A Critical Review on Wind Turbine Power Curve Modelling Techniques and Their Applications in Wind Based Energy Systems

Table 4

Summary of noteworthy contributions.

Author	Models	Data	Evaluation	Features of; applications (suggested/analysed/used)
Diaf et al. [12]	Linear	Ratings of WT; (, , , , etc.)	—	(i) All are polynomial models; (ii) Do not follow curvature of power curve; (iii) Accuracy is poor; (iv) Mostly applied for power prediction for sizing of wind based systems
Diaf et al. [25]	Quadratic		—
Giorsetto and Utsurogi [30]	Binomial		—
Chedid et al. [46]	Cubic		—
Powell [6]	Weibull based	Ratings of WT and	—	(i) Requires shape parameter of site; (ii) Accuracy depends on wind regime; (iii) Applied for capacity factor evaluation
Ai et al. [59]	Manufacturer’s curve fitting; (3 binomial expressions)	Manufacturer’s curve	—	(i) Needs many expressions to represent the shape of curve accurately; (ii) Applied for sizing of hybrid wind PV system
Diaf et al. [55]	Manufacturer’s curve interpolation by cubic splines	Manufacturer’s curve	—
Katsigiannis et al. [60]	Manufacturer’s curve fitting; 9th-order polynomial	Manufacturer’s curve	—	(i) Accurate for the particular data set; (ii) High-order polynomials may not represent the variance of data; (iii) Applied for sizing of hybrid wind, PV, and biodiesel based system
Gottschalk and Dunn [58]	Linear, Weibull based,; cubic splines,; manufacturer’s curve fitting	, , , , and manufacturer’s curve	Visual comparison,; % error in energy production	(i) Polynomial models; (ii) Fitting accuracy with goodness of fit indicators is not evaluated
Nand Kishoreand Fernandez [26]	Linear segmented	Manufacturer’s curve	—	(i) Better accuracy; (ii) Needs many expressions
Liu [54]	New nonlinear formula	Ratings of WT	Visual; comparison	(i) Considers inflection point on curve; (ii) Follows shape of curve more accurately than polynomial models; (iii) Simple method; (iv) Applied for economic load dispatch, reliability analysis, and multiple turbines with and without correlation
Villanueva and Feijóo [33]	3PL and 4PL curve	Manufacturer’s curve	MAE, MAPE, and RMSE	(i) Parameters are derived directly, no need of iterative procedure
Kusiak et al. [1]	4PL curve; Parameter estimation: Technique: least squares and MLM; Algorithm: ES	Actual data of wind farm	AE, RE	(i) Least square better than MLM method; (ii) -NN outperforms other nonparametric models; (iii) MLP best accuracy; (iv) Residual and control chart approach for online monitoring is presented; (v) 4PL least squares and -NN models proposed for detecting anomalies
	Data mining: -NN, MLP,; random forest, M5P tree, and boosting; tree
Kusiak et al. [4]	4PL curve; Parameter estimation: Technique: least squares; Algorithm: ES; Data mining: -NN, MLP, REP tree, M5P tree, and bagging tree	Manufacturer’s curve; Actual data of wind farm	MAE, AE, RE, and mean relative error	(i) -NN outperforms other nonparametric models; (ii) Outlier filtering by residual approach and control chart; (iii) Application for power prediction and online monitoring is suggested
Li et al. [17]	ANN (MLP)	Actual data of wind farm	MSE	(i) Better than the traditional model; (ii) Applied for power prediction
Li et al. [61]	Regression; ANN (MLP)	Actual data of wind farm	RMSE	(i) Comparison of both models; (ii) NN model is more accurate; (iii) Effect of wind direction is considered
Pelletier et al. [62]	ANN (multistage 2-layer MLPs)	Actual data of wind farm	Visual; mean error, MAE	(i) Compared with parametric, nonparametric, and discrete models; (ii) Six inputs variables considered
Üstüntaş and Şahin [8]	Least squares fitting (2nd-order polynomial); CCFL	Actual data of wind farm	RMSE	(i) CCFL model is more accurate than the least squares fitting based model
Lydia et al. [24]	Parametric model: linear segmented, 4PL and 5PL; Parameter estimation: Technique: least squares; Algorithms: GA, EP, PSO, and DE	Actual data of wind farm	RMSE, MAE	(i) 5P logistic model with parameters estimated using DE is the most accurate among parametric models
	Nonparametric model: ANN, clustering,; data mining (model trees)	Actual data of wind farm	RMSE, MAE	(i) ANN model is the most accurate among the nonparametric models
Lydia et al. [36]	5PL	Actual data of wind farm	RMSE, MAE	(i) Used for wind resource assessment
Sohoni et al. [35]	4PL and 5PL	Actual data of wind farm	% error in energy estimation	(i) Applied for wind energy estimation
Schlechtingen et al. [2]	CCFL; ANN; -NN; ANFIS	Actual data of wind farm	MAE, RMSE; MAPE, SD	(i) ANN and NN perform best; (ii) -NN worst performance; (iii) Effect of wind direction, temperature consideration produces less errors; (iv) Application in online monitoring
Stephen et al. [10]	Copula model	Actual data of wind farm	—	(i) Joint probability distribution of wind speed and power is considered; (ii) Applications for condition monitoring are suggested
Gill et al. [11]	Copula model	Actual data of wind farm	, , and chi-square	(i) Joint probability distribution of wind speed and power is considered; (ii) Applications for condition monitoring are suggested
Zeng and Qiao [37]	Wavelet SVM for wind speed prediction	Actual data of wind farm and manufacturer’s power curve	MAE, MAPE, and SD	(i) Outperforms the persistence model for short-term prediction; (ii) Applied for short time power prediction