wind energy

1132 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 4, NOVEMBER 2002

Modeling of Wind Turbines for Power System StudiesTomas Petru and Torbjörn Thiringer

Abstract—In this paper, the modeling of wind turbines for powersystem studies is investigated. Complexities of various parts of awind turbine model, such as aerodynamic conversion, drive train,and generator representation, are analyzed. The results are veri-fied by field measurements made on a stall-regulated fixed-speedwind turbine. The modeling focuses on deriving a representationthat is suitable for use in grid simulation programs.

Index Terms—Grid interaction, model, modeling, power quality,wind turbine.

I. INTRODUCTION

T HE number of wind energy installations is rapidly growingworldwide. With increasing wind power production, it is

important, especially for grid owners, to predict the grid interac-tion of wind turbines in advance. Grid simulation packages, likethe Power System Simulator for Engineering (PSS/E), which arecommonly used for power system behavior studies, usually re-quire reasonably accurate and low-capacity-demanding modelsof all power system components. The low-capacity demand isnecessary with respect to the high number of components usedin the system. Models of the new types of generation units, likewind turbines, have to comply with this requirement.

There are various simulation packages, which in principle de-scribe a complete wind turbine. However, the turbine descrip-tion used in such programs is not viable in grid simulationspackages due to its high computational burden. It is necessary,therefore, to simplify such a description to a level acceptable forgrid simulation programs, which is the intention of this paper.

Approaches to simplified aerodynamic modeling of wind tur-bines have been presented in [1] and [2]. The main idea in thesepapers is to adjust wind speed data in one point (hub level) byvarious filters in order to represent the interaction of turbineblades with the wind speed distribution over the rotor sweptarea. The resulting wind data are then applied to the static powercurve in order to determine the driving torque.

Descriptions of the drive train also vary considerably; how-ever, rather simplified descriptions dominate completely in theliterature since parameters for detailed descriptions are not gen-erally available.

Representations of the generator complexity vary consid-erably in the literature. In [2], no dynamic model is used atall, whereas [3] makes use of a first-order model. In [4], athird-order model is utilized, and in [5], a fifth-order model isemployed.

Manuscript received November 13, 2001; revised April 2, 2002. This workwas supported by Sydkraft AB and the Swedish National Energy Administra-tion.

The authors are with the Department of Electric Power Engineering,Chalmers University of Technology, Göteborg, Sweden (e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPWRS.2002.805017

The general trend is that electrical engineers tend to simplifythe aerodynamic and mechanical components of the overallmodel, whereas mechanical engineers tend to overlook elec-trical performance details of the wind turbine.

Verifications of models with practical measurements on windturbines are rare in the reported literature. Moreover, simula-tions and measurements of wind turbine responses to grid distur-bances have not yet been published. Two cases, where measure-ments and simulations of the impact by wind turbines duringnormal operation have been reported, are [6] and [7]. In [6], re-sults have been reported for the determination of flicker impactby a wind turbine for one wind speed, and in [7], fairly goodagreement between calculations and measurements is reportedfor a broad wind speed range using a rather detailed wind tur-bine model.

From a power quality point of view, prediction of voltagefluctuations caused by variable-speed turbines is not of interestsince their flicker emission is very low [8]. However, predic-tion of voltage fluctuations due to fixed-speed turbines is veryimportant since it is often that this contribution sets the installa-tion limits for these turbines [9].

The aim of this paper is to investigate the modeling require-ments of a wind turbine for power system studies. The impor-tance of aspects such as complexity of the aerodynamic conver-sion description, the drive train, and the generator descriptionare investigated. Moreover, our goal is to verify the simulationresults through on-site measurements.

II. M ODELING INTEREST OFWIND TURBINE CONCEPTS

Three main types of wind turbines are commonly being in-stalled today. The fixed-speed wind turbines with a generatordirectly connected to the grid (see Fig. 1) and variable-speedwind turbines with either a slip-ringed induction generator anda converter in the rotor circuit or with a full power converterin the stator circuit (see Fig. 2). The variable-speed turbines arepitch-regulated, whereas the fixed-speed turbines are either stallregulated or active stall regulated. Active stall regulation meansthat the pitch angle is adjusted slightly at higher wind speeds inorder to always obtain a correct power level.

