Limitations of Small-Signal Modeling of Grid-Connected VSCs under Phase Jumps and Frequency Deviations

The stability of grid-connected voltage source converters (VSCs) is commonly studied by the small-signal model in the synchronous reference (dq) frame. With phase-locked loop dynamic from VSCs, it is inevitable to convert the small-signal model to a common dq frame. When linearizing the frame transformation, the trigonometric functions of the angle are approximated by first-order terms. In this letter, the limitation of such linearization on the dq-transformation is discussed. The accuracy of the model, in presence of phase jumps and frequency variations, are examined. It is found that even under small phase jumps, mismatches are found between the small-signal model (SSM) and a nonlinear model (NM). It is further revealed that during the dynamics of frequency variation, significant mismatches can occur between the SSM and the NM.