Review Article A Critical Review on Wind Turbine Power ...Journal of Energy Region 1 Region 2 Region...
Transcript of Review Article A Critical Review on Wind Turbine Power ...Journal of Energy Region 1 Region 2 Region...
-
Review ArticleA Critical Review on Wind Turbine Power CurveModelling Techniques and Their Applications in Wind BasedEnergy Systems
Vaishali Sohoni, S. C. Gupta, and R. K. Nema
Department of Electrical Engineering, Maulana Azad National Institute of Technology, Bhopal 462051, India
Correspondence should be addressed to Vaishali Sohoni; [email protected]
Received 27 March 2016; Revised 8 June 2016; Accepted 12 June 2016
Academic Editor: Kamal Aly
Copyright © 2016 Vaishali Sohoni et al.This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Power curve of a wind turbine depicts the relationship between output power and hub height wind speed and is an importantcharacteristic of the turbine. Power curve aids in energy assessment, warranty formulations, and performance monitoring of theturbines. With the growth of wind industry, turbines are being installed in diverse climatic conditions, onshore and offshore,and in complex terrains causing significant departure of these curves from the warranted values. Accurate models of powercurves can play an important role in improving the performance of wind energy based systems. This paper presents a detailedreview of different approaches for modelling of the wind turbine power curve. The methodology of modelling depends uponthe purpose of modelling, availability of data, and the desired accuracy. The objectives of modelling, various issues involvedtherein, and the standard procedure for power performance measurement with its limitations have therefore been discussed here.Modelling methods described here use data frommanufacturers’ specifications and actual data from the wind farms. Classificationof modelling methods, various modelling techniques available in the literature, model evaluation criteria, and application of softcomputing methods for modelling are then reviewed in detail. The drawbacks of the existing methods and future scope of researchare also identified.
1. Introduction
Wind energy has emerged as a promising alternative sourcefor overcoming the energy crisis in the world. Wind powerbased energy is one of the most rapidly growing areas amongthe renewable energy sources and will continue to do sobecause of the growing concern about sustainability andemission reduction requirements. The uncertain nature ofwind and high penetration of wind energy in power systemsare a big challenge to the reliability and stability of thesesystems. To make wind energy a reliable source, accuratemodels for predicting the power output and performancemonitoring of wind turbines are needed. The theoreticalpower captured (𝑃) by a wind turbine is given by [1]
𝑃 =1
2𝜌𝐴𝑤𝐶𝑃(𝜆, 𝛽) 𝜐
3
. (1)
The power production of a wind turbine (WT) thusdepends upon many parameters such as wind speed, wind
direction, air density (a function of temperature, pressure,and humidity) and turbine parameters [2]. Much complexityis involved in considering the effects of all the influencingparameters properly. It is therefore difficult to evaluate theoutput power using the theoretical equation given above.Power curve of a wind turbine, which gives the output powerof turbine at a specific wind speed, provides a convenientway to model the performance of wind turbines. A typicalpower curve for a pitch regulated wind turbine is shown inFigure 1. In the first region when the wind speed is less thana threshold minimum, known as the cut-in speed, the poweroutput is zero. In the second region between the cut-in andthe rated speed, there is a rapid growth of power produced. Inthe third region, a constant output (rated) is produced untilthe cut-off speed is attained. Beyond this speed (region 4) theturbine is taken out of operation to protect its componentsfrom high winds; hence it produces zero power in thisregion.
Hindawi Publishing CorporationJournal of EnergyVolume 2016, Article ID 8519785, 18 pageshttp://dx.doi.org/10.1155/2016/8519785
-
2 Journal of Energy
Region1
Region 2
Region3
Region4
Wind speed
Pow
erou
tput
Prated
0 �cut in �rated �cut off
Figure 1: Typical power curve of a pitch regulated wind turbine.
The power curve of a WT indicates its performance.Accurate models of power curves are important tools forforecasting of power and online monitoring of the turbines.A number of methods have been proposed in various worksto model the wind turbine power curve. These methodswhich use data frommanufacturers’ specifications and actualdata from the wind farms have been utilized by manyresearchers in various wind power applications [3, 4]. Theliterature reviewed reveals that appropriate selection of powercurve models can help in improved performance of windenergy based systems. This paper presents current statusof research and future directions of different wind turbinepower curve modelling approaches. The need of modelling,modelling methodology, classification of models, and meth-ods of evaluation have been discussed. The impact of variousparameters on these curves, the standard procedure forpower performance measurement of wind turbines, and theneed for developing site specific curves is also discussed.Various models proposed and used in various studies havebeen compared critically and finally inferences are drawn.
2. Need of Power Curve Modelling
The power curve reflects the power response of a WT tovariouswind speeds. Accuratemodels of the curves are usefulin a number of wind power applications. The objectives ofmodelling the wind turbine power curve have been discussedhere.
2.1. Wind Power Assessment and Forecasting. TheWT powercurve can be used for wind power assessment.Wind resourceassessment of a region in terms of wind speed, wind powerdensity, and wind energy potential is done to identify areassuitable for wind power development [3]. In this process,estimation of energy is done by using the available wind dataand wind turbine power curve. Predicting the output powerof the turbine at a candidate site is also required in sizing andcost optimization studies during the design stage of a windenergy based system. The accuracy in power prediction isimportant as an overestimation can result in poor reliabilityand an underestimation can lead to oversizing of the windenergy conversion system.Wind turbine operators who tradeenergy directly to the electricity market also need to forecastthe power output of their turbines accurately, so that they willbe able to deliver the traded amount of power [2].
Power curves are supplied by the manufacturers in atabular or graphical form. However, a generic equationwhich represents this curve accurately is required in var-ious problems of wind power systems. Derivation of anappropriate function to describe the actual shape of thecurve is a very important task. However, the manufacturer’scurves are created under standard conditions therefore theymay not represent the realistic conditions of the site underconsideration. The turbine performance at the wind farmsis also not ideal due to wear and tear and aging of turbines.Another method tomodel the power curves is to derive themusing the actual data of wind speed and powermeasured fromthe turbines [4]. The data of wind turbines collected by theSCADA (supervisory control and data acquisition) systemcan be utilized for this purpose.This method can incorporatethe actual conditions at the wind farms, thus providing betteraccuracy in power prediction.
2.2. Capacity Factor Estimation. The capacity factor of a WTis defined as the ratio of the average power output to therated output power of the generator and is an indicator ofits efficiency [5]. It is used to estimate the average energyproduction of aWT required for the sizing and cost optimiza-tion studies, optimum turbine-site matching, and rankingof potential sites [5, 6]. The wind turbine power curvemodels are used to estimate the capacity factor of a WT. Acomparative analysis of four power curvemodellingmethodsin estimation of capacity factor of wind turbine generator ispresented in [7].
2.3. Selection of Turbines. The power curve can be used tomake generic comparison between models and can aid in thechoice of turbine from the available options. The selection ofthe turbine characteristics whichmatch with the wind regimeof the site helps in optimizing the efficiency of wind energysystem [8].
2.4. Online Monitoring of Power Curves. Power curves can beused for monitoring the performance of turbines. For this,a benchmark curve which represents the performance of anormally operating turbine is required. This reference curvecan be extracted from measured power output and windspeed data of wind turbines. The actual curve of the turbineto bemonitored can be comparedwith this benchmark curve.The deviations of the actual values from the expected outputcan indicate underperformance or faults [1]. The wind poweroutput of a turbine can be affected by underperformance orvarious faults/anomalies of the turbine such as blade faultsand yaw and pitch system faults [4, 9]. Different types of faultsaffect the turbine system differently and will cause the powercurve to depart from the expected value in a different way.Tools which can characterize and quantify these departurescan aid in early identification of faults. Statistical analysis ofthe outlier data can give indications of the specific reason ofanomaly.Wind turbine conditionmonitoring by use of powercurve copula modelling is suggested in [10, 11] and is a topicof further research. Early recognition of the emerging faultsand timely repair andmaintenance of the equipment can helpin improving the performance of wind turbines.
-
Journal of Energy 3
3. Modelling Issues
A number of aspects require consideration while modellingthe power curves of wind turbines. The selection of modeland methodology adopted depends upon the purpose ofmodelling, available data, impact of various parameters onthese curves, and other related issues.
The following important issues should be taken intoconsideration while modelling of the power curve.
3.1. Difference in Models. The power curves vary with dif-ferent manufacturers and models. Therefore the model usedto describe them should also be different [12]. Also, thereis difference between pitch regulated and stall regulatedturbines. Pitch regulated turbines maintain constant outputfrom the rated to cut-off speed, whereas the stall regulatedturbines have a decreased power output above the rated windspeeds (stall region).
3.2. Cut-In and Cut-Off Behaviour. The turbine behaviournear cut-in and cut-off wind speeds can be difficult to model[8]. These limits are different for different turbine models.When the power curve is derived using the measured data,some nonzero and negative values of power outputs belowcut-in speed can be obtained. The cut-off hysteresis whichoccurs during the period between shut down and restart ofturbine affects the productivity of turbine [13]. Hysteresiseffects can bemore significant with certain wind patterns andterrains such as unsteady and gusty winds requiring frequentstarting and shutting down, resulting in considerable loss ofenergy production. Power curve correction which takes intoaccount this behaviour of turbine at cut-off can reduce thepower prediction errors.
3.3. Single versus Group of Turbines. The manufacturers’curves are suitable for predicting the power output of asingle turbine of a specific type. In a big wind farm anumber of turbines are spread over a wide area. Wind energyproduction involves uncertainties due to stochastic nature ofthe wind and variation of the power curve [14]. The speedand direction of wind encountered by the turbines of a windfarm may not be the same due to variation of wind. Hence,in a wind farm, power produced by turbines with identicalspecifications can also differ, even if the wind speed is thesame. The shadowing effect of turbines causes this differenceas the turbines which operate in wake of other turbinesmay get reduced wind speeds [15]. This difference can alsohappen due to factors such as wear and tear, aging, anddirt or ice deposition on blades. With the growth of windenergy projects it has become essential to develop methodsto monitor the performance of not only a single turbine butalso the wind farm as a whole.Therefore building appropriatemodels to obtain the relationship between wind speed andoutput power when a group of turbines are deployed on awind farm is required.
