Initialization of Wind Turbine Dynamic model

8/12/2019 Initialization of Wind Turbine Dynamic model

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Paper accepted for presentation at PPT 20012001 IEEE Porto Power Tech Conferenceloth 13'h September, Porto, Portugal

Initialization of Wind Turbine Models in PowerSystem Dynamics Simulations

J.G. Slootweg' H. Polinde?Member IEEE

I Electrical Power Systems, Electrical Power ProcessingFaculty of Information Technology and Systems, Delft Universityof Technology

P.O. Box 503 1 , 2600GA Delft, The NetherlandsPhone:+31 15 278 6219, Fax: +31 15 278 1 182, e-mail:[email protected]

Abstract: As a result of increasing environmental concern,increasing amounts of electricity are generated from renewablesources. One way of generating electricity from renewable sources isto use wind turbines. A tendency to erect more wind turbines can beobserved. As a result of this, in the near future wind turbines may

start to influence the behavior of electrical power systems.To investigate the impact of increasing wind turbine penetration,power system dynamics studies need to be carried out. To this end,power system dynamics simulation software is used, in which windturbine models must be integrated to enable the investigation ofincreasing wind turbine penetration on power system behavior. Ifwind turbine models are to be integrated into power systemdynamics simulation software, it must be possible to calculate theinitial conditions of the dynamic model from load flow data to beable to initialize the dynamic simulation correctly. In this paper, asolution to this problem is presented.

Keywords: wind turbine, modeling, simulation, power systemdynamics, grid integration, model initialization, initial conditions

1. INTRODUCTION

As a result of increasing environmental concern, the impact ofconventional electricity generation on the environment isbeing minimized and efforts are made to generate electricityfrom renewable sources. The main advantages of electricitygeneration f rom renewable sources are the absence of harmfulemissions and the infinite availability of the prime mover thatis converted into electricity.One way of generating electricity from renewable sources isto use wind turbines that convert the energy contained inflowing air into electricity. Up to this moment, the amount ofwind power integrated into large scale electrical powersystems only covers a small part of the total power systemload. The rest of the power system load is for the largest partcovered by conventional thermal, nuclear and hydro powerplants.Wind turbines often do not take part in voltage and frequencycontrol and if a disturbance occurs, the wind turbines aredisconnected and reconnected when normal operation hasbeen resumed. Thus, notwithstanding the presence of windturbines, frequency and voltage are maintained by controllingthe large power plants as would have been the case withoutany wind turbines present. This is possible, as long as windpower penetration is still low.However, a tendency to increase the amount of electricity

W.L. Kling'Member IEEE

generated from wind turbines can be observed and they maybegin to influence overall power system behavior, making itdifficult to operate a power system by only controlling largescale power plants. I t is therefore important to study thebehavior of wind turbines in an electrical power system andtheir interaction with other generation equipment and withloads.To investigate the impact of increasing wind turbinepenetration on power system behavior, power systemdynamics studies need to be carried out. To this end, powersystem dynamics simulation software is used and to enablethe investigation of increasing wind turbine penetration, windturbine models must be integrated in power system dynamicssimulation software packages. One of the problems that mustbe solved to make this possible, is the calculation of the initialconditions of the wind turbine from load flow data in order tobe able to initialize the dynamic model correctly.The structure of this paper is as follows. First, the problem ofthe initial condition calculation is commented upon. Then,

models of the three most important actual wind turbineconcepts are described and the system equations for eachconcept are given. To conclude, a solution to the problem ofthe calculation of the initial conditions for each of theseconcepts is discussed and applied to an example wind turbine.

11. THE MODEL INITIALIZATION PROBLEM

A. Power system dynamics simulation softwarePower system dynamics simulation software is used toinvestigate the transient behavior and small signal stability ofpower systems. An example of a power system dynamicssimulation package is PSSIE. Power system dynamicssimulation software can be used when the phenomena ofinterest have a frequency of about 1 to 10 Hz. When the

frequencies of interest are higher, subtransient simulationsoftware, such as ATP, EMTP or the MATLAB Power SystemsBlockset should be used. These packages contain moredetailed and higher order equipment models than powersystem dynamics simulation software.Some advanced software packages offer both transient andsubtransient simulations and are able to automatically switchbetween equipment representations appropriate for thesubtransient and transient domain, depending on the event tobe simulated.

