of Technology (KTH).

Vindforsk – III is funded by ABB, Arise windpower, AQSystem, E.ON Elnät, E.ON Vind Sverige, EBL-kompetanse, Falkenberg Energi, Fortum, Fred. Olsen Renewables, Gothia wind, Göteborg Energi, HS Kraft, Jämtkraft, Karlstads Energi, Luleå Energi, Mälarenergi, o2 Vindkompaniet, Rabbalshede Kraft, Skellefteå Kraft, Statkraft, Stena Renewable, Svenska Kraftnät, Tekniska Verken i Linköping, Triventus, Wallenstam, Varberg Energi, Vattenfall Vindkraft, Vestas Northern Europe, Öresundskraft and the Swedish Energy Agency.

Comments on the work and the final report have been given by a reference group with the following members: Therese Fahlberg from Svenska Kraftnät, Anders Danell from Svenska Kraftnät, Muhammad Reza from ABB, Jonas Persson from Vattenfall, Kjell Gustafsson from Statkraft and Anders Ekberg from Fortum.

Stockholm April 2012

Anders Björck

Programme manager Vindforsk-III

### Sammanfattning

Denna rapport täcker bakgrund och mål för projekt V-311 samt beskriver de resultat som har uppnåtts.

Målet med studien är att undersöka hur storskaliga vindparker som är

geografiskt fördelade i ett kraftsystem påverkar stabiliteten i systemet och om styrning av många vindturbiner bidrar till stabilitet och dämpning.

Studiens fokus är på vindparker med vindturbiner som använder

dubbelmatade asynkrongeneratorer (DFIGs). Dessa är okonventionella generatorer, och deras påverkan på kraftsystemet är annorlunda jämfört med påverkan från konventionella generatorer. Olika oscillationsmoder

uppkommer i kraftsystem där en stor mängd effekt genereras av vindparker och spänningsmönstret förändras.

För att studera vindparkers effekt på kraftsystemstabiliteten har modeller och styrregler utvecklats. En ny metod för styrning av vindparker presenteras och en metod för koordinering av styrning för flera parker fördelade i ett

kraftsystem härleds. Metoderna används för att bevisa vindparkers effektivitet i att dämpa kraftsystemsoscillationer och för att jämföra effektiviteten hos vindparker med effektiviteten hos synkrongeneratorer. Vindturbinernas inverkan utreds med hjälp av linjära och dynamiska simuleringar. Studien bevisar att DFIGs kan användas för dämpning av oscillationer och att de även kan förbättra kritiska felurkopplingstider.

Däremot kan de ha en negativ påverkan på ett kraftsystem i efterdyningarna av stora spänningsstörningar.

### Summary

This report covers the background and aims of project V-311, and describes the results which have been obtained.

The aim of the study is to examine how large scale wind parks distributed in a power system affect the stability of the system, and whether the control of many wind turbines contributes to stability and damping.

The focus of this study is on wind turbines which use doubly fed induction generators (DFIGs). These are unconventional generators, and their effect on power systems is different to that of conventional generators used in most other types of generating plants. Different modes of oscillation appear in power systems where a significant proportion of power is generated by wind parks, and the voltage behaviour of these systems is altered.

In order to examine the effect of wind parks on power system stability, models and control strategies are developed. Additionally a new method for controlling wind parks is presented, and a method for coordinating the control of multiple parks distributed throughout a power system is derived. These methods are used to demonstrate the effectiveness of wind parks in damping power system oscillations, and to compare the performance of wind parks and synchronous generators.

The impact of wind turbines is investigated through the use of linear and dynamic simulations. It has been demonstrated that DFIGs can be used for damping oscillations, and that they can also improve the critical clearing time of faults. However, they may have an adverse impact on a power system after large voltage disturbances.

### Contents

**1**

**Introduction**

**1**1.1 Background ... 1 1.2 Aims ... 3

**2**

**Results**

**4**2.1 Modelling ... 4 2.2 Control ... 5 2.3 Impact on power systems ... 8

**3** **Conclusions ** **12**

### 1

### Introduction

This project is a continuation of the earlier Vindforsk II project V-216.

### 1.1

### Background

As the installed capacity of wind power increases across the world, its impact on power systems is becoming more important. The aim of this study is to examine how distributed large scale wind parks affect the stability of power systems, and whether controlling wind parks contributes to power system stability and damping.

