Agregated Modelling of Wind Parks

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The financial support from the Dutch Organization for Scientific Research

(NWO) is greatly acknowledged.

The authors are with the Faculty of Information Technology and Systems,

Delft University of Technology, P.O. Box 5031, 2600 GA, DELFT, The

Netherlands.

Corresponding author: J.G. Slootweg

E-mail: [email protected]

Tel : +31-15-27 86219

Fax: +31-15-27 81182

Aggregated Modelling of Wind Parks in Power

System Dynamics Simulations

J.G. Slootweg, Member, IEEE, W.L. Kling, Member, IEEE

Abstract - Increasing numbers of wind turbines are connected to

electrical power systems, in order to reduce the adverse

environmental impact of conventional electrical power

generation. A tendency can be observed to erect these turbines in

wind parks, connected to the high voltage transmission grid.

These parks effect the dynamic behaviour of power systems,

because in wind turbines generator types that are different from

the conventional synchronous generator are used.

To investigate the impact of a wind park on the dynamics of the

power system to which it is connected, an adequate model is

required. In order to avoid the necessity of developing a detailed

model of a wind park with tens or hundreds of wind turbines and

their interconnections and to calculate the wind speed signal for

each individual turbine, aggregated wind park models are needed.

In the paper, aggregated models for wind parks equipped with

either constant or variable speed wind turbines are presented. It

is shown that results obtained with an aggregated model and with

a detailed model show a high degree of correspondence, both for

normal operation and for disturbances.

Index Terms - wind power, wind park, aggregated modelling,

simulation, power system dynamics

I. I NTRODUCTION

As a result of increasing environmental concern, the impact of

conventional electricity generation on the environment is being

minimized and efforts are made to generate electricity fromrenewable sources. The main advantages of electricity

generation from renewable sources are the absence of harmful

emissions and the in principle infinite availability of the prime

mover that is converted into electricity. One way of generating

electricity from renewable sources is to use wind turbines that

convert the energy contained in flowing air into electricity. Up

to this moment, the amount of wind power integrated into large

scale electrical power systems only covers a small part of the

total power system load. The rest of the load is for the largest

part covered by conventional thermal, nuclear and hydro

power plants.

Wind turbines hardly ever take part in voltage and frequency

control and if a disturbance occurs, the wind turbines aredisconnected and reconnected when normal operation has been

resumed. Thus, notwithstanding the presence of wind turbines,

frequency and voltage are maintained by controlling the other

power plants as would have been the case without any wind

turbines present. This is possible, as long as wind power

penetration is still low. However, a tendency to increase the

amount of electricity generated from wind can be observed.

Therefore, the penetration of wind turbines in electrical power

systems will increase and they may begin to influence overall

power system behavior. In that case, it will no longer be

possible to run a power system by only controlling large scale

power plants. It is therefore important to study the behavior of

wind turbines in an electrical power system and their

interaction with other generation equipment and with loads.

Further, a tendency to concentrate turbines in wind farms can

be observed in order to use regions with a good wind resourceefficiently and to concentrate the visual impact of modern

wind turbines, that can easily reach heights of more than 100

m, at certain locations. These wind farms are connected to the

high voltage transmission grid and therefore directly influence

the dynamic behavior of an electrical power system. This

increases the need for adequate models.

In this paper, aggregated models of wind parks with both

constant and variable speed wind turbines are presented. The

advantage of an aggregated model is that it eliminates the need

to develop a detailed model of a wind park with tens or

hundreds of wind turbines and their interconnections, and to

calculate the wind speed signal for each individual turbine in

advance. As will be shown, the response of the aggregated andthe detailed models shows a high degree of similarity, both

during normal operation as well as during disturbances.

The topic of aggregated wind park modelling has been treated

earlier, both by the authors of this paper, as well as by other

authors [1-4]. Nevertheless, it has not been treated extensively

in the existing literature, because so far:

For wind parks with variable speed wind turbines, only the

response to wind speed changes been investigated [1].

For constant speed wind turbines, only the fault response

has been investigated [2-4].

In this paper, the response of detailed and aggregated models

of wind parks with constant and variable speed wind turbines

to both wind speed changes and faults will be compared. Thisis important, because presently it is not clear whether

aggregated models adequately represent a wind park both

under normal operating conditions and during disturbances, as

is required [5]. Investigations of the response of wind parks

with constant speed wind turbines to wind speed changes and

the fault response of wind parks with variable speed wind

turbines have not been carried out yet. These will be carried

out in this paper, which therefore makes an important

contribution to the topic of aggregated wind park modelling.

