For conventional HAWT (horizontal axis wind turbines), the rotor speed is maintained constant while the blade tip speed changes continuously. This reduces considerably the power performance of the wind turbine particularly at high wind speeds where the tip speed ratio is small. With growth of variable speed generators, a compact BEM (blade element momentum) analysis is derived to design optimal blades for continuously variable speed HAWTs. First, a generalized quadratic equation on the angular induction factor is introduced which is related to local axial induction factor, blade local speed ratio, and drag to lift ratio. Second, the optimal blade geometry is obtained for which the maximum power coefficient is calculated at different design tip speed ratios and drag to lift ratios by assuming variable operational speed. Third, it is demonstrated that the power performance of the variable speed wind turbine is significantly higher than the conventional constant speed wind turbines. In addition, the present BEM modeling may be useful to reduce the computational effort of iterative numerical methods used in determining off-design power performance of conventional wind turbines with constant speed. (C) 2014 Elsevier Ltd. All rights reserved.