A. Steady-State Voltage Level Influence

Wind turbines affect the voltage level in the point of commonconnection (PCC) due to their power production. The activepower produced by the turbine increases the voltage, whereasthe reactive power can further increase the voltage level or re-duce it.

The impact on the steady-state voltage level by the fixed-speed wind turbine system with an induction generator directlyconnected to the grid is predestined and cannot be controlledduring the operation. There is a capacitor bank connected at the

0885-8950/02$17.00 © 2002 IEEE

PETRU AND THIRINGER: MODELING OF WIND TURBINES FOR POWER SYSTEM STUDIES 1133

Fig. 1. Principle layout of the fixed-speed wind turbine system.

Fig. 2. Principle layout of the variable-speed wind turbine systems. Left:System with a slip-ringed induction generator and a converter in the rotorcircuit. Right: System with a full power converter in the stator circuit.

turbine, which is typically designed to compensate for the in-duction machine no-load reactive power consumption. As theactive power production increases, the reactive power consump-tion rises as well. These outcomes, in combination with the grid

-ratio (ratio between grid reactance and grid resistance),determine if the voltage level in the PCC is increasing with in-creasing power production or not. An -ratio of around twoto three usually gives a very low steady-state voltage impact. Itis so due to the relation between the active and reactive powerproduced/consumed by a common induction machine. On a gridwith a low -ratio (resistive), which is a grid consisting ofmainly cables, the voltage level will increase with increasingpower production. On a grid with a high -ratio (inductive),which is a grid consisting mainly of overhead lines or close toa transformer, the voltage will decrease instead [9]. Here, an

-ratio of 0.6 has been used to represent the resistive gridand an -ratio of 2.7 for the inductive grid.

For variable-speed turbines, the reactive power is controllableand is usually kept close to zero in order to obtain a power factorof one. This means that the voltage level increases as the powerproduction increases. However, if desired, the wind turbine con-verters can produce any reactive power, provided that the ratingof the converter allows it. An example of such a utilization isvoltage level control in the PCC [10].

B. Rapid Voltage Fluctuations, Flicker Emission

As previous authors [8] have pointed out, there is a need topredict the rapid voltage fluctuations caused by fixed-speedstall-regulated turbines while prediction of flicker emissionfrom variable-speed turbines is not of interest. The active-stallregulated systems produce similar rapid power fluctuationsto the purely stall-regulated systems since the pitching ofthe blades are done very slowly. In order to predict the rapidpower fluctuations from fixed-speed turbines, there is a need to

represent the wind field arriving at the turbine, apart from thegenerator and drive train.

In the IEC-standard [11], it is described how the voltage fluc-tuations should be evaluated. A key dimensionless quantity(short-term flicker severity index) should be determined, whichrepresents the amount of voltage fluctuations.

C. Response to Grid Disturbances

The response of wind turbines to grid disturbances is also animportant issue to be involved in the model. Grid disturbancescan either be of the severe type, for instance, a short circuitnearby, or there can also be minor disturbances, for instance,a voltage dip with a duration of a few hundred milliseconds anda dip magnitude of a few percent.

In the case of a fixed-speed turbine, the response to a griddisturbance is mainly governed by the induction generator, es-pecially the immediate response. The other parts (drive train andaerodynamic conversion) are not as important to model in thiscase.

For variable-speed wind turbines, the response to minor griddisturbances depends on the details of the control system of thespecific wind turbine. These are not generally provided by themanufacturers. For this reason, it is impossible to construct agenerally valid model for handling of grid disturbances for thesetypes of turbines.

When a major grid disturbance occurs, the two variable-speedsystems will behave differently. The system with a full-powerconverter in the stator circuit will be able to disconnect imme-diately by just blocking the turn-on pulses for the converter.The system with a converter in the rotor circuit of a slip-ringedinduction machine acts in another way. If the disturbance willcause too high rotor voltages, the rotor windings will be shortcircuited (in order to protect both the rotor and the converter),and the stator of the generator will be disconnected later usingordinary circuit breakers. It may also be desirable that the gen-erator stays online, provided that the generator, wind turbine,and other equipment can handle such an operation. This couldbe of particular interest in the case where there are many tur-bines connected, and the loss of many wind turbines would leadto grid stability problems.

