Concept of Modal Repulsion for Examining the Sub-Synchronous Oscillations in Power Systems

This paper investigates the modal repulsion happened in the sub-synchronous resonance between a synchronous generator and series-compensated transmission line. The investigation is based on the closed-loop model of the series-compensated power system consisted of the torsional and electrical open-loop subsystems. Analytical explanation is presented to show how the SSO modal repulsion is formed as the result of moving close and apart between two open-loop SSO modes. Analysis is carried out to indicate that the peak of the SSO modal repulsion occurs when the two open-loop SSO modes from the torsional and electrical subsystem are closest to each other on the complex plane, which is referred to as the open-loop modal coupling. Estimation on the peak, i.e., the maximum damping degradation of the SSO modes, is derived in the paper. Subsequently, a method of open-loop modal analysis is proposed. Applications of the proposed method of open-loop modal analysis to study the SSOs caused by the DFIGs under the condition of the modal repulsion in the power system are demonstrated and evaluated by example power systems. The concept of modal repulsion explains why the grid connection of the DFIGs may bring about the SSO instability risk in the power system.