voltage stability issues related to implementation of...

THESIS FOR THE DEGREE OF LICENTIATE OF ENGINEERING

Voltage Stability Issues Related to

Implementation of Large Wind Farms

by

Marcia Martins

Department of Energy and Environment

Division of Electric Power Engineering

CHALMERS UNIVERSITY OF TECHNOLOGY

Göteborg, Sweden 2006

Voltage Stability Issues Related to Implementation of Large Wind Farms

MARCIA MARTINS

MARCIA MARTINS, 2006

Department of Energy and Environment,

Division of Electric Power Engineering

Chalmers University of Technology

SE - 412 96 Göteborg - Sweden

Telephone: +46 (0) 31 – 772 1000

Fax: +46 (0) 31 – 772 1633

E-mail: [email protected]

Web page: www.elteknik.chalmers.se

Chalmers Bibliotek, Reproservice

Göteborg, Sweden 2006

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Abstract

This thesis focuses on the impact of voltage stability when introducing large wind farms on the power system. To this purpose fixed speed wind turbines equipped with conventional induction generators were studied.

The investigations have been carried out with respect to short and long-term voltage stability. A comparison with field measurements was performed in order to validate the simulation models used for the investigations.

For short term voltage stability studies, a comparison has been made between induction machines operating as a generator or as a motor. Further investigations have been performed to study the behaviour of the system during and after a short circuit fault at the terminals of the wind park. The investigations have examined factors affecting the short-term voltage stability limit such as: generated power, fault types, fault duration, fault clearing time and retained voltage. The voltage tolerance curve was introduced to describe the stability limit of a system connected to a wind farm.

For long-term voltage stability a comparison was made between wind power plants, thermal power plants and a combination of both the production sources. For both wind power and thermal power the requirement of the Swedish grid code was taken into account. Different control strategies of the reactive power production were analysed for the wind park. An important conclusion is that under normal operation of a wind park, a voltage control mode will be beneficial for the network it is part of.

Keywords:

Voltage stability, short-term voltage stability, long-term voltage stability, voltage collapse, voltage dip, voltage drop, grid code, fixed speed wind turbine, wind farm, wind park.

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Acknowledgments

This project is funded by The Swedish National Energy Agency (Energimyndigheten) whose support is greatly acknowledged.

Great thanks for Dr. Evert Agneholm for guiding me through this research. It remains a privilege to have Dr. Evert Agneholm as my supervisor.

Thanks to Dr. Ola Carlson for his helpful contribution to this project.

Special thanks are extended to Prof. Jaap Daalder for his valuable comments and advices.

My gratitude also goes towards to Dr. Math Bolen who was the supervisor on the beginning of this project.

Further thanks to all my colleagues at Department of Energy and Environment, Chalmers University of Technology. Especially to: Cuiqing Du, Dr. Heike Ullrich, Massimo Bongiorno, Abram Perdana, Roberto Chouhy Leborgne and Dr. Gabriel Olguin.

Finally I would like to express my deep gratitude for the love and support from Valter Nordh and my Family.

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List of Publications

A. M. Martins, Y. Sun, M.H.J. Bollen, “Voltage Stability of Wind

Parks and Similarities with large Industrial Systems”, Nordic Wind Power Conference, March 2004, Gothenburg, Sweden ”

B. M. Martins, A. Perdana, P. Ledesma, E. Agneholm, O. Carlson, “Validation of Fixed Speed Wind Turbine Model for Voltage Stability Simulations”. Submitted to Renewable Energy Journal.

C. M. Martins, E. Agneholm, “ Long-Term Voltage Stability – A Comparison Between Conventional Thermal Power Units

and Fixed Speed Wind Turbines”. To be submitted to IEEE Transactions on Energy Conversions – Wind Power.

Not included on this thesis:

M.H.J. Bollen, G. Olguin, M. Martins, “Voltage dips at the terminals of wind-power installations”, Wiley Interscience Journal - Wind Energy, vol.8, n 3, pp.307-318, July 2005.

O. Carlson, A. Perdana, N. R. Ullah, M. Martins, E. Agneholm “Power System Voltage Stability related to Wind Power Generation”, European Wind Energy Conference, 2006, Athens, Greece.

M. Martins, P. Ledesma, E. Agneholm, O. Carlson, “Voltage Stability of Wind Power Based on Simulations and Field Measurements”, Poster presented at Wind Power Seminar 2004, Gothenburg, Chalmers.

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Table of Contents

ABSTRACT I

ACKNOWLEDGMENTS II

LIST OF PUBLICATIONS III

TABLE OF CONTENTS IV

1 INTRODUCTION 9

1.1 Background and Motivation 9

1.2 Aim and thesis outline 10

2 THEORY 13

2.1 Voltage stability definitions 13

2.2 Importance of a new stability definition involving induction generators 16

2.3 Wind Turbines 17

2.3.1 Conversion of wind energy 17

2.3.2 Wind turbine electrical systems 17

2.3.2.1 General structure 17

2.3.2.2 Wind turbine topologies (electrical systems) 18

2.3.2.3 Power Control Concepts 21

3 VOLTAGE STABILITY ISSUES RELATED TO

IMPLEMENTATION OF LARGE WIND FARMS 23

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3.1 Short term voltage stability (Summary of Paper A) 23

3.1.1 Comparison between wind parks and industrial systems 24

3.1.2 Comparison between simulations and field measurements (Summary of Paper B) 28

3.2 Long-term voltage stability (Summary of Paper C) 29

3.2.1 Factors that influence long-term voltage stability 29

3.2.1.1 Fixed Speed Wind Turbine - Induction Generators 29

3.2.1.2 Synchronous generator current limiters 30

3.2.1.3 Dynamic load 31

3.2.1.4 Transformer on load tap-changer 31

3.2.2 Long-term voltage stability for a grid connected to a wind farm 31

4 CONCLUSIONS AND FUTURE WORK 33

4.1 Conclusions 33

4.2 Future Work 34

REFERENCES 37

APPENDIX 1: PAPERS 39

Section 1 – Introduction

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1 Introduction

Renewable energy is increasing its importance and will become an integral part of the world energy in the future. Apart from hydropower wind energy is one of the most significant renewable sources of electrical power. Great attention has been given to study the impact of wind power on power system stability. Since wind power plants differ from conventional production plants their interaction with the power system diverge from the “classical” behaviour.

1.1 Background and Motivation

Wind power has been used for centuries with different purposes such as: pumping water, propelling boats or grinding corn. The remarkable contribution to the electricity supply started in the mid 1980s.

Since then the interest in wind power has increased with the new demand for clean and sustainable energy sources. Another concern is to plan and built in advance enough generation so that there is sufficient capacity available to meet future load requirements.

Wind power constitutes a significant alternative for the generating of electricity by offering the choice of the use of an energy that needs no fuel and produces no waste or greenhouse gases. For a long time environmental concerns have been the incentive searching for a non-polluting, renewable source of energy that is as cheap as coal and oil.

The installed wind energy capacity has increased significantly around the world during the last years. According to Global Wind Energy Council, the installed capacity, worldwide is 59.3 GW, in Germany 18.5 GW, in Spain 10.0 GW and in the US 9.2 GW. Penetration levels are especially high in Denmark (20%), Spain (5%) and Germany (5%).

In 1997 the Swedish Parliament approved new energy guidelines that assert and emphasize the intent to change to an ecologically sustainable energy production system. According to [7] nuclear power will be replaced slowly by renewable forms of energy. Wind power can be one of the renewable sources that may contribute to accomplish several of the national environmental quality objectives. The Swedish National Energy Agency recommends an


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increase of the use of electricity from renewable sources by 10 TWh/year within the next 10-15 years [8]. In 2004, 400 MW wind energy capacity was installed in the Swedish system which is equivalent to 1% of the total installed electric power in the Swedish system [8].

All over the world wind energy has become very attractive with several attributions; however, there are a number of particularities to take into account. Because wind is an intermittent resource special strategies have to be devised to ensure that electricity supply meets electricity demand. Another important aspect, and of particular concern for this thesis, is related to the integration of large-scale wind power plants into the grid. This aspect may impose challenges. Voltage stability constitutes one of the implications of the wind power integration that requires special attention.

1.2 Aim and thesis outline

Aim of the thesis:

The aim of the thesis is to investigate the impact on short and long-term voltage stability of a grid connected to large wind farms composed of fixed speed wind turbines. Part of the study intends to analyse, categorize and describe the stability problem. The main focus is to identify and characterize stability limits of the system. A comparison with a field measurement is also considered in order to validate the model used in the simulations.

Thesis outline:

The thesis is organized as follows:

Chapter 1 presents a brief introduction with a background and motivation of the project.

Chapter 2 presents the theory of voltage stability definitions and wind turbines. It gives an overview of stability definitions focusing on voltage stability. It also includes a discussion on the importance of a new definition involving the induction generator. After having introduced the voltage stability concepts, the main characteristics of wind turbines are presented providing an overview of the general structure, different control concepts and topologies.

Chapter 3 presents a general overview of the papers which form a part of this thesis. First the studies involving short-term voltage


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stability are discussed based on Paper A. Here a comparison between wind parks and industrial systems is presented and the voltage stability problem involving induction motors and induction generators is described. With the intend to validate different simulator tools, including Digsilent Power Factor used for the investigations in this thesis, the second part presents a summary of a comparison of measurement data and simulations described in Paper B. The last part of this chapter summarizes the investigations of long-term voltage stability comparing thermal power units and fixed speed wind turbines as analysed in Paper C.

Chapter 4 presents the main conclusions of this thesis and proposes issues for future work.

Section 2 – Theory

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2 Theory

2.1 Voltage stability definitions

The concept of voltage stability addresses a large variety of different phenomena depending on which part of the power system is being analysed. For instance it can be a fast phenomenon if induction motors, air conditioning loads or HVDC links are involved. It may be a slow phenomenon if for example a mechanical tap changer is involved. Today it is well accepted that voltage instability is a dynamic process since it deals with dynamic loads and the means of loosing voltage control [2].

Voltage stability: is the ability of a power system to maintain steady voltages at all buses in the system after being subjected to a disturbance. It is the ability of maintaining voltage, so that when load is increased, load power will also increase and voltage and power are controlled. Voltage instability occurs in the form of a progressive fall or rise of voltages of some buses. A possible outcome of voltage instability is the loss of load in an area, or tripping of transmission lines and other elements by their protective systems leading to cascading outages. Loss of synchronism of some generators may result from these outages or from reaching the generator field current limit [1].

The voltage stability definitions presented in this chapter are based on the classification shown in the diagram bellow from IEEE/CIGRE. It presents an overview of the classification of power system stability [1].


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Power System Stability

Rotor Angle

StabilityFrequency

StabilityVoltage

Stability

Small Disturbance

Angle StabilityTransient Stability

Short Term

Large Disturbance

Voltage Stability

Small Disturbance

Voltage Stability

Long TermShort TermShort Term Long Term

Figure 1: IEEE/CIGRE Power system stability diagram.

Voltage Collapse: Voltage collapse is more complex than voltage instability and is usually the result of a sequence of events accompanying voltage instability leading to a low unacceptable voltage profile in a significant part of the power system. When a power system is subjected to a sudden increase of reactive power demand following a system contingency, the additional demand is met by the reactive power reserves of generators and compensators. Generally there are sufficient reserves and the system settles to a stable voltage level. However, it is possible, due to a combination of events and system conditions that lack of additional reactive power demand may lead to voltage collapse, causing a total or partial breakdown of the system. Voltage stability problems normally occur in heavily stressed systems. While the disturbance leading to voltage collapse may be initiated by a variety of causes, the underlying problem is an inherent weakness in the power system [3].

The principal factors contributing to a voltage collapse are [3]:

• the generator reactive power/voltage control limits

• load characteristics

• characteristics of reactive compensation devices, and/or action of voltage control devices such as transformer under-load tap changers (ULTCs).

Large-disturbance voltage stability: refers to the system's ability to maintain steady voltages following large disturbances such as system faults, loss of generation, or circuit contingencies.


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This ability is determined by the system and load characteristics, and the interactions of both continuous and discrete controls and protections. Determination of large-disturbance voltage stability requires the examination of the nonlinear response of the power system over a period of time sufficient to capture the performance and interactions of such devices as motors, under-load transformer tap changers and generator field-current limiters. The study period of interest may extend from a few seconds to tens of minutes [1]. Small-disturbance voltage stability: refers to the system's ability to maintain steady voltages when subjected to small perturbations such as incremental changes in system load. This form of stability is influenced by the characteristics of loads, continuous controls, and discrete controls at a given instant of time. This concept is useful in determining, at any instant, how the system voltages will respond to small system changes. The time frame of interest for voltage stability problems may vary from a few seconds to tens of minutes. Therefore, voltage stability may be either a short-term or a long-term phenomenon [1]. Short-term voltage stability involves dynamics of fast acting load components such as induction motors, electronically controlled loads and HVDC converters. The study period of interest is in the order of several seconds, and analysis requires solution of appropriate system differential equations; this is similar to the analysis of rotor angle stability. Dynamic modeling of loads is often essential. In contrast to angle stability, short circuits near loads are important [1]. Long-term Voltage Stability: involves slower acting equipment such as tap-changing transformers, thermostatically controlled loads and generator current limiters. The study period of interest is up to minutes. Therefore long-term simulations are required for an analysis of the system dynamic performance. Stability is usually determined by the resulting outage of equipment, rather than the severity of the initial disturbance. Instability is due to the loss of long-term equilibrium (e.g., when loads try to restore their power beyond the capability of the transmission network and connected generation), the post-disturbance steady state operating point being small-disturbance unstable or a lack of attraction towards the stable post-disturbance equilibrium (e.g., when a remedial action is applied too late) [1].


