Metamodel based optimization for dynamic blade pitch control on a vertical axis wind turbine using analytical and CFD methods

In this study, the blade pitching motion on a representative (12 kW) vertical axis wind turbine (VAWT) is optimized over a wide range of operating conditions. The pitching is referred to as active blade pitching (ABP) when it is not constrained by a predetermined motion, while the operating condition is referred to as the tip speed ratio (TSR). Computational fluid dynamics (CFD) simulations are used to estimate the instantaneous torque produced by the VAWT blades. The torque is considered the system output and is dependent on the ABP which serves as the system input. This work initially used a preliminary ABP derived using an analytic model; the VAWT was then simulated at a TSR of 2.3 with fixed blades using an analytic-ABP strategy. The simulation with the analytic-ABP generated a 33.4% increase in torque output compared to the fixed pitch strategy simulation. The analytic-ABP curve was then approximated by a function of two variables, via parameterization of the ABP. The parameters of this ABP are the optimization variables of a response surface methodology (RSM) optimization, the objective function being the CFD “black-box” simulation and the output variable being the average torque of a blade. The optimization used a three-level full factorial design (FFD) as the design of experiment (DOE) strategy in order to sample the function with an initial set of points, generate a metamodel, and search for the optimum. The ABP derived from this method, termed the FFD-ABP, was simulated; the results show that it increased the torque output by 15.5% relative to the previous analytic-ABP. A new optimization procedure is proposed in this work. It starts from the simulation results of the analytic-ABP as well as +2° and −2° offset perturbations. The optimization procedure generates an optimal ABP using a modified quadratic regression metamodel over a discretized domain; the metamodel is updated with the response of the first optimal-ABP to generate a second optimal-ABP. The procedure is repeated until the ABP converges into a narrow band. The optimal-ABP simulations resulted in a 6.5% increase in torque output with fewer function calls compared to the previous FFD-ABP. The optimization procedure was extended to several TSRs and the data used to develop a governing function and power performance charts. The governing function was based on a novel nonlinear curve fit model and it estimated the pitch based on the TSR and azimuthal angle. The maximum power operation point is increased by 13% and the torque performance at low TSR is improved.