AckermannTh. (ed) Wind Power in Power Systems

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At the time of reconnection, T

, switch SW 01 was closed and section 1 with wind

turbine WT 01 was reconnected to the entire power system. During the experiment, the

voltage and the current at the low-voltage side of the 0.7/10 kV transformer of wind

turbine WT 01 were measured, as shown in Figure 27.9. The sampling frequency of the

measuring equipment was 1 kHz (Raben et al., 2003) and any delay in the measured

signals produced by the equipment can be neglected.

During islanded operation, the no-load capacitor of wind turbine generator WT 01

was kept grid-connected. This was done to reduce the possibility of a voltage drop at the

terminals of wind turbine WT 01 during islanded operation (Raben et al., 2003).

27.3.2 Measured behaviour

Figure 27.10 presents the measured behaviour of the phase current, I

, and the phase-to-

phase voltage, U

. During islanded operation, the current of the no-load compensated

induction generator of wind turbine WT 01 was not zero, because the induction motors

in section 1 absorbed a certain amount of electric power produced by the induction

generator of wind turbine WT 01; also, some reactive power was exchanged via the

internal power network of section 1, as there was the no-load impedance of the

transformers and the cable charging.

During islanded operation, and shortly after reconnection, higher harmonics of the

fundamental frequency of 50 Hz were seen in the measured current. The higher harmo-

nics were presumably caused by the induction machines. This coincides with the results

of previous studies (Pedersen et al., 2000). The measured voltage showed no (significant)

drop during islanded operation.

At tripping, t ¼T

, there was no DC offset in the measured phase current. However,

there was a noticeable DC offset in the measured phase current at reconnection, t ¼T

There was no DC offset during tripping because the opening of switch SW 01 was an

unbalanced three-phased event (Section 27.2.1 explains the elimination of the DC offset

in the phase current during tripping.) Switch SW 01 was closed at the same time, t ¼T

2000

1800

1600

1400

1200

1000

800

600

400

200

–200

–400

–600

–800

–1000

(a)

Time (s)

Phase current/500 ms

Current (A)

2.2

2.4 2.6

2.8 3 3.2

3.4

3.6

3.8

1200

1000

800

600

400

200

–200

–400

–600

–800

–1000

–1200

(b)

Time (s)

Voltage (V)

2.2

2.4 2.6

2.8 3 3.2

3.4

3.6

3.8

Phase–phase voltage/500 ms

Figure 27.10 Measured behaviour of (a) phase-current and (b) phase-to-phase voltage.

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,

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in all the three phases. The reconnection was therefore a balanced transient event

initiating the DC offset in the phase current.

During and after islanded operation, the voltage magnitude was almost unchanged.

The measured current showed a fluctuating behaviour after reconnecting. The natural

frequency of the current fluctuations was about 7 Hz and could not be explained by the

dynamic behaviour of the induction generator only. The value of the natural frequency

indicated that the current fluctuations were related to the torsional oscillations of the

shaft system of wind turbine WT 01.

27.3.3 Modelling case

The positive-sequence equivalent of the experimental network is implemented in the tool

PSS/E

that is used for the validation. It is essential that the network representation

and its load flow solution are in agreement with the factual conditions of the experi-

ment. SEAS provided the data of the internal power network of the wind farm, includ-

ing for the cables and the transformers, and the manufacturer Bonus Energy supplied

the data of the fixed-speed wind turbines (Akhmatov, 2003a).

The values of the phase current and phase-to-phase voltage, which were measured just

before opening switch SW 01, are used for initialising wind turbine generator WT 01.

The numeric value of the apparent power, S, of the no-load compensated induction

generator of wind turbine WT 01 is computed from:

S ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ Q

ﬃﬃﬃ

; ð27:1Þ

where P denotes the elect ric power of the induction generator of wind turbine WT 01

), and Q ¼Q

Q

, where Q

is the reactive power absorbed by the induction

generator and Q

is the reactive power of the no-load capacitor.

From the measured behaviour of the current and the voltage shown in Figure 27.10,

the numeric value of the apparent power of the no-load compensated induction gen-

erator is estimated to be 80 kVA. This is the value before the islanded operation. Using

this information and the data of the generator and the no-load capacitor, and applying

iterations, we arrive at the initial operational point of the induction generator of wind

turbine WT 01. Assuming a regular wind distribution over the wind farm, other grid-

connected wind turbines (in three other sections) were initialised to the same operational

points.

