The wind turbine power curve shows the relationship between the wind turbine power and hub height wind speed. It essentially captures the wind turbine performance. Hence it plays an important role in condition monitoring and control of wind turbines. Power curves made available by the manufacturers help in estimating the wind energy potential in a candidate site. Accurate models of power curve serve as an important tool in wind power forecasting and aid in wind farm expansion. This paper presents an exhaustive overview on the need for modeling of wind turbine power curves and the different methodologies employed for the same. It also reviews in detail the parametric and non-parametric modeling techniques and critically evaluates them. The areas of further research have also been presented.

A comprehensive review on wind turbine power curve modeling techniques

Wind power is the most reliable and developed renewable energy source over past decades. With the rapid penetration of the wind generators in the power system grid, it is very essential to utilize the maximum available power from the wind and to operate the wind turbine (WT) at its maximal energy conversion output. For this, the wind energy conversion system (WECS) has to track or operate at the maximum power point (MPP). A decent variety of publication report on various maximum power point tracking (MPPT) algorithms for a WECS. However, making a choice on an exact MPPT algorithm for a particular case require sufficient proficiency because each algorithm has its own merits and demerits. For this reason, an appropriate review of those algorithms is essential. However, only a few attempts have been made in this concern. In this paper, different available MPPT algorithms are described for extracting maximum power which are classified according to the power measurement i.e. direct or indirect power controller. Merits, demerits and comprehensive comparison of the different MPPT algorithms also highlighted in the terms of complexity, wind speed requirement, prior training, speed responses, etc. and also the ability to acquire the maximal energy output. This paper serves as a proper reference for future MPPT users in selecting appropriate MPPT algorithm for their requirement.

A review of conventional and advanced MPPT algorithms for wind energy systems

Currently, variable speed wind turbine generators (VSWTs) are the type of wind turbines most widely installed. For wind energy studies, they are usually modelled by means the approximation of the manufacturer power curve using a generic equation. In literature, several expressions to do this approximation can be found; nevertheless, there is not much information about which is the most appropriate to represent the energy produced by a VSWT. For this reason, in this paper, it is carried out a review of the equations commonly used to represent the power curves of VSWTs: polynomial power curve, exponential power curve, cubic power curve and approximate cubic power curve. They have been compared to manufacturer power curves by using the coefficients of determination, as fitness indicators, and by using the estimation of energy production. Data gathered from nearly 200 commercial VSWTs, ranging from 225 to 7500 kW, has been used for this analysis. Results of the analysis presented in the paper show that exponential and cubic approximations give the higher R 2 values and the lower error in energy estimation. With the approximate cubic power curve quite high values of R 2 and low errors in energy estimation are achieved, which makes this kind of approximation very interesting due to its simplicity. Finally, the polynomial power curve shows the worst results mainly due to its sensitivity to the data given by the manufacturer.

Review of power curve modelling for wind turbines

A wind turbine power curve essentially captures the performance of the wind turbine. The power curve depicts the relationship between the wind speed and output power of the turbine. Modeling of wind turbine power curve aids in performance monitoring of the turbine and also in forecasting of power. This paper presents the development of parametric and nonparametric models of wind turbine power curves. Parametric models of the wind turbine power curve have been developed using four and five parameter logistic expressions. The parameters of these expressions have been solved using advanced algorithms like genetic algorithm (GA), evolutionary programming (EP), particle swarm optimization (PSO), and differential evolution (DE). Nonparametric models have been evolved using algorithms like neural networks, fuzzy c-means clustering, and data mining. The modeling of wind turbine power curve is done using five sets of data; one is a statistically generated set and the others are real-time data sets. The results obtained have been compared using suitable performance metrics and the best method for modeling of the power curve has been obtained.

Advanced Algorithms for Wind Turbine Power Curve Modeling

Wind turbine power curve modeling is an important tool in turbine performance monitoring and power forecasting. There are several statistical techniques to fit the empirical power curve of a wind turbine, which can be classified into parametric and nonparametric methods. In this paper, we study four of these methods to estimate the wind turbine power curve. Polynomial regression is studied as the benchmark parametric model, and issues associated with this technique are discussed. We then introduce the locally weighted polynomial regression method, and show its advantages over the polynomial regression. Also, the spline regression method is examined to achieve more flexibility for fitting the power curve. Finally, we develop a penalized spline regression model to address the issues of choosing the number and location of knots in the spline regression. The performance of the presented methods is evaluated using two simulated data sets as well as an actual operational power data of a wind farm in North America.

Wind Turbine Power Curve Modeling Using Advanced Parametric and Nonparametric Methods

Critical analysis of methods for mathematical modelling of wind turbines

The literature review reveals that though numerous models are available for estimating solar radiation; however, impact of these estimations on the energy yield of PV system and its economics has n...

A revisit to solar radiation estimations using sunshine duration: analysis of impact of these estimations on energy yield of a PV generating system

This paper discusses a method for estimating the hourly temperature at a location, if the ambient maximum and minimum temperatures of a particular day, along with the maximum temperature on the previous day and the minimum temperature of the following day, are known. The impact of estimated temperature on the energy yield of a photovoltaic (PV) module is also discussed with the help of a mathematical model. Algorithms have been developed for relevant computations and implemented using MATLAB. Hourly meteorological data of Bhopal and Trivandrum, India, have been considered for studying, analyzing, and validating the results. A PV module (BP 3215) manufactured by BP Solar Ltd. has been considered for analyzing the results in terms of energy generation. The statistical error parameters calculated for the estimated hourly temperature indicate a reasonable degree of accuracy of estimation. The values of mean absolute error (MAE) and root mean square error (RMSE) are superior to those of other models and that o...

Estimation of Hourly Temperature at a Site and its Impact on Energy Yield of a PV Module

* Professor, School of energy & environment management,UIT-RGPV, State Technological University of MP State, Bhopal ; e-mail : vksethi@rgtu.net Reader, Electrical & Electronics Engineering, UIT-RGPV, State Technological University of MP State, Bhopal ; csrajeshwari@ rediffmail.com *** Reader, Electrical & Electronics Engineering, UIT-RGPV,State Technological University of MP State, Bhopal ; vinaythapar@ rediffmail.com **** Associate Engineer, SECoE, Eaton Technologies Pvt. Ltd.,Pune, India ; navankurbeohar@gmail.com ** e-mail : e-mail : e-mail : Abstract

http://www.nitttrbpl.ac.in/journal/volume1/paper7.pdf

Vinay Thapar

Papers

Critical analysis of methods for mathematical modelling of wind turbines

A revisit to solar radiation estimations using sunshine duration: analysis of impact of these estimations on energy yield of a PV generating system

Estimation of Hourly Temperature at a Site and its Impact on Energy Yield of a PV Module

Evaluating effect of insolation on pv cell output using matlab/simulink

Impact of factors influencing the performance of hybrid energy system