Concept of Modal Repulsion for Examining the Subsynchronous Oscillations Caused by Wind Farms in Power Systems

This paper investigates the torsional subsynchronous oscillations (SSOs) of synchronous generators caused by the grid-connected wind farms. The investigation does not rely on the representation of a wind farm by an aggregated wind generator and is based on a multi-input and multi-output closed-loop model. The model is comprised of the wind farm subsystem, which includes all the wind farms, and the subsystem of rest of power system (ROPS). Theoretical analysis proves that the open-loop SSO modal coupling of wind farm subsystem and ROPS subsystem results in the closed-loop SSO modal repulsion on the complex plane. Subsequently, damping of torsional SSOs decreases and growing SSOs may occur when the closed-loop modal repulsion is strong. Hence, closed-loop modal repulsion explains and reveals the mechanism about why the wind farms may cause the torsional SSOs in the power system. In addition, a method of open-loop modal analysis is proposed to detect the SSO instability risk brought about by the wind farms. The detection is based on the estimation of degree of closed-loop modal repulsion and only needs the modal information of open-loop subsystems. An example power system with wind farms is presented to demonstrate analysis and conclusions made in the paper.