The operational points of the induction motors of the disconnected wind turbine

generators are not given but are estimated from the measured current and voltage

during islanded operation. During islanded operation, the measured value of the phase

current peak is in the range of 60–65 A, and the voltage magnitude does not change

significantly. This current repres ents mainly the electric power absorbed by the induc-

tion motors in section 1 of the wind farm. Using the above-described procedure for

initialising wind turbine gen erator WT 01, the operational points of the induction

motors are estimated. The induction motors absorb approximately 10 kW per (discon-

nected) wind turbine.

Despite our efforts carefully to represent the experimental cond itions in the simula-

tion case, there will always be a small number of uncertainties and missing data. The

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manufacturer did not provide the damping coefficients that are required for the two-

mass model equations, for instance. The representation is simplified and the damping

coefficients are set to zero in the simulations.

In dynamic simulations, the wind turbine generator is computed with the transient

fifth-order model. For the induction motors, however, the standardised PSS/E

model

CIMTR4 is used – that is, the common third-order model of induction motors (i.e. the

current transients in the induction motors during reconnection are neglected). The

no-load capacitor of wind turbine WT 01 is modelled in accordance with the dynamic

interface of the tool PSS/E

. Therefore, the transients in the capacitor current are also

neglected, even though there are probably such current transients in the measurements

(Larsson and Thiringer, 1995).

27.3.4 Model validation

The main target is to validate the user-written dynamic model of Type A wind turbines,

which was implemented in the tool PSS/E

. This model contains the fifth-order model

of induction generators and a shaft system representation with the two-mass model. For

reasons of comparison, the same simulations are carried out using of the following

models:

A model with the fifth-order model of induction generators and the lumped-mass

model (i.e. assuming a very stiff shaft system);

a model contai ning the common third-order model of induction generators and the

two-mass model of the shaft system.

The simulation tool PSS/E

operates with positive-sequence equivalents of the net-

work models and computes the phasor values of voltages and currents. Figure 27.11

shows the simulated behaviour, in phasor values, of the voltage and the current. For the

validation, we therefore compare the measured phase values with the computed phasor

values. As demonstrated in Section 27.2.1, the current phasor follows the magnitude

behaviour of the phase current with developed DC offset. The behaviour simulated with

the dynamic wind turbine model is in agreement with the measured behaviour. The

simulated current phasor is correctly initiated, drops to around 60 A (peak-phase)

during islanded operation, contains the fundamental frequency transients during recon-

nection and shows an oscillating behaviour with the natural frequency of around 7 Hz.

The wind turbine model containing the lumped-mass model of the mechanical system

underpredicts values for the current trans ients at reconnection. Furthermore, it does not

predict oscillations of the current after reconnecting.

The wind turbine model with the common third-order model of induction generators

underpredicts values of the current at reconnection, because the fundamental frequency

transients in the machine current are neglected. This model does, however, predict

current oscillations with the natural frequency of around 7 Hz.

The oscillating behaviour of the current phasor is related to the shaft torsional mode

and to the natural frequency of the generator itself. The simulated generator rotor

speed shown in Figure 27.12 illustrates this. When representing the shaft system with the

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2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

400

500

600

700

800

900

1000

1100

1200

300

200

100

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Voltage (V)

Current (kA)

Time (s)Time (s)

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Time (s)

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Time (s)

(a)

(c)

(b)

(d)

PSS/E

fifth-order, two-mass model

PSS/E

fifth-order, two-mass model

PSS/E

fifth-order, two-mass model

PSS/E

fifth-order, two-mass model

Figure 27.11 Computed behaviour of (a) current phasor and (b) voltage phasor, both computed

with the dynamic wind turbine model containing the fifth-order generator model and the two-mass

shaft model. Current-phasor computed with the model containing (c) the fifth-order generator model

and the lumped-mass model of the mechanical system and (d) the third-order generator model and

the two-mass shaft model. 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,

005

004

003

002

001

–005

–004

–003

–002

–001

0.002

0.004

0.006

0.008

0.010

–0.01

–0.008

–0.006

–0.004

–0.002

Speed deviation (p.u.)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (s)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (s)

(a) (b)

PSS/E

lumped-mass model

PSS/E

two-mass model

Figure 27.12 Computed behaviour of the generator rotor speed deviation (minus slip) for (a) the

two-mass model and (b) the lumped-mass model. Note: The curves are to different scales.