3.4. Influencing Factors. A number of factors can cause thepower curve to deviate from the theoretical value [1, 2]. The
important influencing factors are given here and need dueattention during modelling.
(i) Wind Conditions at the Site. Wind is highly stochastic innature. The wind speed and direction change continuously.Thewind at a particular site is affected byweather phenomenaand topology of the site. The turbulence of wind at a givenlocation affects the power production [16]. Obstacles liketrees, buildings, and other high structures influence the wind.
(ii) Air Density.The pressure, temperature, and humidity ofsite affect the air density [17], hence affecting the powerproduced. Effect of varying air density has been consideredfor developing site specific curves [18]. It is shown in [2]that temperature has the highest influence on air density andconsidering its effect along with the wind direction resultedin improved performance of models.
(iii) Extrapolation of Wind Speed.The wind speed changeswith height.Thiswind shear effect is affected by the roughnessof terrain. The power curve uses the wind speed measured atthe hub height of turbine, but this height varies with differentmodels and manufacturers, and it is not always possible tomeasure the wind speed at this height. A number of methodshave been used in the literature to express the variation ofwind speed with height [12]. Also the wind speed measuredat the masts is different from the speed at the turbine locationand sometimes when the wind speed values at the particularsite are not available the wind speed measurements from anearby location are used to determine the wind profile ofthis site. The accuracy of conversion of the measured windspeed to wind speed at hub height and at the turbine locationdepends on factors such as the vertical wind profile at the site,position of masts relative to the turbine, and themethod usedfor extrapolation.
(iv) Turbine Condition.The power curve is affected by thecondition of turbine and associated equipment. Aging andwear and tear of turbine, anomalies and faults, blade condi-tion, yaw and pitch misalignments, controller settings, andso forth cause the power curve to depart from actual values[1, 11].
3.5. IEC 61400-12-1 Standard [19]. IEC 61400-12-1, the com-monly adopted international standard for power perfor-mance measurement, is found to be of relevance. The pro-cedure for measuring the power performance characteristicsof single wind turbines is specified in this standard. It isthe most accepted standard for power curve measurementof single wind turbines. The standard describes the measure-ment methodology for the measured power curve which isdetermined by simultaneousmeasurement of wind speed andpower output at the test site. A previous site calibration isrequired for certain terrain conditions. The annual energyproduction is calculated by applying the measured powercurve to reference wind speed frequency distributions sup-plemented by sources of uncertainty and their effects. Thestandard prescribes derivation of power curve using the hubheight wind speed measured with a cup anemometer in the
-
4 Journal of Energy
suitable measurement sector, but if the wind speed has alarge variation over the rotor swept area then there can be asignificant difference between the hub height wind speed andwind speed averaged over the whole rotor swept area. Themeasurement methods and accuracy of measuring instru-ments can cause variance in measurements and can lead tolarge prediction errors. The impact of other measurementoptions such as consideration of rotor equivalent wind speedin which speed is measured at heights over the full rotorplane with the use of remote sensing technology (LIDAR andSONAR) and nacelle based anemometry is a topic of furtherresearch [20].
The IEC standard uses ten-minute averaged data groupedinto wind speed intervals of 0.5m/s (method of bins). This10-minute averaging of data introduces systematic averagingerrors and short wind fluctuations are killed off. Wind at aspecific site can be affected by a number of factors such astopology of the site and obstacles and weather phenomena.Although the IEC power curve considers the wind conditionof the current site it may not always be appropriate to applyto the wind conditions of other sites. Research efforts aretherefore required to develop site specific power curves.These curves can incorporate the wind conditions of theparticular site, thus giving better results [18, 19].
Appropriate selection of modelling method is an impor-tant requirement for during planning and operation stage ofwind based system and helps in improving the performanceof the system. The methods which consider only wind speedas input may not take into account the variance caused byvarious influencing parameters. Methods which consider theinfluence of these parameters on the power curve can resultin more accurate models. Wind at a specific site can beaffected by a number of factors such as topology of the siteand obstacles and weather phenomena. It is shown in [18]that the use of developed site power curves, which usedthe knowledge of site and turbine parameters for modelling,resulted in more accurate energy assessment than the turbinepower curve.The issues discussed above if addressed properlycan result in efficient models of power curves.
4. Wind Speed Modelling
Wind power generated is highly correlated with the windspeed distribution across the region where the wind farmis situated and depends upon the type of WT deployed inthe wind farm. The accuracy in prediction of wind energycan be achieved by modelling the wind speed and powersimultaneously.The wind speed at a site varies randomly andits variation in a certain region over a period of time canbe represented by different probability distribution functions(PDF). Selection of appropriate PDF to describe the actualwind speed distribution of the site is crucial for accuracy inpower prediction.
Themost commonly used and accepted distribution is thetwo-parameter Weibull distribution [5, 21]. It is a versatilePDF, is simple to use, and is found to be accurate for most ofthe wind regimes encountered in nature. However, Weibulldistribution is not suitable for certain wind regimes, forexample, those having high frequencies of null winds, and
0 5 10 15 20 25 30 350
5
10
15
20
25
30
Wind speed (m/s)
Out
put p
ower
(MW
)
Figure 2: Power curve using actual data for a group of wind turbinesat a wind farm (NREL) [66].
for short time horizons [1, 22]. The Weibull PDF is givenby
𝑓 (V) =𝑘
𝑐(V𝑐)
𝑘−1
exp(−V𝑐)
𝑘
. (2)
Another widely used distribution is Rayleigh PDF [18]in which the shape parameter of (2) is taken as 𝑘 = 2.It is a simple PDF and can describe the wind regime withsufficient accuracy when little detail is available about thewind characteristics of a site.Thewind speed distribution hasalso been described in the literature using several other PDFswhich include lognormal, beta, and gamma distributions[23]. A detailed review of different PDFs for wind speedmodelling and techniques for estimation of their parametersis given in [22]. Appropriate PDF and parameter estimationtechnique should be selected for modelling the wind speedfor a particular site.
5. Power Curve Models Classification
The power curve modelling methods can be classifiedinto discrete, deterministic/probabilistic, parametric/nonpara-metric, and stochasticmethods or they can be classified on thebasis of data used for modelling.
5.1. Discrete Models. In this method as described in IEC61400-12 all the wind speeds are discretized into 0.5m/sbins [19]. The power output for each bin is then modelled.This is a simple method as it does not require mathematicalfunctions for describing the curve. Also it takes into accountthe nonlinear wind speed-power output relation. However alarge number of data are required in this method to developa reliable model.
5.2. Deterministic and Probabilistic Models. A deterministicpower curve model assumes a fixed relation between theoutput power and wind speed. But when a fleet of windturbines are deployed on a wind farm, turbines of the sametypemay produce different amount of power even if the windspeed is the same (Figure 2). A probabilistic power curvemodel incorporates these power variations to characterize therelationship between wind speed and actual output powers.Most of themodels available in the literature are of determin-istic nature and are constructed by using the manufacturers’
-
Journal of Energy 5
power curve data. A probabilistic model proposed in [14]characterizes the dynamics of output power by a normaldistribution with varying mean and constant standarddeviation. The method given in the paper accommodatesthe uncertainty of output power. The probabilistic nature ofwind power output can also be modelled by deriving curvesusing actual data of power output and wind speed of turbinesdeployed in a wind farm. This method requires a largenumber of historical data but results in accurate models[4, 24].
5.3. Parametric and Nonparametric Models. A parametricmodel defines the relationship between input and outputby a set of mathematical equations with a finite numberof parameters. In a nonparametric model, no assumptionis made about the functional form of the phenomenonunder observation. Parametric models of WT power curvecan be built by utilizing a set of mathematical expressionshaving a fixed number of parameters, which are usuallycollected together to form a single parameter vector 𝜃 =(𝜃1, 𝜃2, 𝜃3, . . . , 𝜃
𝑛). Nonparametric models are used when it
is difficult to define the underlying theory upon which theparametric model can be constructed [24].
5.4. Models Based on Presumed Shape, Curve Fitting, andActual Data. The models of power curves can be classifiedaccording to the data being used for modelling. Models ofpower curve based on presumed shape of curve utilize onlythe cut-in, cut-off, and rated speeds and the rated powerof the selected turbine for calculating the parameters ofexpressions used in the model [12, 25, 26]. These ratings areavailable from the specifications of the turbines. When themanufacturer’s power curve data is available, models can bedeveloped by fitting one or more appropriate expressionsto the actual curve. The parameters of the expression beingfitted to the actual curve are generally calculated by usingthe least squares method [4].Themodels derived from actualdata of wind farm need the actual wind speed and poweroutput data from an operational wind farm. If the effect ofthe influencing parameters is also included in the model,then the data of the included parameters is also required.This data can be obtained from the wind farm’s SCADA sys-tem.
5.5. Stochastic Models. The stochastic method consists ofcharacterizing the power performance of wind turbine byevaluating dynamic response against the fluctuating windspeed inputs [27, 28].The dynamic power output is separatedinto a deterministic stochastic part in this model. In [29] theMarkov chain theory is used to describe the power outputof WT. The resulting model is independent of turbulenceintensity; however, the effect of other influencing parametersis not taken into account in this method.
6. Power Curve Modelling Approaches
Various approaches have been used in the literature formodelling of WT power curve. These methods, their merits,limitations, and application areas are discussed here.
6.1. Parametric Models. The power delivered by a WT can beexpressed as
𝑃 =
{{{{
{{{{
{
0 V < V𝑐, V > V
𝑓
𝑞 (V) V𝑐< V < V
𝑟
𝑃𝑟
V𝑟≤ V ≤ V
𝑓.
