An important aspect to be taken into account regarding functions to model WT power curves is the number of parameters. This number can rise up to six in the case of logistic functions.
However, when dealing with fewer than three, the adaptability of the function to model the WT power curve is almost null. Therefore, the number of parameters considered in this survey ranges from three to six. i.
e. 3PL, 4PL, 5PL and 6PL.The parameters of the logistic function have been estimated using genetic algorithms (GA), evolutionary programming (EP), particle swarm optimization (PSO) and differential evolution (DE) 13.
The objective of all these methods is to minimize the difference between the estimated and actual power. Objective Function = Where Pe(Yi) is the power estimated by the logistic expressions, Pa(i) is actual power.B. Four parameter Logistic RegressionThe focus is to find a logistic function with the minimum number of parameters and the best performance when modeling WT power curves.
So, generally 4PL and 5PL is used. The equation of 4PL is: 11 The vector parameters of the logistic function, a, m, n and ? determine its shape.Power curve models developed based on these showed more accuracy than several non-parametric techniques like neural networks etc.
C. Five parameter Logistic RegressionThe five parameter logistic function was originally used in biological applications and was first applied in wind turbine power curve modeling in 15. The equation of 5PL is: 13 Where a is the minimum asymptote, b is steepness of the curve, c is the inflection point of the curve, and d is the maximum asymptote g is the asymmetry factor .However, a 4PL curve is symmetric about the inflection point whereas, the power curves are asymmetric. Models which can incorporate this asymmetry can therefore produce even better results. In this paper, first the wind speed is predicted using various statistical models and after that the power curve is fitted using the predicted value from the model with minimum error.