The project focuses on the analysis of doubly fed induction generators (DFIGs). Many of the newer, larger wind turbines now being produced are variable speed turbines which use DFIGs. These are induction generators which have their stator winding connected to the grid, while their rotor winding is coupled to a power electronics converter, which is in turn connected to the grid. Variable speed operation becomes possible with the use of the converter, and because of this, wind turbines of this type can be controlled to extract more energy from the wind than fixed-speed induction generators. The converter can also be controlled to improve the dynamic response of the wind turbine.

A schematic of a DFIG is shown in Figure 1.

**Figure 1 Doubly fed induction generator system **

DFIGs are unconventional generators, and their effect on power systems is different to that of conventional generators which are used in most other types of generating plants. Different modes of oscillation appear in power systems where a significant proportion of power is generated by wind parks, and the voltage behaviour is altered.

An analogy with mechanical systems can be used to briefly describe power system oscillations. Most generators in a power system are rotating machines. Their rotation can be described by their position and speed, much like the oscillation of a pendulum. Figure 2 shows a mechanical equivalent of a power system.

If the generators begin to swing out of phase, then oscillations begin to appear on the lines connecting them. If these oscillations become too large, then a generator may break away from the other generators. Undamped oscillations in power systems may also result in fault tripping of protection equipment.

**Figure 2 Mechanical analogy **

The earlier Vindforsk II project showed that large scale wind parks affect the dynamics of power systems, and that wind turbines with appropriate control methods can contribute to system stability and damping of power oscillations with low frequencies. In that project an analysis was performed in a small test system and linear control methods were used. Additionally a simple model for wind turbines was used in the simulations.

In this continuation project a more detailed wind turbine model is used in a larger electric power system which reflects the dynamics of the Nordic power system. Additionally a method for controlling wind parks is presented, and a method for coordinating the control of multiple parks distributed through the system is derived. This method is used to demonstrate the effectiveness of wind turbines at damping power system oscillations, and to compare the performance of wind parks and synchronous generators.

### 1.2

### Aims

The aims of the continuation project include the following:

Investigating different modelling practices

Deriving smart control methods for wind turbines

Examining the effect of wind turbines on larger power systems.

These aims have been fulfilled in the following publications:

[Article 1] investigated the impact of using more simplified wind turbine models for control development

[Article 6] investigated more realistic and detailed wind turbine models [Article 3] showed the effectiveness of a nonlinear signal as feedback in

a power oscillation damping scheme for wind turbines

[Article 4] derived a method for implementing a power oscillation damping controller with nonlinear feedback in multiple wind turbines [Article 2] examined the impact of a large wind park in power systems

with VSC-HVDC

[Article 5] examined the impact of multiple large wind parks in large power systems.

### 2

### Results

### 2.1

### Modelling

Many different models and control strategies were investigated in [Article 6]. A wind turbine model was extended for use in further studies. The model was developed so that it included the effect of pitching wind turbine blades on mechanical wind power input. The wind speed was assumed to be constant in all simulations, and this assumption was reasonable for the short time scales examined. The mechanical power to the generator could be altered by controlling the pitch angle.

By increasing the pitch angle the power input and rotational speed of the turbine can be reduced. The relationship between pitch angle, speed and power is shown in Figure 3.

**Figure 3 Power coefficient **

Limiters were also added to the wind turbine power electronics converter, so that the power rating of the converter was not violated. The power rating determines the extent to which the wind turbine can control larger disturbances.

More simplified models were examined in [Article 1] for the purpose of deriving new nonlinear control schemes, but these were not further used in this study.

### 2.2

### Control

For small disturbances the dynamics of a power system can be represented by a linearised version of the system. The eigenvalues of the linear system show dynamic properties of the system. Each eigenvalue is made up of a real and an imaginary part. The eigenvalues describe modes of oscillation, with the frequency described by the imaginary part of the eigenvalues, and the damping described by the negative of the real parts. The eigenvalues can be plotted in the complex plane, as shown in Figure 4.

