AckermannTh. (ed) Wind Power in Power Systems

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

, that has to be calcul ated as it is used as an input signal to the control system of the

VSC (see Section 26.5).

The order of the DFIG model can be reduced from six to four by omitting the stator

flux transients in Equation (26.23). Then the derivatives of the stator flux linkages will

be set to zero. Such a model is often referred to as the transient stability model or the

neglecting stator transients model (see Thiringer and Luomi, 2001; or see Section

24.4.3.3). Equation (26.23) is then simplified to:

¼ i

þ j

: ð26:48Þ

In power system analysis, this simplification is co mmonly used in transient and small

signal stability programs where the grid transients are neglected, too, since the power

system is modelled with phasor models, also called fundamental frequency models,

instead of instantaneous value models (Thiringer and Luomi, 2001).

26.9 Conclusions

This chapter presented a 6th-order DFIG. Special atten tion was paid to the used vector

method and the bidirectional transformations between the stator and rotor refer ence

frame.

The detailed modulation scheme of the VSC connected to the rotor of the induction

generator was not described, as it was assumed that the switching frequency of the VSC

36 36.2 36.4 36.6

0.5

1.0

1.5

2.5

Time (s)

Rotor current (p.u.) and Mode

36 36.2 36.4 36.6

305

310

315

320

325

330

335

340

Time (s)

Rotor speed ω

(rad/s)

Mode

Figure 26.6 Rotor current, mode of operation, and speed of the machine !

during a three-phase

fault in the power system

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is infinite. The VSC and its control was condensed and lumped together in a unique

module.

A sequencer was described, the task of which is to protect the VSC from high currents

as well as to optimise the behaviour of the system. Transient conditions require changes

of mode in the sequencer. There are three different modes generated by the sequencer.

The DFIG model was tested in a small power system that was simulated in instan ta-

neous value mode. Our model was not verified against an actual installation of a DFIG

model. Finally, we described how the order of the DFIG model can be reduced.

References

[1] Akhmatov, V. (2002) ‘Variable-speed Wind Turbines with Doubly-fed Induction Generators, Part I:

Modelling in Dynamic Simulation Tools’, Wind Engineering 26(2) 85–108.

[2] A

ngquist, L. (1984) Complex Vector Representation of Three-phase Quantities. Technical report TR YTK

84-009E, ASEA Drives, Va

stera

s, Sweden.

[3] Centeno Lo

pez, E. (2000) ‘Windpower Generation Using Double-fed Asynchronous Machine’, B-EES-

0008, masters thesis, Department of Electric Power Engineering, Royal Institute of Technology, Stock-

holm, Sweden, and ABB Power Systems, Va

stera

s, Sweden.

[4] Fankhauser, H., Adielson, T., Aneros, K., Edris, A.-A., Lindkvist, L., Torseng, S. (1990) ‘SIMPOW – A

Digital Power System Simulator’, reprint of ABB Review 7 pp. 27–38.

[5] Kova

cs, P. K. (1984) Studies in Electrical and Electronic Engineering, 9: Transient Phenomena in Electrical

Machines, Elsevier, Amsterdam.

[6] Novak, P., Jovik, I., Schmidtbauer, B. (1994) ‘Modeling and Identification of Drive-system Dynamics in a

Variable-speed Wind Turbine’, in Proceedings of the Third IEEE Conference on Control Applications,

August 24–26, 1994, volume 1, Institute for Electrical and Electronic Engineers (IEEE), New York,

pp. 233–238.

[7] Thiringer, T., Luomi, L. (2001) ‘Comparison of Reduced-order Dynamic Models of Induction Machines’,

IEEE Transactions on Power Systems 16(1) 119–126.

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Full-scale Verification of

Dynamic Wind Turbine Models

Vladislav Akhmatov

Dedicated to my true friend C. E. Andersen

27.1 Introduction

The incorporation of wind power into elect ric power systems is progressing faster than

predicted. In Denmark, for example, the total installed capacity was approximately

3000 MW of grid-connected wind power in mid-2003. About 2400 MW of this capacity

is installed in Western Denmark (Jutland – Funen) and 600 MW in Eastern Denmark

(Zealand and Lolland – Falster; for more details, see Chapter 10).

In addition, the large offshore wind farm at Rødsand in Eastern Denmark started

operating in late 2003. The Rødsand wind farm comprises 72 2.3 MW fixed-speed wind

turbines (Type A) from the manufacturer Bonus Energy.