0- 7803- 7139- 9 /01 /$10 . 00 02001IEEE


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The main difference between dynamics simulation softwareand subtransient simulation software is that in the first onlythe fundamental harmonic component is taken into account.This approach enables the representation of the network by aconstant impedance or admittance matrix, like in load flowcalculations. Further, it reduces the number of differentialequations, because no differential equations are associatedwith the network and fewer with generating equipment andbecause it enables the use of a larger simulation time step [l ].As a result of this approach, power system dynamicssimulation software alternately executes a load flow, tocalculate node voltages and branch flows, and a dynamiccalculation, to calculate the response of the dynamicequipment models to changes in their terminal voltage,current andor frequency and to determine the new values ofthe state variables. This sequence is depicted in figure 1.

Loadflow DynamicsStart calculatio? calculation

Numsncal

cDmp1ex p o w er

values o fstate

variables- -

Figure I Dynamic simulation activity sequence

B Model initializationAs can be seen from figure 1, a simulation run using a powersystem dynamics simulation package starts with preparing aload flow case and solving this using the load flow calculationmodule of the software. Thereafter, the dynamic simulationmodel must be initialized.This comes down to calculating the initial conditions of thedynamic equipment models from the load flow data. If this isnot done correctly, state variables and other quantities do notstay at the value at which they are initialized, but startchanging at the start of the dynamic simulation. In thissituation, it may take much time to reach a new equilibriumand numerical instability can occur before an equilibrium isreached. Further, if an equilibrium results, it can be differentfrom the original load flow case that was initially planned tobe investigated [2].These outcomes are undesirable and therefore attentionshould be paid to the calculation of the initial conditions ofdynamic equipment models. Some of these models have beenused for long, such as synchronous generator models andexciter and governor models. The calculation of the initial

conditions of these model categories does not pose specialproblems and is integrated in power system dynamicssimulation software. However, in order to be able to integratenew equipment models into dynamic simulation software, notonly an equipment model must be available, but the problemof the calculation of the model's initial conditions must besolved as well. For models of the three currently most widelyused wind turbine concepts, a solution to this problem ispresented in this paper.

111. MODELS OF ACTUAL WIND TURBINE CONCEPTS

A . IntroductionThe three most important currently applied wind turbineconcepts are the following:

A constant speed wind turbine, which consists of a directlygrid coupled squirrel cage induction generator. The wind

turbine rotor is coupled to the generator through agearbox. The power extracted from the wind is limitedusing the stall effect. This concept will be further referredto as concept 1.A variable speed wind turbine with doubly fed (woundrotor) induction generator. The rotor winding is fed usinga back-to-back voltage source converter. Like in concept1, the wind turbine rotor is coupled to the generatorthrough a gearbox. In high wind speeds, the powerextracted from the wind can be limited by pitching therotor blades. This concept will be further referred to asconcept 2.A variable speed wind turbine with a direct drivesynchronous generator. The synchronous generator mayhave a wound rotor or may be excited using permanent

magnets. It is grid coupled through a back- to-backvoltage source converter or a diode rectifier and voltagesource converter. The synchronous generator is a lowspeed multi pole generator, therefore no gearbox isneeded. Like in concept 2, the power extracted from thewind is limited by pitching the rotor blades in high windspeeds. This concept will be further referred to as concept3.

For a more elaborate description of these wind turbineconcepts and their advantages and disadvantages, ref: [3]should be consulted.Further, three remarks must be made. First, when calculatingthe initial conditions of a dynamic model from load flow data,the model is calculated through from the output to the input.The initial values of the output are determined in the loadflow case and the initial values of the state variables and othervalues have to be calculated from these load flow data.Therefore, the description and modeling of the components ofthe each of the wind turbine concepts will be discussedstarting from the grid connection point.Second, when calculating the initial conditions, the system isassumed to be in steady state. Therefore, all time derivativesare equal to zero and will not be included in the wind turbinemodel equations. Further, the following is assumed whenderiving the equations describing each of the systems:


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Magnetic saturation is neglected in the generator modelsFlux distribution is sinusoidalConverter losses are neglected

Third, the rotor is modeled as an algebraic relationshipbetween wind speed and rotor. power. This is considereddetailed enough for power system dynamics studies [4]. Inthis way, the use of the blade element method which wouldresult in lengthy computations and the need for detailed rotorblade descriptions can be avoided.It is difficult to calculate the per unit value of the powerextracted from the wind, because mechanical wind turbinecharacteristics such as rotor diameter and nominal rotor speedcome into play. Therefore all equations are in per unit, exceptthe equations describing the rotor. These equations are onlyvalid for a 2 MW wind turbine with the characteristics givenin table 1 . For wind turbines with different nominal powerand/or mechanical characteristics, new numerical

approximations for the power coefficient cp should bedeveloped.