**Figure 4 System eigenvalues **

If one eigenvalue lies in the right half of the complex plane, then the system has negative damping, and is unstable. For this reason it is necessary to move all of the eigenvalues into the left half plane and ordinarily into the region shown in Figure 5 where the angle has been specified. The damping ratio can be formally defined as

### z

### =

### cos

### q

where### q

is the smallest angle for which all of the eigenvalues lie in the region. The damping ratio describes how quickly oscillations are damped.It is common to move eigenvalues further into the left half plane by using a linear controller. When this type of controller is used in a conventional synchronous generator, the controller is called a power system stabilizer (PSS). When controllers performing similar functions are used in the power electronics converter of a wind turbine, the controller is called a power oscillation damping (POD) controller.

**Figure 5 Eigenvalue region **

The parameters for each POD are chosen to move critical eigenvalues further into the left half plane.

It was shown in the earlier project that a signal based on the speeds of synchronous machines in a power system can be used to control wind turbines for power oscillation damping. In [Article 4] a nonlinear signal was examined for power oscillation damping, which had been used for power electronics based controllable components. It was based on the speeds and angles of all of the synchronous generators in the power system and was found by determining which generators swung against each other at the frequency of the least damped mode of oscillation. In the systems examined the least damped oscillation was of low frequency, and occurred between different regions. These types of oscillations are called inter-area modes.

The effect of one POD controller was presented in [Article 3].

Traditional methods for tuning PSSs in synchronous generators have involved tuning each new PSS as it is installed, without retuning the PSSs in earlier generators. When wind power turbines are installed simultaneously, a more efficient way of utilising their POD controllers is to tune them simultaneously. A method for simultaneously choosing the magnitude of the signals for each generator was derived in [Article 4]. This method used linear matrix inequalities (LMIs) and was useful for coordinating the control between multiple wind parks without using iterative methods. The LMI method used in [Article 4] and [Article 5] searches for a set of feedback gains so that all of the system eigenvalues lie in the region shown in Figure 5. If such a set can be found, then the least damping ratio of the system is at least

### cos

### q

.To demonstrate the method a small test system, shown in Figure 6, was used. This system comprises two areas which swing against each other.

Re Im

*θ*
*Accept able*

**Figure 6 Two area system **

The PODs in the wind parks were tuned in two different ways. The first uses the nonlinear signal tuned by the LMI method, and the second uses the traditional linear signals where the PODs are tuned one after the other.

The inter-area oscillation can be examined by looking at the power flow along the lines connecting the two areas and also the voltage near one of the wind parks. Some of the results are shown in Figure 7.

Case 1: Power Case 1: Voltage

Case 2: Power Case 2: Voltage

**Figure 7 Comparison of feedback signals. No POD control [red], nonlinear **
**PODs in wind turbines [green], linear PODs in wind turbines [blue] **

The system with no PODs installed is shown in red, and it is clear that oscillations are present in the system. The two types of PODs work well, but for Case 2 the linear POD, shown in blue, does not restore the power to the equilibrium point, and in fact the system is unstable. The nonlinear POD, however, shown in green, has the desired effect.

### 2.3

### Impact on power systems

Studies were performed on a larger test system, the Nordic 32A test system, which was intended to reflect some of the properties of the Nordic power system. One such property is the oscillation between the north and south regions of the system. The Nordic 32A system is shown in Figure 8.

The effect of one wind park equipped with a linear POD controller was described in [Article 2] in a large power system with VSC-HVDC transmission, shown in Figure 9. A method for coordinating the VSC-HVDC POD controller with wind power production was also presented. The results of this coordination are shown in Figure 10.

The effect of multiple wind parks was shown in Figure 11. The locations of the parks were chosen to maximise the impact of the wind park controllers on power system oscillations. Four wind parks were installed in the north and the south of the system, making up just over 30 percent of the installed capacity in the system.

A comparison was made between the performance of wind parks utilising PODs and the performance of conventional generators utilising PSSs. The inter-area oscillation can be examined by looking at the power flow along the lines connecting the two areas, and the phase portrait of the system. The phase portrait shows the speed and frequency difference between two groups of swinging machines, which are the signals used in the nonlinear POD signal. The portraits display the collective behaviour of all synchronous machines in the system, and are shown in Figure 11.