(1)

The wind farm is connected

to the transmission network of the national transmission system operator (TSO) of

Denmark. Further large offshore projects have recently gone under consideration in

Denmark, and incorporation of 400 MW offshore wind power due in the year 2008 in

Denmark has been announced.

The majority of the electricity-producing wind turbines in Denmark are Type A wind

turbines. This type is also called the Danish concept. They are scattered across the

(1)

For definitions of wind turbine Types A–D, see Section 4.2.3.

Wind Power in Power Systems Edited by T. Ackermann

Ó 2005 John Wiley & Sons, Ltd ISBN: 0-470-85508-8 (HB)

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country and are connected to the local distribution power networks. That means that

the majority of wind turbines connected to the Danish power grid are based on the same

concept as those at the Rødsand offshore wind farm.

Such a large penetration of wind power into electric power networks reduces the

amount of electric power supplied by centralised power plants and may affect the opera-

tion of the power networks. Therefore, it is important to know what consequences the

dynamic interaction between large wind farms and the power system has before the wind

farm is connected to the grid. Technical documentation has to be provided and it has to

show that the wind turbines comply with the technical specifications set by the power

system operator. The power system operator has to grant the large wind farm permission

to be connected to the grid (for more details on these issues, see Chapters 7 and 11).

It is necessary to develop and implement dynamic simulation models of wind turbines

for the existing simulation software tools that are applied in the analysis of power

system stability. The results of such analyses will be used for planning net-reinforcements

and the incorporation of dynamic reactive compensation, for revising protective relay

settings in the transmission power system and other practical arrangements, which can

be complex, expensive and time-consuming. The analysis may also take into considera-

tion economic interests of different companies and be used in the decision-making

process regarding suppliers to a large wind farm project. Therefore the analysis will focus

on the accuracy, credibility and documentation of the dynamic wind turbine models.

We use dynamic wind turbine models to investigate short-term voltage stability in the

context of connecting large amounts of wind power to the grid. The models have to

include suffici ently accurate representations of all the components of the wind turbine

construction that are relevant to such investigations. We will clarify, explain and

document the accuracy of the dynamic wind turbine models and their possible

shortcomings by validating the models. In general, the validation process should be

finished before the models are applied in the analysis of the short-term voltage stability.

Thus, validation becomes an integral part of the development of dynamic wind turbine

models and their implementation into dynamic simulation tools.

27.1.1 Background

The validations we will present here have their background in projects regarding the

incorporation of large amounts of wind power into the East Danish power system and,

more specifically, regarding the analysis of short-term voltage stability. The majority of

the small wind turbine sites in Denmark and the large offshore wind farm at Rødsand

consist of Type A wind turbines (Akhmatov, 2003a). Figure 27.1 illustrates this wind

turbine concept. It shows a three-bladed rotor, a shaft system with a gearbox, and an

induction generator with a shorted rotor-circuit. These basic components need accurate

representation and validation.

We use the simulation tool Power System Simulator for Engineering (PSS/E

(2)

When

we carried out our analysis, the dynamic simulation tool PSS/E

did not contain any

(2)

PSS/E

is a trademark of Shaw Power Technologies Inc. (PTI), New York, USA.

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model of Type A wind turbines that was sufficiently complex (Akhmatov, Knudsen and

Nielsen, 2000). Therefore, it was necessary to develop a user-written dynamic model of

Type A wind turbines to implement it into the PSS/E

tool and to verify it. This project

was carried out at the Danish company NESA (Akhmatov, Knudsen and Nielsen, 2000).

The simulation tool PSS/E

and modelling details are discussed briefly in Chapter 24.

This chapter describes the validation of the user-written dynami c model of Type A

wind turbines that was developed and implemented into the simulation tool PSS/E

NESA. It includes partial validation and an example of a full-scale validation of the

dynamic wind turbine model.

27.1.2 Process of validation

When analysing short-term volta ge stability, Type A wind turbines are treated as

complex electromechanical systems (Akhmatov, Knudsen and Nielsen, 2000). The

dynamic wind turbine model contains representations of the induction generator and

the shaft system, the aerodynamic model of the turbine rotor and blade-angle control.

First, representation of the individual parts of the wind turbine construction and its

generator can be validated. At this poi nt the models of the induction generator, the shaft

system and the turbine rotor can be validated separately. This is called partial validation

and it is necessary always to specify which part of the dynamic wind turbine model is to

be validated. If the individual parts of the wind turbine model are found to be suffi-

ciently accurate, the complete model of fixed-speed wind turbines is considered to be

sufficiently accurate too. However, partial validation does not necessarily take into

account the links between different parts of the model.