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2.2 Importance of a new stability

definition involving induction

generators

When an induction generator is subjected to a severe fault in the connected grid, a significant increase occurs in its rotor speed. Even after the voltage recovers the generator rotor speed keeps increasing and it will not return to the pre-fault value. Further description of this phenomenon is given in Chapter 3.

[4] brings up an important discussion and a proposal for a definition of instability involving induction generators. Voltage instability at present clearly defines an induction machine in motor operation that stalls. However, the definition is not the same for an induction machine operating as a generator. The voltage stability definition [1], [2] and [3] refers to a balance between load demand and load supply. In this case no load is involved, but instead there is an induction machine operating as a generator in a run away situation. The existing stability concepts for power systems, covered at [1], [2] and [3], do not include this phenomenon.

[4] proposes an adjustment in the voltage stability definition to include induction generators and an introduction of a new type of stability named: “rotor speed stability”. Rotor speed stability is related to the torque-speed dependence of asynchronous generators whereas rotor angle stability is related to the torque-angle dependence of synchronous generators. The suggested definition in [4] is:

“Rotor speed stability refers to the ability of an induction (asynchronous) machine to remain connected to the electric power system and running at a mechanical speed close to the speed corresponding to the actual system frequency after being subjected to a disturbance.”

The definition above represents an important initiative to describe the phenomenon. Careful and precise definitions in the future are needed to cover the stability of induction generators.

In this thesis and following the definitions at [1], the term “short-term voltage stability” will still be used when also referring to the rotor speed stability phenomenon.


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2.3 Wind Turbines

2.3.1 Conversion of wind energy

Wind power is converted by the rotor of a wind turbine into rotational power that is transferred to a generator, either directly or through a gearbox increasing the rotor speed. The mechanical power is converted into electrical power in the generator. From the generator the electrical power is transferred to the grid.

The instantaneous power windP available in the wind flowing

through an area vA can be described as:

3..2

1wvairwind vAP ρ= (1)

Where airρ is the mass density of air and wv is the velocity of the

wind. The fraction of the wind captured by a wind turbine is given by a factor pC , the power performance coefficient. This coefficient

is based on the theoretical maximum power that can be extracted from the wind, the so called Betz limit. It can be expressed as:

%59..2

1 3 == pwvairBetz CvAP ρ (2)

2.3.2 Wind turbine electrical systems

2.3.2.1 General structure

The most common wind turbine structure used today is the horizontal axis with three blades. In the past, two-bladed wind turbines have also been used. However, two-bladed wind turbines must operate at higher rotational speeds than a three-bladed wind turbine. To operate at such speeds the individual blades in a two-bladed wind turbine need to be lighter and stiffer and therefore they are more expensive [10], [11].


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Figure 2: Typical structure of the nacelle for a horizontal three-blade grid connected wind turbine.

2.3.2.2 Wind turbine topologies (electrical systems)

Wind turbines can operate either at fixed speed or at variable speed.

Fixed Speed: This technique totally dominated the first ten years of wind turbine development during the nineties of the last century. Operation at constant speed means that regardless of the wind speed, the wind turbine’s rotor speed is fixed and determined by the frequency of the grid, the gear ratio and the generator design.

Usually fixed speed wind turbines are equipped with a squirrel cage induction generator connected to the grid, with a soft starter and a capacitor bank for reducing the reactive power consumption. They are designed to achieve maximum efficiency at a particular wind speed. Wound rotor synchronous generators have also been also applied; however, at present, the most common one is the induction generator. Figure 3 illustrates a fixed speed wind turbine based on the squirrel-cage induction generator.

The fixed speed wind turbine has the advantage of being simple, robust, reliable and well proven. The cost of its electrical parts is low. Its disadvantages are an uncontrollable reactive power


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consumption, mechanical stress and limited power quality control [5].

Fixed speed wind turbines can have pitch control, stall and active stall control.

Figure 3: Fixed Speed

Variable speed: The tendency in the last few years among the installed and planned wind parks is to use variable speed wind parks. This concept represents the trend in modern wind turbine technology. They are designed to achieve maximum aerodynamic efficiency over a wide range of wind speeds. This concept brings the possibility to adapt (accelerate or decelerate) the rotational speed of the wind turbine to the wind speed. The electrical system is usually equipped with an induction generator or synchronous generator and connected to the grid through a power converter. At present, there are two types of topologies which are believed to be some of the most promising solutions: doubly fed induction generator (DFIG) and full size converter.

In the DFIG system, a frequency converter is connected to the rotor circuit of the induction generator. Variable speed is achieved by controlling the rotor currents. The possible speed variation of the generator is proportional to the power of the converter, i.e. a speed variation of ±20 % gives a power rating of the converter of 20% of the rated power of the wind turbine. The most advanced types of this system shall be able to ride-through a voltage drop according to the grid codes. A DFIG system is shown in Figure 4. In this system, only a part of the power passes the frequency converter and thereby the cost of the converter and the system losses are lower compared with the full size converter where all the power passes through the converter.


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Figure 4: Doubly fed induction generator

In a system with a full power converter the control of the current is total and thereby the control of active and reactive power is precise. During a voltage dip it is possible to keep control of the current, which gives good performance during grid disturbances and full capability to ride-through faults. The system consists of a rectifier, an inverter and a generator. Sometimes a DC/DC-converter is also included to raise the low and variable generator rectifier voltage to a constant DC-voltage. The generator can be a synchronous generator with electric excitation or permanent magnets, but it can also be an induction generator, see Figure 5.

GRID

DC/DC Converter

ac

dcac

dc dc

dc

Generator rectifierGrid inverter

Filter

Gen

Figure 5: Full size converter

The advantages of a variable speed wind turbine are an increased energy capture, improved power quality and reduced mechanical stress on the wind turbine. The disadvantages are losses in power electronics, the use of more components and the increased cost of equipment because of the power electronics. The introduction of variable speed wind turbines increases the number of applicable generator types and also introduces several degrees of freedom in the combination of generator type and power converter type.


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2.3.2.3 Power Control Concepts

In the same way as for other production plants, wind turbines are designed to produce electrical energy at a minimum cost. In practice it means that the maximum output of the wind turbine is restricted to wind power of around 15 meters per second. Considering the incidence of stronger winds it is necessary to waste a part of the excess energy of the wind in order to avoid damage to the wind turbine. Therefore all wind turbines are designed with some sort of power control.

The prevalent methods in modern wind turbines are: pitch control, stall control, and active stall control. In general, all three types of control (or a combination) can be applied for the fixed speed wind turbines whereas for the variable speed wind turbines pitch control is most commonly used.

Pitch control: Wind turbines with this type of control have the ability to change the power performance coefficient pC by turning

the rotor blades around their longitudinal axis. The blades can be turned out or into the wind as the power output becomes too high or too low, respectively. At high wind speeds the mean value of the power output is kept close to the rated power of the generator.

The advantages of this type of control are good power control, assisted start-up and emergency stop. Some disadvantages are the extra complexity arising from the pitch mechanism and higher power fluctuations at high wind speeds.

Stall control: is the simplest, most robust and cheapest method where the blades are locked onto the hub at a fixed angle (contrary to the pitch controlled turbine). Thus, it is the aerodynamic performance of the blades that provides the power control. The rotor stalls (looses power) when the wind speed exceeds a certain level. Compared to pitch control, the slow aerodynamic power control causes less power fluctuations. Some drawbacks of the method are lower efficiency at low wind speeds, no assisted start-up and variations in the maximum steady-state power due to variations in air density and grid frequencies.

Active stall control: the active stall control is similar to the pitch control at low speeds. The stall of the blade is actively controlled by pitching the blades. At high wind speeds the blades enters a deeper stall by slightly being pitched into the direction opposite to that of a pitch-controlled turbine. Instead of pitching the blades


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out of the wind, the attack angle of the blades is increased provoking a stall situation.

The active stall wind turbines achieve a smoother limited power, without high power fluctuations as in the case of pitch-controlled wind turbines. This control type has the advantage of being able to compensate variations in air density. The combination with the pitch mechanism makes it easier to carry out emergency stops and to start-up the wind turbine.

Section 3 –Voltage stability issues related to implementation of large wind

farms

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3 Voltage stability issues

related to implementation of

large wind farms

This chapter presents a summary of important aspects of the papers and explains some of the stability issues related to implementation of large wind farms. The papers are organized as follows:

Paper A

“Voltage Stability of Wind Parks and Similarities with Large Industrial Systems”: presents a description of the voltage stability problem of a power system having either an induction motor or an induction generator. A detailed analogy is made by pointing out similarities and differences. The main discussion concerns voltage drop and short-term voltage stability after a fault.

Paper B

“Validation of Fixed Speed Wind Turbine Model for Voltage Stability Simulations”: presents an investigation of the models used in the simulations and comparing them with the field measurement data.

Paper C:

“Long-Term Voltage Stability – A Comparison Between Conventional Thermal Power Units and Fixed Speed Wind Turbines”: by comparing both types of generation a beneficial side of the wind power is highlighted when it is acting as a voltage control.

3.1 Short term voltage stability (Summary

of Paper A)

Short-term voltage stability for a grid connected to a wind farm has to be analyzed taking into account the behaviour of induction generators requiring a large amount of reactive power immediately after a fault in the grid has been cleared. This


farms

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mechanism may lead to a voltage stability problem with a risk of voltage collapse as a final consequence.

The equations (1) and (2) in Paper A are essential to understand the stability problem involving an induction generator. The reduction in the electromagnetic torque during a fault in the grid is the starting point for leading the generator to speed up.

Depending on the fault location in the grid, the generator can recover to stable operation or not. A detailed description is given in Paper A illustrating the stable and unstable situation for motor and generator operation.

Voltage tolerance curve

The 'Voltage-tolerance Curve' is introduced in order to qualify the voltage stability limit of the installations. The voltage tolerance curve is a common tool to study the compatibility between the power supply and equipment sensitive to voltage dips (in this case the wind park). It indicates the most severe voltage dips that can be tolerated without leading to incorrect operation of the equipment. For the investigations presented in Paper A the voltage-tolerance curve was constructed by applying a three phase to ground fault, varying the maximum clearing time in combination with the retained voltage. Retained voltage means the voltage left during the voltage dip. The duration that gives the transition between stable and unstable operation becomes one point in the voltage-tolerance curve.

3.1.1 Comparison between wind parks and

industrial systems

In Paper A, Appendix 1, a comparison was made between the behaviour of wind parks and large industrial systems. A grid connected to a large wind park of 200 fixed speed wind turbines totalling 500 MVA was studied.

The main difference between motors and generators is that, after a disturbance in the grid, induction motors will decrease the speed whereas induction generators will keep speeding up.

Some of the similarities are related to the layout of the system. Either wind parks or industrial systems have the same rule for the maximum cable length based in the voltage drop along the cables.


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A difference comes for the voltage drop along an impedance. In Paper A is presented a well known (approximated) expression for the voltage drop along an impedance R+jX due to a load P+jQ is presented. Below is described how these expressions are obtained for motor and generation operation.

Induction Motor

jXI−

ZmotorP

motorQ

motorUE

+

−

+

−

I

φcosI

φsinII

E

RI−

φ

motorU

Figure 6: Circuit with a motor and phasor diagram

jXRZ += , in general RX > .

UEUmotor ∆−= (3.1)

ZIEUmotor −= (3.2)

φφ sincos jIII −= (3.3)

[ ])sincos)(( φφ jIIjXREUmotor −+−= (3.4a)

[ ])sincos()sincos( φφφφ RIXIjXIRIEUmotor −++−= (3.4b)

[ ])sincos()sincos( φφφφ RIXIjXIRIUE motor −++=− (3.4c)

The angle between motorU and E is small, so the imaginary part of

motorUE − is neglected.

Therefore:

)sincos( φφ XIRIUE motor +≈− (3.5)

UUE motor ∆=−


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φφ sincos XIRIU +≈∆ (3.6)

Assuming ..1 upU = :

φcospupu IP ≈ (3.7)

φsinpupu IQ ≈ (3.8)

Then:

pupupu XQRPU +≈∆ (3.9)

motorP : active power consumed by the motor

motorQ : reactive power consumed by the motor

motorU : bus voltage, motor side

E : ideal voltage source

I : load current from voltage source

jXRZ += :constant impedance

U∆ : voltage drop

Induction generator:

genUE

+

−

+

−

I

ZgenP genQ

I

RI

genU

E

jXI

φ

Figure 7: Circuit with a generator and phasor diagram.

jXRZ += in general RX > .


farms

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UEU gen ∆+= (3.10)

ZIEU gen += (3.11)

φφ sincos jIII −−= (3.12)

[ ])sincos)(( φφ jIIjXREU gen −−++= (3.13a)

[ ])cossin()sincos( φφφφ XIRIjXIRIEU gen +−+−+= (3.13b)

[ ])cossin()sincos( φφφφ XIRIjXIRIEU gen +−+−=− (3.13c)

The angle between genU and E is small:

EXIRIj <<+ )cossin( φφ (3.14)

)sincos( φφ XIRIEU gen +−≈− (3.15)

UEU gen ∆=−

φφ sincos XIRIU +−≈∆ (3.16)

Assuming ..1 upU = :

φcospupu IP ≈ (3.17)

φsinpupu IQ ≈ (3.18)

Then:

XQRPU +−≈∆ (3.19)

genP : active power generated by the generator

genQ : reactive power consumed by the generator

genU : bus voltage, generator side

E : ideal voltage source

I : load current from generator

jXRZ += :constant impedance


farms

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3.1.2 Comparison between simulations and field

measurements (Summary of Paper B)

Discussions have been going on about the fixed speed wind turbine model used for voltage stability simulations. In many studies the induction generator model neglects stator transients [15], [16], [17], but still there is no full agreement on this point [14]. The same occurs for the drive train model, depending on the purpose of the investigation, one-mass model [17] or two-mass model [15], [16], [14] are used.