Wind turbine characteristic Value forconcept 1

Rotordiameter [m] 75

Value forconcepts 2and 3

1 5

Nominal rotor speed [RF'M]

Minimum rotor speed [ W M ]

16.7 18

9.a.

B Steady state equ ations describing conceptI

Seen from the grid, the first component is the squirrel cageinduction generator, which is described by the following perunit equations in the d-q reference frame using the generatorconvention, i.e. positive currents are outputs [ 11.Voltage equations:

v*= R,i,+ oS((L sa+ m)iqs+ miqr)vqs= Rsiqs- q( ( Ls a+Lm)idp+mib)

O = Rriqr-sws((L,+ Lm)idr+ mih)O = Rrib+ sos((Lnr+ m)iqr+ miqs) (1)

Real and reactive power:P = drirtr+Q= vqsidF- JqS (2)

s 4s

In these equations v is voltage, i is current, R is resistance, L

is inductance, omega is frequency and s is slip. The indices dand q stand for direct and quadrature component respectively,m stands for mutual, s for stator, r for rotor and U for leakage.P is active power and Q is reactive power. The rotor slipequals

Nominal wind speed [d s ]

3)

I 124

in which p is the number of poles and om s the mechanical

frequency of the generator rotor.The generator is coupled to the rotor with a shaft. Windturbine shafts are relatively flexible, therefore it is importantto incorporate the shaft in the model in power systemdynamics studies [5]. In steady state, the following per unitequation describes the wind turbine shaft:

(4)

in which T is torque in P.u., y is the angle between the bothends of the shaft [el. rad] and K, is the shaft stiffness.The rotor is modeled using the following algebraic relationbetween wind speed and mechanical power extracted:

P, = p Cp(a)AR;

cP(A)= 46.4((--A 0.01)- 2.0))e 16.52-

(5 )

with1

(6)in which P, is the power extracted from the airflow [W], p theair density [kg/m3], cp the performance coefficient or powercoefficient, L the tip speed ratio vt/vw,, he ratio between bladetip speed v, and wind speed upstream the rotor v, [ d s ] andA the area covered by the rotor [m2].

C . Steady state eq uations describing concept 2In this concept, the first components seen from the grid arethe doubly fed induction generator and the converter feedingthe rotor winding. The voltage equations describing thedoubly fed induction generator are the following [6]:

v = R,i,+ ms((Lsa+Lm)iqs+ miql)vqs= R,iqs- as Lsa+ m)idr+ mi*)

vqr= Rriqr- sos((Lra+Lm)idr+ midr)v*= Rri,+ sos((Lra+Lm)iqr+ miqs) (7)

A doubly fed induction generator is capable of generatingreactive power. Reactive power can be delivered by the statoror by the grid side of the converter. It is assumed that the gridside of the converter operates at unity power factor and thatany reactive power is delivered by the stator. In that case, thefollowing equations apply for real and reactive power:

P = s+ r = vdFi,+v i + vdFidc+ qsiq,Q= vqSi*- vdriqs 8)

in which the index c stands for converter. The other symbolshave the same meaning as in equations 1 ) and (2). Note thatfrom (S), it follows that the converter only takes part intoactive power generation, not in reactive power generation.In the case of a variable speed wind turbine, the shaft can beneglected, because the power electronic converter decouplesthe electrical and mechanical behavior. Therefore, the shaftproperties are hardly reflected in the wind turbines responseto wind speed changes or grid faults. Therefore, no equationsdescribing the wind turbine shaft will be taken into account.The rotor is modeled using the following equations:

qs qs

P,= p cp(a,e)ARv; 9)


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equations in each other is basic calculus and will therefore notbe carried out here. Note that because P and Q are quadraticquantities, the equations are not linear. A symbolicmathematics package such as MAPLE can be usedadvantageously to solve the equations. Equations in which therotor speed versus power characteristic P o,,,) occurs, had tobe solved numerically, because it is difficult to obtain aclosed form solution.