0-7803-7967-5/03/$17.00 ©2003 IEEE

Paper accepted for presentation at 2003 IEEE Bologna Power Tech Conference, June 23th-26th, Bologna, Italy



II. WIND TURBINE TYPES

Three different wind turbine types are currently widely

applied. The first is the directly grid coupled squirrel cage

induction generator, used in constant speed wind turbines. The

wind turbine rotor is coupled to the generator through a

gearbox. In most constant speed wind turbines, the power

extracted from the wind is limited using the stall effect during

high wind speeds. This means that the rotor is designed in sucha way that its aerodynamic efficiency decreases in high wind

speeds, thus preventing extraction of too much mechanical

power from the wind. When the stall effect is used, no active

control systems are necessary. Pitch controlled constant speed

wind turbines have, however, also been built.

The second type is the doubly fed (wound rotor) induction

generator, which allows variable speed operation. The rotor

winding is fed using a back-to-back voltage source converter.

Like in the first type, the wind turbine rotor is coupled to the

generator through a gearbox. In high wind speeds, the power

extracted from the wind is limited by pitching the rotor blades.

The third type is a direct drive synchronous generator, also

allowing variable speed operation. The synchronous generator can have a wound rotor or be excited using permanent

magnets. It is grid coupled through a back-to-back voltage

source converter or a diode rectifier and voltage source

converter. The synchronous generator is a low speed multi

pole generator, therefore no gearbox is needed. Like in the

second type, the power extracted from the wind is limited by

pitching the rotor blades in high wind speeds. The three wind

turbine types are depicted in figure 1. For a more elaborate

description of the various wind turbine types, the reader is

referred to text books [6].

Figure 1. Schematic representation of frequently occurring wind turbine

types: constant speed wind turbine, variable speed wind turbine with doubly

fed (wound rotor) induction generator, variable speed wind turbine with direct

drive synchronous generator .

III. AGGREGATED MODELLING OF WIND PARKS

A. Power System Dynamics Simulations

The models presented in this paper are meant to be used for

power system simulations, also referred to as fundamental

frequency simulations or electromechanical transient

simulations. This type of simulations can be applied to study

phenomena with frequencies of about 0.1 to 10 Hz. The typical problems investigated using power system dynamics

simulation software are voltage and rotor angle stability.

In order to be able to quickly carry out the simulation of

phenomena in the band width of interest, it should be possible

to use a relatively long simulation time step. Therefore, high

frequency phenomena are neglected in power system dynamics

simulations by using a load flow model for the network and by

neglecting short time constants in the generator and controller

models by assuming that the new steady state is reached

immediately. This approach not only allows the use of a longer

simulation time step, but also reduces the number of

differential equations, because there are no longer differential

equations associated with the network, whereas the number of differential equations associated with the generators and the

controllers is reduced [7].

In section III.B, the modelling of the individual wind turbines

will be discussed, whereas in section III.C the development of

an aggregated park model from the model of an individual

wind turbine is described.

B. Wind Turbine Modelling

1) Constant Speed Wind Turbine Model

A model of a constant speed wind turbine for power system

dynamics simulations consists of a rotor model, a shaft model

and a squirrel cage induction generator model. Here, thefollowing set of equations is used to describe the rotor of a

constant speed wind turbine

(1)

in which Pw is the power extracted from the wind [W], is the

air density [kg/m3], c p is the performance coefficient, Ar is the

area swept by the rotor [m

2

], vw is the wind speed [m/s] and the tip speed ratio, equal to the rotor blade tip speed vt [m/s]

divided by the wind speed vw. Before the wind speed is

inserted in equation (1), it passes through a low pass filter in

order to approximate the smoothing effect of the large rotor

surface for wind speed components with a high frequency.

The shaft is described by the following set of equations, in

which f is the nominal grid frequency [Hz], T is torque [p.u.],

is the angular displacement between the two ends of the shaft

[electrical radians], is rotational speed [p.u.], H is the inertia

constant [s] and K s is the shaft stiffness [p.u. torque/electrical



Figure 2. General variable speed wind turbine model [1], [10]

radians]. The indices wr, m and e mean wind turbine rotor,

generator mechanical and generator electrical respectively.

(2)

The generator model in the constant speed wind turbine

concept is a standard induction machine model in which the

d/dt terms in the stator equations are neglected in order to be

comply with the assumptions on which power system dynamics

simulations are based. The model’s equations can be found in

the literature [7].