D. Simulation Models

The fixed-speed systems must incorporate the description ofthe aerodynamics, generator, and drive train in order to pre-dict their steady-state impact. When the response to grid distur-bances is of interest, it is mainly the generator description thataffects the response of the turbine.

For the variable-speed systems, the dynamic behavior duringsteady-state operation does not need to be represented for thereasons mentioned earlier. This means that these systems cansimply be described as active and reactive power sources thatare functions of the average wind speed.

To simulate the response of variable-speed systems to all griddisturbances, the details of the control and protection of thepower electronic converters must be known and implementedin the simulation program.


III. W IND TURBINE MODELING

A. Wind Field and Aerodynamic Conversion

According to [12], a wind field for a wind turbine can be con-structed with the knowledge of some basic parameters—windspectrum, average wind speed, turbulence intensity, roughnessof the surrounding terrain, and the height and rotor size of a windturbine. In [12], it is suggested that the wings be divided into anumber of sections and that the randomly generated wind sig-nals be distributed along the center of each wind section i.e., inrings with the hub as center. In [7], a fixed-speed stall-regulatedturbine was modeled. A configuration with three rings and 45points per ring was found to be sufficient.

For each step of the calculation, the randomly generated windsignals arriving at each blade section can be determined withthe knowledge of the rotor position. If necessary, interpolationis used to calculate the wind speed at a given point. With theknowledge of the blade geometry, pitch angle, rotor speed, andwind speed, the forces acting on the blades can be determined[13].

Generation of wind speeds in one and three dimensions wereperformed. The resulting effect on the power quality impact ofa turbine was evaluated [7], and it was found that it is sufficientto only use wind speed in the longitudinal (axial) direction.

In a time-critical application, it may be unacceptable to deter-mine the driving shaft torque, as described above, for each timestep. An alternative approach that is applicable to fixed-speedsystems, which is less time consuming, has been suggested in[1] and [2] and makes use of the aerodynamic filter approach.First, a time series of wind data with the required properties, i.e.,mean wind speed and turbulence intensity, at one point only (atthe hub level) is generated [14]. This signal is the input to theaerodynamic filters, and the outgoing signal is the equivalentwind speed representing the wind field impact. This resultingwind signal can then be applied to the curve of the tur-bine to determine the driving shaft torque.

The first filter is the spatial filter (SF)

(1)

where 0.55, , m is the turbine radius,m/s is the average wind speed at the hub height, andis the

decay factor over the disc ( ).The SF damps higher frequency components present in the

wind. In this way, the filtering property of the rotor bladesis represented. The transfer function in (1) can be simplifiedto a first-order transfer function with a negligible effect onits characteristic

(2)

where Hz is the cut-off frequency of the filter.The second filter represents the rotational sampling of the

wind by the turbine rotor and is therefore called the rotational

Fig. 3. Damping factor and cut-off frequency as a function of mean windspeed: Solid line-TI= 0:05; dashed line-TI= 0:1; dotted line-TI= 0:2.

Fig. 4. Wind field model (black) and simplified aerodynamic model (gray).

sampling filter (RSF), which, in this paper, is slightly modifiedto

(3)

where , is the number of blades, r/min isthe rotor speed, andis the damping factor.

This filter amplifies the variations at a frequency regionaround the blade passing frequency. In other regions, this filterhas a gain of nearly one.

Fig. 3 presents the damping factor of the RSF and the cut-offfrequency of the SF as functions of mean wind speed fordifferent turbulence intensities (TI). The damping factor andcut-off frequencies of the filters were determined using thedetailed aerodynamic simulation approach discussed earlier onthe experimental 180-kW turbine, which is used for verificationin this paper. The technical data of the turbine is attached inthe Appendix. It must be stressed, however, that the tuningperformed here is valid for this specific turbine only. Moreinformation on the tuning of the aerodynamic filters can befound in [15].

Fig. 4 presents the calculated shaft torques determined usingthe detailed aerodynamic method and the filter method. As canbe noted, the simplified approach makes it possible to repre-sent the formation of the shaft torque up to a frequency of about2 Hz, which is the blade passing frequency of the investigated


Fig. 5. Simulated drive train model.