Second, full-scale validation can be carried out. This also focuses on validating the

representations of the different parts of the wind turbine construction. In addition, it

validates the interaction and links between different parts of the wind turbine construc-

tion. We will illustrate full-scale validation using an example where the interaction of the

electric parameters (the machine current) and the mechanical parameters (the generator

rotor speed) are verified against measurements (Raben et al., 2003).

Wind

Wind turbine

Gearbox

Induction generator

Capacitor

Grid

Figure 27.1 A fixed-speed wind turbine equipped with an induction generator. Note:LS¼low

speed; HS ¼high speed. Reprinted from Akhmatov, V. Analysis of Dynamic Behaviour of

Electric Power Systems with Large Amount of Wind Power, Ph.D. thesis, Technical University

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We can distinguish between two types of validation processes. First, a user-written

model that is implemented into a given simulation tool can be verified against the

standardised model of the same component of the other simulation tool (Knudsen

and Akhmatov, 1999). This requires that the standardised model already be verified

and documented by the supplier of the simulation tool. Second, the user-written model

is validated against measurements. In this case, the measurements come either from

planned experiments in the field (Pedersen et al., 2003) or from transient events or

accidents that have occurred in the power network.

Probably the easiest and cheapest way of validation is to carry it out against stan-

dardised models of another simulation tool. The validating process is then characterised

by the following:

The cases that are simulated with the two simulation tools can be set up so that they

are as similar to each other as possible. Possible uncertainties and discrepancies

between the two cases are minimised.

The cases contain only those components for which representation is necessary for the

validation.

The network representation around the validated component is reduced.

The component model can be validated during simulated operational conditio ns or

during transient events, which are not always reasonable to apply in experiments

(Raben et al., 2003).

The results of the validation need careful interpretation.

We have to keep in mind that validation is still being carried out with use of a

simulation model, even though it is standardised in the given simulation tool. The

standardised model may still have shortcomings regarding the model assumptions and

the area of application.

An example of this is the common third-order model of induction generators, CIMTR3,

which is the standardised model of the simulation tool PSS/E

. This model includes a

representation of the rotor flux transients, but it does not contain the stator flux transients

(see Chapter 24). The common third-order model is very suitable for simulating unba-

lanced, three-phased events in the power network (Pedersen et al., 2003). The disconnection

of a three-phased line is an example of such an unbalanced event. However, the common

third-order model will predict inaccurate results in the case of balanced, three-phased,

short-circuit faults with a significant voltage drop at the induction generator terminals

(Knudsen and Akhmatov, 1999). Consequently, it can be very useful to include in the

validating process other simulation tools and their standardised and validated models of

the same component. However, this requires a careful interpretation of the results.

The validation of user-written models against measur ements in the field is charac-

terised by the following:

Experimental work needs careful planning and preparation. Preparation includes

obtaining permission from authorities, the power system controller and the wind

turbine manufacturer (Raben et al., 2003).

The disturbances the wind turbines and the power network can be subjected to are

often limited. It is not always possible to obtain permission, for example, to execute

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experiments and subject a power system with grid-connected wind turbines to a

balanced, three-phase, short-circuit fault, even though the results of such experiments

would be valuable for validating the dynamic wind turbine model.

Measurements can be affected by components, control systems and parts of the power

network that are not part of the componen t to be validated. It may become necessary

to include representations of these compon ents in the network representation that is

used for the validation. Careful planning of the experimental work can reduce this

undesirable effect, though.

The validation is likely to be complicated by uncertainties with respect to network

configuration, the data of the components and the control systems affecting the

measurements and so on. A careful representation of the simulation case can minimise

such uncertainties.

The simulated and the measur ed behaviour have to be in agreement, otherwise the

model is incomplete and the interpretation of the results of the validation process is

ambiguous.

Even though there may be difficulties regarding (a) planning and executing measure-

ments in the field, (b) collecting data and (c) minimising uncertainties, the validation

results reached with the use of measurements have a high credibility. The reason for this is

that simulations aim at reproducing measured behaviour under similar conditions in

simulations. If this is not achieved, the usefulness of the simulation will be under question.