(3)
The relationship between power output and wind speedof a WT between cut-in and rated speed is nonlinear (region2 of Figure 1). The relation 𝑞(V) can be approximated byvarious functions using polynomial and other than polyno-mial expressions. The pitch regulated turbines maintain aconstant power output in region 3 of Figure 1, whereas thestall regulated turbines have decreased power output in thisregion; thus the power in this region for a stall regulatedturbine should not be modelled as a constant. The governingequations for different approximations of power curve aregiven in Table 1.
6.1.1. Polynomial Function Approximation. The nonlinearwind speed-power relationship, 𝑞(V), can be approximatedby various polynomial expressions. Different models usinglinear, quadratic, cubic, and higher powers of speed or theircombinations have been used in the literature.
(i) The most simplified model based on a linear curve,which describes region 2 of power curve by a straightline, is used in many applications [12, 39–42].
(ii) A quadratic model represents the nonlinear portionof the curve by an equation of degree 2. 𝑞(V) hasbeen approximated by a quadratic equation in [25] todescribe the relation between output power and windspeed of a WT. A binomial expression discussed in[30] has been adopted by many researchers [43, 44]to determine output power of wind turbines. Regions2 and 3 of Figure 1 for a stall regulated WT can bedescribed by using two different binomial expressionsas in [45].
(iii) Model based on cubic law approximates region 2 ofpower curve by cubic law. A model which describesthe nonlinear power-wind speed relationship by acubic law is discussed in [46]. This model is usedfor power output calculations in [26, 31, 47]. A cubicexpression for region 2 and a linear expression forregion 3 are chosen to describe the power curve in[48].
The models given above use the WT specifications ofrated power and cut-in, cut-off, and rated wind speed onlyto determine the equations for power curve.
(i) A methodology based on Weibull’s parameter isproposed in [6]. This model based on Weibull shapeparameter is used by many researchers [49, 50] forcalculating the power output of WT.
(ii) A linearized segmented model discussed in [24, 51]carries out a piecewise linear approximation of the
-
6 Journal of Energy
Table 1: Expressions of parametric models.
Model Expressions of 𝑃 and 𝑞 Parameters
Linear [12] 𝑞 (V) = 𝑃𝑟
(V − V𝑐)
(V𝑟− V𝑐)
—
Quadratic [25] 𝑞 (V) = 𝑃𝑟(V − V𝑐
V𝑟− V𝑐
)
2
—
Binomial [30] 𝑞 (V) = (𝑎 + 𝑏V + 𝑐V2) 𝑃𝑟
𝑎 =1
(V𝑐− V𝑟)2[V𝑐(V𝑐+ V𝑟) − 4V
𝑐V𝑟
(V𝑐− V𝑟)2
2V𝑟
]
𝑏 =1
(V𝑐− V𝑟)2[4 (V𝑐+ V𝑟)(V𝑐− V𝑟)3
2V𝑟
− 3 (V𝑐+ V𝑟)]
𝑐 =1
(V𝑐− V𝑟)2[2 − 4
(V𝑛+ V𝑟)3
2V𝑟
]
Cubic [31] 𝑞 (V) = 𝑎V3 − 𝑏𝑃𝑟
𝑎 =𝑃𝑟
(V𝑟
3 − V𝑐
3)
𝑏 =V3𝑟
(V𝑟
3 − V𝑐
3)
Weibull based [6] 𝑞 (V) = 𝑎 + 𝑏V𝑘𝑎 =
𝑃𝑟V𝑐
𝑘
(V𝑐
𝑘 − V𝑟
𝑘)
𝑏 =𝑃𝑟
(V𝑐
𝑘 − V𝑟
𝑘)
Double exponential [32] 𝑃 = exp (−𝜏1exp (−𝜐𝜏
2)) 𝜏
1and 𝜏
2to be estimated
4PL [1, 33] 𝑃 = 𝑎(1 + 𝑎𝑚𝑒𝜐/𝜏
1 + 𝑎𝑚𝑒𝜐/𝜏)
𝜃 = (𝑎,𝑚, 𝑛, 𝜏)
(1) From manufacturers’ curve [33]𝑎 = 𝑃
𝑟
𝑛 = 𝑒2𝑠V𝑖𝑝/(𝑃𝑟−𝑃𝑖𝑝)
𝑚 = 𝑛(
2𝑃𝑖𝑝
𝑃𝑟
− 1)
𝜏 =
(𝑃𝑟− 𝑃𝑖𝑝)
2𝑠
(2) Parameters obtained by evolutionary techniques forSCADA data in [1]
4PL [34, 35] 𝑃 = 𝑓 (V, 𝜃) = 𝐷 + (𝐴 − 𝐷)1 + (V/𝐶)𝐵
𝜃 = (𝐴, 𝐵, 𝐶,𝐷)
𝐴 = minimum asymptote𝐵 = Hill slope𝐶 = inflection point (point of curve where the curvaturechanges direction)𝐷 = maximum asymptote(parameters obtained by evolutionary techniques)
5PL [24, 35, 36] 𝑃 = 𝑓 (V, 𝜃) = 𝐷 + (𝐴 − 𝐷)
(1 + (V/𝐶)𝐵)𝐺
𝜃 = (𝐴, 𝐵, 𝐶,𝐷, 𝐺)
𝐴 = minimum asymptote𝐵 = Hill slope𝐶 = inflection point (point of curve where the curvaturechanges direction)𝐷 = maximum asymptote𝐺 = asymmetry factor(parameters obtained by evolutionary techniques)
curve by using the equation of a straight line. Theresulting curve follows the actual curve more accu-rately.
(iii) The power curve of wind turbine has also been mod-elled by other than polynomial functions. The powercurve that is modelled in [52] uses a exponentialequation whereas a double exponential equation isused in [32].
(iv) A polynomial regression parametric model is devel-oped from real data as a benchmark method in [53].Three nonparametric methods are also proposed inthis study.
6.1.2. Approximations Considering Inflection Point on theCurve. All the polynomial expressions given above do nottake into account the inflection point on the power curves.
-
Journal of Energy 7
In most real power curves there is an inflection point onthe curve at which its curvature changes sign. Models whichconsider this inflection point can describe the actual shapeof the curve more accurately than the above models. Anew formula for power curve interpolation which considersinflection point on the curve is proposed in [54]. A doubleexponential model is proposed in [32] to fit the data in twoinflection zones using a single equation. Functions basedon four- and five-parameter logistic approximations alsoconsider this inflection point on the curve and are promisingapproaches for modelling of power curve.
(i) The shape of awind power curve can be approximatedby a four-parameter logistics (4PL) function [1, 34]. Aprocedure to obtain the parameters of the 4PL func-tionmodelmodelled frommanufactures power curvedata has been proposed in [33]. The four parametersof the function are obtained directly from the powercurve instead of using an optimization process in thiswork. The paper also proposes manufacturer’s powercurve approximation using a three-parameter model.The power curve is derived from the SCADA data ofwind farms using a 4PL approximation in [1, 4, 24]. Itis shown in [1] that this model can be used for onlinemonitoring of power curves. Another form of four PLexpression is used for extracting power curve fromactual wind speed and power curve data of a windfarm in [35]. The method is applied for wind energyestimation of the selected wind farm site. Literaturereviewed reveals that the four-PLmodel produces lesserrors in representing the power curve than themeth-ods based on polynomial approximation. However a4PL curve is symmetric about the inflection pointwhereas the power curves are asymmetric. Modelswhich can incorporate this asymmetry can thereforeproduce even better results. Cubic splines can be usedfor asymmetric data. A cubic spline is the smoothestcurve that passes through the exact data points. Asthe power curves are quite smooth their asymmetrycan be approximated by a cubic spline interpolationtechnique [55–57], but the disadvantage with a splinefit is that it does not represent the random variationof data.
(ii) A five-parameter logistic (5PL) approximationincludes a fifth parameter (𝐺 in Table 1) to control thedegree of asymmetry [58].Thismethod canmodel theasymmetry effectively and can be used for modellingthe WT power curve [36]. A 5PL model howeverhas the possibility of becoming ill-conditioned; thusevaluation of parameter vector becomes difficult. A5PL model derived from the SCADA data of windfarm is applied for energy estimation of the farm in[35] and it is shown that it produces less error in theestimated energy compared to the 4PL model.
6.1.3. Model Based on Curve Fitting of Manufacturer’s Curve.The power curve models obtained by means of curve fittingof the manufacturer’s curve are used in several applications.The characteristic equation of wind generator is fitted with
three binomial expressions for 𝑞(V) in [59] to get the accuracyin fitting. A ninth-order polynomial for power curve fittinghas been used in [60] and it has been found that it givesaccurate correlation with the real data, producing exclusivelypositive values for the generated power between cut-in to cut-off range. High-order polynomials may produce better fittingresults for a particular set of data; however they may notrepresent the variance of data and should be used carefully.Thepower curvemodels by curve fitting of themanufacturer’scurve are analyzed in [55–57].
6.2. Parameter Estimation. The parametric models of WTpower curve express the shape of the curve by a set of mathe-matical equations. Determination of the coefficients of theseequations requires fitting the data to the selected model. Thetechniques and algorithms used in various works for param-eter estimation of power curve models are discussed here.
6.2.1. Techniques for Parameter Estimation
(i) Least SquaresMethod.The least squaresmethodminimizesthe summed square of residuals to obtain the parametersof the model and is the most commonly used and acceptedmethod [4, 24].
(ii) Maximum Likelihood Method (MLM). Another approachused in the literature is to determine the parameters ofpower curve model by maximum likelihood method. In thismethod the parameters of a statistical model are estimated bymaximizing the likelihood function. It was found in [1] thatthis method did not perform well in comparison to the leastsquares method.
6.2.2. Algorithms for Parameter Estimation. The parametersof the parametric models especially those using the 4PL and5PL approximations are difficult to evaluate. The parameterestimation becomes more difficult when the models arederived from the actual data of wind turbines. Developingaccurate models of wind turbines and optimization for hugedata sets are a very complicated process. Modern nontradi-tional solution techniques for parameter estimation enhancethe accuracy, reduce the computational time, and are easyto implement. Various evolutionary techniques have beenapplied for determining the parameter vector 𝜃 of logisticfunction based power curve models [4, 24].