A recorded data set from a fixed speed wind turbine of 180 kW, 0.4 kV from Alsvik was used to validate the models in three different simulator programs: PSS/E, Digsilent Power Factory and Matlab. The data after a disturbance of voltage, current, active and reactive power was recorded. Paper B describes in detail the models used in the simulations and it makes a comparison with the field measurements.

The results presented in Paper B show good agreement between the measured data and the simulations for both induction generators models: either neglecting stator transients or taking them into account. Since there is no big difference in both models, the model neglecting the stator transients is accurate enough to simulate the study case.

The mechanical model was also verified comparing an one-mass model and a two-mass model. An one-mass model is a lumped model where the masses of the wind turbine, gear box and generator rotor are lumped into a single rotating mass and the wind turbine shaft is not included in the model. In the two-mass model the wind turbine and the generator are represented separately and the shaft is included, see Paper B, Fig. 1. The simulations show a significant difference between these two models. When using a one-mass model the active power oscillations during the fault are considerable lower than when using a two-mass model. The recovering time for voltage and rotor speed is faster when using one-mass model as compared to a two-mass model. Thus, an unstable situation when using an one-mass model can easily be overlooked.

The investigations in Paper B show that the differences in the frequency oscillations between the measurements and simulations are due to the inertia (J) of the generator and stiffness (K) of the mechanical coupling. The very fast transient at the first moment


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depends on the time constant. The results are primarily related to the electromechanical transients, not the electromagnetic transients.

3.2 Long-term voltage stability (Summary

of Paper C)

From a perspective of long-term voltage stability Paper C presents a study where fixed speed wind turbines are compared with conventional thermal power plants. For simulation purposes a simplified network was used representing a main production area, a transmission system and a load with some generation. The wind farm is composed of fixed speed wind turbines with induction generators equipped with capacitor banks for reactive power compensation. For simulation purposes the mechanical model is represented as an one-mass model wind turbine. The model of the system also includes a transformer tap changer, a dynamic load and armature and current limiters.

The investigations were carried out considering a variation on the active power generation of the production plants. For the wind park, different control strategies of the reactive power production were applied. The purpose of the analysis was to investigate how the presence of wind power influences long-term voltage stability. The results displayed an important aspect of the wind park control strategies.

3.2.1 Factors that influence long-term voltage

stability

Long-term voltage stability is primarily related to slower acting equipment such as generator current limiters, dynamic loads and transformers tap-changers. These components should be modelled properly, if system stability is investigated. The same is true for fixed speed wind turbine model.

3.2.1.1 Fixed Speed Wind Turbine - Induction Generators

When using induction generators, special attention has to be given to reactive power compensation. For the simulations done in Paper C, shunt capacitors were used and two different control strategies were applied:


farms

30

Reactive power control: is used for compensating the reactive losses in the wind park and transformer. In the point of the connection to the grid the reactive power is controlled, i.e. no exchange with the grid occurs irrespectively of the voltage level.

Voltage control: is used for controlling the voltage in the point of connection to the grid. In case of an active power production less than maximum available shunt capacitors are connected and disconnected at various voltage levels. For severe voltage instability situations all shunt capacitors will be connected after the voltage decrease. This behaviour will also correspond to the behaviour of a SVC which acts very fast.

3.2.1.2 Synchronous generator current limiters

Since voltage problems can be due to generators performance, it is important to consider the reactive capability limits of synchronous generators in long-term voltage stability studies. Therefore models of the field and armature current limiters are included in the voltage regulator of the synchronous generator.

Field current limiter: protects the field winding from overheating due to a prolonged field overcurrent. The limiter may be activated after a load increase when for some reason the system suffers a deficiency of the transmission capacity. After activation the generator behaves as a fixed voltage source behind a reactance. This represents an increase of the reactance in the system leading to an increased risk of a voltage collapse. A description is given in [12]. The settings for the time delay was 4 seconds and for the field current limit 3.0 p.u.. The block diagram used to model the field current limiter is shown in Paper C, Appendix, Figure 13.

Armature current limiter: limits the increase in temperature of the generator due to the increase of the RI2 power losses. When activated, the generator behaves like a constant current source. As a result the voltage regulator will reduce the excitation of the generator and thereby the reactive power production. The settings for the time delay was 4 seconds and for the field current limit 1.05 p.u.. The block diagram used to model the field current limiter is shown in Paper C, Appendix, Figure 14.


farms

31

3.2.1.3 Dynamic load

During voltage instability the impact of the load is essential to consider as the load recovery can further aggravate the situation when the voltage starts to decline. Paper C gives a detailed description of the dynamic load model used in the investigations.

3.2.1.4 Transformer on load tap-changer

Tap-changers provide voltage control by restoring the load voltage level. They can be the cause of long-term voltage instability in their attempt to restore the load voltage. Increasing the voltage may lead to a load increase and as a result the transmission voltage level is deteriorated. If this process continues it may eventually lead to voltage collapse. The time delay of the tap-changer model for the studies in Paper C has been set to 30 seconds constant time per step.

Based on the simulations performed it can be observed that if no tap-changer is included in the transformer model, the voltage collapse will take longer time to occur even for critical levels of load demand.

The interaction between dynamic load, tap-changer and generator current limiters is also described in this paper.

3.2.2 Long-term voltage stability for a grid

connected to a wind farm

When studying voltage stability it is important to consider the grid code requirements for absorbing and supplying reactive power. By taking the Swedish grid code as an example, the only requirement for wind power is that it shall be able to control the reactive power production and consumption to 0 MVAr at the connection point to the grid.

Simulations were done based on the system described. DigSilent Power Factory simulator software was used to carry out all investigations. The problem that leads to voltage instability is caused by the trip of one of the two transmission lines, followed by the tap-changer action and load recovery until the current limiters are activated. In Paper C, three different scenarios were investigated: the system is supplied by only thermal power, the system is supplied by only wind power and the system is supplied by both thermal and wind power.


farms

32

When the system is supplied by the induction generators from the wind farm, the reactive power demand increases with the loading of the machine. In order to compensate this reactive power, shunt capacitors, HVDC light or a SVC can be used. Paper C uses shunt capacitors and describes two alternatives that have been applied: reactive power control and voltage control of the wind park. When using only reactive power control the load level supply is reduced with a decrease of the active power generation. In this case the reactive power consumption by the induction generators is determining the voltage stability limit for the system. However if voltage control is used, higher amounts of load can be supplied. Even at 0 MW of generated power (no wind incidence), a considerable amount of load can survive after a loss of a transmission line. The simulations demonstrated that the wind farm under normal operating conditions can provide reactive power to the grid regardless of the amount of wind. From a power system point of view wind power may be used as a contributor to voltage control. The Swedish grid code states that on the connection point the reactive power exchange with the wind park shall be 0MVAr. It is recommended to revise this statement and include a new requirement stating that wind farms must be equipped with voltage control.

Section 4 – Conclusion and future work

33

4 Conclusions and future

work The main conclusions and proposals for future work are presented in this section.

4.1 Conclusions

In this thesis the main issue investigated is how large wind farms composed by fixed speed wind turbines affect voltage stability of power systems.

Comparisons were made in order to facilitate the analysis of the behaviour of a wind farm. By comparing induction generators with induction motors and wind power plants with thermal power plants it was possible to evaluate their performance and to define the limits of the wind farm and its interaction to the grid and vice-versa.

The main difference between motors and generators is that, after a disturbance in the grid, induction motors will decrease the speed whereas induction generators will keep speeding up.

For the short-term voltage stability investigations the “voltage tolerance curve” was introduced in order to describe the stability limit of a system when connected to a wind farm. The voltage tolerance curve defines the stable and unstable areas for different voltage dips related to maximum fault clearing time.

A comparison with field measurements was also performed in order to validate the simulation models used for the investigations. The conclusions of this evaluation define which models shall be used in the simulations in order to have good agreement with experimental results. The main conclusions are the following:

• An induction generated model where stator transients are neglected is of sufficient accuracy describe voltage stability.

• Electromechanical oscillations can only be represented with a sufficient accuracy by a two-mass mechanical model in case of short-term voltage stability.


34

• The introduction of mechanical damping is necessary to achieve a good agreement between the measurements and the simulations.

Long-term voltage stability studies were done based on a comparison of wind farms with thermal power plants. The main conclusions is that the integration of a large wind farm acting as a voltage control may be beneficial for power system performance. Irrespective of the amount of the incidence of wind blowing, (i.e. even if the active power production would be close to 0 MW) the wind farm can provide reactive power to the system. This means that the power system performance will be able to contribute to keep the voltage stable for a reasonable amount of power demand.

Based on the analysis performed it is recommended that the grid code includes a requirement stating that wind farms shall be equipped with voltage control. The present restriction that wind power is not allowed to have an exchange of reactive power with the grid may then be removed.

4.2 Future Work

Power system stability studies deal with a large number of different aspects and the complexity is increased when combined with wind power studies. Future work of this combination should include the following topics:

• Frequency stability: of special interest is wind park behaviour during storms. Initially the power production of the wind park will increase to a maximum but when it becomes too windy the wind park will be closed down. The wind park power production will then change from maximum to zero in a short period of time. If wind power constitutes a sizeable part of the total generation, frequency instability will become a major issue.

• Doubly fed induction generator (DFIG): DFIG consists of a induction generator with a variable speed wind turbine combined with a power electronic converter. After a voltage disturbance it differs from fixed speed wind turbines. DFIG will disconnect from the grid in order to protect the power electronic converter which is very sensitive to overcurrents. This sudden loss of generation may lead to further voltage and frequency disturbances

• Full power converter: the current is controlled and thus the control of active and reactive power is very precise.


35

However, it is an expensive system. The current control is kept even during a voltage dip giving a good performance during any grid disturbance and full capability to ride-through. Further studies with this converter concept combined with induction or synchronous generators verifying the advantages and disadvantages related to costs have to be considered.

• Grid Codes: when analysing the advantages and disadvantages of different generator types it is important on the one hand to check their ability to fulfil the grid codes. On the other hand suggestions for modifications or renewal of existing codes are important to consider.

• Dimensioning criteria for connecting large wind parks to the existing transmission systems is another issue of main importance.

37

References

[1] P. Kundur, J. Paserba, V. Ajjarapu, G. Andersson, A. Bose, C. Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. Van Cutsem, V. Vittal. “Definition and classification of power system stability IEEE/CIGRE

joint task force on stability terms and definitions”. Power Systems, IEEE

Trans. Vol. 19. 2004; pp. 1387 – 1401.

[2] C. Taylor, Power Systems Voltage Stability, McGraw-Hill Inc.: New York, 1994.

[3] P. Kundur, Power Systems Stability and Control, McGraw-Hill Inc.: New York, 1994.

[4] O. Samuelsson, S. Lindhal, ”On Speed Stability”, IEEE Transactions On Power Systems, vol. 20, nº 2, pp. 1179-1180, May 2005.

[5] T. Ackerman, Wind Power in Power Systems, John Wiley & Ltd, 2005.

[6] M. Kazmierkowski, R. Krishnan, F. Blaabjerg, Control in Power Electronics: Selected Problems, Academic Press, 2002.

[7] Energimyndigheten. Climate Report 2001. Technical Report ER 6:2002, Swedish National Energy Agency, www.stem.se, 2002. ISSN 1403-1892.

[8] Energimyndigheten. Energy in Sweden 2004. Article Number 1664 ET 19-2004, Swedish National Energy Agency, www.stem.se, 2004.

[9] Energimyndigheten. Energy in Sweden 2004-OH-Pictures. Article Number 1677, Swedish National Energy Agency, www.stem.se, 2004.

[10] Å. Larsson , “The Power Quality of Wind Turbines”, Ph.D. dissertation, Dept. Electric Power Engineering. Chalmers University of Technology, Sweden, 2000.

[11] R. David Richardson, G. Mcnerney, “Wind Energy Systems”, Proceedings of IEEE, 1993.

[12] S. Johansson, “Long-term Voltage stability in Power Systems”, Ph.D. dissertation, Dept. Electric Power Engineering. Chalmers University of Technology, Sweden, 1998.

[13] J. G. Slootweg, W.L. Kling, “Modelling and analysing impacts of wind power on transient stability of power systems”, Wind Energy vol. 25, nº 6, 2001, vol. 26, nº 1, 2002.

[14] V. Akhmatov, H. Knudsen, “Modelling of Windmill Induction Generators in Dynamic Simulation Programs”, International Conference on Electric Power Engineering, PowerTech Budapest 1999, 29 Aug.-2 Sep. 1999, p. 108.

38

[15] P. Ledesma, J. Usaola, J.L. Rodríguez, “Transient Stability of Fixed Speed Wind Farm”, Renewable Energy, vol. 28/9, pp. 1341-1355, Feb. 2003.

[16] T. Petru, T. Thiringer, “Modelling of Wind Turbines for Power System Studies”, IEEE Transactions on Power Systems, vol. 17, nº 4, pp. 1132-1139, Nov. 2002.

[17] Z. Saad-Saoud, N. Jenkins, “Simple Wind Farm Dynamic Model”, IEEE Proceedings on Generation, Transmission and Distribution, vol. 142, nº 5, pp. 545-548, Sep. 1995.

Appendix 1: Papers

PAPER A

M. Martins, Y. Sun, M.H.J. Bollen, “Voltage Stability of Wind

Parks and Similarities with large Industrial Systems”, Nordic Wind Power Conference, 2004, Gothenburg, Sweden.

PAPER B

M. Martins, A. Perdana, P. Ledesma, E. Agneholm, O. Carlson, “Validation of Fixed Speed Wind Turbine Model for Voltage

Stability Simulations”. Submitted to Renewable Energy Journal.