There will, however, always be discrepancies between simulated and measured beha-

viour. Such discrepancies have to be minimised by accurate modelling and by discovering

and explaining the possible sources of these discrepancies. If the validation process is

carried out accurately, such discrepancies are small and are often caused by uncertainties

in the network representation and data (Akhmatov, 2003a; Pedersen et al., 2003).

27.2 Partial Validation

In the following, we will present cases with a partial validation of the dynamic wind

turbine model. The cases are validated against simulations and measurements.

27.2.1 Induction generator model

Here we will describe the validation of the user-written model of induction generators that

is implemented in the simulation tool PSS/E

at NESA. This is a transient fifth-order

model (i.e. it contains a representation of the fundamental frequency transients of the

machine current). The validation is carried out against simulations with the standar-

dised model of the tool Matlab/Simulink

(3)

The simulated sequence is a three-phase,

short-circuit fault that lasts 100 ms. We chose to validate the user-written model in

PSS/E

against simulations with the standardised model of induction generators of

Matlab/Simulink

for the following reasons:

(3)

Matlab/Simulink

is a trademark of The MathWorks Inc; Natrick, USA.

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A balanced, three-phase, short-circuit fault is a common transient event that has been

analysed in investigations on transient voltage stability (Knudsen and Akhmatov,

1999). Therefore it is necessary to ensure that the user-written model in the tool PSS/

gives a sufficiently accurate response for this kind of fault.

It can be difficult to obtain permission to carry out an experiment with such a

disturbance in the grid because this is a serious incident.

The tool Matlab/Simulink

is applied and recognised worldwide.

The tool Matlab/Simulink

contains the standardised and verified model of induction

generators, which is a three-phase, physical representation. The model is suitable for the

simulation of balanced as well as unbalanced transient events in the power network.

The validation process is based on a simple network equivalent. It contains an

induction generator connected to an infinite bus through a 0.7/10 kV transformer and

a line with an impedance corresponding to the short-circuit ratio (SCR) of 6.7. Figure

27.2 shows the network equivalent. The network equivalent models are implemented

both in the simulation tool PSS/ E

(the positive-sequence equ ivalent) and the tool

Matlab/Simulink

(the three-phase representation). The implementation for each

simulation tool is as similar as possible. The induction generator works at the rated

operation point and supplies 2 MW. Table 27.1 includes the data.

=2MW

=2.7 MW

=1%, e

=6%

= 0.5 MVAR

0.7/10

SCR = 6.7

Z /2

100

Infinite bus

Figure 27.2 Model of a network equivalent with an induction generator (IG). Note:SCR¼ short-

circuit ratio; P

¼generator electric power; C

¼no-load compensation; S

¼transformer power

capacity; e

¼real part of transformer impedance; e

¼imaginary part of transformer impedance.

Reprinted from Akhmatov, V. Analysis of Dynamic Behaviour of Electric Power Systems with

Large Amount of Wind Power, Ph.D. thesis, Technical University of Denmark, Kgs. Lyngby,

Table 27.1 Data of a 2 MW induction generator. Reprinted from Akhmatov, V. Analysis of

Dynamic Behaviour of Electric Power Systems with Large Amount of Wind Power, Ph.D. thesis,

the copyright holder

Parameter Value Parameter Value

Rated power (MW) 2 Stator resistance (p.u.) 0.048

Rated voltage (v) 690 Stator reactance (p.u.) 0.075

Rated frequency (Hz) 50 Magnetising reactance (p.u.) 3.80

Rated slip 0.02 Rotor resistance (p.u.) 0.018

Generator rotor inertia (s) 0.5 Rotor reactance (p.u.) 0.12

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Figure 27.3 illustrates the simulated behaviour of the voltage and the generator rotor

speed, which is applied to validate the transient fifth-order model of induction genera-

tors. For a comparison, the behaviour computed with the use of a common third-order

model in the tool PSS/E

(neglecting fundamental frequency transients in the machine

current) is plotted in the same figure.

As expected (Knudsen and Akhmatov, 1999), the simulated results of the transient

fifth-order model of induction generators in the tool PSS/E

are in agreement with the

results of the standardised model of the tool Matlab/Simulink

. The common third-

order model of induction generators predicts overpessimistic results with respect to

maintaining short-term voltage stability, for the following reasons:

The common third-order model predicts more overspeeding of the induction genera-

tor during the grid fault, compared with the results of the fifth-order model. An

explanation of this phenomenon is given in Chapter 24.