Fig. 6. Comparison of shaft power using a soft shaft description (gray) and astiff shaft description (black), respectively.

turbine. More filters could be added in order to adjust the mag-nitudes of the higher frequency components and, in this way,increase the frequency region where the torque is accuratelydetermined. One example mentioned in [1] and [2] is an “in-duction lag filter.” The performed simulations have, however,shown that omitting the induction lag filter has no detectableimpact on the power quality prediction capability of the pre-sented models. Instead, it was found that the resulting flickeremission was rather strongly dependent on the tuning of the twoused filters.

An approach suitable for fixed-speed stall-regulated turbinesis to determine the shaft torque in advance using the wind fieldapproach according to [12] and save this to a file. This approachwas found to be more accurate and less time-consuming duringthe grid simulation then the aerodynamic filter approach and hasthus been used in this paper.

B. Drive Train Representation

Since detailed knowledge (by others than the manufacturers)of the drive train parameters is rather rare, the drive train modelhas been developed considering the availability of data. Thedrive train model suggested here consists of the inertia of boththe turbine and the generator. The connecting shaft is modeledas a spring and a damper. In Fig. 5, the drive train of the windturbine used in this paper is presented. Fig. 6 presents the spectraof the calculated output power from the induction generator ex-posed to the calculated shaft torque for both a stiff and a softshaft representation. It can be noted that above a frequency of0.5 Hz, there is a major discrepancy between the two model rep-resentations. The conclusion is that it is essential to incorporatea soft shaft in the drive train model.

Fig. 7. Equivalent circuit of the induction generator, reactive powercompensating capacitor, and grid.

The equations for the drive train are

(4)

(5)

(6)

(7)

where kg m is the turbine moment of inertia, kg m isthe generator moment of inertia,kg m s is the stiffnessof the shaft, kg m s is the absorption of the shaft,

N m is the input torque, N m is the generatorelectromagnetic torque, , rad/s are the angular speed ofthe turbine and of the generator, respectively, and, radare the angle of the turbine and of the generator, respectively.

All quantities are referred to the high-speed side of thegearbox.

C. Generator Description

The classical description of the induction machine for tran-sient studies is the fifth-order model [16]. When the reactivepower compensating capacitor is involved in the model, thesupply grid representation must be represented as well, and theoverall model order is increased by four to a ninth-order model.The equivalent circuit of the ninth-order model is presented inFig. 7, and the electric equations of the model are describedin (8)–(11), where (9)–(10) are the electric equations of thefifth-order induction machine model.

(8)

(9)

(10)

(11)

Imag

where , V are the grid and stator voltages,, , Aare the grid, stator, and rotor currents, rad/s is the syn-chronous angular frequency, rad/s is the rotor angular fre-quency, rad/s is the rotor angular speed, , , arethe grid, stator, and rotor resistances,, H are the stator


Fig. 8. Simulated response to a torque step. Upper plot: Fifth-order model(black), third-order model (gray), and first-order model (black dashed). Lowerplot: Fifth-order model (black), ninth-order model (gray).

Fig. 9. Simulated response to a voltage dip. Lines as in Fig. 8.

and rotor leakage inductances,, H are the grid and mainmagneting inductances, and is the number of pole pairs.

Usually, models of lower order than the fifth-order model areused for power system studies. A third-order model in which thestator flux transients of the fifth-order model have been ignored[19] is common. The rotor flux transients are sometimes alsoneglected, thus leading to a first-order model of the inductionmachine.

Fig. 8 presents the response of the mentioned models to a loadtorque step (from 50 to 100% of the nominal torque), and Fig. 9presents the response to a voltage dip of 10%.

It is observed that for the third-, fifth- and ninth-order model,the response to the shaft torque disturbances is very similar,whereas the response of the first-order model differs. The con-clusion here is that for shaft torque disturbances, the third-ordermodel is an appropriate choice.

The response to the voltage dip reveals more differences be-tween the models. The first-order model does not provide anyacceptable result, whereas the other three models manage to pro-vide similar results, although their differences are clearly vis-ible. The fifth- and ninth- order model also predicts the surgecurrents during the first line periods, and the ninth-order modelalso predicts a very high-frequency oscillation due to the ca-pacitor. The conclusion is again that the third-order model is anappropriate choice, unless a bandwidth of above 20–30 Hz isdesired, which is usually not the case.