PAPER C

M. Martins, E. Agneholm, “ Long-Term Voltage Stability – A Comparison Between Conventional Thermal Power Units

and Fixed Speed Wind Turbines”. To be submitted to IEEE Transactions on Energy Conversion – Wind Power.

NORDIC WIND POWER CONFERENCE, 1-2 MARCH, 2004, CHALMERS UNIVERSITY OF TECHNOLOGY 1

Abstract— Stability investigations have been carried out to

study behavior of the system during and after a short circuit

fault for both wind parks and large industrial systems. The

main phenomenon that determines the behavior is the large

reactive power taken by the induction machines immediately

after the fault has been cleared. This mechanism leads to a

voltage stability problem with a risk of voltage collapse as a

final consequence. A commercial power system analysis

package has been used to study this phenomenon in detail. The

so-called "voltage tolerance curve" has been used to quantify

the voltage stability limit of the installations. The voltage

tolerance curve is a common tool to study the compatibility

between the power supply and equipment sensitive to voltage

dips. It indicates the most severe voltage dips that can be

tolerated without leading to incorrect operation of a piece of

equipment. The voltage tolerance curves will be given for both

systems and for different operational states. These studies

confirm the strong similarities expected in voltage-stability

between the systems. The differences between the systems are

discussed and explained in the paper.

Index Terms— Voltage stability, voltage drop, voltage dips

(sags), power quality, wind power installations.

I. INTRODUCTION

ind parks are composed of several induction machines

as generating units. Certainly a large percentage of

electrical machines found in industrial systems are induction

motors. Because of this, similarities in design and operation

of both systems are to be expected. By realizing these

similarities, the existing knowledge on industrial power

systems can be used for the design of future wind parks.

The direction of the active power flow is however

different in industrial systems as in wind parks. This will

account for some differences. This paper will address some

of the similarities and differences between these two

systems.

II. LAY-OUT OF THE SYSTEM

An example of the design for a large wind park is shown

in Figure 1. The wind park connects a number of wind

turbines, typically all of the same size. In this case the

turbines are supplied at 960 Volt, each with a dedicated

transformer. Ten of these generator-transformer units are

supplied through a 150/20 kV transformer; 20 of these

groups are supplied through two parallel 400/150 kV

transformers. A similar structure can be found in many

industrial power systems at medium voltage. The difference

can be found at low voltage because the industrial system

contains a mixture of large and small machines whereas the

wind park contains only large machines.

400kV

15000MVA

400kV

150kV

500MVA

Total

20 strings with

10 wind turbines

each

Total

10 wind turbines

Total

10 wind turbines

Total

10 wind turbines

Figure 1: Example of a large wind park.

Like in industrial systems the location of the machines is

not determined by the power system requirements. Figure 2

shows the geographical layout of a 500 MVA wind farm,

consisting of 200 turbines, 700 m between each other, and

integrated into the transmission network at 150 kV voltage

level. The 150/20-kV transformers are located on top of

each string of 10 transformer-turbine combinations. More

details of the system can be found in [1].

14 km

7 km

14 km

7 km

Figure 2: Layout of a large wind park with 200 turbines: each dot

represents a 2.5 MVA turbine.

The layout of the system is ruled by the voltage drop

along the cables and by the loading of the cables and the

transformers. This results in two rules that decide the

maximum cable length:

• the total load should not exceed the rating of the

cable;

Marcia Martins1, Yu Sun2, Math H.J. Bollen3

1Chalmers University of Technology, Gothenburg, Sweden, [email protected]

2University of Strathclyde, Glasgow, United kingdom, [email protected]

3STRI AB, Ludvika, Sweden, [email protected]

Voltage Stability of Wind Parks and Similarities with

large Industrial Systems

W


• the voltage should be within the permitted range

for every load at every load condition.

The first rule can be applied alternatively by fixing the

cable length and choosing a cable cross-section such that the

total load can be supplied. In either way the first rule will

result in exactly the same cable length for motor as for

generator operation.

The second rule is slightly different. A well known

(approximated) expression for the voltage drop along an

impedance R+jX due to a load P+jQ is applied.

The 150 kV bus is taken as the reference voltage for the

voltage drop calculation.

For motor operation the expression is:

XQRPU +=∆ (1)

For generator operation the voltage drop is:

XQRPU +−=∆ (2)

For large cable cross-sections the reactive part of the

voltage drop (XQ) will normally dominate, but the

difference between (1) and (2) is still enough to make a

difference. Simulations for the system in Figure 1 showed a

significant difference in voltage at the machine terminals

between motor operation and generator operation. The

difference is amplified because the relation between voltage

and reactive power. A lower terminal voltage will result in a

lower speed for the motor which in turn results in more

reactive power consumption.

Another difference between motor and generator

operation is that the lowest voltage is not necessarily with

highest current for generator operation.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Active power (pu)

Reactive power (pu)

V=0.7Vnom V=0.8Vnom

V=0.9Vnom

V=Vnom

Figure 3: Reactive power consumed by an induction generator as a

function of the generated active power and voltage.

The voltage drop or rise with induction generators

depends on the amount of power generated by the turbine.

The reactive power consumption is related to the active

power production according to the relation shown in Figure

3. The voltage drop, according to (2), as a function of the

generated active power is plotted in Figure 4. In this case a

small voltage drop results for zero active power, but in all

other cases the voltage rises (negative voltage drop =

voltage rise).

Figure 4: Voltage drop at the end of the cable as a function of the

generated power.

The relation between active power and voltage drop

depends on the machine parameters and on the X/R ratio of

the feeder. The result is different for each case.

III. STABILITY FOR GENERATORS

During a short circuit fault close to the terminals of an

induction machine, the short circuit current rises because of

the machine contribution and the generator terminal voltage

drops. Due to this voltage dip, the output electrical power

and the electromagnetic torque suffer a significant

reduction. Only a small amount of electrical power can be

fed into the grid. As the mechanical power remains constant

the machine will speed up.

The electromagnetic torque developed inside an induction

machine at any given speed is proportional to the square of

the terminal voltage as follows:

2)( VsKTe = (1)

eT : electromagnetic torque; K : constant values depending

on the parameters of the machine; s : machine slip speed;

V : terminal voltage

Thus a 30% reduction in voltage leads to a 50% reduction

in electrical torque. As electrical and mechanical torque are

in balance before the fault, suddenly 50% of the mechanical

torque has to be used to accelerate the machine.

The dynamic behavior of the rotor is governed by the

swing equation given below:

em TTdt

dJ −=

ω (2)

J : moment of inertia of the rotating mass; ω : rotor

angular speed; mT : mechanical torque applied to the rotor;

Te: electrical torque.

After clearance of the fault the voltage at the machine

terminal recovers. Before any energy can be transferred

between the rotor and the stator (thus between the

mechanical and the electrical side of the machine) the air-

gap field has to build up. Building up this magnetic field

requires a high reactive current (the "magnetic inrush").

Thus current leads to a voltage drop at the machine


terminal: the voltage does not fully recover, thus the

electrical torque does not fully recover. If the electrical

torque during recovery remains lower than the mechanical

torque the machine will keep on accelerating: it looses

synchronism. The result for the power system is a voltage

collapse situation: unless the protection removes the

generators they will gradually pull down the rest of the

system. Figures 5a, 5b and 5c show an example for an

unstable case.

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (seconds)

Voltage Phasor Magnitude (p.u.), Speed (p.u.)

Speed

Voltage

2'

1

3''7''

6'

Figure 5a: Unstable case: asynchronous generator voltage and speed.

0 0.5 1 1.5 2 2.5 3100

150

200

250

300

350

Time (seconds)

Current Phasor Magnitude (kA)

Figure 5b: Unstable case: asynchronous generator current.

0 0.5 1 1.5 2 2.5 3-400

-300

-200

-100

0

100

200

300

Time (seconds)

Active Power (M

W), Reactive Power (M

VAr)

Active power

Reactive power

Figure 5c: Unstable case: asynchronous generator active and reactive

power.

Even after the magnetic field has built up again, the

generator is still running at a speed significantly above its

nominal speed. It will require a higher reactive power (the

"mechanical inrush") leading to a continued reduction in

voltage (the "post-fault voltage dip").

An example for a stable case is shown in Figures 6a, 6b

and 6c.

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (seconds)

Voltage Phasor Magnitude (p.u.), Speed (p.u.)

Speed

Voltage

1 1

2' 3'

3''

Figure 6a: Stable case: asynchronous generator voltage and speed

0 0.5 1 1.5 2 2.5 3100

150

200

250

300

350

Time (seconds)

Current Phasor Magnitude (kA)

Figure 6b: Stable case: asynchronous generator current

0 0.5 1 1.5 2 2.5 3-300

-200

-100

0

100

200

300

Time (seconds)

Active Power (M

W), Reactive Power (M

VAr)

Active power

Reactive power

Figure 6c: Stable case: asynchronous generator active and reactive power.

A. Generators versus Motors

There are a number of differences between generators and

motors for the stability issues discussed before. The first

difference concerns safety. A motor will slow down during

a fault. In the worst case it will reach zero speed: stand still.

A generator on the other hand will speed up: there is no

limit to its speed. With generators it is thus extremely

important to have a very reliability overspeed protection,

preferably mechanically.

In the Figures 7 and 8 the short term voltage stability of

induction motors are described. Before the short-circuit

occurs the motor is in a stable operation at point 1. The

electrical torque of the generator and the mechanical torque

of the load are then equal, i.e. the speed of the motor will be

constant. If a three phase short-circuit occurs at the motor


terminal the voltage will go down to zero. This will result in

an electrical torque that is zero and also a reactive power

consumption that is zero. This is indicated with 2 in Figures

7 and 8.

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Speed (pu)

Torque (pu)

1

2’’

2

2’

3

3’

3’’

4

5’

5’’

V=0*Vnom

V=0.5*Vnom

V=0.8*Vnom

V=Vnom

Tmech=k*n2

Figure 7: Motor operation: speed-torque curve, for different voltage levels

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Speed (pu)

Reactive power (pu)

5’

3’

3’’

4

1

5’’

V=0.5*Vnom

V=0.8*Vnom

V=Vnom

2 3 V=0*Vnom

Figure 8: Motor operation: speed-reactive power curve, for different

voltage levels.

If the short-circuit occurs somewhere else in the system the

voltage will not go down to zero and consequently not the

electrical torque and reactive power consumption. These

situations are indicated in the Figures 7 and 8 by 2’ and 2’’.

During the time it takes before the faulted object is

disconnected the speed of the motor will decrease. In the

Figures 7 and 8 this is indicated by point 3, 3’ and 3’’,

respectively. In reality the speed decrease will be higher

with a lower motor voltage if the fault clearing time is equal.

However, this is not indicated in the Figure 7.

If the voltage totally recovers the operation point will be 4

in the Figures 7 and 8. As the electrical torque is higher

than the mechanical torque the machine will speed up and

go back to operating point 1 in the Figures 7 and 8.

As can be seen in the Figures 7 and 8 the reactive power

consumption of the motor at operating point 4 will increase

as compared to normal operation. Therefore it is likely that

the motor terminal voltage will not recover totally directly

after the fault is cleared. If the motor terminal voltage was

close to zero it is possible that the voltage will be lower and

instead of full recovery it will recover from operating point

3 to 3’’ or 3’. In operating point 3’’ the electrical torque is

also higher than the mechanical torque and the speed can

recover to operating point 5’’. However, in operating point

3’ the electrical torque is lower than the mechanical torque

resulting in a further decrease of the speed down to

operating point 5’. As can be seen in the Figure 8 the

reactive power consumption will increase even more during

this time resulting in a further voltage decrease. The voltage

collapse is now a fact.

For the induction generator the short-term voltage stability

phenomena are described using induction generator

characteristic as shown in Figures 9 and 10.

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5-2

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Speed (pu)

Torque (pu)

V=Vnom

V=0.8*Vnom

V=0.5*Vnom

Tmech=k*n2

V=0*Vnom

1

2

2’

2’’

3

3’’

3’

4

5’’

6

6’

6’’

6’’’

7’

7’’

7’’’

Figure 9: Generator operation: speed-torque curve, for different voltage

levels.

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Speed (pu)

Reactive power (pu)

V=0.5*Vnom

V=0.8*Vnom

V=Vnom

V=0*Vnom

1,2’’

4

2

6’’’

6’’

6’

63

3’

3’’

5’’

2’

Figure 10: Generator operation: speed-reactive power curve, for different

voltage levels.

Before a short-circuit occurs the generator is in a stable

operation at point 1. The electrical torque of the generator

and the mechanical torque of the load are then equal, i.e. the

speed of the generator is constant. If a three-phase short-

circuit occurs at the generator terminal the voltage will drop

to zero. This will result in an electrical torque that is zero

and reactive power consumption that is zero. This is

indicated by the number 2 in the Figures 9 and 10.

If the short-circuit occurs somewhere else in the system the

voltage will not drop to zero and consequently neither will

the electrical torque and reactive power consumption. These

situations are indicated in the figures by 2’ and 2’’. During

the time it takes before the faulted object is disconnected,

the speed of the generator will increase. This is indicated in

the Figures 9 and 10 by points 3, 3’ and 3’’, respectively.

If the voltage totally recovers the operation point will be 4

in the Figures 9 and 10. As the electrical torque is higher


than the mechanical torque the generator will speed down

and go back to operating point 1 in the Figures 9 and 10.