The mechanical parameter, which is the generator slip, and the electric parameters of

the induction generator are strongly coupled. If the prediction of the overspeeding is

too high, the prediction of the reactive absorption will be too high as well.

(b)

184

182

180

178

176

174

172

170

Speed, (rad/s)

168

166

164

162

160

158

186

156

0.6 0.7 0.8 0.9 1.0 1.1 1.2

Time (s)

1.3 1.4 1.5 1.6 1.7 1.8 1.9

0.5

PSS/E

fifth-order model

PSS/E

third-order model

184

182

180

178

176

174

172

170

Speed, (rad/s)

168

166

164

162

160

158

186

156

(a)

0.6 0.7 0.8 0.9 1.0 1.1 1.2

Time (s)

1.3 1.4 1.5 1.6 1.7 1.8 1.90.5 2

Matlab/Simulink

(c)

600

500

400

Voltage (V)

300

200

100

700

0.6 0.7 0.8 0.9 1.0 1.1 1.2

Time (s)

1.3 1.4 1.5 1.6 1.7 1.8 1.9

0.5

Matlab/Simulink

(d)

600

500

400

Voltage (V)

300

200

100

700

0.6 0.7 0.8 0.9 1.0 1.1 1.2

Time (s)

1.3 1.4 1.5 1.6 1.7 1.8 1.9

0.5

PSS/E

fifth-order model

PSS/E

third-order model

Figure 27.3 Simulated behaviour of the generator rotor speed: (a) using Matlab/Simulink

and

(b) using PSS/E

. The terminal (RMS phase–phase) voltage: using (c) Matlab/Simulink

, and

(d) using PSS/E

. Reprinted from Akhmatov, V. Analysis of Dynamic Behaviour of Electric

Power Systems with Large Amount of Wind Power, Ph.D. thesis, Technical University of

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Consequently, the common third-order model of induction generators predicts a slower

voltage re-establishing after the grid fault than does the transient fifth-order model.

In this particular case, the common third-order model predicts voltage instability,

whereas according to the transient fifth-order model of induction generators the

voltage is re-established.

Knudsen and I reached the same conclusion when validating against the standardised

induction generator model of the Alternative Transient Program (ATP) simulation tool

(Knudsen and Akhmatov, 1999). Chapter 24 briefly describes the ATP tool. This was

also the first time that the validity and accuracy of the common third-order model of

induction generators were questioned as to whether the model should be used in the

analysis of short-term voltage stability.

Wind turbine generators are equipped with protective relays. This means that several

electrical and mechanical parameters are monitored, and if one of the monitored

parameters exceeds its respective relay settings the wind turbine generators will be

disconnected. One of the monitored parameters is the machine current. Figure 27.4

shows the computed behaviour of the machine current during the grid fault. As can be

seen, the machine currents computed with the transient fifth-order model in the tool

PSS/E

and with the standardised model of the tool Matlab/Simulink

are in

agreement. The machine current computed with the common third-order model in the

tool PSS/E

does not coincide with the result of the tool Matlab/Simulink

This needs further explanation. The transient fifth-order model takes the following

into account when computing the behaviour of the machine current:

A three-phased, short-circuit fault is a balanced transient event, meaning that the fault

occurs at the same moment in all three phases. The phase current can be characterised

by the DC offset, and the current phasor contains the fundamental frequency transi-

ents. The computed current behaviour during the faulting time shows this.

The short-circuit fault is cleared sep arately in each phase of the faulted three-phased

line. This happens when the phase-currents pass zero in the respective phases. The

fault clearance is therefore an unbalanced event. It does not initiate the DC offset in

the pha se currents, and the fundamental frequency transients in the current phasor

are eliminated after the fault is cleared.

The standardised model of induction generators in the tool Matlab/Simulink

automatically takes this behaviour into account because Matlab/Simulink

operates

with three-phased representations of electric machines and power networks.

The transient fifth-order model of induction generators in the tool PSS/E

adapted to this behaviour. This is necessa ry because the simulation tool PSS/E

operates with positive-sequence equivalents of power network models.

Additionally, the phase current behaviour is plotted. This phase current is modelled in

Matlab/Simulink

and is included here in order to demonstrate that the current phasor

follows the behaviour of the magnitude of the phase current with developed DC offset.

This observation is important for the validating process described in Section 27.3.

According to the current behaviour shown in Figure 27.4, the common third-order

model of induction generat ors underpredicts values of the machine current during the

610 Full-scale Verification of Dynamic Wind Turbine Models