Bak, Thomas

Knudsen, Torben

Soltani, Mohsen

English

    Aalborg UniversitetPrediction Models for Wind Speed at Turbines in a Farm with Application to ControlKnudsen, Torben; Soltani, Mohsen; Bak, ThomasPublished in:Extended Abstracts for Euromech Colloquium 508 on Wind Turbine WakesPublication date:2009Document VersionPublisher's PDF, also known as Version of recordLink to publication from Aalborg UniversityCitation for published version (APA):Knudsen, T., Soltani, M., & Bak, T. (2009). Prediction Models for Wind Speed at Turbines in a Farm withApplication to Control. In Extended Abstracts for Euromech Colloquium 508 on Wind Turbine Wakes E.T.S.I.Industriales Universidad Politécnica de Madrid.General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            ? You may not further distribute the material or use it for any profit-making activity or commercial gain            ? You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: November 29, 2020PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationConclusionPrediction Models for Wind Speed at Turbinesin a Farm with Application to ControlTorben Knudsen, Mohsen Soltani and Thomas BakAalborg UniversityOctober 22, 2009PredictionModelsT. Knudsenet.al.The AeolusprojectOverallcontrolengineeringviewWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationConclusionThe Aeolus projectThis work is part of the EU-FP7 project with the title:Distributed Control of Large - Scale Oshore Wind Farms(Aeolus).PredictionModelsT. Knudsenet.al.The AeolusprojectOverallcontrolengineeringviewWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationConclusionOverall control engineering viewThe problem from a control point of viewWind FarmControllerNetworkOperatorPowerDemandPowerReferenceProduced Power, Wind Speed and Direction, Faigue Load, Pitch Angle, Rotation SpeedWind FarmAvailablePowerWindProduced PowerFigure: Block diagram illustrating the centralised control problem.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolMotivationand objectivesResults fromthe literatureand newchallengesEstimationof eectivewind speedMeasurementsSystemIdenticationConclusionWind speed models for farm level controlMotivation and objectivesMotivationModern control design methods is model based.Prediction models are used explicitly (MPC) or implicitly(LQG).A wind farm model includes the dynamics of the wind eld.The important time scale is the average time for wind totravel between turbines which is typically 1 minute.The objective is then:Develop a method for making models for wind speedsat turbine positions in a wind farm where the availablemeasurements are standard signals from the turbines.The models must be suitable for prediction.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolMotivationand objectivesResults fromthe literatureand newchallengesEstimationof eectivewind speedMeasurementsSystemIdenticationConclusionResults from the literature and new challengesResults from the literatureIn Sørensen (2005) it is concluded that the the predictionof wind speeds from upwind turbines is not useful.Nielsen (2004) reports useful models for point wind speedat separation 300 m but a very weak relation over 600 m.Point wind speed coherence functions in e.g. Panofsky(1984) also support the above statement.New challengesTry to develop methods that improves predictionperformance over distances typical for a wind farm.A hypothesis is that the eective wind over the rotorshould be more predictable.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedEstimationtaskApproachesfrom theliteratureEstimationmodelResultinglterMeasurementsSystemIdenticationConclusionEstimation of eective wind speedEstimation taskEstimation of eective wind speed can be approached as astandard estimation problem.ẋ = f (x , u,w) ,y = h(x , u, v)Given the system model above in SS form and the input uoutput y estimate the state x .x is the state which would include the eective wind speed.u is the input i.e. blade pitch and generator torque orpower referencew is process noise which maybe drives the wind model.y is measurements e.g. rotor speed, generator speed,produced power and maybe more.v is measurement noise.