6.3. Data Preprocessing. Thepower curve derived from actualwind speed and power output data of wind turbines usesSCADA data from the wind turbines. This data is proneto errors due to measurement, sensor, and communicationssystem errors. The data is also affected by nonproduction ofturbines when it is shut down by the control system for somereason other than anomalous operation. SCADA system canhave null entries or erroneous data which can result ininaccurate models. Hence it is necessary to remove thesemisleading entries before using this data for further analyses.The most common method is to remove the data manually.These outliers can be identified by visual inspection [11] ofwind speed power output plot and can be removed before
-
8 Journal of Energy
proceeding for development of model. However the methodcan lead to inaccurate results as the data from SCADAsystem is voluminous and it is difficult to differentiatebetween correct and erroneous data.These outliers have beenremoved by different statistical methods in various worksbefore development of models. In [4] the analysis of residualstogether with control charts is used to filter potential outliers.The outliers can be detected by classical least mean square(LMS) method which minimizes the sum of the squares overall the measurements and if a measurement is found to befar away from the correct value it prevails in the resultingfitting; however, in this method a single outlier point candestroy the fitting. In [32] least median of squares method isused for data preprocessing in which instead of the sum asin LMS method sum of medians is minimized to identify theoutliers. It is shown that this method is very robust; howeverit requires iterative solution. The wind data preprocessingis done in four steps in [63] which include validity check,data scaling, missing data processing, and lag removal. In[64] a probabilisticmethod developed around a copula-basedjoint probability model for power curve outlier rejection isproposed. A data mining approach to process the raw datahas been proposed in [65]. Appropriate method for datapreprocessing is important requirement for development ofan efficient model.
6.4. Evaluation of Model. After developing the model fromthe data, it is important to determine whether this modelappropriately represents the behaviour of the actual data forthe power curve. The evaluation of the developed modelsin various applications is done on the basis of a number ofperformance metrics. The root mean square error (RMSE),goodness of fit statistics used by awide number of researchers,estimates of the standard deviation of random component inthe data, and a value closer to zero indicate a better fit. The𝑅-squared statistic is the square of the correlation betweenthe actual and the predicted values that measures how closelythe fit explains variation in the data. An 𝑅-squared valuecloser to one indicates a good fit [38]. Other criteria used inthe literature include the mean absolute error (MAE), meanabsolute percentage error (MAPE), the sum of squares error(SSE), SD (standard deviation), and chi-square 𝑅 [2, 4, 8, 11,17]. The most commonly used criteria are given in Table 2.
Selection of appropriate model analyzed on the basis ofsuitable criteria is a very important task for improving theperformance of wind power plants. Many models used in theliterature have not been evaluated for goodness of fit withactual curve data or their suitability for specific applications.Thepolynomialmodels of [54, 57] are compared by observingthe visual fit. Models in [2, 11] are compared by MAE, RMSE,MAPE, and SD performance metrics; however, suitability ofthese models for wind power applications is not evaluated.Also as these models will ultimately be used in wind energyapplications it is not appropriate to judge their suitability onthe basis of goodness of fit parameters alone, but it should alsobe examined how successfully they can be employed for theparticular applications.
Table 2: Model evaluation indices.
ExpressionAbsolute error (AE)[1] AE =
𝑦𝑚 (𝑖) − 𝑦𝑎(𝑖)
Relative error (RE) [1] RE =𝑦𝑚− 𝑦𝑎
𝑦𝑎
× 100
Mean absolute error(MAE) [24] MAE =
1
𝑁
𝑁
∑
𝑖=1
𝑦𝑚 (𝑖) − 𝑦𝑎 (𝑖)
Mean absolutepercentage error(MAPE) [37]
MAPE = 1𝑁
𝑁
∑
𝑖=1
𝑦𝑚(𝑖) − 𝑦
𝑎(𝑖)
𝑦𝑎(𝑖)
Root mean squareerror (RMSE) [24] RMSE = [
1
𝑁
𝑁
∑
𝑖=1
(𝑦𝑚(𝑖) − 𝑦
𝑎(𝑖))2
]
1/2
𝑅-squared [38] 𝑅2 = 1 −∑𝑁
𝑖=1(𝑦𝑎(𝑖) − 𝑦
𝑚(𝑖))2
∑𝑁
𝑖=1(𝑦𝑎(𝑖) − 𝑦
𝑎𝑚(𝑖))2
𝑁= number of data, 𝑦𝑚(𝑖) = 𝑖th modelled value, 𝑦
𝑎(𝑖) = 𝑖th actual value, and
𝑦𝑎𝑚(𝑖) = mean of actual value.
6.5. NonparametricModels. Various nonparametricmethodscan be used for modelling of WT power curves. The SCADAdata collected from the wind farms is voluminous and usuallycontains errors. It may be difficult to obtain the relationbetween input and output using a functional form. Nonpara-metric methods can be suitable for deriving power curvesfrom this data. After preprocessing of data, model extractioncan be done using different methods. Nonparametric modelscan also incorporate the effect of parameters other than windspeed on the power curves more easily than the parametricmodels. The models can be trained by taking these otherparameters as inputs to the models [17, 18]. Developmentsin soft computing techniques offer promising approaches forpower curve modelling. Various advanced algorithms canbe utilized to generate accurate nonparametric power curvesfor various applications. Table 3 summarises details of somenonparametric models from the literature.
6.5.1. Neural Networks. Artificial neural networks (ANN)inspired by biological nervous system emulate the naturalintelligence of human brain [67] and can learn the nonlinearrelationship between input and output data sets by use of acti-vation function within the hidden neurons. Neural networksare used to estimate power generation of turbines at a windfarm in [17]. A separatemultilayer perception (MLP) networkfor each turbine uses ten-minute averages of wind speedand direction from two meteorological towers as inputs andpower generated by the turbine as the output. A comparativeanalysis of regression and ANNmodels for WT power curveestimation is done in [61] and it is shown that neural networkmodels perform better than the regression models. HoweverANN has a black box approach and it is difficult to developan insight about meaning associated with each neuron andweight [68]. ANN based multistage modelling has been usedin [62] to model the wind turbine power curve. The windspeed and air density are used as inputs in the first stage andthe normalized power output obtained from this stage, windspeed data turbulence intensity, is used to train the secondANN stage. It is claimed that this method has produced
-
Journal of Energy 9
Table 3: Details of some nonparametric models from various studies.
Ref.
Data set Model
Interval Data Number ofvalues Model ParametersStructure/transferfunction (TF)/trainingmethod
[4] 10min SCADA data100 WTs
Total 4347Training 3476Testing 871
𝑘-NN 𝑘 = 100 Euclidian distancemetric
[17] 10min
12 WTs(wind speed anddirection from
twometeorological
towers)
Training1500 patterns for
each WTANN
Number of hidden layers= 1
Number of hidden layerneurons = 8
(i) Separate MLPnetwork for each WT(ii) Training-patternmode(iii) TF-hyperbolic (alllayers)
[8] — Measured data100 kWWT —Fuzzy
clusteringNumber of cluster
centers = 8
(i) CFL(ii) Subtractiveclustering
[24] 10min
Data set 1generated withmethod in [9]
Total 1008Training 50%Testing 50%
ANN Number of hidden layerneurons = 5
(i) Feed forward backpropagation(ii)Training:Levenberg-Marquardt(iii) TF: hidden layertransig(iv) TF: output layerpurlin
Data set 2Total 4388
Training 50%Testing 50%
Data sets 3, 4,and 5
Total 2208Training 50%Testing 50%
Data sets1–5 as above As above
Fuzzyclustering
Number of clustercenters = 8 Fuzzy 𝐶-means
[2] 10min
SCADA (three2MWWTs)(model type 1:wind speedModel type 2:wind speed and
direction,temperature)
32796Training 60%Validation 40%
Fuzzyclustering
Number of clustercenters
Type 1 = 3Type 2 = 6
CCFL
MLPNN
Number of hidden layers= 2
(i) Training-gradientdescent(ii) TF: hiddenlayer-sigmoid(iii) TF: outputlayer-linear
𝑘-NN Type 1 𝑘 = 150Type 2 𝑘 = 3 —
ANFIS
(i) FIS structure Sugenotype(ii) Training-hybridlearning(iii) MembershipfunctionsInput space-generalizednormalOutput space-linear(iv) Number of MFs = 3
better results compared to the parametric, nonparametric,and discrete models.
6.5.2. Clustering Methods. Clustering is grouping of similardata into classes or clusters. A wind farm having many windturbine generators has variable power outputs due to varia-tion of wind speed. Efficient power curve can be found by
applying clustering methods. Power curve characterizationby cluster centre, fuzzy C-means, and subtractive clusteringmethods is done in [69]. Fuzzy clustering applies the conceptof fuzzy sets to cluster analysis and belongingness of eachpoint of data set to a group is given by amembership function.The method has the advantage of adapting noisy data. FuzzyC-means clustering uses fuzzy partitioning to partition acollection of vectors into 𝑐 fuzzy groups and finds a cluster
-
10 Journal of Energy
centre 𝑐𝑖in each group. The performance of FCM depends
upon the initial cluster centres.The method proposed in [70]to decide the number of clusters and their initial values forinitializing iterative optimization based clustering algorithmsis used in [8] to set up cluster centre fuzzy logic (CCFL)modelof power curve. This cluster estimation method is used as abasis for identifying fuzzy models and the effect of number ofcluster centres and cluster neighbourhood distance on RMSE iscalculated. On comparison of CCFL model with polynomialmodel fitted by least square method it is concluded thatthe RMSE obtained with the fuzzy logic method is muchlower than that obtained with the least square polynomialmodel.
