World wind energy output is steadily increasing in both production scale and capacity of harvesting wind. Hydrostatic transmission systems (HTSs) have been used mostly in offshore wind turbine applications. However, their potential has not been fully utilized in onshore wind turbines, partially due to concerns related to hydraulic losses. In our prior work, it was shown that the annual energy production from a hydrostatic wind turbine can match or exceed that of a mechanical drive wind turbine with appropriate optimal control techniques. In this paper, we present an optimal control technique that can further improve energy production of a hydrostatic wind turbine, particularly in low speed regions. Here, the overall loss equation of the HTS is developed and used as a cost function to be minimized with respect to system model dynamics. The overall loss function includes the losses due to both the aerodynamic efficiencies and the hydrostatic efficiencies of the motor and pump. A nonlinear model of HST is considered for the drive train. Optimal control law was derived by minimizing the overall loss. Both unconstrained and constrained optimization using Pontryagin’s minimum principle were utilized to derive two distinct control laws for the motor displacement. Simulation results showed that both the controllers were able to increase power output with the unconstrained optimization offering better results for the HTS wind turbine in the low speed regions (3 m/s–8 m/s).
Optimal Control of Wind Turbines under Islanded Operation