**Figure 8 CIGRE system Nordic 32A **
4071
4072
4011
4012
4022 4021
4031 4032
4042
4041
4046
4043 4047
4044
4045
4051
4061
4062
4063
1011
1012
1013
1014
1022
1021
2031
2032
1044
1043
1041 1045
1042
50% 50%
37,5%
40%
40%
**External**
**South **
**West**
**Central**
**North**
400 kV
220 kV
130 kV

**Figure 9 Damping. No PODs [red], POD only in wind park [blue], POD only in **
**VSC-HVDC [green] and PODs in both [black] **

**Figure 10 Damping ratio with coordination [red] and without coordination **
**[green] **

The fault shown was located at a bus where voltage support equipment is installed. When a fault occurs here, there was a loss of support, and the machines which were able to contribute to voltage stability tried to

compensate. If the fault is cleared quickly, after 0.1 seconds, no problem arises, and the wind parks are able to damp oscillations more quickly than the conventional generators. This was the case for many small disturbances. If the fault is cleared after a longer time, 0.25 seconds, the DFIGs in the wind parks try to compensate for the loss of voltage support, but their effect is limited by the size of their converters. The critical clearing time, is 0.33 seconds without wind parks, but is decreased by over 20 percent to 0.26

the maximum angle of the combined system increasing with increasing clearing time, with generators breaking away from each other if the fault is not cleared within 0.26 seconds.

Clearing time 0.1 seconds Clearing time 0.1 seconds

Clearing time 0.25 seconds Clearing time 0.25 seconds

**Figure 11 Dynamic results for wind parks [blue] and conventional generators **
**[red] **

### 3

### Conclusions

This study has fulfilled the objectives of project V-311, by examining how large scale wind parks distributed in a power system affect the stability of the system, and by studying whether the control of many wind turbines

contributes to power system stability and damping.

The study has focused on wind turbines using DFIGs. These have been modelled in such a way as to better reflect the general behaviour of these turbines, and added features have been added to the models used earlier. A nonlinear signal, often used in power electronics based controllable

components, has been used as a feedback signal to the wind park controller to create a POD function. A method using LMIs has been derived to

simultaneously find a suitable POD coordination for multiple wind turbines so that a power system satisfies a specified damping ratio. The effect of DFIG POD controllers on power system damping has been compared to the signals normally used in PSSs, and was shown to perform more effectively. A method for coordinating VSC-HVDC control and wind power production has also been presented.

The impact of wind parks on power system has been investigated through the use of linear and dynamic simulations. It has been shown that even one wind park can make a contribution to power system damping. The performance of multiple wind parks with PODs has been compared to that of conventional synchronous generator power plants with PSSs in a large power system. It has been demonstrated that DFIG based wind parks can be used for damping oscillations. However, they may adversely affect on power systems after large voltage disturbances.

### 4

### Publications

The results of this project are described in the following articles:

[Article 1] Katherine Elkington and Mehrdad Ghandhari. “Comparison of Reduced Order Doubly Fed Induction Generator Models for Nonlinear Analysis”. In: Electrical Power & Energy Conference (EPEC). Oct. 2009.

[Article 2] Katherine Elkington, Hector Latorre, and Mehrdad Ghandhari. “Operation of Doubly Fed Induction Generators in Power Systems with VSC-HVDC Trans- mission”. In: Proceedings International Conference on AC and DC Power Trans- mission. Oct. 2010.

[Article 3] Camille Hamon, Katherine Elkington, and Mehrdad Ghandhari. “Doubly-fed Induction Generator Modeling and Control in DigSilent PowerFactory”. In: International Conference on Power System Technology. Oct. 2010.

[Article 4] Katherine Elkington and Mehrdad Ghandhari. “Power Oscillation Damping Controllers for Doubly Fed Induction Generators in Wind Parks”. In: IET Renewable Power Generation (2012). Provisionally accepted.

[Article 5] Katherine Elkington and Mehrdad Ghandhari. Wind power stabilising control: Demonstration on the Nordic Grid. Tech. rep. Submitted.Royal Institute of Technology (KTH), 2012.

[Article 6] Katherine Elkington, J. G. Slootweg, Mehrdad Ghandhari, and Wil Kling. “Wind Power in Power Systems”. In: ed. by Thomas Ackermann. 2nd ed. To be published. John Wiley & Sons, Ltd, 2012. Chap. 42.

[Article 7] Katherine Elkington. “Analysis of the dynamic impact of large wind parks on power system stability”. Forthcoming. PhD thesis. Royal Institute of Technology (KTH), 2012.