6.5.3. Data Mining. Data mining refers to extracting ormining knowledge from large amounts of data [71]. Devel-opments in data mining offer promising approaches formodelling power curves of wind turbines. Selection of appro-priate data mining method and algorithm is important toget accurate, stable, and robust power curve. Data drivennonparametric models using multilayer perception (MLP),random forest, M5P, boosting tree, and 𝑘-nearest neighbour(𝑘-NN) algorithms are developed in [1] along with the 4PLparametric models. Performance of these models for onlinemonitoring of the power curves was analyzed and the leastsquare 4PL parametric and 𝑘-NNmodels were found to be ofhigh fidelity to be used as reference curves for monitoring ofpower curves. Control chart approach is used for detectingthe outliers and indicating the abnormal conditions of theturbine. However in another study [2] the performance of 𝑘-NN was found to be poor. Different data mining algorithms,namely, MLP, REP tree, M5P tree, bagging tree, and 𝑘-nearest neighbour algorithms, are used to build models forpower prediction and online monitoring in [4]. Principlecomponent analysis and 𝑘-NN algorithm are used for datareduction and filtering of outliers is done by residual andcontrol chart approach. In [2] four data mining techniques,namely, bagging, M5P algorithm, REP tree algorithm, andM5 rules, were used for constructing the nonparametricpower curve models. Model trees are type of decision treeswith linear regression functions at the leaves and are appliedfor modelling the power curves in a few applications [2,24]. Much detail of these models is not given in thesestudies. More information on model trees can be found in[72, 73].
6.5.4. Adaptive Network-Based Fuzzy Inference System(ANFIS) Model. Adaptive network-based fuzzy inferencesystem (ANFIS) is a fuzzy inference system implementedin the framework of adaptive networks and thus integratesthe best features of fuzzy systems and neural networks [68].A fuzzy inference system using fuzzy if-then rules is basedon human knowledge and reasoning processes. In ANFIS,tuning of nonlinear signal relations can be done by con-structing a set of fuzzy rules with appropriate membershipfunction parameters tuned in a training phase [67].Application of ANFIS for wind turbine power curvemonitoring is proposed in [2]. This method of modellingis compared with earlier best performing methods, namely,
ANN, CCFL, and 𝑘-NN methods, found in the liter-ature. Effect of including direction of wind and ambient tem-perature on the prediction error is evaluated. Data for pitchregulated turbines is used for the modelling.
6.5.5. Joint Probability of Wind Speed and Power. Anotherapproach of modelling is to consider the joint probabilitydistribution of power and wind speed instead of consideringthe implied function of the two variables. Considering jointprobability of the two variables instead of their individualprobabilities can incorporate measures of uncertainty intoperformance estimates [11]. SCADA wind speed and powermeasurement data from wind turbines are used to estimatebivariate probability distribution functions and constructpower curve using copula modelling technique in [10]. Theapplication of empirical copulas is proposed to approximatethe complex form of dependency between active power andwind speed. Usefulness of copula analysis for turbine condi-tion monitoring and early recognition of faults is suggestedin this paper. It is shown that different fault modes producedifferent signatures in 𝑅, 𝑅2, and chi2 statistics and can beused to identify the type of turbine fault.
6.5.6. Wavelet Support Vector Machine. Wavelet analysis is atechnique to analyze the nature of signals and is a promisingtool for nonstationary signals. In support vector machinesthe data is mapped into higher-dimensional feature spacevia nonlinear mapping. The power curve of WT is used forwindpower prediction in [37]. Anovelwavelet support vectormachine based model for wind speed prediction is proposedin this paper and its performance is found to be effective forshort time prediction.
A number of works in literature also include comparativeanalyses of various parametric and nonparametric methods[2, 8, 57, 74]. Seven different functions have been comparedin [75] for modelling the power curves of six differentturbines. In [53] four models are developed from availableoperational power output data. The polynomial regressionbased parametricmodel is used as a benchmarkmodel.Threenonparametric methods in addition to the above methods,namely, locally weighted polynomial regression, cubic splineregression, and a penalized spline regression model, areproposed in this study.
7. Selection of Modelling Method
Anumber ofmodels andmodellingmethodologies have beenproposed in various works formodelling ofWT power curve.The choice of appropriate model and methodology adoptedfor a specific application is important and is a difficult task.The model selection for a particular application is done onthe basis of availability of data, complexity of model, desiredaccuracy, and type of turbine and its power curve. On thebasis of reviewed literature the following points are identifiedfor selection of modelling methodology.
(i) Wind power curve models required for initial windresource assessment need handy methods for estima-tion of energy. Wind power output calculation and
-
Journal of Energy 11
energy estimation which are done during designingof wind based systems need a power curve modelwith fair degree of accuracy. When only specificationvalues (cut-in, cut-off, and rated speeds and therated power) for a wind turbine are available, thepolynomial models based on presumed shape canbe used. These models can also be used as a handytool for calculation of wind turbine output duringdesign stage of wind farms because of the simplicity ofcalculations. When the manufacturers’ curve data isavailable it is preferable to fit a polynomial function tothe data as it results in better accuracy. These modelsare thus suitable for modelling of single turbinesfor predicting power for small systems where fairlyaccurate accuracy is desired.
(ii) For power prediction and selection of turbines fordesigning of large wind based systems a very goodaccuracy is required as oversizing can result in lossof revenue and undersizing can hamper the reliabilityof the system. Accurate prediction is also required forwind farm operators for energy trading. The 4PL and5PL functions may therefore be used for these appli-cations to develop models from the manufacturers’curve data.
(iii) When the SCADA data from a nearby wind farm isavailable and it is desired to assess the power outputof a prospectivewind farmwith good accuracy havinga group of turbines or when the models is to be usedfor online monitoring of curves, it is appropriate toextract model from SCADA data of the wind farmwith appropriate extrapolations.These models can bederived using the 4PL and 5PL parametric methodsor one of the nonparametric methods such as ANNor ANFIS. The models can also incorporate the effectof other influencing parameters in themodels. Choiceof parameters depends upon terrain, wind conditions,obstacles, correlation of parameters, and so forth.Thecopula method of defining the power curve using ajoint probability distribution function of wind speedand power can be used for condition monitoringapplications.
8. Discussions and Prospects
Various methods of modelling ofWT power curve have beenreviewed. Several methods of modelling have been proposedand used in various studies (Figure 3). A summary of note-worthy contributions is given in Table 4. The salient featuresof these models are summarised in Table 5. The inferencesdrawn, the deficiencies, and the suggestions proposed aregiven below.
(i) Most of the parametric models used in the literatureuse polynomial approximations tomodel wind powercurve models. These models are mostly used forpredicting power output of turbines for sizing andcost optimization applications. These models do notconsider the inflection point on the power curveaccurately and can result in large prediction errors.
However they are simple to use and can be utilized forpredicting power during initial resource assessmentand designing of small systems if very good accuracyis not desired. 4PL and 5PL parametric models canfollow the actual shape of the power curve moreaccurately.These novel methods can result in reducedpower prediction errors and can be applied for powerand energy assessment during design of large systemsand forecasting of power for energy trading wheregood accuracy is a crucial requirement.
(ii) The deterministic methods which use manufacturer’sdata for modelling are suitable for single turbines andnot appropriate formodelling a group of turbines.Theprobabilistic methods which consider the variation ofboth power andwind speed are suitable formodellingpower curve for a fleet of turbines.
(iii) Power curve models extracted from actual data ofwind farms can incorporate actual conditions at a siteand are suitable for modelling a group of turbines.These curves can be derived from the available databy parametric and nonparametric methods.
(iv) The parametric models derived from actual windfarm data used in the literature include linear seg-mented and 4PL and 5PL models. Nonparametricmethods used are neural networks, clustering meth-ods, data mining, ANFIS, and copula models. Datamining techniques can offer good results as the dataavailable from the wind farms is voluminous andfrequent updating of data is easier. ANN and ANFISmodels perform well for power prediction and onlinemonitoring applications. These curves derived fromactual data can help in minimizing power predictionerrors.
(v) The 4PL and data mining technique based modelsextracted from actual data of wind farms have beenanalyzed in the literature for their application inonline monitoring. It is indicated that the monitoringof the power curves can be used to detect anomaliesand statistical analysis of the outlier data can giveindications of the specific reason of anomaly. Appli-cation of 5PL model for online monitoring of curve isnot yet researched.
(vi) Thewind power output of a turbine can be affected byvarious faults/anomalies or underperformance of theturbine, such as blade faults and yaw and pitch systemfaults. Different types of faults affect the turbine sys-tem differently and cause the power curve to departfrom the expected value in a different way. Toolswhich can characterize and quantify these departurescan aid in early identification of faults. Likely linkbetween copula statistics and WT faults/anomaliesis indicated in the literature should be investigated.Further research should also focus on considering thejoint probability distribution of these variables.
(vii) Applications of advanced algorithms for developingimproved parametric and nonparametric methodsneed to be explored.
-
12 Journal of Energy
Table4:Summaryof
noteworthycontrib
utions.
Author
Mod
elsData
Evaluatio
nFeatures
ofapplications
(sug
geste
d/analysed/used)
Diafetal.[12]
Linear
Ratin
gsof
WT
(V𝑐,V𝑓,V𝑟,𝑃𝑟,etc.)