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedEstimationtaskApproachesfrom theliteratureEstimationmodelResultinglterMeasurementsSystemIdenticationConclusionApproaches from the literatureModels used are either one or two inertia drive trainmodels.The literature investigated uses a Kalman lter (KF) toestimate rotor torque.From this rotor torque plus rotor speed and pitch a directcalculation of wind speed is performed based on cP tables.Consequently, no wind speed model is used.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedEstimationtaskApproachesfrom theliteratureEstimationmodelResultinglterMeasurementsSystemIdenticationConclusionEstimation modelOne inertia drive train model plus wind speed modelState equationsI ω̇r = Tr − Tg ,v̇t = −a(t)vt + n1 ,v̇m = n2 ,Tr =12ρv3r Acp(λ, β)1ωr, λ =ωrRvr,Tg =pµωr,vr = vt + vmTower was initially included both gave to poor observability.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedEstimationtaskApproachesfrom theliteratureEstimationmodelResultinglterMeasurementsSystemIdenticationConclusionMeasurement equationsωm = ωr + v1 ,vn = vr + v2PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedEstimationtaskApproachesfrom theliteratureEstimationmodelResultinglterMeasurementsSystemIdenticationConclusionDetailed wind speed modelThe wind turbulence model is time varying as it dependson average wind speed.This improves performance.dvt = −a(vm)vtdt + dw1 ,dvm = dw2 ,w ∈W (Q) ,Q =(Q11(vm) 00 Q22), Q11(vm) =πv3mt2iLa(vm) =πvm2LPredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedEstimationtaskApproachesfrom theliteratureEstimationmodelResultinglterMeasurementsSystemIdenticationConclusionResulting lterBased on the above models.A extended continuous-discrete Kalman lter has beendeveloped.It has acceptable observability.An reasonably white prediction errors.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedEstimationtaskApproachesfrom theliteratureEstimationmodelResultinglterMeasurementsSystemIdenticationConclusionAn example of the obtained estimates is seen below0 100 200 300 400 500 6009101112131415161718  VnVeKFVmKFFigure: Comparison of nacelle wind speed and estimated eectivewind speed.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsThe OWEZfarmExample of 1days measure-mentsSystemIdenticationConclusionMeasurementsVestas kindly provided 1 second measurements from the OWEZfarm for the project.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsThe OWEZfarmExample of 1days measure-mentsSystemIdenticationConclusionThe OWEZ farmFigure: Layout of OWEZ. The six turbines in the red box is the onesthere are measurements for.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsThe OWEZfarmExample of 1days measure-mentsSystemIdenticationConclusionExample of 1 days measurements0 1 2 3 4 5 6 7 8 9x 104051015WTG02WindSpeedTime (sec.)0 1 2 3 4 5 6 7 8 9x 104250300350WTG02WindDirection0 1 2 3 4 5 6 7 8 9x 10451015WTG02RotorSpeed0 1 2 3 4 5 6 7 8 9x 1040100020003000WTG02ProducedPower0 1 2 3 4 5 6 7 8 9x 10402040WTG02PitchAngle0 1 2 3 4 5 6 7 8 9x 104260280300320340360380WTG02NacelleDirectionFigure: Time plot for signals from WT02 for one day 2009-02-11.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationLinear modelsModelstructuresEstimationandValidationNacelle windspeedEective windspeedOne minutepredictionConclusionSimple linear time invariant modelsFor single input single output (SISO) systems a linear timeinvariant (LTI) model can be dened as follows.y(t) = G (q−1)u(t − nk) + H(q−1)e(t) , e(t) ∈ ID(0, σ2)G (q−1) =B(q−1)A(q−1), H(q−1) =C (q−1)D(q−1)PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationLinear modelsModelstructuresEstimationandValidationNacelle windspeedEective windspeedOne minutepredictionConclusionSelected model structuresArxDel ARX model with delay. na = nb = 2, nk =60,C (q−1) = 1,D(q−1) = A(q−1).BJDel Box-Jenkins model with delay.na = nb = nc = nd = 2, nk = 60.Per Persistence model, no input from upwind i.e.ŷ(t + k |t) = y(t) ∀ k .A(q−1) = 1− q−1,B(q−1) = 0.