Fig. 10. Comparison of measured and simulated spectra. Measured= upperblack; fifth-order= gray; first-order= lower black.

The literature provides some more discussions on the fifth-order model complexity. Magnetizing inductance saturation canbe represented by modification of the machine equations [17],although the order of the model remains unchanged. Skin ef-fect and iron losses are accounted for by increasing the order ofthe induction machine model by two. When initial response tomajor grid disturbances, such as short circuits, need to be de-termined, it is necessary to represent both skin effect and satu-ration of leakage inductances in order to achieve a high accu-racy. However, saturation, iron losses, and skin effect all playan unimportant role in the prediction of the induction machineresponse to low-frequency disturbances (below 30 Hz) [18] andare thus seldom represented in studies dealing with the low-fre-quency dynamics of the induction machine.

IV. PERFORMANCE OF THEMODELS AT

STEADY-STATE OPERATION

A comparison of the measured versus the simulated reactivepower output of a 180-kW fixed-speed stall-regulated wind tur-bine is presented in Fig. 10. The simulations presented have uti-lized the wind field approach with the results (predeterminedshaft torque) saved in advance. Measured voltages have beenused as inputs instead of using constant voltages. This is veryimportant since the induction generator is not only exposed todisturbances on the machine shaft but to disturbances comingfrom the connected grid as well [7]. A soft shaft description isconsidered in the models. The models differ in the descriptionof the induction generator, and presented results are from thefifth- and first-order model, respectively. The third-order modelrenders very similar results as the fifth-order model and is, ac-cordingly, not presented in the figure.

The third- and fifth-order model predict the reactive powerresponse well, although there is a slight discrepancy toward themeasurements in the frequency range of 7–10 Hz. The first-order model predicts similar results as the two other models upto about 4 Hz but then underestimates the reactive power fluc-tuations for higher frequencies.

The periodic power pulsations of the turbine are not simulatedhere. The reason is that they are turbine specific and, thus, haveto be empirically found for each turbine, and the goal in thispaper is to try to be as general as possible. In [20], it was foundthat the magnitude and phase of the periodic power pulsations


Fig. 11. P on grid withX=R-ratio of 0.6. : measured with periodic powerpulsations removed. Squares: fifth-order model. Diamonds: fifth-order modelwith constant voltages. Circles: first-order model.

Fig. 12. P on grid withX=R-ratio of 2.7. Markers as in Fig. 11.

could be modeled as a function of rotor position and wind speed.Thus, the implementation of the periodic power pulsations in thewind turbine model can be made in a fairly convenient way, ifthis is desired. However, a cost is that one additional equation isneeded in order to determine the rotor position.

In Figs. 11 and 12, the resulting measured and calculatedflicker emission to the grid by the wind turbine is presentedfor two grids with different ratios. Since the third-ordermodel yields very similar results to the fifth-order model, re-sults obtained using the third-order model are not presented.Apart from the fifth-order model, results using the first-ordermodel of the induction machine are also presented. Finally, re-sults using the fifth-order model but with constant voltages asinputs are presented.

It can be noted that if grid voltage variations are not takeninto consideration, the result can be very erroneous, especiallyfor the inductive grid. Taking the grid voltage variations into ac-count gives a very good agreement for the inductive grid. Theprediction of the flicker emission on the resistive grid is not asgood. The reason for this is unknown. However, it is very im-portant to point out the fact that this mismatch is of little impor-tance since, as pointed out in [9], for a resistive grid, it is thesteady-state voltage limit that sets the limitation for a wind tur-bine installation.

Fig. 13. Recorded rapid voltage dip.

Fig. 14. Active power response to a rapid voltage dip. Upper plot: solid black=measured; solid gray= fifth-order with soft shaft. Lower plot: solid black=fifth order with stiff shaft; solid gray= third order with soft shaft; dashed black= first order with soft shaft.

Fig. 15. Reactive power response to a rapid voltage dip. Lines as in Fig. 14.

