Delay-dependent stability of pitch control system in a large wind turbine plant

Abstract

The use of hydraulic pressure drive unit as actuator element in the pitch control scheme of a large wind turbine plant introduces inevitable time-delay in the feedback loop. This delay has an adverse impact on the performance and stability of the closed-loop system; nevertheless, if the delay magnitude exceeds a critical margin, the closed-loop system is driven to instability. In a large wind turbine plant, owing to its massive tower structure and enormous blade span, unstable, or for that matter, even marginally stable operation is highly detrimental. If the unboundedly evolving or sustained oscillations in pitch angle, signifying unstable or marginally stable operation respectively, are not curtailed using efficient braking systems, it might lead to the loss of whole structure. Hence, in this paper, the problem of delay-dependent stability of time-delayed pitch control system of a large wind turbine plant has been addressed using the classical Lyapunov-Krasovskii functional approach combined with Wirtinger inequality. The derived stability criterion which is in LMI framework, is tested on a benchmark wind turbine plant. In the sequel, simulation results are also provided to validate the effectiveness of the presented analytical results.