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationLinear modelsModelstructuresEstimationandValidationNacelle windspeedEective windspeedOne minutepredictionConclusionEstimation and ValidationFor estimation the rst 4 hours is used.And for cross validation the next 4 hours is used asillustrated in the gure.0 0.5 1 1.5 2 2.5 3x 104051015Time WTG02WindSpeedE0 0.5 1 1.5 2 2.5x 10451015WTG03WindSpeedETime PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationLinear modelsModelstructuresEstimationandValidationNacelle windspeedEective windspeedOne minutepredictionConclusionPerformance measuresThe RMS error is the standard error estimate for thepredictions.RMS =√√√√ 1NN∑t=1(y(t)− ŷ(t|t − k))2The Fit is how much of the standard deviation in theoutput that is explained by the model.Fit = 1− RMSσ̂yPredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationLinear modelsModelstructuresEstimationandValidationNacelle windspeedEective windspeedOne minutepredictionConclusionResults for nacelle wind speedFit (%)Pred. hor. ArxDel BJDel Per1 sec. 37.558 42.233 28.53530 sec. 23.943 32.062 -9.15960 sec. 23.937 31.548 -6.071∞ 23.937 32.153RMS (m/s)1 sec. 0.816 0.755 0.93430 sec. 0.994 0.888 1.18760 sec. 0.994 0.894 1.227∞ 0.994 0.886Table: Predictability for nacelle wind speed using one upwindturbines and LTI models.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationLinear modelsModelstructuresEstimationandValidationNacelle windspeedEective windspeedOne minutepredictionConclusionResults for eective wind speedFit (%)Pred. hor. ArxDel BJDel Per ArxDel4To21 sec. 94.466 94.520 94.380 94.45430 sec. 68.346 67.928 59.516 64.84660 sec. 66.862 66.056 52.501 61.178∞ 65.208 65.736 55.140RMS (m/s)1 sec. 0.055 0.054 0.056 0.05530 sec. 0.314 0.318 0.402 0.34960 sec. 0.329 0.337 0.472 0.386∞ 0.345 0.340 0.445Table: Predictability for eective wind speed using one upwindturbines and LTI models.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationLinear modelsModelstructuresEstimationandValidationNacelle windspeedEective windspeedOne minutepredictionConclusionOne minute prediction exampleThe gure below zooms in on one of the largest gusts in thevalidation data.It is clear that a simple prediction model based on the rst orsecond upwind turbine outperforms the persistence method.Prediction of EWS6000 6200 6400 6600 6800 700077.588.599.51010.511Time (sec)Wind speed (m/s)  MeasuredPerArxDelBJDel−simArxDel4To2Figure: Example of predictions with a gust. Legend: Per is based ona persistence model. ArxDel is based on a ARX(2,2,60) (na, nb, nk)model from WT 3 to 2. ArxBJ is based on a BJ(2,2,2,2,60)(na, nb, nc , nd , nk) model from WT 3 to 2. ArxDel4To2 is based ona ARX(2,2,120) model from WT 4 to 2. All are 1 minute predictionsexcept BJDel-sim which is pure simulation. Data: 2009-02-11PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationConclusionConclusionEective wind speed estimationIn this paper an estimator for eective wind speed isdeveloped.This estimator includes the wind speed in a more correctway compared to the estimators found in the literature.Using the estimator the eective wind speed for sixturbines in the OWEZ farm has been estimated.The eective wind speed is more suitable for predictionscompared to the nacelle wind speed.PredictionModelsT. Knudsenet.al.The AeolusprojectWind speedmodels forfarm levelcontrolEstimationof eectivewind speedMeasurementsSystemIdenticationConclusionPredictability in a real wind farmBased on simple classical models the prediction error forthis eective wind speed can be reduced with 30% using aupwind turbine compared to the persistence method.This reduction is for a prediction horizon of 1 minute and adistance of 632 m.The smallest standard deviation for this prediction error is0.33 m/s corresponding to a 95% condence interval at±0.66 m/s which can be suciently small to be useful.When the distance is approximately doubled to 1277 m thereduction goes from 30% to approximately 15%.

Prediction Models for Wind Speed at Turbines in a Farm with Application to Control

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Prediction Models for Wind Speed at Turbines in a Farm with Application to Control

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