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,

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two-mass model, the behaviour of the generator rotor speed shows oscillations with the

natural frequency of around 7 Hz. This is similar to the current phasor behaviour. The

reason is the strong coupling between electrical and mechanical parameters in induction

generators (Akhmatov, Knudsen and Nielsen 2000).

When using the lumped-mass model, the generator rotor speed does not show such

oscillating behaviour. Consequently, there are no oscillations in the simulated current

phasor.

To summarise this discussion, only the dynamic wind turbine model containing the

fifth-order model of induction generators and the two-mass representation of the shaft

system gives sufficiently accurate results. This full-scale validation also demonstrates

that the links between the various parts of the dynamic wind turbine model have been

accurately implemented.

27.3.5 Discrepancies between model and measurements

Having shown that the dynamic wind turbine model with the fifth-order induction

generator model and the two-mass model of the shaft system gives sufficiently accurate

results, we will now evaluate and explain possible discrepancies between the simulations

carried out with this model and the measurements.

First, the simulated results do not include higher harmonics of the fundamental electric

frequency, which are there in the measurements. The reason is that this user-written model

is implemented in the tool PSS/E

, which is a fundamental frequency tool. This is one of

the restrictions of this dynamic wind turbine model and of the simulation tool.

Second, during reconnection, the fundamental frequency transients of the simulated

current phasor are somewhat lower than in the measur ed phase current. This can be

explained by the fact that the induction motors and the no-load capacitor are modelled

according to the interface of the tool PSS/E

. That means that during balanced

transient events the fundamental frequency transients are neglected in the simulated

current. However, such transients have probably influenced the measured phase current

during reconnection.

Last, the damping of the current oscillations is lower in the simulated behaviour than

it is in the measured behaviour. The reason is that the simulations are carried out with

the damping coefficients set to zero. However, there is always finite damping in the real

wind turbine construction and its generator.

This validation sh ows only relatively small discrepancies between simulated and

measured behaviour. The discrepancies were minimised by accurately implementing

the network model equivalent into the simulation tool and by accurate modelling.

27.4 Conclusions

Validation is an important and indispensable part of modell ing electricity-producing

wind turbines in dynamic simulation tools. The dynamic wind turbine models are to be

used for analysing power system stability in the context of connecting large amounts of

wind power to the grid. Therefore, the dynamic wind turbine models have to be based

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on sufficiently accurate assumptions and to predict accurate responses of the wind farms

to transient events in power networks. There is no point in applying models that have

not been validated and that are inaccurate.

The results presented here demonstrate that it is possible to develop and implement in

existing simulation tools dynamic wind turbine models of sufficient accuracy and

complexity. The focus here was on the validation of the user-written dynamic model

of Type A wind turbines implemented in the simulation tool PSS/E

, for use by the

Danish power company NESA. Type A wind turbines may be considered the simplest

among the existing wind turbine concepts. Even for this concept, thou gh, modelling and

validation has been challenging.

The dynamic wind turbine model contains (a) the transient fifth-order model of

induction generators, (b) the two-mass representation of the shaft system and (c) the

aerodynamic rotor model and the model of blade-angle control. The common third-

order model of induction generators should not be used to investigate balanced transient

events with a significant voltage drop. The lumped-mass model of the shaft system does

not pred ict accurately the inter action between the wind turbines and the electric power

network during grid disturbances. It is also important to choose the details of the

aerodynamic rotor model in accordance with the target of the investigation.

The dynamic wind turbine model was validated against measurements and also

against simulations. Here, the partial validation has demonstrated that the main parts

of the dynamic wind turbine model are developed and implemented in the simulation

tool with sufficient accuracy. The full-scale validation showed that all the parts of the

complete model and also the links between them are represented with sufficient accuracy.