—(i)
Allarep
olyn
omialm
odels
(ii)D
ono
tfollowcurvatureo
fpow
ercurve
(iii)Ac
curacy
ispo
or(iv
)Mostly
appliedforp
ower
predictio
nforsizingof
windbasedsyste
ms
Diafetal.[25]
Quadratic
—Giorsetto
andUtsu
rogi[30]
Bino
mial
—Ch
edid
etal.[46
]Cu
bic
—
Powell[6]
Weibu
llbased
Ratin
gsof
WTand
𝑘—
(i)Re
quire
sshape
parameter
ofsite
(ii)A
ccuracydepend
sonwindregime
(iii)Ap
pliedforc
apacity
factor
evaluatio
n
Aietal.[59]
Manufacturer’s
curvefi
tting
(3bino
mialexpressions)
Manufacturer’s
curve
—(i)
Needs
manyexpressio
nsto
representthe
shapeo
fcurve
accurately
(ii)A
ppliedforsizingof
hybrid
windPV
syste
mDiafetal.[55]
Manufacturer’s
curveinterpo
latio
nby
cubic
splin
esManufacturer’s
curve
—
Katsigiannise
tal.[60]
Manufacturer’s
curvefi
tting
9th-orderp
olyn
omial
Manufacturer’s
curve
—(i)
Accurateforthe
particular
dataset
(ii)H
igh-orderp
olyn
omialsmay
notrepresent
thev
arianceo
fdata
(iii)Ap
pliedforsizingof
hybrid
wind,PV
,and
biod
ieselbased
syste
m
GottschalkandDun
n[58]
Linear,W
eibu
llbased,
cubics
plines,
manufacturer’s
curvefi
tting
V 𝑐,V𝑓,V𝑟,𝑃𝑟,and
manufacturer’s
curve
Visualcomparis
on,
%errorinenergy
prod
uctio
n
(i)Po
lyno
mialm
odels
(ii)F
ittingaccuracy
with
good
nessof
fitindicatorsisno
tevaluated
NandKishoreand
Fernandez[26]
Linear
segm
ented
Manufacturer’s
curve
—(i)
Bette
raccuracy
(ii)N
eeds
manyexpressio
ns
Liu[54]
New
nonlinearformula
Ratin
gsof
WT
Visual
comparis
on
(i)Con
sidersinfl
ectio
npo
into
ncurve
(ii)F
ollowsshape
ofcurvem
orea
ccurately
than
polyno
mialm
odels
(iii)Simplem
etho
d(iv
)App
liedfore
cono
micload
dispatch,reliabilityanalysis,
andmultip
leturbines
with
andwith
outcorrelation
Villanu
evaa
ndFeijó
o[33]
3PLand4P
Lcurve
Manufacturer’s
curve
MAE,
MAPE
,and
RMSE
(i)Parametersa
rederiv
eddirectly,
noneed
ofiterativ
eprocedu
re
Kusia
ketal.[1]
4PLcurve
Parameter
estim
ation:
Techniqu
e:leastsqu
ares
andMLM
Algorith
m:E
SAc
tualdataof
wind
farm
AE,
RE(i)
Leastsqu
areb
etterthanMLM
metho
d(ii)𝑘
-NNou
tperform
sother
nonp
aram
etric
mod
els(iii)MLP
bestaccuracy
(iv)R
esidualand
controlchartapproach
foro
nlinem
onito
ringispresented
(v)4
PLleastsqu
ares
and𝑘-N
Nmod
elsp
ropo
sedford
etectin
ganom
alies
Datam
ining:𝑘-N
N,M
LP,
rand
omforest,
M5P
tree,andbo
ostin
gtre
e
Kusia
ketal.[4]
4PLcurve
Parameter
estim
ation:
Techniqu
e:leastsqu
ares
Algorith
m:E
SDatam
ining:𝑘-N
N,M
LP,R
EPtre
e,M5P
tree,
andbaggingtre
e
Manufacturer’s
curve
Actualdataof
wind
farm
MAE,
AE,
RE,and
meanrelativ
eerror
(i)𝑘-N
Nou
tperform
sother
nonp
aram
etric
mod
els(ii)O
utlierfi
lterin
gby
resid
ualapp
roachandcontrolchart
(iii)Ap
plicationforp
ower
predictio
nandon
linem
onito
ringissuggested
Lietal.[17]
ANN(M
LP)
Actualdataof
wind
farm
MSE
(i)Be
tterthanthetraditio
nalm
odel
(ii)A
ppliedforp
ower
predictio
n
Lietal.[61]
Regressio
nANN(M
LP)
Actualdataof
wind
farm
RMSE
(i)Com
paris
onof
both
mod
els(ii)N
Nmod
elismorea
ccurate
(iii)Eff
ecto
fwinddirectionisconsidered
Pelletie
retal.[62]
ANN(m
ultistage
2-lay
erMLP
s)Ac
tualdataof
wind
farm
Visual
meanerror,MAE
(i)Com
paredwith
parametric
,non
parametric
,and
discretemod
els(ii)S
ixinpu
tsvaria
bles
considered
Üstü
ntaş
andŞahin[8]
Leastsqu
ares
fittin
g(2nd
-order
polyno
mial)
CCFL
Actualdataof
wind
farm
RMSE
(i)CC
FLmod
elismorea
ccuratethantheleastsquaresfi
tting
basedmod
el
-
Journal of Energy 13
Table4:Con
tinued.
Author
Mod
elsData
Evaluatio
nFeatures
ofapplications
(sug
geste
d/analysed/used)
Lydiae
tal.[24]
Parametric
mod
el:lin
earsegmented,4P
Land
5PL
Parameter
estim
ation:
Techniqu
e:leastsqu
ares
Algorith
ms:GA,E
P,PS
O,and
DE
Actualdataof
wind
farm
RMSE
,MAE
(i)5P
logisticmod
elwith
parameterse
stim
ated
usingDEisthem
ostaccuratea
mon
gparametric
mod
els
Non
parametric
mod
el:ANN,cluste
ring,
datamining(m
odeltre
es)
Actualdataof
wind
farm
RMSE
,MAE
(i)ANNmod
elisthem
ostaccuratea
mon
gthen
onparametric
mod
els
Lydiae
tal.[36]
5PL
Actualdataof
wind
farm
RMSE
,MAE
(i)Usedforw
indresource
assessment
Soho
nietal.[35]
4PLand5P
LAc
tualdataof
wind
farm
%errorinenergy
estim
ation
(i)Ap
pliedforw
indenergy
estim
ation
Schlechtingenetal.[2]
CCFL
ANN𝑘-N
NANFIS
Actualdataof
wind
farm
MAE,
RMSE
MAPE
,SD
(i)ANNandNNperfo
rmbest
(ii)𝑘
-NNworstperfo
rmance
(iii)Eff
ecto
fwinddirection,
temperature
considerationprod
uces
lesserrors
(iv)A
pplicationin
onlin
emon
itorin
g
Stephenetal.[10]
Cop
ulam
odel
Actualdataof
wind
farm
—(i)
Jointp
robabilitydistr
ibutionof
windspeedandpo
wer
isconsidered
(ii)A
pplications
forc
onditio
nmon
itorin
gares
uggeste
d
Gill
etal.[11]
Cop
ulam
odel
Actualdataof
wind
farm
𝑅,𝑅2,and
chi-squ
are
(i)Jointp
robabilitydistr
ibutionof
windspeedandpo
wer
isconsidered
(ii)A
pplications
forc
onditio
nmon
itorin
gares
uggeste
d
Zeng
andQiao[37]
Wavele
tSVM
forw
indspeedpredictio
n
Actualdataof
wind
farm
and
manufacturer’s
power
curve
MAE,
MAPE
,and
SD(i)
Outperfo
rmsthe
persistence
mod
elforsho
rt-te
rmpredictio
n(ii)A
ppliedforsho
rttim
epow
erpredictio
n
-
14 Journal of Energy
Table 5: Comparison of modelling methods.
Models Data requiredfor modelling Merits Demerits Applications
Polynomialmodels(linear,quadratic,binomial, cubic,and Weibullbased)
V𝑐, V𝑓, V𝑟, and 𝑃
𝑟
of turbine
(i) Simplicity(ii) Limited data required(iii) Parameter calculation is easy
(i) Do not follow curvature ofpower curve(ii) Accuracy is poor(iii) Sometimes more than oneexpression are used todescribe the shape of curve
Suitable for power predictionand energy estimation duringinitial resource assessmentand designing of small systems
Manufacturer’scurve fitting
Manufacturer’scurve (i) Need less data
(i) Requires manufacturer’spower curve data(ii) Fairly accurate(iii) Many expressions may berequired for accuraterepresentation of curve
Suitable for power predictionand energy estimation duringinitial resource assessmentand designing of small systems
Cubic splines Manufacturer’scurve (i) Exact fit(i) Variance of data is nottaken into account Power prediction
4PL model
Manufacturer’scurve, actualdata of windfarm
(i) Consider inflection point oncurve; hence shape of curve isrepresented more accurately thanthe earlier models(ii) One expression is required
(i) Asymmetry of curve notmodelled
Online monitoring;further research on powerprediction during design andpower forecasting applicationsis required
5PL model
Manufacturer’scurveactual data ofwind farm
(i) Consider inflection point oncurve and asymmetry of curve ismodelled more accurate than theearlier and 4PL models(ii) One expression is required
(i) Parameter estimation isdifficult
Further research on powerprediction during design andpower forecasting and onlinemonitoring applications isrequired
ANN Actual data ofwind farm(i) Found to be accurate than othermethods (i) Black box approach
Wind power assessment forsizing and power forecasting,and online monitoringapplications, suitable forgroup of turbines
Clustering Actual data ofwind farm(i) More accurate than theregression method
(i) Accuracy depends on thenumber of cluster centres
Wind power assessment forsizing and power forecasting,and online monitoringapplications, suitable forgroup of turbines
𝑘-NN Actual data ofwind farm(i) Performance variable in differentstudies
(i) Accuracy depends on valueof 𝑘(ii) Less training time asinstance based scheme
Wind power assessment forsizing and power forecasting,prediction, andonline monitoringapplications, suitable forgroup of turbines
Modeltrees(REP, M5P,and baggingtree)
Actual data ofwind farm (i) Fairly accurate
(i) Much research notavailable
Applicability in powerprediction andonline monitoring to beexplored
ANFIS Actual data ofwind farm
(i) Integrates best features of fuzzysystems and neural networks(ii) Accurate method(iii) Fewer parameters required intraining therefore faster trainingcompared to NN(iv) Tunable membership functions
(i) Computational complexity
Wind power assessment forsizing and power forecastingfor energy trading Onlinemonitoring applications,suitable for group of turbines
Copula model Actual data ofwind farm
(i) Considers joint probabilitydistribution of wind speed andpower(ii) Includes measures ofuncertainty in performanceestimates
(i) Needs advanced methodfor parameter estimation ofmarginals
Applications for conditionmonitoring to be investigated
-
Journal of Energy 15
WT power curve
Binning (IEC) method
Based on stochastic method Dynamic model
Deterministic/probabilistic method
Deterministic
Probabilistic
Parametric/nonparametric method
Parametric
Polynomial
Linear
Quadratic
Cubic
Weibull
Cubic splines
fitting
Exponential
Inflection point
considered
Double exponential
3PL, 4PL, and 5PL
Nonparametric
ANN
Clustering
ANFIS
Datamining
Copula
SVM, wavelet
Presumed shape based on manufacturers specifications
Manufacturers power curve data
Manufacturers curve/SCADA data of wind farm
SCADA data of wind farm
Manufacturer’s curve
Figure 3: Wind turbine power curve models.