As seen in Figure 10, the reactive power consumption of

the generator at operating point 4 will be greater in

comparison to normal operation. Therefore, it is likely that

the generator terminal voltage will not recover entirely

directly after the fault is cleared. If the generator terminal

voltage was close to zero it is possible that the voltage will

be lower and instead of full recovery it will recover from

operating point 3 to 3’’ or 3’. At operating point 3’’, the

electrical torque is also higher than the mechanical torque

and the speed can recover to operating point 5’’. However,

at operating point 3’, the electrical torque is lower than the

mechanical torque resulting in a further increase in speed to

operating point 7’.

As can be seen in the Figure 10, the reactive power

consumption will increase even more during this time

resulting in a further voltage decrease. Voltage collapse is

now a fact.

If the fault clearing time is longer, resulting in operating

point 6, even a full recovery of the voltage to operating

point 6’’’ is not enough for avoiding a voltage collapse and

instead the operating point will be 7’’’.

B. Influence of generated power

For a given configuration of the wind park, the stability

of the system has been studied. As discussed above the

generator looses synchronism when the electrical torque

after voltage recovery is not sufficient to slow down the

machine. The fault-clearing time has been varied to

determine that maximum-permissible fault-clearing time

without reaching instability. This "critical fault-clearing

time" is plotted in Figure 11 as a function of the generated

power.

Generated power input (MW)

Ma

xim

um

cle

arin

g tim

e (se

co

nd

s )

Over stability limit

Safe operation

Figure 11: Critical fault-clearing time as a function of generated power.

For increasing generated power the machine will

accelerate faster during the fault thus reaching instability

faster. This explains the sharp decrease in critical fault-

clearing time with generated power.

This study shows that stability problems can be expected

mainly when the wind park is producing maximum power.

As this occurs only during part of the time, it may be

decided to allow the wind park to become instable for the

worst case: maximum power generation and maximum

fault-clearing time for a nearby fault. The calculation of the

likelihood that such a case occurs and the assessment of the

risk is outside of the scope of this paper.

C. Effect of fault type and duration

As another part of this study the size of the wind park has

been varied for a given system fault level, a given wind park

configuration, constant fault duration and constant

generated power per turbine (thus constant wind speed). The

maximum wind park size is determined that gives a stable

recovery after the fault. Next this is repeated for different

fault-clearing times (60 ms, 80 ms, 100 ms, 150 ms, 200 ms,

300 ms and 500 ms) and different fault types. The results

are shown in Figure 12. This figure can be used to

determine the maximum size of wind park that can be

connected without leading to instability after a nearby fault.

Single phase fault

Phase to phase fault

Two phase to ground fault

Three phase fault

Inst

alle

d W

ind

ca

pa

city

(M

VA

)

Fault Duration (ms) Figure 12: Maximum installed capacity as a function of fault-clearing

time for different fault types.

The fault duration should be chosen as the maximum

value that can be expected under reasonable circumstances.

For medium-size wind parks, where tripping does not

adversely affect the supply to other customers, the zone 1

fault-clearing time may be used. For large wind parks, for

which tripping could cause severe problems for the

transmission system, it may be more appropriate to use the

zone 2 fault-clearing time.

For a three-phase fault and a fault-clearing time longer

than about 370 ms, the system is always instable, even for

very small installed capacity. This corresponds with the

"critical speed" as explained in Figure 9.

For non-symmetrical faults more wind power can be

installed before the system becomes instable. For a given

installed capacity a longer fault-clearing time is allowed.

This can be explained by considering the positive-sequence

voltage. A symmetrical fault close to the terminals of the

wind park leads to a drop to zero of the positive-sequence

voltage. For a non-symmetrical fault, a non-zero value of

the positive-sequence voltage remains. Next to that a

negative-sequence voltage appears. The positive-sequence

voltage governs the average torque and thus the increase in

speed. The negative-sequence voltage leads to torque

oscillations. The result is that non-symmetrical faults are

less severe than symmetrical faults from a stability

viewpoint. They should however not be neglected during


the design. Non-symmetrical faults are typically much more

common that symmetrical faults. Also may the fault-

clearing time be longer for non-symmetrical faults than for

symmetrical faults.

D. Voltage Tolerance Curve

A common way of describing the performance of

equipment connected to industrial power systems during

faults in the grid is by means of a so-called "voltage-

tolerance curve". This curve indicates which voltage dips

will lead to mal-operation of the equipment. Such a curve

can also be determined for a wind park, e.g. in the following

way. Voltage dips of constant retained voltage and varying

duration are applied at the terminals of the wind park. The

duration that gives the border between stable and instable

operation becomes one point in the voltage-tolerance curve.

The total curve is obtained by repeating this for different

retained voltage. The result for the wind-park under study is

shown in Figure 13.

Re

tain

ed

Vo

ltag

e (p

.u)

Maximum clearing time (seconds)

Stable

Area

Instable

Area

Figure 13: Voltage-tolerance curve for a wind park.

The maximum dip duration (maximum fault-clearing time

from the viewpoint of the network operator) is about 100 ms

for zero retained voltage and increases with increasing

retained voltage. With increasing retained voltage the

during-fault electrical torque (the "braking torque")

increases so that the machine speeds up less and will take

longer time to reach instability.

The advantage of presenting the stability limit in this way

is that the results can be directly compared with voltage dip

statistics. One should however keep in mind that the voltage

tolerance curve is different for different fault types

(different types of dips) as shown in Figure 12. For a correct

comparison the classification of three-phase voltage dips

presented in [3] and [4] should be used. Applying the curve

and the supply performance in the correct way will result in

the number of times per year that the turbine will become

instable due to a fault in the grid.

IV. OTHER DESIGN ISSUES

Several other design issues are of importance both the

industrial power systems and to large wind power

installations.

An important design criterions the required reliability of

the supply. For industrial installations the reliability often

needs to be very high as an interruption of plant operation is

associated with high costs due to lost production. In many

production processes loss of a small component may already

lead to a complete stoppage. Therefore the supply is often

redundant down to the lowest voltage level. In wind power

installations the loss of the supply to one turbine will only

lead to the loss of that turbine. Obviously there are costs

associated with this loss of production but they are not

sufficiently high to justify a redundant supply down to the

turbines. Therefore the power system inside of a wind park

is typically radial without any redundancy. However at the

higher voltage level (150 kV in the example used in this

paper) it is worth installing some redundancy because loss

of a component may otherwise lead to loss of the complete

production. Without redundancy it will also be needed to

completely stop the production for maintenance to be

performed at 150 kV.

The choice of neutral point earthing is not much affected

by motor or generator operation. For industrial systems the

reliability requirements may make that resistance earthing is

somewhat more attractive than for wind power installations.

Some industrial installations have a very fluctuating load.

The supply should be such that it can cope with the worst

case: typically highest currents during a longer time. For

wind power installations one may decide to not design for

the worst case but instead reduce the production somewhat

during long periods of strong wind. One may even underrate

some of the components somewhat as high wind will also

provide good natural cooling. In industrial systems the peak

load may come with any wind speed.

V. CONCLUSION

A comparison has been made between industrial power

systems and large wind park installations. It was assumed

that in both cases the load consists of mainly induction

machines. The main discussion concerned voltage drop and

stability after a fault.

The wind power installation has a lower voltage drop

because of the active-power flow into the grid. In the

example studied in this paper, the voltage even increases

with increasing production. Note that this is often reported

as a disadvantage of installing wind power. This observation

is correct for wind power connected to distribution level, but

not for the kind of large wind parks discussed here. For such

installations no other customers are connected at medium

voltage levels so that no limits exist for the voltage.

Obviously the generators have to be able to cope with the

range of voltages that can be expected.

Stability after a fault is a more severe issue for wind

power installations than for industrial power systems. The

first difference is that motor loads will reach stand-still in

the worst case whereas there is no such natural limit for

generator operation. Apart from that may there be a "critical

speed" above which the generator will not be able to re-

synchronise, not even for an infinite grid.

ACKNOWLEDGMENT

This work was partly funded by the Swedish Energy


Authorities.

REFERENCES

[1] Y. Sun, Stability and dynamics of large wind farms, MSc Thesis,

Chalmers University of Technology, Dept. Electric Power

Engineering, Gothenburg, Sweden, 2003.

[2] R.C. Dugan, M.F. McGranaghan, H.W. Beaty, Electric power systems

quality. New York: McGraw-Hill, 1996.

[3] M.H.J. Bollen, Understanding power quality – Voltage sags and

interruptions. New York: IEEE Press, 2000.

[4] M.H.J. Bollen, G. Olguin, M. Martins, Voltage dips at the terminals of

wind-power installations. Nordic Wind Power Conference 2004,

Gothenburg, Sweden.

[5] P. Kundur, J. Paserba, V. Ajjarapu, G. Andersson, A. Bose, C.

Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. Van

Cutsem, V. Vittal. Definition and classification of power system

stability IEEE/CIGRE joint task force on stability terms and

definitions. Power Systems, IEEE Trans. Vol. 19. 2004; pp. 1387 –

1401.

1

Validation of a fixed speed wind turbine dynamicmodel with measured data

M. Martins, A. Perdana, P. Ledesma, E. Agneholm, O. Carlson

Abstract— Power systems dynamic studies involving fixed-speed wind turbines normally use a wind turbine model consist-ing of two lumped masses, an elastic coupling and a simplifiedinduction generator model. However, validations of this modelagainst measured data are rarely reported in the literature. Thispaper compares a recorded case obtained in a fixed-speed, stallregulated 180 kW wind turbine through a grid disturbance withsimulations performed with this model.

The paper also includes a study of the performance oftwo induction generator models, neglecting and including theelectromagnetic transients in the stator respectively. It also finallydiscusses the convenience of representing the elastic coupling andthe effect of mechanical damping.

I. INTRODUCTION

O ver the last decade the wind energy installed capacityhas increased rapidly in the world, growing from 2,500

MW in 1992 to 48,000 MW in 2005 [1], i.e. at a growth rateof near 30 % per year. Although not uniformly, almost threequarters of this power has been installed in Europe. Penetrationlevels are specially high in Denmark (20 %), Germany (5 %)and Spain (5 %). More specifically, some regions meet alreadya great amount of the demanded power from the wind energy:Navarra in Spain meets already 50 % and Schleswig-Holstein,in Germany 30 %. According to the European Comissiontargets wind energy will continue to grow in Europe and willreach 69,900 MW in 2010 [2].

The nature of the wind energy and the wind energy conver-sion systems are different from the conventional generationand therefore careful studies must be addressed to integratethe wind power into the power system. Some of these studiesinvolve the use of dynamic models of the wind turbines [3]:

At a local scale, the contribution of the wind farms tothe fault currents must be studied in order to design aproper protection scheme.At a system-wide scale the power system dynamics andstability issues after a disturbance must be studied.

In particular, the need of new grid code specifications for theconnection of wind farms enforce the use of wind turbinedynamic models for the design of such specifications and forthe prove of grid code compliance.

A large percentage of the installed wind turbines are fixed-speed, stall-regulated turbines with induction generators. Thistechnology is simpler and is preceding the variable-speedtechnology. Hence, several dynamic models have already been

M. Martins, A. Perdana, E. Agneholm and O. Carlson are with the Energyand Environment Department, Chalmers University of Technology.

P. Ledesma is with the Departamento de Ingenierıa Electrica, UniversidadCarlos III de Madrid.

developed and used in previous works, although validations ofthese models with field measurements are rarely reported inthe bibliography [5].

Most of the fixed-speed wind turbine models for voltagestability simulations use an induction generator model, whichneglects stator transients [5], [6], [7], [8], [9], [11], althoughthere is no full agreement on this point [10]. As for the drivetrain model, several models ranging from one to four lumpedmasses [6] have been used depending on the purpose of thestudy, although one-mass [7], [8] or two-masses [5], [9], [10],[11] models are the most commonly used.

The availability of recorded voltage and current data in afixed-speed wind turbine after a grid disturbance offers a goodopportunity to validate these models with field measurements.This paper performs such a validation on the most commonfixed-speed wind turbine models found in the bibliography.The results of such a validation is intended to increase theconfidence of the electric utilities and system operators inthe fixed-speed wind turbine models, in order to perform thenecessary studies to integrate the wind energy into the powersystem.

II. WIND TURBINE MODEL

II-A. Mechanical modelThe two-masses model represented in Fig. 1 has been used

to represent the mechanical coupling between the low-speedshaft and the high-speed shaft. The equations of the modelare:

dθtg

dt= ωg − ωt (1)

dωt

dt=

1

2Ht

(τwind + Kθtg + D(ωg − ωt)) (2)

dωg

dt=

1

2Hg

(−τem − Kθtg − D(ωg − ωt)) (3)

where θtg is the angle between the turbine and the generator,ωt, ωg , Ht and Hg are the turbine and generator rotor speedand inertia, respectively, K and D are the drive train stiffnessand damping constants, τwind is the torque provided by theturbine and τem is the electromagnetic torque. All parametersare in per unit.

II-B. Induction generator modelTwo main induction generator models are used when per-

forming power system dynamic studies:A detailed model which includes electromagnetic tran-sients both in the stator and the rotor circuits, containingfour electric state variables.

2

g

em

t

wind

H H

D

K

τ τ

Fig. 1: Mechanical model

v’ +jv’

dsR X’

d ds

i +ji

q

qss s

v’ +jv’qs

Fig. 2: Induction generator model neglecting stator transients

A simplified model which neglects stator transients,containing two electric state variables1.