and equations or each of ihe

Concept 1

K n O W n P, vds, Vqsvariables

Unknown iqs,iqr, Q> , Y

Numberof 1)+ 2)+ 4)equations =7

concepts

Concept 2 Concept 3 Concept3with with

wound permanentrotor magnets

P, Q, vds, Pc Qo v d o Pc, c, vds?vq\ vqo p, Vqa

ldsr l q s r l d r r Vdr. vqs Q@ &. vqs3

p,, pn

. . .iqr, Vdri Vqrr I d o lqo I ds , I d 0 I q o I d s

s, U Iqs. wm vfdi l q s r o m g, Q , g

3)+ 7)+ 8) 12)+ 13) 12)+ 14)+P( ) + I41 + I51=8 +P O,) +P(%)

+V,( ) +V,(%J=9+Q,(%VJ=1 I

B Example generator characteristicsIn the next paragraphs, for each concept the initial conditionswill be calculated. The parameters of the generators used inconcept 1 and 2 can be found in [7] and of the generator usedin concept 3 in [8] respectively and are not reproduced here.

C Initial conditions o concept IThe initial conditions of a concept 1 model can be calculatedusing algorithm depicted in figure 4. As an example, thisalgorithm is applied to a wind turbine of 2 MW nominalpower that is generating 1 MW of real power, i.e. 0.5 P.u.,with a terminal voltage of vd,=l.02 p.u. and v,,=0.25 p.u. Theresults of each of the steps are given in table 3.

D Initial conditions o concept 2The initial conditions of a concept 2 model can be calculatedusing the algorithm depicted in figure 5. In this algorithm thegenerator losses are neglected by setting the mechanical

power extracted from the wind equal to the electrical powergenerated in the load flow case. This very much simplifies thecalculations and introduces only a minor error in the initialconditions, because the generator losses are small.As an example, the algorithm is applied to a wind turbine of 2MW nominal power that is generating MW of real power,i.e. 0.5 p.u. and 0.4 MVAr reactive power, i.e. 0.2 p.u. at aterminal voltage of vd,=l.02 p.u. and vq,=0.25 p.u. The resultsof each of the steps are given in table 3.

I 1. Use (1 ) and (2) to calculate ids, o, ido o,, s and Q I

11

2. Calculate copper losses using p,=~~i,:+i,:,+~,(i,,'+i,,Z)

3. Calculat e rotor speed using 3)

1I 4. Calculate torque using P=Tw I

15. Calculate y using 4)

16. Calculate wind speed using (5) and (6)

Figure 4. Algorithm or calculation of initial conditions of a concept 1 wind

turbine fro m lo adflow data

PCP , P=P ,

2. Calculate wind speed using IO) nd I 1

14. Calculate v, vqp dp , i& iqsusing (7) and (6)

Figure 5. Algorithm or calculation of initial conditions of a concept 2 windturbine fro m lo adflow daia

E Initial conditions o concept 3The initial conditions of a concept 3 model can be calculatedusing the algorithm depicted in figure 6. In this algorithm, thegenerator losses are again neglected, like in the case ofconcept 2 an for the same reasons. As an example, thealgorithm is applied to a wind turbine of 2 MW nominalpower that is generating 1 MW of real power, i.e. 0.5 p.u. and0.4 MVAr reactive power, i.e. 0.2 p.u. .at a terminal voltage ofv,,=1.02 p.u. and v,,=0.25 p.u. Further, it is assumed that

and that in case of the permanent magnet rotor bpmquals 1.3p.u. The lower equation of (16) only applies to a generatorwith a wound rotor. Other control strategies for terminal

voltage and reactive power can be used without rendering theproposed algorithm invalid. The results of each of the stepsare given in table 3.

F Initial conditions o concepts 2 and 3 at nominal powerWhen concepts 2 and 3 generate nominal power in the load.flow case, there is no unique relation between generatedpower and rotor speed, as can be seen from the right part offigure 3 (up from 18 rpm). This is caused by the fact that atwind speeds above nominal the pitch angle controller


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becomes active and limits the power extracted from theairflow to the nominal power, no matter what the actual windspeed is.Therefore, when a concept 2 or concept 3 wind turbinegenerates nominal power in the load flow case, the actualrotor speed and the wind speed or the pitch angle have to begiven. The other values can then be calculated in the sameway as when the wind turbine is initialized below nominalpower. In figures 5 and 6, the right arrow corresponds to analternative algorithm that can be used in that situation.

V. CONCLUSIONS

In this paper, a method was presented to calculate the initialconditions of dynamic models of the most important actualwind turbine concepts from data provided in a load flow case.This is an important result that facilitates the integration ofwind turbine models in power systems dynamics simulationsoftware.