V. RESPONSE OF THEWIND TURBINE TO GRID DISTURBANCES

In Fig. 13, a measured rapid voltage dip with a magnitudeof about 10% is presented, and in Figs. 14 and 15, the mea-sured and calculated active and reactive power responses arepresented. The wind turbine model using a fifth-order represen-tation of the generator manages to predict the response well,whereas the third-order representation cannot predict the initial


Fig. 16. Recorded slow voltage dip.

Fig. 17. Reactive power response to a slower voltage dip. Upper plot: solidblack= measured; solid gray= fifth order. Lower plot: solid black= thirdorder; solid gray= first order.

surge currents. When a first-order representation of the gener-ator is used, no result of value is obtained.

In Fig. 16, a measured slower voltage dip that does not leadto any significant change in the active power production ispresented. The reactive power response is more pronounced,and the results by various model complexities are presented inFig. 17. Since there was no important difference using a softand a stiff shaft, only results obtained using a soft shaft arepresented. In this case, it can be observed that since no 50-Hzoscillations are involved, the third-order generator represen-tation provides similar results compared with the fifth-orderrepresentation. Again, insufficient results are obtained when afirst-order model of the generator is used.

VI. CONCLUSIONS

In this paper, the modeling requirements of wind turbinesfor power quality studies are investigated. Measurements ona 180-kW fixed-speed stall-regulated wind turbine are used toverify the results.

It is found that the aerodynamic filter approach to simplifythe determination of the torque acting on the drive-train of afixed-speed turbine is adequate when predicting the shaft torqueup to a frequency of 2 Hz for the turbine investigated here. Asthe rotational speed of the turbine is reduced, which happensas the turbines are getting larger, this limit frequency is also

lowered. However, use of the filter approach for the determi-nation of flicker emission from a turbine is not recommended.The tuning of the filter requires a large number of simulations,and the flicker emission results vary much on details in the de-termination procedure. Instead, calculation of the shaft torquein advance using a detailed wind field approach and storage ofthe result in a file is recomended.

The minimum requirement for the modeling of the drive trainis to use a soft shaft and the turbine and generator inertia. Moredetailed modeling could be useful; however, parameters for moredetailedmodelingof thedrive trainareusuallynotavailable.

When the flicker emission is evaluated, it is important (forinductive grids, it is extremely important,) to take the voltagedisturbances from the connected grid at the wind turbine siteinto account.

To simulate the surge current during the first line periods aftera faster grid disturbance, the fifth-order representation of thegenerator is needed. However, usually, this is not of interestwhen power system simulations are performed, and then, thethird-order generator representation is quite sufficient.

To conclude, it was found that a third-order generator repre-sentation, together with two drive train equations and a precalcu-lated shaft torque signal, are sufficient to represent a fixed-speedwind turbine for power system simulations. For a variable-speedwind turbine, the control and protection of the converter andgenerator systems must be included in a model.

APPENDIX

A. Wind Turbine Data

location Alsvik wind farm Island of Gotland,Sweden;

rated power 180 kW;hub height 30 m;rotor diameter 23.2 m;number of blades three;rotor speed 42 r/min;blade profile NACA-63 200;gearbox ratio 23.75.

B. Drive Train Data

turbine inertia 102.8 kgm;generator inertia 4.5 kgm ;stiffness of the shaft 2700 Nm/rad;absorption of the shaft -(all data referred to the high speed shaft).

C. Generator Data

nominal voltage 400 V;number of pole-pairs three;stator resistance 0.0092 ;rotor resistance (referred to thestator)

0.0061 ;

stator leakage inductance 186 H;rotor leakage inductance(referred to the stator)

427 H;

magnetizing inductance 6.7 mH.


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Tomas Petrureceived the M.Sc. degree from the University of West Bohemia,Pilsen, Czech Republic, in 1997. He is pursuing the Ph.D. degree with the De-partment of Electric Power Engineering, Chalmers University of Technology,Göteborg, Sweden.

His area of research is modeling wind turbines for power system studies.

Torbjörn Thiringer received the Ph.D. degree in 1996 from Chalmers Univer-sity of Technology. Currently, he is an Associate Professor at the Department ofElectric Power Engineering at Chalmers University of Technology, Göteborg,Sweden. His area of interest is control and modeling of induction machines,particularly for wind turbine applications.

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