Validation of various windmill brake state models used by blade element momentum calculation P. Pratumnopharat * , P.S. Leung Mechanical Engineering Division, School of Computing, Engineering and Information Sciences, Northumbria University, Ellison Place, Newcastle upon Tyne, NE1 8ST, UK article info Article history: Received 18 October 2010 Accepted 23 March 2011 Available online 5 May 2011 Keywords: Blade element momentum theory Windmill brake state model Tip loss model Wind turbine performance Axial induction factor abstract The concept of windmill brake state model is considered in this paper. Blade Element Momentum (BEM) calculation often calculates the value of thrust coefficient in windmill brake state. Unfortunately, thrust coefficient predicted by momentum theory deviated dramatically from the experimental data when the value of axial induction factor is greater than 0.5. To solve this problem and to increase the accuracy of the prediction, windmill break state model including tip loss effect must be applied to equations of thrust coefficient. The problem of interest is that which windmill break state model is suitable for the wind turbine model being simulated. The purpose of this paper is to compare the rotor power predicted by six different windmill brake state models. The aerodynamic code based on BEM theory has been imple- mented in Matlab and validated with the simulated result of AWT-27 wind turbine model reported by National Renewable Energy Laboratory (NREL). Six windmill brake state models to be compared are Glauert’s characteristic equation, classical brake state model, advanced brake state model, Wilson and Walker model, modified advanced brake state model, and Shen’s correction. The predicted power curves obtained from each windmill brake state model are compared to the measured power curve of AWT-27/ P4. It has been shown that Shen’s correction gives the highest correlation to the measured data with r-square of 0.970 and the predicted annual energy production (AEP) is different from measured data by only 6.3%. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction In predicting performance of wind turbines, the Blade Element Momentum (BEM) theory is still commonly used by wind turbine designers and researchers. The BEM theory has significant advantages in computational speed [1,2] and ease of implementation. Histori- cally, Glauert [3] originated the basic concepts of aerodynamic anal- ysis of airscrew propellers and windmills. In 1974, Wilson et al. [4,5] extended Glauert’s work for application to wind turbines and pre- sented a step-by-step procedure for calculating performance char- acteristics of wind turbines. The accuracy of the BEM codes is dependent on two-dimensional wind tunnel test which is normally known to over-predict thrust and under-predict peak torque [6,7]. In addition, the BEM theory does not include the effects of three- dimensional flow velocities due to the rotation of the blade [7,8]. In recent years, researchers have optimized and modified the BEM calculation to provide more accurate results. Several strategies in solving the non-linear equations, e.g. iterative techniques of the induction factors and convergence rate accelerator of the induction loop [9], are proposed. There are many corrections proposed to increase the precision of prediction. Windmill brake state model is the one to be considered because the BEM calculation often calculates the value of thrust coefficient in this state of operation. Referring to Stoddard’s work in 1977 [10], the behaviour of wind turbine rotors were correlated with known experimental data for helicopters reported by Glauert in 1926 [11]. Stoddard’s work showed that thrust coefficient predicted by momentum theory deviated dramatically from the Glauert’s experimental data (without tip loss effect) when the value of axial induction factor is greater than 0.5. To solve this problem and to increase the accuracy of the prediction, several researchers applied tip loss effect to the thrust coefficient equation and then proposed windmill break state models. The problem of interest is that which windmill break state model is suitable for the wind turbine model being simulated. The objective of this article is to compare the wind turbine power curves predicted by BEM theory with six different windmill brake state models listed in Table 1 . Also, the predicted results are compared with the existing measured power curve of AWT-27/P4 wind turbine [12]. To achieve this objective, the authors imple- ment the aerodynamic code based on BEM theory in Matlab and validate the code with the existing WT_Perf code [13]. * Corresponding author. E-mail address: panu.pratumnopharat@northumbria.ac.uk (P. Pratumnopharat). Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene 0960-1481/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2011.03.027 Renewable Energy 36 (2011) 3222e3227