(viii) Appropriate evaluation of the developed models isa very important requirement in modelling. Theright choice of an evaluation metric is importantand depends on the data and analysis requirements.Models developed in the literature have used differ-ent performance metrics. The reviewed articles donot highlight the reason of preferring a particularcriterion for evaluation. Different statistical measurescan have different interpretations and appropriateselection of error metrics is crucial for analysis ofthe models. Moreover these models will ultimately beused in wind energy applications; therefore it is notappropriate to judge their suitability on the basis ofgoodness of fit parameters alone, but it should alsobe examined how successfully these models can beemployed for the particular applications.
(ix) Power curves of wind turbines provided by themanufacturers are used for power prediction in mostof the wind energy applications. These curves are
developed under standard test conditions. The IEC61400-12-1 is the most accepted standard for powercurvemeasurement of single wind turbines.Thewindconditions at the practical sites can be different fromthose at the test site. IEC curve may not alwaysrepresent the wind conditions of other sites. Furtherresearch should focus on development of site specificpower curves.
(x) The discrete model prescribed in IEC 61400-12 issimple, but a large amount of data is required todevelop a reliable model.
(xi) The stochastic model that is proposed in some worksis independent of turbulence intensity but does notinclude the effect of other influencing parameters.
(xii) Future works should also include the effect of variousinfluencing parameters on the power curves.
-
16 Journal of Energy
9. Conclusions
Accurate modelling of WT power curves is crucial forsuccessful design and operation of any wind energy conver-sion system. This paper presented an overview of differentapproaches used for modelling of wind turbine power curve.There are several methods ofmodelling which have their ownadvantages and disadvantages. Polynomial approximationbased power curve models which have been used widely aresimple to use and can be utilized for predicting power duringinitial resource assessment and designing of small systems.The four- and five-parameter logistic function based powercurve models which consider the inflection point on thesecurves are promisingmethods which can help in reduction ofpower prediction errors and improved performance in onlinemonitoring of these curves. Alsomost of themodels in earlierworks are developed from manufacturers curves of windturbines. However, the manufacturer supplied curves areturbine specific and represent their behaviour under standardtest conditions. They can be applied for power predictionof single turbines and for sites with steady winds. Improvedmodels are required which can represent the conditions atlarge wind farms with a group of turbines installed and siteshaving complex terrains. Power curves derived from actualwind speed and output power data from wind farms can takeinto account various site specific factors resulting in bettermodels. A wind farm’s SCADA data is a valuable resourcewhich can be exploited for this purpose. Nonparametricmethods of power curve modelling used in the literatureinclude neural networks, clustering, datamining, ANFIS, andcopula models. The nonparametric methods are suitable forextracting models from large data. Moreover, these modelscan incorporate the effect of parameters other than windspeed on the power curves more easily than the parametricmodels. Literature survey reveals that ANN and ANFISnonparametric methods perform well among other modelsfor power prediction and online monitoring applications.Further research should focus on development of site specificpower curves. Future models should be able to minimize theprediction errors and should be suitable for online monitor-ing of turbines. Methods which can quantify the power curvedepartures from expected values for identification of turbinefaults should be explored. As the power output of wind tur-bines is strongly dependent onwind speed of a potential windfarm site, selection of appropriate wind speed model alongwith the power curve model is an important requirementfor accurate prediction of wind farm output. Different windspeed modelling techniques have also been reviewed brieflyin this paper. It can be concluded that selection of appropriatemodel, solution technique, and proper algorithms for aparticular application is important for efficient modellingand can contribute significantly to developing reliable andefficient wind energy based power system.
Nomenclature
𝑃: Power output of wind turbine (W)V: Wind speed (m/s)𝐴𝑤: Area swept by the rotor blades (m2)
𝜌: Air density (kg/m3)𝜆: Tip speed ratio𝛽: Pitch angle (degree)𝐶𝑝: Power coefficient of wind turbine
𝑘: Shape parameter Weibull PDF𝑐: Scale parameter Weibull PDFV𝑐: Cut-in wind speed of turbine (m/s)
V𝑟: Rated wind speed of turbine (m/s)
V𝑓: Cut-off (or furling) wind speed of turbine(m/s)
𝑃𝑟: Rated power of wind turbine (W)
𝜂𝑤: The efficiency of WTG and thecorresponding converter
𝜃: Vector parameter of parametric models.
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
References
[1] A. Kusiak, H. Zheng, and Z. Song, “On-line monitoring ofpower curves,” Renewable Energy, vol. 34, no. 6, pp. 1487–1493,2009.
[2] M. Schlechtingen, I. F. Santos, and S. Achiche, “Using data-mining approaches for wind turbine power curve monitoring:a comparative study,” IEEE Transactions on Sustainable Energy,vol. 4, no. 3, pp. 671–679, 2013.
[3] S. Mathew, Wind Energy-Fundamentals, Resource Analysis andEconomics, Springer, Berlin, Germany, 2006.
[4] A. Kusiak,H. Zheng, andZ. Song, “Models formonitoringwindfarmpower,”Renewable Energy, vol. 34, no. 3, pp. 583–590, 2009.
[5] F. A. L. Jowder, “Wind power analysis and site matching of windturbine generators in Kingdom of Bahrain,”Applied Energy, vol.86, no. 4, pp. 538–545, 2009.
[6] W. R. Powell, “An analytical expression for the average outputpower of a wind machine,” Solar Energy, vol. 26, no. 1, pp. 77–80, 1981.
[7] T.-P. Chang, F.-J. Liu, H.-H. Ko, S.-P. Cheng, L.-C. Sun, and S.-C. Kuo, “Comparative analysis on power curve models of windturbine generator in estimating capacity factor,” Energy, vol. 73,pp. 88–95, 2014.
[8] T. Üstüntaş and A. D. Şahin, “Wind turbine power curve esti-mation based on cluster center fuzzy logic modeling,” JournalofWind Engineering and Industrial Aerodynamics, vol. 96, no. 5,pp. 611–620, 2008.
[9] J.-Y. Park, J.-K. Lee, K.-Y. Oh, and J.-S. Lee, “Development of anovel power curve monitoring method for wind turbines andits field tests,” IEEE Transactions on Energy Conversion, vol. 29,no. 1, pp. 119–128, 2014.
[10] B. Stephen, S. J. Galloway, D. McMillan, D. C. Hill, and D. G.Infield, “A copula model of wind turbine performance,” IEEETransactions on Power Systems, vol. 26, no. 2, pp. 965–966, 2011.
-
Journal of Energy 17
[11] S. Gill, B. Stephen, and S. Galloway, “Wind turbine condi-tion assessment through power curve copula modeling,” IEEETransactions on Sustainable Energy, vol. 3, no. 1, pp. 94–101, 2012.
[12] S. Diaf, M. Belhamel, M. Haddadi, and A. Louche, “Technicaland economic assessment of hybrid photovoltaic/wind systemwith battery storage in Corsica island,”Energy Policy, vol. 36, no.2, pp. 743–754, 2008.
[13] L. Horváth, T. Panza, and N. Karadža, “The influence of highwind hysteresis effect on wind turbine power production atBura-dominated site,” in Proceedings of the European WindEnergy Conference and Exhibition (EWEC ’07), pp. 1017–1022,Milan, Italy, May 2007.
[14] T. Jin and Z. Tian, “Uncertainty analysis for wind energy pro-duction with dynamic power curves,” in Proceedings of the IEEE11th International Conference on Probabilistic Methods Appliedto Power Systems (PMAPS ’10), pp. 745–750, IEEE, Singapore,June 2010.
[15] J. R. McLean, “WP2.6-Equivalent wind power curves,” Tech.Rep. EIE/06/022/SI2.442659, 2008.
[16] E. Hedevang, “Wind turbine power curves incorporating tur-bulence intensity,”Wind Energy, vol. 17, no. 2, pp. 173–195, 2014.
[17] S. Li, D. C. Wunsch, E. A. O’Hair, and M. G. Giesselmann,“Using neural networks to estimate wind turbine power gen-eration,” IEEE Transactions on Energy Conversion, vol. 16, no. 3,pp. 276–282, 2001.
[18] Z. O. Olaofe and K. A. Folly, “Wind energy analysis basedon turbine and developed site power curves: a case-study ofDarling City,” Renewable Energy, vol. 53, pp. 306–318, 2013.
[19] International standard IEC 61400-12-1, Wind turbines- Powerperformance measurement of electricity producing wind tur-bines, 2005.
[20] H. Mellinghoff, Development of Power Curve MeasurementStandards, DEWEK2012: 11, DeutscheWindenergie-Konferenz,Bremen, Germany, 2012.
[21] S. A. Akdağ and A. Dinler, “A new method to estimate Weibullparameters for wind energy applications,” Energy Conversionand Management, vol. 50, no. 7, pp. 1761–1766, 2009.
[22] J. A. Carta, P. Ramı́rez, and S. Velázquez, “A review of windspeed probability distributions used in wind energy analysis.Case studies in the Canary Islands,” Renewable and SustainableEnergy Reviews, vol. 13, no. 5, pp. 933–955, 2009.
[23] V. Lo Brano, A. Orioli, G. Ciulla, and S. Culotta, “Quality ofwind speed fitting distributions for the urban area of Palermo,Italy,” Renewable Energy, vol. 36, no. 3, pp. 1026–1039, 2011.
