The increasing shortage of fossil fuels has urged the development of renewable energy. In recent decades, the technology of using wind energy resources has becoming mature, the most prominent of which are horizontal axis wind turbines (HAWTs). Compared with the HAWTs, vertical axis wind turbines (VAWTs) also possess great research significance and application market because of the lower cost and more stable structure. However, the relatively low power coefficient of VAWTs has long been the bottleneck for its further widespread use.

From the previous researches, the selection of figures will have a great influence on the efficiency of VAWTs. In this paper, a stochastic numerical optimization of the figure of a φ-shape Darrieus wind turbine is performed by using heuristical search algorithm. Firstly, the power coefficient of a Darrieus type VAWT with given shape parameters is quickly calculated by the program script that edited by python. The program adopted the "Double Multiple Stream Tube (DMST)" model, which is based on the "Blade Element Momentum" (BEM) theory with NACA0015 chosen as the type of the airfoil. Then, the Evolutionary Strategy (ES) as well as the Covariance Matrix Adaptation Evolutionary Strategies (CMA-ES) are chosen as the the methods for the optimization. R(radius), B(blade number) and β(radius/half-height) of the VAWT are shape variables to be investigated under certain inlet wind velocities and the objective function is the result from the DMST script.

The result shows that, the CMA-ES not only can present an evolutionary model with a 16.9% higher power coefficient, but also cut computational expenses comparing to the general ES method with a higher accuracy at the same time. Combined with the DMST, this algorithm may provide a quick and reliable reference for the preliminary design of a VAWT under a certain wind environment.


Both environmental friendliness and economic feasibility make wind energy a valuable renewable energy. Therefore, the utilization of wind power is one of the most promising technologies. Among them, the wind turbine is regarded as a typical representative to capture wind sources, which has rapidly matured and sophisticated (Leith et al., 1996; Tapia et al., 2003; Spera, 1994).

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