2) Variable Speed Wind Turbine Model

A variable speed wind turbine is a much more complicated

system than a constant speed wind turbine. First, the rotor

model is different, because the performance coefficient

depends not only on the tip speed ratio , but also on the pitch

angle . In nearly all variable speed wind turbines, the power

extracted from the wind in high wind speeds is limited by

reducing the aerodynamic efficiency of the rotor through

pitching the blades. Second, a rotor speed controller is needed,

because the variable speed capability leads to the necessity to

control the rotor speed. Third, a pitch angle controller must be

incorporated in the model. To conclude, variable speed wind

turbines are in principle capable of taking part in grid voltage

control because they can vary reactive power output.

Detailed models of the two variable speed wind turbine types

that match the assumptions applied in power system dynamics

simulation have been presented by the authors in earlier papers

[8], [9]. It has also been shown that it is possible to model both

variable speed wind turbine types with one general variable

speed wind turbine model in power system dynamics

simulations [10]. Although the two concepts are fundamentally

different, the differences are mainly related to the different

generator concepts and controller algorithms of the power

electronic converter. These, however, for the largest disappear

when the power electronic converters are modelled as

fundamental frequency current sources and are hence hardly

reflected in the frequency bandwidth that is of interest in

power system dynamics simulations. It is therefore possible to

use the general variable speed wind turbine model depicted in

figure 2 [1], [10].

C. Model Aggregation

1) Aggregated Wind Speed Modelling

The wind speed can be considered to consist of four terms,

namely an average value, a ramp component, a gust

component and turbulence [11], [12]. In deriving the wind

speed signal for the aggregated wind park model, it is assumed

that the wind speed can be split up in a fully deterministic and

a fully stochastic part. The stochastic part consists of theturbulence. In the aggregated park model, this term is

neglected, because in a wind park the effect of turbulence on

the aggregated output power is reduced due to the smoothing

effect of the large number of wind turbines, as can be

concluded from measurements carried out at existing wind

parks [13].

The fully deterministic part consists of the average value and,

if present, the gust and ramp component. The average value

can be assumed to be the same throughout the park. The gust

and ramp components travel through the park and the time at

which they arrive at the individual turbines depends on the

average wind speed, the angle of attack and the wind park

layout. The start and stop times of the gust and the ramp ateach individual wind turbine can thus be calculated from a

single wind speed signal applied to the aggregated wind park

model as a whole, taking into account the wind direction and

the park layout. The wind speed signal is specified by the start

and stop times of the gust and the ramp relative to the centre of

the wind park and the wind direction.

2) Aggregation of Constant Speed Wind Turbines

The way in which constant speed wind turbines can be

aggregated has been discussed in the literature [2]-[4]. In this

paper, it is assumed that the wind park can be represented with

one single constant speed wind turbine. The characteristics of

this wind turbine can be calculated using the followingequations

(3)

in which S is the MVA rating and C the size of the

compensating capacitor. The index eq means aggregated

equivalent wind turbine, m means mechanical and i indicates

the individual wind turbines in the wind park.

A specific problem in the aggregation of the turbines is posed

by the internal infrastructure of the wind park. Here, the only

components of the internal wind park infrastructure that are

included in the aggregated model are the transformers at the

wind turbines and, if present, at the point of common coupling(PCC). The reason for this is that transformers have a

relatively high impedance, whereas the cables within the park

are rather short and therefore have a low impedance when

compared to the transformers. Their impedance is therefore

neglected. The impedance of the cable from the PCC to the

point of grid connection is kept, because it can be quite long,

particularly for off shore wind parks. The resulting aggregated

wind park model is depicted in figure 3.



Figure 4. Simplified variable speed wind turbine model for use in an

aggregated model of a wind park with variable speed wind turbines Figure 6.Investigated wind park connection schemes

Figure 3. Aggregated model of wind park with n constant speed wind turbines

3) Aggregation of Variable Speed Wind Turbines

The instantaneous power generated by a variable speed windturbine is dependent on the actual value of the rotor speed,

rather than on the wind speed. Therefore, adding the

mechanical power of the individual wind turbines, as was done

with constant speed wind turbines according to the right

equation of (3), would introduce an error. It would be assumed

that there exists an instantaneous relation between wind speed

and generated power, which is, however, not true. Therefore,

in the aggregated model of a wind park with variable speed

wind turbines, the rotor speed of the individual turbines is kept

track of and the electrical power of the individual turbines is

added, rather than the mechanical power.

The variable speed wind turbine model is simplified before

aggregation, using the following considerations: When it is assumed that the performance coefficient c p(,)

always equals its maximum value, the c p(,) characteristic

can be omitted from the model and be replaced by a

constant equal to the maximum of c p. Only a minor error

results from this simplification, as the rotor speed versus

power control characteristic is such, that c p is kept at its

maximum as much as possible. This assumption is thus

equivalent to assuming an ideal rotor speed controller.

