Modal Frequency and Damping Evaluation of Grid Connected VSCs in Sub-Synchronous Range Based on Motion Equation Method

With the increasing use of voltage source converters (VSCs), a new type of sub-synchronous oscillation problems related with VSCs have occurred when connected to weak ac grid. Several studies have tried to analyze these oscillation problems, but most used the impedance method from the circuit equivalent perspective. Actually, the circuit equivalent and mechanical equivalent can be transformed each other. To understand the sub-synchronous oscillation problems related with VSCs from the perspective of mechanical equivalent, this paper reveals that the dynamical interaction between VSC's DC-link voltage control loop and phase-locked loop (PLL) is similar to the mass interaction in SG's two-mass shaft model based on the motion equation method, and proposes a quantitative method to evaluate VSC's modal characteristics in sub-synchronous range. Results are all verified in MATLAB/Simulink. In addition to the impedance method, this paper provides another perspective to understand the sub-synchronous oscillation problems related with VSCs.