There were only relatively small discrepancies between the results of the dynamic

wind turbine model and measurements. There will always be such discrepancies because

of uncertainties in the data of the wind turbine and the power network and restrictions

of the simulation tool and the dynamic wind turbine model. These discrepancies can be

minimised by careful modelling.

Dynamic wind turbine models (of different wind turbine concepts) should be imple-

mented, in the near future, in the existing simulation tools that are applied to analyse

power system stabili ty. Individual validations are expensive and therefore simulation

tool suppliers should commercialise and standardise the dynamic wind turbine models

whenever possible. In this way such models would become accessible to every user,

which would be generally advantageous. These standardised models should be validated

in cooperation with wind turbine manufacturers, organisations involved in large wind

farm projects or independent research organisations; the validation reports should also

be published.

References

[1] Akhmatov, V. (2001) ‘Note Concerning the Mutual Effects of Grid and Wind Turbine Voltage Stability

Control’, Wind Engineering 25(6) 367–371.

[2] Akhmatov, V. (2003a) Analysis of Dynamic Behaviour of Electric Power Systems with Large Amount of

Wind Power, PhD thesis, Technical University of Denmark, Kgs. Lyngby, Denmark, available at

http://www.oersted.dtu.dk/eltek/res/phd/00-05/20030403-va.html.

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[3] Akhmatov, V. (2003b) ‘On Mechanical Excitation of Electricity-producing Wind Turbines at Grid

Faults’, Wind Engineering 27(4) 257–272.

[4] Akhmatov, V., Knudsen, H., Nielsen, A. H. (2000) ‘Advanced Simulation of Windmills in the Electrical

Power Supply’ International Journal of Electrical Power and Energy Systems 22(6) 421–434.

[5] Akhmatov, V., Knudsen, H., Nielsen, A. H., Pedersen, J. K., Poulsen, N. K. (2003) ‘Modelling and

Transient Stability of Large Wind Farms’, Electrical Power and Energy Systems, 25(2) 123–144.

[6] Eltra (2000) ‘Specifications for Connecting Wind Farms to the Transmission Network’, ELT1999-411a,

Eltra Transmission System Planning, Denmark.

[7] Hinrichsen, E. N., Nolan, P. J. (1982) ‘Dynamics and Stability of Wind Turbine Generators’, IEEE

Transactions on Power Apparatus and Systems, 101(8) 2640–2648.

[8] Kazachkov, Y. A., Feltes, J. W., Zavadil, R. (2003) ‘Modeling Wind Farms for Power System Stability

Studies’ presented at IEEE Power Engineering Society General Meeting, Toronto, Canada.

[9] Knudsen, H., Akhmatov, V. (1999) ‘Induction Generator Models in Dynamic Simulation Tools’, Inter-

national Conference on Power System Transients IPST’99, Budapest, Hungary, pp. 253–259.

[10] Larsson, A., Thiringer, T. (1995) ‘Measurements on and Modelling of Capacitor-connecting Transients

on a Low-voltage Grid Equipped with Two Wind Turbines’, International Conference on Power System

Transients IPST’95, Lisbon, Portugal, pp. 184–188.

[11] Øye, S. (1986) ‘Unsteady Wake Effects Caused by Pitch-angle Changes’, in IEA R&D WECS Joint Action

on Aerodynamics of Wind Turbines, 1st Symposium, London, U.K., pp. 58–79.

[12] Pedersen, J. K., Akke, M., Poulsen, N. K., Pedersen, K. O. H. (2000) ‘Analysis of Wind Farm Islanding

Experiment’, IEEE Transactions on Energy Conversion 15(1) 110–115.

[13] Pedersen, J. K., Pedersen, K. O. H. Poulsen, N. K., Akhmatov, V., Nielsen, A. H. (2003) ‘Contribution to

a Dynamic Wind Turbine Model Validation from a Wind Farm Islanding Experiment’, Electric Power

Systems Research 64(2) 41–51.

[14] Raben, N., Donovan, M. H., Jørgensen, E., Thisted, J., Akhmatov, V. (2003) ‘Grid Tripping and

Re-connection: Full-scale Experimental Validation of a Dynamic Wind Turbine Model’, Wind Engineering

27(3) 205–213.