The non-linear rotor speed versus control characteristic is

replaced by a first order approximation.

When the integrator in which the rotor speed is stored is

limited, e.g to 1.1, the pitch angle controller can be

omitted, as it is no longer needed for limiting the speed.The simplified variable speed wind turbine model that results

from the above, with which each of the turbines in the

aggregated park model is represented, is depicted in figure 4.

The power generated by the aggregated wind park model

equals the sum of the outputs of the simplified models depicted

in figure 4. Thus, as mentioned above, the electrical power is

added, rather than the mechanical power. If the wind turbines

in the park are equipped with voltage controllers, one voltage

controller is attached to the aggregated model. With respect to

the internal park infrastructure, the same approach that was

used in case of the aggregation of the constant speed wind

turbines is applied, i.e. the transformers and grid connection

are kept and the cables within the park are neglected. Theresulting aggregated model is depicted in figure 5.

Figure 5. Aggregated model of wind park with n variable speed wind turbines

IV. SIMULATION R ESULTS

A. Simulated Cases

In order to investigate the accuracy of the aggregated wind

park models presented above, a number of simulation runs has

been carried out. First, two wind park connection schemes

were developed in order to allow a broad comparison of the

detailed and aggregated model. Both consist of ten wind

turbines with a nominal power of 2 MW each, one connected

as a string and the other as a star. The investigated wind park

layouts are depicted in figure 6. Then, simulations are carried

out and the response of the detailed and aggregated wind park

models are compared.

First, the response to a wind speed change is investigated by

applying a wind speed sequence to the detailed and aggregated

models. The wind speed sequence consists of an average value

corresponding to a generated power of 0.75 p.u., a gust with an

amplitude of 3 m/s and a duration of 10 s and a ramp with a

duration of 30 s and an amplitude of 4 m/s. In both cases, the

wind comes from ‘above’ in figure 6. The simulation run takes

90 s. The gust and the ramp start 30 s and 50 s in the string

connected wind park and at 85 s and 105 s in the star

connected wind park, relative to the park’s centre. Different

gust and ramp starting times are used in order to observe the

effect of the wind speed change in case of both connection

schemes within the same time frame.



Then, the fault response of the aggregated model is

investigated by comparing it to that of the star scheme. A

simulation run of 10 s is used and the wind speed is assumed

to be constant. After 1 s, a fault with a duration of 150 ms is

applied at the PCC.

B. Simulation Results

In figure 7, the simulation results are depicted. Because the

interaction of the wind park with the power system is the main point of interest in power system dynamics simulations, the

quantities on which the comparison of the detailed (solid lines)

and aggregated (dotted lines) models is based, are the active

and reactive power flowing from the PCC to the system and

the voltage at the PCC. The left and middle figures depict the

response to a wind speed change, the right the fault response.

The upper figures correspond to the constant speed wind

turbines, the lower to the variable speed wind turbines.

It can be concluded from the figures that in all cases, there is a

high degree of correspondence between the detailed and the

aggregated model. The observed differences in case of the

constant speed wind turbines are mainly caused by the neglect

of turbulence. However, the effect of turbulence on theaggregated output power of a wind park will become smaller,

the more wind turbines the park contains. In practice, most

wind parks will consist of far more than ten turbines. It is

therefore not considered necessary to modify the aggregated

model of the park with constant speed wind turbines in order

to include the effect of turbulence. In case of variable speed

wind turbines, turbulence is hardly reflected in the output

power, due to the functioning of the rotor as an energy buffer.

The difference between the active power in case of the

variable speed wind turbines is mainly due to the

simplifications applied in deriving the simplified variable

speed wind turbine model depicted in figure 4 from a detailed

model. The different rotor speed versus power characteristicleads to small differences in generated active power. In turn,

these lead to differences in reactive power and PCC voltage.

In case of the fault response, the differences between the

detailed and the aggregated model can hardly be observed.

They are similar to those occurring in case of a wind speed

change but are hided by the larger scale of the graphics.

V. CONCLUSIONS

In this paper, aggregated models of a wind park with constant

speed and with variable speed wind turbines for use in power

system dynamics simulations are presented and verified by

comparing their response to that of detailed wind park models.The use of aggregated models reduces the modelling effort for

the user and the amount of data to be entered, because no

longer a detailed model of the wind park infrastructure and of

the individual turbines is required. Further, it eliminates the

need to specify the wind speed at each individual wind turbine

within the park.