The following is a brief description of both models.II-B.1. Model including stator transients: The asyn-

chronous machine equations, expressed in a reference framerotating at synchronous speed, and taking positive currentsgoing out from the machine, are [13], [7]:

λds = Xsids + Xmidr (4)λqs = Xsiqs + Xmiqr (5)

vds = −Rsids + ωsλqs −dλds

dt(6)

vqs = −Rsiqs − ωsλds −dλqs

dt(7)

λdr = Xridr + Xmids (8)λqr = Xriqr + Xmiqs (9)

0 = −Rridr + sωsλqr −dλdr

dt(10)

0 = −Rriqr − sωsλdr −dλqr

dt(11)

τem = λqridr − λdriqr (12)

where the subindexes s, r stand for the rotor and statorquantities respectively, and the subindexes d, q stand for thecomponents aligned with the d, q axis in the synchronousrotating reference frame. λ represent the flux linkages, u thevoltage and i the current. ωs and ωg are the synchronousand generator rotor speed, respectively, while s is the slipdefined as s =

ωs−ωg

ωs. The electric parameters of the machine

Rs, Xs, Xm, Rr and Xr stand for the stator resistance andreactance, mutual reactance and rotor resistance and reactance,respectively. All variables are in per unit.

II-B.2. Model neglecting stator transients: Neglecting sta-tor flux linkage transients is common when performing stabil-ity simulations [13]. It is done by neglecting terms dλds

dtand

dλqs

dtin (6) and (7), thus being equivalent to assume infinitely

fast electromagnetic transients in the stator windings.

1This model is sometimes referred in the literature as the third order model,accounting for the two electric state variables and the generator speed. Thus,the detailed model is referred as the fifth order model.

1.51 1.52 1.53

−300

−200

−100

0

100

200

300

400

500

600

Time (s)

Vol

tage

(V)

Measured data of phase aMeasured data of phase bMeasured data of phase cSimulated curve of phase aSimulated curve of phase bSimulated curve of phase c

Fig. 3: Extract from voltage measurements

Rearranging (4) to (12) in a convenient way leads to thewell-known model [12], [13], which represents the machineconnected to the grid as a voltage source v′

d + jv′

q behind atransient impedance Rs + jX ′

s as shown in Fig. 2. The rate ofchange of the voltage source and the electromagnetic torqueare governed by the following equations:

dv′

d

dt= −

1

T ′

o

[v′

d − (Xs − X ′

s)iqs] + jsωbasev′

q (13)

dv′

q

dt= −

1

T ′

o

[v′

q + (Xs − X ′

s)ids] − jsωbasev′

d (14)

τem = v′

dids + v′

qiqs (15)

where s is the slip, T ′

o = Xr/Rr and X ′

s = Xs − X2

m/Xr.This model is suitable for integration with conventional tran-

sient stability software programs, where grid electric variablesare represented as phasors and hence only the fundamentalfrequency component is preserved.

III. VALIDATION PROCEDURE

Model validation has been performed using a sample of dataobtained on a 180 kW stall-regulated fixed-speed wind turbineover a period of 4 seconds. The relevant parameters of thewind turbine are shown in appendix I. The available data arethe instantaneous voltage and current at the machine terminals,with a sampling frequency of 256 Hz. As an example, Fig. 3shows the recorded voltage at each phase over 25 ms timeframe.

The dynamic model validation procedure shown in Fig. 4has been developed taking the available data into account.Positive-sequence line-to-ground voltage and current phasorshave been obtained from the recorded data using the transfor-mation [4]:

[

vkx

vky

]

= T

vka

vkb

vkc

(16)

where vka , vk

b , vkc are the kth recorded voltage data and vk

x,vk

y are the rectangular coordinates of the kth instance of thevoltage phasor. The transformation matrix T is calculated as

T =1√

2

[

cos(θk) cos(θk−

2π3

) cos(θk + 2π3

)− sin(θk) − sin(θk

−2π3

) − sin(θk + 2π3

)

]

3

currentsampling

model validation

vx,y

grid

simulation

windmill

voltagesampling

transf.3 => 2

a,b,c

3 => 2

va,b,c

P, Qsimulated

x,yi

transf.

i

P, Qmeasured

compensatingcapacitors

Fig. 4: General procedure for the validation of the models

0 1 2 3 40.34

0.35

0.36

0.37

0.38

0.39

0.4

Time (s)

Lin

e−to

−lin

e vo

ltage

mod

ule

(kV

)

Fig. 5: Voltage profile

θk = ωtk + φo

where tk is the time at which the kth measurement samplewas obtained, ω is the grid frequency and the angle φo hasbeen chosen so that the initial voltage angle is zero. The sametransformation is applied to the current replacing v by i in(16).

Voltage and current phasors are easily obtained expressingvk

x + jvky and ikx + jiky in polar coordinates.

Model validation has been performed over the wind turbineactive and reactive power output. Wind turbine output powermay be obtained as

Sk = 3(vkx + jvk

y )(ikx − jiky) (17)

P k = real(Sk) (18)Qk = imag(Sk) (19)

where Sk, P k and Qk are the apparent, active and reactivepower, respectively at time tk.

0 1 2 3 4310

311

312

313

314

315

316

317

318

Time (s)

Stat

or v

olta

ge fr

eque

ncy

(rad

/sec

)

Fig. 6: The stator voltage frequency

0 1 2 3 4−100

−50

0

50

100

150

Time (s)

Act

ive

pow

er (k

W)

Fig. 7: Measured wind turbine active power

IV. RECORDED CASE

Fig. 5 and Fig. 6 show the measured voltage and the statorvoltage frequency over the recorded period. The stator voltagefrequency fs is simply obtained from

fs =dθ

dt(20)

While Fig. 7 and Fig. 8 show the behavior of the active andreactive power. It can be seen in Fig. 7 that the wind turbine isworking at a low-power operating point (approximately at 0.05pu), which corresponds to a low wind speed. The consumptionof reactive power is relatively high (approximately 0.33 pu)despite the reactive power compensation of 0.11 pu.

Regarding Fig. 5 to Fig. 8 two different transients may beobserved:

1. At time 0.5 s the terminal voltage drops by approxi-mately 5 %, followed by a slow recovery and a slightfrequency oscillation due to angle oscillation. Activepower suffers oscillations of around 10 kW in amplitudehaving similar profile with the stator voltage frequencyoscillation. Reactive power absorbtion decreases as aresult of the voltage decay, and slightly increases afterthe transient in order to recover rotor flux.

4

0 1 2 3 4−100

−50

0

50

100

Time (s)

Rea

ctiv

e po

wer

(kV

A)

Fig. 8: Measured wind turbine reactive power

2. At time 1.6 s there is a sharp voltage decay of about10 %, followed by voltage and angle oscillations. It canbe seen from Fig. 6 that the frequency variation is ap-proximately 0.05 Hz along the recorded data. There arealso high active power oscillations of more than 50 kWin amplitude, again the power oscillation shows a similarprofile with the stator voltage frequency oscillation. Thebehavior of the reactive power after the disturbance ismainly governed by voltage oscillations.

Since the second transient has a more rapid and largervoltage drop than the first transient, hence the second tran-sient is considered to be representatively enough to explainphenomena in the first transient. Consequently only the secondtransient will be discussed in the following sections.

V. SOFTWARE TOOLS

Two different transient stability simulation programs havebeen used to simulate the recorded case:

1. PSS/E, a power system simulation tool by Siemens PTI.As there was no any wind turbine model available in thestandard library, a user-defined model for the turbineand the induction generator has been developed andimplemented.

2. Power Factory by DIgSILENT. This program allows toperform simulations both neglecting and regarding statortransients, hence facilitating the comparison between thetwo induction generator models. The fixed speed windturbine model provided in the standard library has beenused.

The models implemented in the tools above were validatedagainst the same models implemented in Matlab/Simulink.

Since most models provided by these programs are blackboxes with no access to the source code, the coincidence ofthe simulations when using the wind turbine model in bothprograms has reinforced the confidence in the results.

VI. SIMULATIONS

VI-A. Simulations regarding stator transients

Fig. 9 shows a detail of the power oscillations obtained fromthe measurement and simulation with the detailed generator

1.5 2 2.5 3−150

−100

−50

0

50

100

150

Act

ive

Pow

er (k

W)

Time (seconds)

MeasuredSimulated

Fig. 9: Simulated and measured active power regarding statortransients

1.5 2 2.5 3−150

−100

−50

0

50

100

150

Rea

ctiv

e Po

wer

(kV

Ar)

Time (seconds)

MeasuredSimulated

Fig. 10: Simulated and measured reactive power regardingstator transients

model described in section II-B.1. The mechanical modeldescribed in section II-A despite absent of the mechanicaldamping. It may be seen that, in spite of the presence of a 50Hz, the results provided by the detailed model shows fairlygood agreement with the measured data. Several considera-tions may be obtained from these figures:

The power oscillations in simulations and measurementshave a similar frequency.The fast transients in the first few cycles in the simulationand the measurement have a similar magnitude.The amplitude of the simulated and measured poweroscillations are similar during the first oscillation afterthe transient. Later, the simulated oscillations are higherthan the measured.

Fig. 10 shows a comparison between the measured andsimulated reactive power. It may be seen that:

There is a good accordance between the measurementsand the simulations, although there is a shift in thereactive power after the second disturbance. This shiftcould be due to the disconnection of some compensatingcapacitors as a result of the disturbance. Unfortunately

5

1.5 2 2.5 3−150

−100

−50

0

50

100

150A

ctiv

e Po

wer

(kW

)

Time (seconds)

MeasuredSimulated

Fig. 11: Simulated and measured active power of detailedmodel after dc-offset removal.

1.5 2 2.5 3−150

−100

−50

0

50

100

150

Rea

ctiv

e Po

wer

(kV

Ar)

Time (seconds)

MeasuredSimulated

Fig. 12: Simulated and measured reactive power of detailedmodel after dc-offset removal.

there are no recorded data of such events, so that it isnot possible to confirm this supposition.

The presence of 50 Hz ripple in the simulation output activeand reactive power in Fig. 9 and Fig. 10 respectively, which isnot shown in the measurement data, can be originated owingto an unsymmetrical input voltage. This can be confirmed afterexamining the measurement data carefully, it was found thatthe sum of the 3-phase voltage is not zero. The most possiblereason causing the unsymmetrical is dc-offset contained in themeasurement data. This dc-offset can take place, for example,due to inaccurate value of resistors used to obtain neutral pointin the voltage measurement sensor. Therefore, to get betteragreement of the output power, the dc offset must be filteredout using high pass filter. As shown in Fig. 11 and Fig. 12, afterfiltering dc-offset out from the input voltage, the output powershows a better agreement with the measurement. However the50 Hz oscillations is still apparent in the simulation duringfirst few cycles after fault was initiated. This discrepancy isprobably because of transient voltage unbalance during thatperiod which cannot be traced precisely using the availablemeasurement data due to a low sampling frequency of the

1.5 2 2.5 3−150

−100

−50

0

50

100

150

Act

ive

Pow

er (k

W)

Time (seconds)

MeasuredSimulated

Fig. 13: Simulated and measured active power neglectingstator transients

1.5 2 2.5 3−150

−100

−50

0

50

100

150

Rea

ctiv

e Po

wer

(kV

Ar)

Time (seconds)

MeasuredSimulated

Fig. 14: Simulated and measured reactive power neglectingstator transients

data.

VI-B. Simulations neglecting stator transients

The same case has been simulated using a reduced orderinduction generator model which neglects the stator transients,such as described in section II-B.2. Fig. 13 shows the windturbine active power output obtained with a model neglectingstator transients. The figure shows that, unlike in the detailedmodel, a high and fast transient 1.6 s is not obtained in thereduced order model simulations. This is natural since this isan electromagnetic transient, which cannot be simulated in aphasor-oriented program such as PSS/E. On the other, sidethe subsequent oscillations with a frequency in the order of 8Hz, are well simulated as can be seen regarding Fig. 11 andFig. 13.

Those results above are in accordance with the resultsreported by other authors [5], [6], [7], [8], [9], [11] andreinforces the opinion that the induction generator reducedorder model represents accurately wind turbine electromechan-ical transients. Furthermore as reported in [15], despite thefact that the detailed model provides a better prediction on

6

1.5 2 2.5 3−150

−100

−50

0

50

100

150A

ctiv

e Po

wer

(kW

)

Time (seconds)

MeasuredSimulated

Fig. 15: Simulated and measured active power including amechanical damping

1.5 2 2.5 3−150

−100

−50

0

50

100

150

Rea

ctiv

e Po

wer

(kV

Ar)

Time (seconds)

MeasuredSimulated

Fig. 16: Simulated and measured reactive power including amechanical damping

instantaneous peak transient current, it provides no additionalaccuracy in the simulation of the dc-offset in the machineterminal currents when the model is used together with analgebraic or phasor network model. This kind of networkmodel representation is common in power system stabilitytools such as PSS/E.

VI-C. Introduction of a mechanical damping

No damping was provided among the wind turbine param-eters. However, a mechanical damping will surely exist, andthe active power oscillations obtained in Fig. 13 suggested theconvenience to include such a damping in the model.

Fig. 15 and Fig. 16 show the comparison between the mea-sured and simulated active and reactive power, respectively,when including a damping constant D = 3pu. Accordance inthe active power after the first oscillation improves notably,so that the simulations provide very accurate results forthe active power. However it must be noted that neglectingmechanical damping provides results not so accurate but moreconservative, and that the mechanical parameters of the drive

1.5 2 2.5 3103

103.5

104

104.5

105

105.5

106

106.5

107

Spee

d (r

ad/s

ec)

Time (seconds)

Gen. speedTurbine speed

Fig. 17: Simulated generator and turbine rotor speed usingtwo-mass model

1.5 2 2.5 3103

103.5

104

104.5

105

105.5

106

106.5

107

Spee

d (r

ad/s

ec)

Time (seconds)

Gen. speedTurbine speed

Fig. 18: Simulated generator and turbine rotor speed usingone-mass model

train of a wind turbine are often not well known and difficultto estimate.

Regarding reactive power, the introduction of the dampingmakes not much difference in the results, while it appears thesame reactive power shift discussed in the previous section.