[15] Snel, H., Schepers, J. G. (Eds) (1995) ‘Joint Investigation of Dynamic Inflow Effects and Implementation

of an Engineering Method’, ECN-C-94–107, Netherlands Energy Research Foundation, ECN, Petten,

The Netherlands.

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Impacts of Wind Power on Power

System Dynamics

J. G. Slootweg and W. L. Kling

28.1 Introduction

In most countries, the amount of wind power generation integrated into large-scale

electrical power systems covers only a small part of the total power system load. However,

the amount of electricity generated by wind turbines is increasing continuously. Therefore,

wind power penetration in electrical power systems will increase in the future and will start

to replace the output of conventional synchronous generators. As a result, it may also

begin to influence overall power system behaviour. The impact of wind power on the

dynamics of power systems should therefore be studied thoroughly in order to identify

potential problems and to develop measures to mitigate those problems.

The dynamic behaviour of a power system is determined mainly by the generators.

Until now, nearly all power has been generated with conventional directly grid-coupled

synchronous generators. The behaviour of the grid-coupled synchronous generator under

various circumstances has been studied for decades and much of what is to be known is

known. However, although this generator type used to be applied in wind turbines in the

past, this is no longer the case. Instead, wind turbines use other types of generators, such

as squirrel cage induction generators or generators that are grid-coupled via power

electronic converters. The interaction of these generator types with the power system is

different from that of a conventional synchronous generator. As a consequence, wind

turbines affect the dynamic behaviour of the power system in a way that might be

different from synchronous generators. Further, there are also differences in the interac-

tion with the power system between the various wind turbine types presently applied, so

that the various wind turbine types must be treated separately. This also applies to the

various wind park connection schemes that can be found discussed in the literature.

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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This chapter discusses the impact of wind power on power system dynamics. First, we

present the concepts of power system dynamics and of transient and small signal

stability, as well as the most important currently used wind turbine types. Then, we will

study the impact of these wind turbine types and of various wind farm interconnection

schemes on the transient stability of the power system. For this, we will analyse the

response to disturbances, such as voltage and frequency changes. Finally, we will deal

with the impact of wi nd power on the small signal stability of power systems and use

eigenvalue analysis for this purpose.

28.2 Power System Dynamics

Power system dynamics investigates how a power system responds to disturbances that

change the system’s operating point. Examples of such disturbances are frequency

changes because a generator trips or a load is switched in or disconnected; voltage

drops due to a fault; changes in prime mover mechanical power or exciter voltage, and

so on. A disturbance triggers a response in the power system, which means that various

properties of the power system, such as node voltages, branch currents, machine speeds

and so on, start to change. The power system is considered stable if the system reaches a

new steady state and all generators and loads that were connected to the system before

the disturbance are still connected. The original power system is considered unstable if,

in the new steady state, loads or generators are disconnected.

Two remarks must be made at this point. First, when a system is stabl e, the new

steady state can either be identical to or different from the steady state in which the

system resided before the disturbance occurred. This depends on the type of distur-

bance, the topology of the system and the controllers of the generators. Se cond, that a

power system is unstable does not necessarily mean that a disturbance leads to a

complete blackout of the system. Rather, the system’s topology is changed by protection

devices that disconnect branches, loads and/or generators during the transient phenom-

enon, in order to protect these. In most cases the changed system will be able to reach a

new steady state, thus preventing a complete blackout. However, although the ‘new’

system that results after the changes is stable, the ‘old’ system was unstable and stability

has been regained by changing the system’s topology.

There are two different methods to investigate the dynamics of a power system in

order to determine whether the system is stable or not. The first method is time domain

analysis. The type of time domain analysis that we use here is also referred to as

dynamics simulation, fundamental frequency simulation or electromechanical transient

simulation (see also Chapter 24). This approach subjects the system to a disturbance

after which its response (i.e. the quantitative evolution of the system’s properties over

time) is simulated. In this way, it can be decided whether the system is stabl e or not. In

the case of instability, strategies can be designed to change the system’s topology in such

a way that stability is regained with minimum consequences to loads and generators.

The second method is frequency domain analysis, also referred to as an analysis of the

small signal properties of the system or as eigenvalue analysis. Frequency domain

analysis studies a linearised representation of the power system in a certain state. The

linearised representation makes it possible to draw conclusions as to how the power

630 Impacts on Power System Dynamics