Wind energy is central to many international climate goals which promote the transition to carbon-free energy sources. Most commercial wind turbines at present are horizontal axis wind turbines (HAWTs). However, vertical axis wind turbines (VAWTs) can fill two gaps in wind energy: offshore floating wind energy and urban wind energy, in part due to their insensitivity to the incoming wind direction, low center of gravity, high power density, and low noise production. Historically, VAWTs have suffered from fatigue issues, low power efficiency, and difficulty in self-starting. Active variable blade pitch control can address these issues. It can be used to maximize the power efficiency, minimize blade load fluctuations to alleviate fatigue, and minimize torque fluctuations. Numerous studies on VAWT blade pitching have been done in the past, both numerical and experimental, and both with fixed and variable blade pitch. Numerical studies use models with varying accuracy. If pitch optimization is conducted, the most common objective is maximizing the power coefficient, C_p. However, blade pitch control can also be used to improve the loading characteristics on a VAWT.

In this study, individual active variable blade pitch control optimization is performed with multiple objectives, recognizing that there are multiple uses of pitch control for VAWTs. The goal of this study is to develop an optimal pitch function(s) that maximizes C_p and minimizes the fluctuations in rotor normal force and torque. The pitch angle is implemented as a third-order sinusoidal function. This is a numerical study, which uses the two-dimensional actuator cylinder (2D AC) model. The unified non-dominated sorting genetic algorithm III (U-NSGA-III) is used to perform pitch function optimization. The multiple objectives are 1) maximize C_p, 2) minimize rotor normal load fluctuations, and 3) minimize rotor torque fluctuations. The objectives are built up in successive optimization cases resulting in three optimization problems, a single-, two-, and three-objective optimization problem, respectively. Solutions are found which achieve all three objectives at the same time. Adding the second and third objectives changes the optimal solutions, and the multiple objectives are important to consider because only maximizing C_p leads to an increase in unfavorable normal load and torque fluctuations.

When only maximizing C_p is considered, the power coefficient can be increased by 17.3% over the base case (with zero pitch). The power coefficient can be increased by 10.3% over the base case without increasing the normal load fluctuations or the torque fluctuations. The normal load fluctuations can be reduced by 22.1% compared to the base case while maintaining the power coefficient and torque fluctuations. The torque fluctuations can be reduced by 13.9% compared to the base case while maintaining the power coefficient and normal load fluctuations. The optimal pitch functions which maximize C_p and/or minimize the torque fluctuations require high variations in the pitch angle throughout the rotor revolution. Meanwhile, optimal pitch functions which minimize the normal load fluctuations require fewer oscillations (they resemble more first-order sinusoids). For the majority, the optimal pitch functions pitch the blade outward in the upwind half and inward in the downwind half of the revolution, though adjusting the pitch angle around the transitions between the upwind and downwind halves can increase the power coefficient. Optimal pitch functions which minimize the normal load fluctuations reduce the angle of attack and loads throughout most of the revolution and shift the loading on the rotor toward the downwind half as compared to the upwind half. Minimizing the torque fluctuations requires pitch functions with relatively large amplitudes. The pitch functions spread out the blade loading and power generation across the revolution by reducing the loads and power generation in the middle of the upwind and downwind regions and increasing them around the transitions between the upwind and downwind regions. In some cases, the optimal pitch functions are transferable to other operating conditions and turbine designs. They can lead to an increase in C_p for a certain range of tip speed ratios, however, the optimal pitch functions depend on the tip speed ratio. The optimal pitch functions and their effectiveness are similar when the turbine has three compared to two blades. Implementing an optimal pitch function found in this study can increase the power output of VAWTs while not compromising their structural integrity and/or alleviate fatiguing load fluctuations while maintaining the power output. Optimal blade pitching can lead to a significant improvement in the operating performance of VAWTs.