Analysis, Simulation, and Experiments of Dynamics and Control of a Hydrostatic Wind Turbine Under Partial Load¹

$Kω2$ control, also called torque control, is a popular method for maximizing wind turbine power. For hydrostatic wind turbines, torque control becomes pressure control with p_c = K′ω² because pressure is proportional to torque. Inverse Kω² control is an alternative approach using rotor speed control with ω_c = (p/K′)^1/2. This work analyzes the dynamics of hydrostatic wind turbines using forward and inverse Kω² control with P-, proportional derivative, proportional integral, and proportional integral derivative-control for feedback. Dimensionless, linearized models are used. Analysis shows that the mechanical rotor dynamics are much slower than the hydrostatic transmission dynamics and that frictional and leakage losses are negligible. Linear perturbation of the nonlinear model reveals that the closed-loop control is not in Evan's form so that closed-loop poles and zeros both vary with the loop gain. Pole and zero root locus analysis shows how systems responses change with controller gains. Both control approaches require derivative controller action to sufficiently dampen their responses; both are also fundamentally limited in speed of response by a slow stable pole regardless of controller loop gains. Nonlinear system simulation shows that both control approaches track the maximum power point with nearly identical transient behavior and have nearly identical power losses when using suboptimal values of the control law gain, $K$⁠. Pressure control has a gain margin of infinity and a phase margin of 99.3 deg, while speed control has a gain margin of 22.4 dB and a phase margin of 73.8 deg showing that pressure control is more robust than speed control. Experiments using the power regenerative hydrostatic test stand at the University of Minnesota show that the control approaches have different transient responses but capture comparable power under steady and turbulent conditions.