[24] M. Lydia, A. I. Selvakumar, S. S. Kumar, and G. E. P. Kumar,“Advanced algorithms for wind turbine power curvemodeling,”IEEE Transactions on Sustainable Energy, vol. 4, no. 3, pp. 827–835, 2013.
[25] S. Diaf, G. Notton, M. Belhamel, M. Haddadi, and A. Louche,“Design and techno-economical optimization for hybrid PV/wind system under various meteorological conditions,” AppliedEnergy, vol. 85, no. 10, pp. 968–987, 2008.
[26] L. Nand Kishore and E. Fernandez, “Reliability well-beingassessment of PV-wind hybrid system using Monte Carlosimulation,” in Proceedings of the International Conference onEmerging Trends in Electrical and Computer Technology (ICE-TECT ’11), pp. 63–68, Tamil Nadu, India, March 2011.
[27] P. Milan, M. Wachter, and J. Peinke, “Stochastic modeling andperformancemonitoring ofwind farmpower production,” Jour-nal of Renewable and Sustainable Energy, vol. 6, no. 3, Article ID033119, 2014.
[28] E. Anahua, F. Böttcher, S. Barth, J. Peinke, and M. Lange,“Stochastic analysis of the power output for a wind turbine,”in Proceedings of the EuropeanWind Energy Conference (EWEC’04), London, UK, November 2004.
[29] E. Anahua, S. Barth, and J. Peinke, “Markovian power curves forwind turbines,”Wind Energy, vol. 11, no. 3, pp. 219–232, 2008.
[30] P. Giorsetto and K. F. Utsurogi, “Development of a new pro-cedure for reliability modeling of wind turbine generators,”IEEE Transactions on Power Apparatus and Systems, vol. 102, no.1, pp. 134–143, 1983.
[31] M. K. Deshmukh and S. S. Deshmukh, “Modeling of hybridrenewable energy systems,” Renewable and Sustainable EnergyReviews, vol. 12, no. 1, pp. 235–249, 2008.
[32] E. Sainz, A. Llombart, and J. J. Guerrero, “Robust filtering forthe characterization of wind turbines: improving its operationandmaintenance,” Energy Conversion andManagement, vol. 50,no. 9, pp. 2136–2147, 2009.
[33] D. Villanueva and A. E. Feijóo, “Reformulation of parameters ofthe logistic function applied to power curves of wind turbines,”Electric Power Systems Research, vol. 137, pp. 51–58, 2016.
[34] D. Rodbard, “Statistical quality control and routine data proc-essing for radioimmunoassays and immunoradiometric assays,”Clinical Chemistry, vol. 20, no. 10, pp. 1255–1270, 1974.
[35] V. Sohoni, S. C. Gupta, and R. K. Nema, “A comparative analysisof wind speed probability distributions for wind power assess-ment of four sites,” Turkish Journal of Electrical Engineering andComputer Sciences, 2016.
[36] M. Lydia, S. Suresh Kumar, A. Immanuel Selvakumar, and G.Edwin Prem Kumar, “Wind resource estimation using windspeed and power curve models,” Renewable Energy, vol. 83, pp.425–434, 2015.
[37] J. Zeng and W. Qiao, “Short-term wind power predictionusing a wavelet support vector machine,” IEEE Transactions onSustainable Energy, vol. 3, no. 2, pp. 255–264, 2012.
[38] Curve fitting toolbox, for use with MATLAB, User’s Guide,Version 1.The Mathworks, 2002.
[39] H.Yang, L. Lu, andW.Zhou, “Anovel optimization sizingmodelfor hybrid solar-wind power generation system,” Solar Energy,vol. 81, no. 1, pp. 76–84, 2007.
[40] L. Xu, X. Ruan, C. Mao, B. Zhang, and Y. Luo, “An improvedoptimal sizing method for wind-solar-battery hybrid powersystem,” IEEE Transactions on Sustainable Energy, vol. 4, no. 3,pp. 774–785, 2013.
[41] X. Liu andW. Xu, “Minimum emission dispatch constrained bystochastic wind power availability and cost,” IEEE Transactionson Power Systems, vol. 25, no. 3, pp. 1705–1713, 2010.
[42] Y. M. Atwa, E. F. El-Saadany, M. M. A. Salama, R. Seethapathy,M. Assam, and S. Conti, “Adequacy evaluation of distributionsystem including wind/solar DG during different modes ofoperation,” IEEE Transactions on Power Systems, vol. 26, no. 4,pp. 1945–1952, 2011.
[43] R. Karki, P. Hu, and R. Billinton, “Reliability evaluation consid-ering wind and hydro power coordination,” IEEE Transactionson Power Systems, vol. 25, no. 2, pp. 685–693, 2010.
[44] P.Wang, Z. Gao, and L. Bertling, “Operational adequacy studiesof power systems with wind farms and energy storages,” IEEETransactions on Power Systems, vol. 27, no. 4, pp. 2377–2384,2012.
[45] L. Lu, H. Yang, and J. Burnett, “Investigation on wind powerpotential onHongKong islands—an analysis ofwind power andwind turbine characteristics,” Renewable Energy, vol. 27, no. 1,pp. 1–12, 2002.
-
18 Journal of Energy
[46] R. Chedid, H. Akiki, and S. Rahman, “A decision supporttechnique for the design of hybrid solar-wind power systems,”IEEE Transactions on Energy Conversion, vol. 13, no. 1, pp. 76–83, 1998.
[47] L. Wang and C. Singh, “Adequacy-based design of a hybridgenerating system including intermittent sources using con-strained particle swarm optimization,” IEEE Transactions onPower Systems, vol. 27, no. 4, pp. 2377–2383, 2007.
[48] A. K. Kaviani, G. H. Riahy, and S.M. Kouhsari, “Optimal designof a reliable hydrogen-based stand-alone wind/PV generatingsystem, considering component outages,” Renewable Energy,vol. 34, no. 11, pp. 2380–2390, 2009.
[49] B. S. Borowy and Z. M. Salameh, “Optimum photovoltaic arraysize for a hybrid wind/PV system,” IEEE Transactions on EnergyConversion, vol. 9, no. 3, pp. 482–488, 1994.
[50] B. S. Borowy and Z. M. Salameh, “Methodology for optimallysizing the combination of a battery bank and PV array in awind/PV hybrid system,” IEEE Transactions on Energy Conver-sion, vol. 11, no. 2, pp. 367–375, 1996.
[51] M. G. Khalfallah and A. M. Koliub, “Suggestions for improvingwind turbines power curves,”Desalination, vol. 209, no. 1–3, pp.221–229, 2007.
[52] C. Carrilo, A. F. O. Montaño, J. Cidras, and D. Dorado, “Reviewof power curve modelling for wind turbines,” Renewable andSustainable Energy Reviews, vol. 21, pp. 572–581, 2013.
[53] S. Shokrzadeh, M. Jafari Jozani, and E. Bibeau, “Wind turbinepower curve modeling using advanced parametric and non-parametric methods,” IEEE Transactions on Sustainable Energy,vol. 5, no. 4, pp. 1262–1269, 2014.
[54] X. Liu, “An improved interpolation method for wind powercurves,” IEEE Transactions on Sustainable Energy, vol. 3, no. 3,pp. 528–534, 2012.
[55] S. Diaf, D. Diaf, M. Belhamel, M. Haddadi, and A. Louche,“A methodology for optimal sizing of autonomous hybridPV/wind system,” Energy Policy, vol. 35, no. 11, pp. 5708–5718,2007.
[56] F. O. Hocaoğlu, Ö. N. Gerek, and M. Kurban, “A novel hybrid(wind-photovoltaic) system sizing procedure,” Solar Energy, vol.83, no. 11, pp. 2019–2028, 2009.
[57] V. Thapar, G. Agnihotri, and V. K. Sethi, “Critical analysisof methods for mathematical modelling of wind turbines,”Renewable Energy, vol. 36, no. 11, pp. 3166–3177, 2011.
[58] P. G. Gottschalk and J. R. Dunn, “The five-parameter logistic:a characterization and comparison with the four-parameterlogistic,”Analytical Biochemistry, vol. 343, no. 1, pp. 54–65, 2005.
[59] B. Ai, H. Yang, H. Shen, and X. Liao, “Computer-aided designof PV/wind hybrid system,” Renewable Energy, vol. 28, no. 10,pp. 1491–1512, 2003.
[60] Y. A. Katsigiannis, P. S. Georgilakis, and E. S. Karapidakis,“Hybrid simulated annealing-tabu search method for optimalsizing of autonomous power systems with renewables,” IEEETransactions on Sustainable Energy, vol. 3, no. 3, pp. 330–338,2012.
[61] S. Li, D. C. Wunsch, E. O’Hair, and M. G. Giesselmann, “Com-parative analysis of regression and artificial neural networkmodels for wind turbine power curve estimation,” Journal ofSolar Energy Engineering, vol. 123, no. 4, pp. 327–332, 2001.
[62] F. Pelletier, C. Masson, and A. Tahan, “Wind turbine powercurve modelling using artificial neural network,” RenewableEnergy, vol. 89, pp. 207–214, 2016.
[63] M. Schlechtingen and I. Ferreira Santos, “Comparative analysisof neural network and regression based condition monitoringapproaches for wind turbine fault detection,” Mechanical Sys-tems and Signal Processing, vol. 25, no. 5, pp. 1849–1875, 2011.
[64] Y. Wang, D. G. Infield, B. Stephen, and S. J. Galloway, “Copula-based model for wind turbine power curve outlier rejection,”Wind Energy, vol. 17, no. 11, pp. 1677–1688, 2014.
[65] L. Zheng, W. Hu, and Y. Min, “Raw wind data preprocessing:a data-mining approach,” IEEE Transactions on SustainableEnergy, vol. 6, no. 1, pp. 11–19, 2015.
[66] National Renewable Energy Laboratory (NREL) western dataset, station ID 2 dataset year 2006, http://wind.nrel.gov/Web nrel/.
[67] S. R. Jang, C.-T. Sun, and E. Mizutani, Neuro-Fuzzy and SoftComputing-a Comp