VI-D. Convenience of Using Two-Mass Model

Initial investigations were also made to verify the mechani-cal model. Comparisons between field measurements and bothmodels: one-mass and two-mass models were made. One-massmodel comprehends a lump model where the masses of windturbine, gear box and generator rotor are lumped into a singlerotating mass. In this case the inclusion of wind turbine shaftis neglected. For two mass model the wind turbine and thegenerator rotor are represented separately and the shaft isincluded as shown in Fig. 1. The results show a significantdifference in the active power amplitude. For one mass modelthe active power oscillations during the fault have considerablelower amplitude than the two masses model. The reason forthe difference relies on the fact that during the fault there isa different behavior for the generator and turbine speed as

7

shown in Fig. 17. The shaft twist is reduced to zero due torelaxation of the shaft during the fault. The fault duration inthis case is short to affect the turbine speed since its inertia ismuch larger than the generator rotor inertia. Only the generatorrotor will be affected by the short fault duration [14]. Forone mass model there are almost no oscillations after a shortfault duration as shown in Fig. 18 and the recovering timefor voltage and rotor speed can be faster than in a two massmodel [16]. This fact can hide an unstable situation.

VII. CONCLUSION

The following conclusions may be obtained from the study:

There is a good accordance between the measured poweroscillations and the simulated ones when using bothinduction generator models, neglecting and regardingstator transients. Hence, the simplified model whichneglects stator transients is accurate enough to simulatethe studied case.A two-masses mechanical model is necessary to accu-rately represent the electromechanical oscillations, andprovides a good accordance between the measurementsand the simulations.Introduction of mechanical damping is necessary toachieve a good accordance between the measurementsand the simulations, while neglecting mechanical damp-ing provides higher oscillations and hence more conser-vative results.As there are no major technologic differences betweenfixed-speed stall-regulated wind turbines of differentsizes, the results may be extrapolated to larger windturbines. However, the study is limited to the availabledata, and further validation of the model with other windturbines, other operating points closer to the rated power,and different disturbances should be desirable.

APPENDIX IPARAMETERS

Tables I to IV show the relevant parameters of the study. Allthe per unit parameters have been calculated on a 210 kVA,400 V base system.

Parameter Value UnitsRated power 180 kWHub height 30 mRotor diameter 23.2 mRotor rated speed 42 r.p.m.Gearbox ratio 23.75

TABLE I: Turbine parameters

Parameter Value UnitsTurbine inertia constant Ht 2.6 sGenerator inertia constant Hg 0.22 sStiffness constant K 141.0 p.u.Damping factor (when applied) D 3.0 p.u.

TABLE II: Drive train paramers

Parameter Value UnitsRated power 210 kVARated voltage 415 VStator resistance Rs 0.0121 p.u.Stator leakage inductance Xs 0.0742 p.u.Mutual inductance Xm 2.7626 p.u.Rotor resistance Rr 0.0080 p.u.Rotor leakage inductance Xr 0.1761 p.u.

TABLE III: Generator parameters

Parameter Value UnitsGrid rated voltage 400 VCapacitor bank susceptance B 0.11 p.u.

TABLE IV: Other parameters

ACKNOWLEDGMENT

Financial support from Swedish National Energy Adminis-tration, Nordic Energy Research, Svenska Kraftnat and Vatten-fall are greatly acknowledge. The authors would like to thankTorbjorn Thiringer for providing the field measurements andfor his valuable comments to the study.

REFERENCES

[1] C. Ender, International Development of Wind Energy Use - Status, DEWIMagazine, no. 27, pp. 36-43, Aug. 2004.

[2] European Wind Energy Association (EWEA) and European Comission’sDirectorate General for Transport and Energy (DG TREN), Wind Energy- The Facts, Dec. 2003, available at <http://www.ewea.org>.

[3] Union for the Coordination of Transmission of Electricity, UCTE PositionPaper on Integrating Wind Power in the European Power Systems -Prerrequisites for Successful and Organic Growth, May 2004, availableat <http://www.ucte.org>.

[4] P.C. Krause, O. Wasynczuk and S.D. Sudhoff, Analysis of ElectricMachinery, IEEE Press, 1995.

[5] T. Petru and T. Thiringer, Modeling of Wind Turbines for Power SystemStudies, IEEE Transactions on Power Systems, vol. 17, no. 4, pp. 1132-1139, Nov. 2002.

[6] G. S. Stavrakakis and G. N. Kariniotakis, A General Simulation Algorithmfor the Accurate Assessment of Isolated Diesel-Wind Turbine SystemsInteraction. Part I: A General Multimachine Power System Model, IEEETransactions on Energy Conversion, vol. 10, n. 3, Sep. 1995.

[7] L. Holdsworth, X.G. Wu, J.B. Ekanayake and N. Jenkins, Comparisonof Fixed Speed and Doubly-Fed Induction Wind Turbines during PowerSystem Disturbances, IEE Proceedings on Generation, Transmission andDistribution, vol. 150, n. 3, pp 343-352, May 2003.

[8] Z. Saad-Saoud and N. Jenkins, Simple Wind Farm Dynamic Model, IEEProceedings on Generation, Transmission and Distribution, vol. 142, n.5, pp. 545-548, Sep. 1995.

[9] P. Ledesma, J. Usaola and J.L. Rodrıguez, Transient stability of a fixedspeed wind farm, Renewable Energy, vol. 28/9, pp. 1341-1355, Feb. 2003.

[10] V. Akhmatov, H. Knudsen, Modelling of Windmill Induction Generatorsin Dynamic Simulation Programs, International Conference on ElectricPower Engineering, PowerTech Budapest 1999, 29 Aug.-2 Sep. 1999, p.108.

[11] C. Carrillo, A.E. Feijoo, J. Cidras, J. Gonzalez, Power Fluctuations inan Isolated Wind Plant, IEEE Transactions on Energy Conversion, vol.19, n. 1, pp. 217-221, Mar. 2004.

[12] D.S. Brereton, D.G. Lewis and C.C. Young, Representation of InductionMotor Loads during Power System Stability Studies, AIEE Transactions,vol. 76, pp. 451-461, Aug. 1957.

[13] P. Kundur, Power System Stability and Control, McGraw-Hill, 1994.[14] V. Akhmatov, Analysis of Dynamic Behaviour of Electric Power Systems

with Large Amount of Wind Power, PhD Thesis, Technical University ofDenmark, ISBN 87-91184-18-5. Apr. 2003.

[15] Y. Kazachkov, S. Stapleton, Modeling Wind Farms for Power SystemStability Studies, Power Technology Newsletter, Issue 95, Apr. 2004.

[16] S.K. Salman, A.L.J. Teo, Windmill Modeling Consideration and factorsInfluencing the Stability of a Grid-Connected Wind Power-Based Embed-ded Generator, IEEE Trans. on Power System, vol. 18, pp. 793-802, May2003.

1

Abstract—This paper presents long-term voltage stability

studies of a power system at different scenarios. The model of the

system studied includes a production area, transmission lines and

a load area. In the load area, the generated power is either based

on thermal power, fixed speed wind turbines or a combination of

thermal and wind power. The model of the system also includes a

transformer tap-changer, a dynamic load and generator field and

armature current limiters. The generators are dimensioned

according to grid codes. Simulations have been performed with a

variation in the active power generation of the production plants.

For the wind parks, investigations have also been performed on

different control strategies of the reactive power production. It

has been demonstrated that these control strategies play an

important role for the long-term voltage stability of the power

system.

Index Terms—long-term voltage stability, voltage collapse,

wind power production, wind turbine, grid code, fixed speed

wind turbines.

I. INTRODUCTION

HE introduction of large-scale wind power in power systems brings up a number of questions regarding

various stability aspects. One of these is the long-term voltage instability that has been the reason for many voltages collapses during the years [5]. Historically many power systems have been based on hydro units and thermal units. Both of these production sources use synchronous generator that has the possibility either to produce or absorb reactive power and thereby continuously contribute to the voltage control of the power system. However, the generators used for large scale wind power applications are mostly based on fixed speed induction generators, double fed induction generators or generators equipped with full converters. These types of generators can produce and consume reactive power in various ways. The fixed speed induction generator can only consume reactive power and therefore it has to be combined with shunt capacitors or an SVC in order to fulfill the grid codes given by the independent system operator. In this paper the fixed speed induction generator will be studied in more detail and compared with conventional thermal power plants from a long-term voltage stability point of view. However, most of the principles analyzed may be also valid for other types of wind turbine technologies.

This work was supported by the Swedish National Energy Agency.

II. LONG-TERM VOLTAGE STABILITY

According to [4, 5, 6], long-term voltage stability involves slower acting equipment such as tap-changing transformers, thermostatically controlled loads and generator current limiters. The study period of interest is up to minutes, and long-term simulations are required for an analysis of the system dynamic performance. Stability is usually determined by the resulting outage of equipment, rather than the severity of the initial disturbance. Instability is due to the loss of long-term equilibrium (e.g., when loads try to restore their power beyond the capability of the transmission network and connected generation), the post-disturbance steady state operating point being small-disturbance unstable or a lack of attraction towards the stable post-disturbance equilibrium (e.g., when a remedial action is applied too late). The disturbance can also be a sustained load buildup (e.g., morning load increase). In many cases static analysis can be used to estimate stability margins, covering a wide range of system conditions and scenarios. Where the timing of control actions is important, the analysis shall be complemented with quasi-steady-state time domain simulations.

III. STUDIED SYSTEM

A power system comprises three parts: the transmission system, the generation system and the distribution system where the load demand is included. Using this approach a simplified network can be built to represent any power system, for instance the Swedish system with a significant amount of power supply coming from the north of the country combined with the thermal power plants in the south where also a possible integration of wind power into the grid is analyzed. A system as in Fig. 1 has been modelled by using the Digsilent Power Factory power system analysis package. The transmission corridor consists of two 400 kV transmission lines of 300 km length. Area 1 has been modelled as an infinite source. The load is situated at the 24 kV level and has been varied to find the operational limits of the system. During voltage instability the impact of the load voltage dependency is essential to consider. Therefore, a dynamic load model is used to model the load recovery [3]. A 400/24 kV transformer with 15% reactance has been included to model the reactive power losses between the transmission system and the 24 kV load. It is important to represent the transformer tap-changers since they can be the cause of long-term voltage instability in their attempt to restore the voltage and thereby the power on the load level.

Long-Term Voltage Stability – A comparison between conventional thermal power units and fixed speed wind turbines M. Martins, Chalmers University of Technology, Sweden, E. Agneholm, Gothia Power, Sweden

T

2

Fig. 1: The studied system.

Voltage collapse is rarely a concern when all lines are in operation. The transmission system security is typically guaranteed such that the loss of any single component will not lead to any violation of the operational limits. Thus, even after loss of one of the two lines the system should be stable for a certain load level. Therefore the system after a loss of one of the two transmission lines will be analyzed in this paper.

A. The thermal unit

A 283 MVA, 255 MW synchronous generator represents the thermal unit. Since voltage problems can be due to generators performance, it is important to consider the reactive capability limit of synchronous generators in long-term voltage stability studies. From the stability point of view the performance of synchronous generators have certain limitations related to their construction. Such limitations are related to the limits in the reactive power generation capabilities like the field current limit and the armature current limit. Therefore these limiters are included in the voltage regulator of the synchronous generator. A capability diagram displays possible operating areas where the generator thermal limits are not violated. In Fig. 2 the capability diagram including the field and armature current limiters are presented.

s

t

X

E 2

itat IE lim

iδ

E tEsX

Fig. 2: Synchronous generator reactive capability curve.

1) Field current limiter

The purpose of having a field current limiter is to protect the field winding from overheating due to prolonged field overcurrent. The block diagram used to model the field current limiter is shown in Appendix, Fig. 13.

The interaction between the current limited and the load characteristic occurs if for some reason a system has a deficiency of transmission capacity leading to a voltage stability problem and the current limiter is activated after further load increase. The generator may then be seen as a fixed voltage source behind a reactance. From the system point of view it will be like an increase of the reactance in the system which will weaken the system leading to a risk for a voltage collapse. A description is given in [1]. 2) Armature current limiter

The armature current results in an RI2 power loss and the energy associated with this loss must be removed in order to limit the increase in temperature of the generator. If the armature current limiter is exceeded the voltage regulator will reduce the excitation of the generator and thereby the reactive power production. The block diagram used to model the armature current limiter is shown in Appendix, Fig. 14.

B. Dynamic load

During voltage instability the impact of the load is essential to consider. Therefore, a dynamic load model is used to model

the load recovery. The recovery time, pT , or qT of the model

is in the time frame of minutes. The load model is based on [2,

3] and includes a static part of the active )(VPs and reactive

power )(VQs and a transient part of the active )(VPt and

reactive power )(VQt . In [2] a load state is introduced as:

( ))(VPPTx tdpp −=

( ))(VQQTx tdqq −=

Here dP is the active power demand and dQ the reactive

power demand. The exponential load recovery is then given by:

)()()(1

VPPVPVPxT

x sdstp

p

p +−=+−=&

)()()(1

VQQVQVQxT

x sdstq

q

q +−=+−=&

The static load voltage dependent characteristics give the stationary and transient behavior as:

s

V

VPVPs

α

=

0

0)( ,

s

V

VQVQs

β

=

0

0)(

t

V

VPVPt

α

=

0

0)( ,

t

V

VQVQt

β

=

0

0)(

Here: 00 ,QP are the active and reactive power consumption

at pre-fault voltage, V is the supplying voltage [kV], 0V is the

pre-fault value of the supplying voltage [kV], 00 ,βα are the

steady state active and reactive load voltage dependence

respectively and tt βα , are the transient active and reactive

load voltage dependence respectively.