REFERENCES

[ l ] P. Kundur, Power system stability and control, NewYork, US:McGraw-Hill, Inc., 1994.[2] P. Lacassel, L.Gerin-Lajoie, D. McNabb, P.-J. LagacC, J. Mahserediian,New Initialization method for controls in transient analysis , 200IEEE

Power Engineering Society Winter Meeting, Jan. 28-Feb. 1, 2001, paper66-09.[3] S. Heier, Grid integration of Wind Energy Conversion Systems,Chicester, UK: John Wiley Sons Ltd., 1998.

[4] V. Akhmatov, Some aspects of new windmill technologies on voltagestability , Seminar on Control Concepts of Wind Turbines, 23 Oct., 2000.[5] V. Akhmatov, H. Knudsen, A.H. Nielsen, Advanced simulationofwindmills in the electric power supply , International Journal of ElectricalPower & Energy Systems, v01.22, no.6, 2 000, pp.421-434.[6] P.C. Krause, 0 Wasyn czuk, M.S. Hildebrandt, Reference frameanalysis of a slip energy recovery system ,IEEE Transactions on energyconversion, vo1.3, no.2, June 1988, pp.404-408.[7] J.G. Slootweg, H. Polinder, W.L. Kling, Dynam ic Modelling of a WindTurbine with Doub ly Fed Induction Gcnerator , 20 01IEEE PowerEngineering Society Summer Meeting, July 15-19, 2001.[8] J.G. Slootweg, H. Polinder, W.L. Kling, Dynamic Mod elling of a WindTurbine with Direct Drive Synchronous Generator and Back to back VoltageSource Converter and its Controls , 2001 European W ind EnergyConference and Exhibition, Copenhagen, Denmark, July 2-6,2001,

P=P

2. Calculate wind speed using (10) and (1 1)

4. Calculate v and for wound rotoralso Q, using ,(w,) a nd Q,(w,,v,)

J5 Calculate vd., vq,, id., ig,. v,, and i, for wound rotor using (13)

usina (11) and 115)and 14) or Q,, v, vq, ids, for permanent magnet rotor

Figure 6. Algorithm fo r calcu lation of initial conditions of a concept 3 windturbine,from oadjlow data.

Table 3 Results yielded when the solution algorithms are applied to an?dotherwise.

Concept 3with

woundrotor

a m pl e. V a h

Step

unless indic

Concept 2

are in per un

Concept 1 Concept 3with

permanentmagnets

0,=15.2W M

BIOGRAPHIES

J.G. Slootweg received his MSc degree in electncalengineenng from Delft University of Technology onSeptember 23rd, 1998. During his education he stayed inBerlin for six months, to hear lectures at TU Berlin and toconduct research at the Dynamowerk of SiemensAG Heis currently working on a PhD on large scale integrationof dispersed generation into existing electric grids at theElectncal Power Sy stems Laboratory of Delft UT

H. Polinder received his MSc degree in electncalengineering in 1992 and his PhD degree in 1998 bothfrom Delft University of Technology. Cu rrently, he is anassistant professor at the Electrical Power ProcessingLaboratory at the same university, w here he gives courseson electncal machines and dnves. His main researchinterest is the field of generator systems in renewableenergy, such as wind energy and wave energy

W.L. Kling received his MSc degree in electncalengineenng from the Technical University of Eindhovenin 1978. Currently he is a part time professor at theElectnc Power Systems Laboratoryof Delft UT. Hisexpenence lies in the area of planning and operation ofpower systems He is involved in scientific organizationssuch as Cigre andIEEE He is the Dutch representative inthe CigrC Study Committee 37 Planning andDevelopment of Power Systems.

i =O. 3 7iq,=0.49idr=-0.47iqr=-O. 6Q=-0.40~=-0.0049

w,=15.2RPM

a = 15.2RPM

2 P,=0.006 2 v,=9.5 m/s v,=9.5 mJs

w,=1.0049 s=-0.015 idp 0.5 1,g-O.072

v,=9.5 m l s

id,=0.51iqc=-O.072

3

4 T=0.50 i,= 0.51i,,=-0.072v,,=-O.O 10v,,=-0.009

id,=-0.61i,;0.42

v,=0.72Q =O

v,=0.72

vd,=0.27v,,=0.67i,=0.25i,,=0.64v,=1.32i,=1.09

vd,=0.32vq,=0.65idq=0.26iq,=0.64Q,=-0.035

5 y=l.68 el.rad

6 vW=9.2m/s I I

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Initialization of Wind Turbine Dynamic model