When the response of the aggregated model was compared

with a detailed model, it was concluded that notwithstanding

the applied simplifications, the agreement between the

responses of the aggregated and detailed wind park models is

very close, both for a wind speed change and a fault.

VI. R EFERENCES

[1] J.G. Slootweg, S.W.H. de Haan, H. Polinder, W.L. Kling, “Aggregated

modeling of wind parks with variable speed wind turbines in power system

dynamics simulations”, 14th Power Systems Computation Conference,

Sevilla, Spain, 24-28 June 2002.

[2] R.M.G. Castro, J.M. Ferreira de Jesus, “A wind park reduced-order model

using singular perturbations theory”, IEEE Transactions on Energy

Conversion, v.11, n.4, December 1996, p.735 -741.

[3] R.M.G. Castro, J.M. Ferreira de Jesus, “An aggregated wind park model”,

13th PSCC Power Systems Computation Conference, Trondheim, Norway, v.2, p. 1302-1307, 28 June 28-July 2, 1999.

[4] V. Akhmatov, H. Knudsen, “An aggregate model of a grid-connected,

large-scale, offshore wind farm for power stability investigations-importance

of windmill mechanical system”, International Journal of Electrical Power &

Energy Systems, v. 25, n. 9, p. 707-719, July 2002.

[5] J.G. Slootweg, W.L. Kling, “Modeling of Large Wind Farms in Power

System Simulations”, Proceedings of the IEEE PES Summer Meeting,

Chicago, July 25-29, 2002.

[6] S. Heier, Grid integration of Wind Energy Conversion Systems, Chicester,

UK: John Wiley & Sons Ltd., 1998.

[7] P. Kundur, Power system stability and control, New York: McGraw-Hill,

Inc., 1994.

[8] J.G. Slootweg, H. Polinder, W.L. Kling, “Dynamic Modelling of a Wind

Turbine with Direct Drive Synchronous Generator and Back to back Voltage

Source Converter and its Controls”, 2001 European Wind Energy Conference

and Exhibition, Copenhagen, Denmark, July 2-6, 2001.[9] J.G. Slootweg, H. Polinder, W.L. Kling, “Dynamic Modelling of a Wind

Turbine with Doubly Fed Induction Generator”, 2001 IEEE Power

Engineering Society Summer Meeting, Vancouver, Canada, July 15-19, 2001.

[10] J.G. Slootweg, S.W.H. Haan, H. Polinder, W.L. Kling, “General Model

for Representing Variable Speed Wind Turbines in Power System Dynamics

Simulations”, IEEE Transactions on Power Systems, v. 18, n. 1, February

2003, p. 144-151.

[11] O. Wasynczuk, D.T. Man, J.P. Sullivan, “Dynamic behavior of a class of

wind turbine generators during random wind fluctuations”, IEEE

Transactions on Power Apparatus and Systems, v.100, n.6, June 1981,

p.2837-2845.

[12] P.M. Anderson, A. Bose, “Stability simulation of wind turbine systems”,

IEEE Transactions on Power Apparatus and Systems, v.102, n.12, Dec. 1983,

p.3791-3795.

[13] J. Cadogan, M. Milligan, Y. Wan, B. Kirby, “Short-term output

variations in wind farms: implications for ancillary services in the unitedstates”, Wind Power for the 21st Century, Kassel, Germany, September

25-27, 2000.

VII. BIOGRAPHIES

J.G. Slootweg (M ‘01) received his MSc degree in

electrical engineering from Delft University of Technology

on September 23rd, 1998. During his education he stayed

in Berlin for six months, to hear lectures at TU Berlin and

to conduct research at the Dynamowerk of Siemens AG.

He is currently working towards a PhD on the effects of

large scale integration of new technology on power system

dynamics. The research is carried out at the Electrical

Power Systems Laboratory of Delft UT.

W.L. Kling (M ’95) received his MSc degree in electrical

engineering from the Technical University of Eindhoven in

1978. Currently he is a part time professor at the Electric

Power Systems Laboratory of Delft UT. His experience lies

in the area of planning and operation of power systems. He

is involved in scientific organizations such as Cigré and

IEEE. He is the Dutch representative in the Cigré Study

Committee C1 System Development and Economics.



Figure 7. Simulation results. From left to right: response of star connected wind park to a wind speed change, response of string connected wind park to a wind

speed change and fault response of wind park. The upper three figures depict active and reactive power and PCC voltage of a wind park with constant speed

wind turbines, the lower three figures depict active and reactive power and PCC voltage of a wind park with variable speed wind turbines. The solid lines

correspond to the detailed model and the dotted lines to the aggregated model of the wind park.

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Agregated Modelling of Wind Parks