3

Examples of dynamic loads in the distribution networks that are included in the model are: electrical heating, air conditioning, refrigerators and freezers.

C. Transformer on-load tap-changer

Tap-changers provide voltage control by restoring the load voltage level. They can be the cause of long-term voltage instability in their attempt to restore the load voltage. During this process the transmission level voltage is deteriorated with a possible voltage collapse. The time delay of the tap-changer model for the studies in this paper has been set to 30 seconds per step. Based on simulations performed it can be observed that if no tap-changer is included in the transformer model, the voltage collapse will take longer time to occur even for critical levels of load demand. The time it takes for the system to collapse can be prolonged with 30 to 50 minutes. The simulations also show that the voltage collapse can happen gradually, i.e. the voltage will keep declining for longer time reaching unacceptable levels. It means that the presence of the tap-changer not only contributes but can also speed up the voltage collapse in critical situations.

D. The fixed speed wind turbine

The investigations in this paper have used a fixed speed wind turbine as a model for all studies. A fixed speed wind turbine consists of an induction generator connected directly to the grid. For simulation purposes the mechanical model is represented as an one-mass model wind turbine. An one-mass model comprehends a lumped model where the masses of wind turbine, gear box and generator rotor are lumped into a single rotating mass. Since long-term voltage stability is studied the period of interest may be several or many minutes and therefore a lumped model is adequate to be used for this purpose. However, for short-term voltage stability purposes a two-masses model would be required to accurately represent the electro mechanical oscillations [7]. When using induction generators the reactive power demand increases with the loading of the machine (Fig. 3). In order to compensate this reactive power, shunt capacitors or a SVC can be used. In this paper shunt capacitors are installed in order to be able to fully compensate at 100% loading and 90% voltage. This is in accordance with the grid codes [9], see section IV. During the simulations two alternatives of using the shunt capacitors have been applied: reactive power control and voltage control of the wind park. Reactive power control is used for compensating the reactive losses in the wind park and transformer. In the point of connection to the grid the reactive power is 0 MVAr irrespectively of the voltage. Voltage control is used for controlling the voltage in the point of connection to the grid. In case of an active power production less than maximum available shunt capacitors are connected and disconnected at various voltage levels. For severe voltage instability situations all shunt capacitors will be connected after the voltage decrease. This behavior will also correspond to the behavior of a SVC which acts very fast.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Active power (pu)

Reactive power (pu)

V=0.7Vnom V=0.8Vnom

V=0.9Vnom

V=Vnom

Fig. 3: Reactive power consumed by an induction generator as a function of the generated active power for different voltage levels (Vnom = nominal voltage).

IV. GRID CODES

Due to the deregulation of the electricity market and the large-scale introduction of wind power based on various technologies there has been a focus on introducing grid codes for production plants. The grid codes cover a variety of requirements during normal and disturbed conditions. When studying long-term voltage stability the requirements related to supplying and absorbing reactive power is important to consider. In this paper the Swedish grid code will be treated as an example. However, the method is general and can also be applied for other grid codes [9]. The Swedish grid code states that for thermal and hydro plants it shall be possible to produce and consume reactive power according to

• Produce reactive power corresponding to a 1/3 of maximum active power when the voltage is within 90-100% of rated voltage. Both reactive power and voltage are referred to the high voltage side of the step-up transformer, i.e. the losses in the transformer must be taken into account.

• Produce reactive power corresponding to a 1/3 of maximum active power production when the voltage is above 100%. This shall be possible until the generator terminal voltage exceeds 105%.

• Thermal units shall be able to reduce the reactive power production to 0 MVAr seen from the upper side of the transformer.

For wind power the only requirement is that it shall be able to control the reactive power production and consumption to 0 MVAr at the connection point to the grid. No voltage levels are given in the grid codes but an assumption is that it shall be possible to fulfill the requirement down to 90% voltage.

V. SIMULATIONS

The simulations were performed using the system presented in Fig 1. DigSilent Power Factory simulator software was used to carry out all investigations. In order to analyze the long-term voltage stability, three different scenarios of the system in Fig. 1 were used:

4

A. Area 2 supplied by only thermal power; B. Area 2 supplied by only wind power; C. Area 2 supplied by thermal plus wind power.

A. Area 2 supplied only by thermal power

The disturbance applied to the system (Fig. 1) is initiated by the trip of one of the two transmission lines. As described in section III-D the system will be exposed to a tap-changer action and load recovery until the current limiters are activated. The voltage will instantaneously go down both on the load level and on the transmission level when the line is disconnected. As a result the active power demand will decrease. However, the load will recover and when also the tap changer starts to act the load will recover even more. As a result the voltage on the transmission level will drop, see Fig. 5. Fig. 4 shows the maximum load in Area 2 as a function of the active power production in the thermal unit. If for each production level the load is increased an additional MW the voltage collapse will be a fact. Normally thermal power plants are operated close to their maximum power production since the efficiency of the plant usually is designed for this point of operation. In Fig. 4, however, it can be seen that if the active power production is reduced some the total load in the load area can be higher as compared to if full active power production is achieved. This can be explained by the fact that when the active power production is reduced there will be access to more reactive power from the generator. This reactive power results in an increased voltage in the transmission system in the load area. As the voltage increases it will be possible to transfer more power from Area 1 to Area 2.

50 100 150 200 250 300940

950

960

970

980

990

1000

1010

1020

1030

Synchronous Generator P(MW)

Load P(MW)

Fig. 4: Relation between load limit level and synchronous generator active power production.

1) Interaction between dynamic load, tap changer and

generator current limiters

Using the models described for dynamic load, tap changer and generator current limiters a simulation was carried out to illustrate the phenomenon of voltage instability verifying the combined effects of these components. The disturbance on the system in Fig. 1 is initiated by a trip of one of the two transmission lines (wind power is not included) at 100 seconds. At the instant when the line is disconnected, the

voltage and power demand drop at the load side (Fig. 5, 6). In [1] this phenomenon is analyzed in detail.

50 100 150 200 250 300 3500.75

0.8

0.85

0.9

0.95

1

1.05

Time (seconds)

Voltage (p.u.)

Secondary voltage

Primary voltage

Fig. 5: Voltage collapse seen on both sides of the transformer located at the load end.

Thirty seconds after the disturbance, the tap changer starts to restore the voltage level at the load side (Fig. 7). For every tap step, the voltage at the load side increases and therefore the load power increases. This also leads to a current increase at the load side of the transformer. This increased current is amplified on the primary side by the transformer and as a result gives an increased voltage drop on the primary side. The field current limiter is activated at 140 seconds whereas the armature current limiter is activated at 280 seconds followed by the voltage collapse in the next 20 seconds (Fig. 9). The generator reactive power production will be reduced when the current limiters are activated. When the generator reaches its field current limit, its terminal voltage drops. In addition to that the tap changer continues to restore the load voltage resulting in a current increase and an additional voltage drop on the primary side. At 310 seconds the voltage collapse is a fact.

50 100 150 200 250 300 3500

50

100

150

200

250

300

Time (seconds)

Active power (MW), Reactive power (MVAr)

Active power

Reactive power

Fig. 6: Synchronous generator active and reactive power.

5

50 100 150 200 250 300 350-7

-6

-5

-4

-3

-2

-1

0

1

Time (seconds)

Tap position

Fig. 7: Tap changer activation.

50 100 150 200 250 300 350

2.5

2.6

2.7

2.8

2.9

3

3.1

3.2

3.3

Time (seconds)

Field Current (p.u.)

If limit = 3 p.u.

Fig. 8: Field current limiter activation (current is limited to 3 p.u.).

50 100 150 200 250 300 3500.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Time (seconds)

Armature current (p.u.)

Ia limit = 1.05 p.u.

Fig. 9: Armature current limiter activation (current is limited to 1.05 p.u.)

B. Area 2 supplied only by wind power

The simulations as performed when only having thermal power have been repeated when only having a large wind farm connected to Area 2 as shown in Fig. 1. The wind farm is modelled as three aggregated induction generators and one 400/0.96 kV transformer. The wind farm has 250 wind turbines, of 2MW each, i.e. in total 500 MW. The presence of the wind power installation leads to the injection of active power in the system and an increase of reactive power consumption. The solution chosen in this paper is to equip the wind farm with capacitor banks providing

reactive power compensation. The studies were made considering the two situations mentioned in section III-D.

0 50 100 150 200 250 300 350 400 450 500700

750

800

850

900

950

1000

1050

Induction Generator P(MW)

Load P(MW)

with voltage control

with reactive power control

Fig. 10: Relation between load and power generation of a system with only wind power input.

The curve with reactive power control demonstrates a considerable reduction on the load level supply when decreasing the active generated power. In this case the reactive power consumption by the induction generators is determining the voltage stability limit for the system. The reactive power consumption is well indicated by the non linear proportion between the load and the generated power presented in Fig. 10. The curve with voltage control shows a significant improvement. Higher amounts of loads can be supplied when the wind farm is producing from 25% to 75% of the total generated power. Even when no wind incidence will appear, i.e. if the wind farm would go down to around 0 MW power generation, still a considerable level of load could survive after loss of a line. It demonstrates that the wind farm can always provide reactive power to the grid regardless of the amount of wind. From the power system point of view wind power offers the benefit of operating as a voltage control for the system when not producing active power, i.e. during most of the time. Fig. 11 shows the behavior of the voltage on primary and secondary sides when the wind farm is producing 150 MW, with a load demand of 900 MW. A simulation was done in order to compare the behavior after a disturbance when having reactive power control and when having voltage control.

50 100 150 200 250 300 350 4000.7

0.75

0.8

0.85

0.9

0.95

1

1.05

Time (seconds)

Voltage (p.u.)



Primary voltage

Secondary voltage

Secondary voltage

Primary voltage

Fig. 11: Voltages for a wind farm with voltage and reactive power control.

6

C. Area 2 supplied by both thermal and wind power

In Fig. 12 it is evident that the combination of both types of power suppliers raises the amount of load that the system can sustain after the disconnection of a transmission line. For the curve with voltage control, once again, it can be observed that even when the wind farm has very low incidence of wind the system can keep the voltage stable for high load levels after the loss of a transmission line. When comparing with a system with only thermal power the load levels are lower. Once more it is shown that the wind farm will provide reactive power to the system even though the amount of wind is not sufficient to produce active power.

0 50 100 150 200 250 300 350 400 450 5001000

1050

1100

1150

1200

1250

1300

1350

Induction Generator P (MW)

Load P (MW)



Fig. 12: Relation between load and power generation of a system supplied by both thermal and wind power.

VI. CONCLUSIONS

From the long-term voltage stability point of view wind farms do not have the same influence on the power system as a conventional power plant. Conventional power plants normally produce maximum or close to maximum active power whereas wind power normally produces much less than maximum active power. As the grid codes are related to maximum active power production, normally there will be a substantial amount of reactive power available from the wind farm. In this paper fixed speed wind turbines combined with shunt capacitors has been studied but other technologies with doubly fed induction generator or generators equipped with full converters can be applicable. Also a combination of these techniques with a SVC or connection via HVDC light can be possible. However, the essential idea from the investigations done in this paper is to illustrate that the impact of the integration of a large wind farm acting as a voltage control is entirely helpful on the power system performance when referring to long-term voltage stability. From the studies it can be noticed that wind power is able to supply highest amount of load demand when producing from 25% to 75% of the total wind power capacity. Considering wind variation, statistically the average of wind power production is around 30% of the rated capacity. Thus a wind farm at this level is capable to maintain voltage stability for its highest power demand.

Another relevant aspect is that, irrespective of the amount of the incidence of wind blowing, i.e. even if the active power production would be close to 0 MW the wind farm still can provide reactive power to the system. This means that the power system performance will be able to keep the voltage stable for a reasonable amount of load power demand. All these considerations are made based on wind farms located in close proximity to the power system, i.e. the power system can take advantage of the reactive power. Based on the analysis performed it is recommendable that the grid code includes a requirement stating that wind farms have to be equipped with voltage control and not only controlling reactive power.

ACKNOWLEDGMENT

Financial support from the Swedish National Energy Agency is greatly acknowledged.

APPENDIX

Dynamic load model: αs = 0.38, αt = 2.26, βs = 2.68, βt = 5.22, P0 = 0.10 p.u., Tpr = 127.6 s, Tqr = 75.3 s. Transformer tap-changer model: Controller time constant = 0.01 p.u., tap step = 0.01 p.u., time delay = 30 s. Current Limiters model: Field current limiter (Fig. X): If limit = 2.987 p.u., T3 = 10s, T4 = 600 s, Tc = 4 s, VCMIN = -100 p.u., VCMAX = 100 p.u., KC = 10 p.u. Armature current limiter (Fig. X): Ia limit = 1.05 p.u., T3 = 10s, T4 = 600 s, Tc = 4 s, VCMIN = -100 p.u., VCMAX = 100 p.u., KC = 10 p.u.

KC+

-1

1+sTc

VD

VCMAX

VCMIN

VFC

IF

IFLIM V1

VBVref

Ut

+

-

+

+

Fig. 13: Block diagram for field current limiter.

KC+

-1

1+sTc

VD

VCMAX

VCMIN

VSC

IS

ISLIM V1

Q

VBVref

Ut

+

-

+

+

Fig. 14: Block diagram for armature current limiter.

7

REFERENCES

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“Validation with a Fixed Speed Wind Turbine Dynamic Model with Measured Data”. Paper submitted to “Renewable Energy” Journal.

[8] Å. Larsson , “The Power Quality of Wind Turbines”, Ph.D. dissertation, Dept. Electric Power Engineering. Chalmers University of Technology, Sweden, 2000.

[9] Svenska Kraftnät, ”Grid Code for Wind Power Integration”. (date???)

voltage stability issues related to implementation of...

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