Lyapunov-Based Robust Stability of Converter-Interfaced Wind Turbines for Inertial Frequency Support

Converter-interfaced wind turbines (WTs) can contribute to inertial frequency regulation through appropriate control of the converter interface. The kinetic energy (KE) of the WT rotor blades is the transient power reserve for inertial frequency support. This work demonstrates that the partial loss of power extracted from the wind when the WT decelerates to release its KE into the network restricts the maximum deviation of the WT rotational speed from the Maximum Power Point (MPP). For higher amount of transient deviation from the MPP, the WT is found to be susceptible to instability. These insights are drawn from Lyapunov's theory for the robust stability of non-linear dynamic systems, applied to the converter-interfaced WT system. The state-space equations governing the operation of the system around the MPP, and modeling of the wind power output are presented. Further, this work quantifies the stability-constrained maximum allowable deviation from the MPP speed, and presents a formulation using Lyapunov's methods to compute this quantity. The robust stability limit provides insights for designing the inertial frequency support contribution of the WT. For this, a control method that uses a virtual synchronous generator (VSG) control loop in the converter interface is presented.