Abstract
Stability assessment and control design of future power electronic dominated grids require efficient and adequate modeling methods. This article deals with modeling and stability analysis of a three-phase grid following voltage-source converters (VSCs). First, a general complex domain model is presented for the VSC considering both balanced and unbalanced operation conditions. Then, a linear time-periodic (LTP) model for the small-signal stability analysis is derived based on the Wirtinger calculus. Next, the space transformation analysis (i.e., modal analysis) for the linear time-invariant (LTI) system is generalized to the LTP system. It is revealed that the frequency-coupling effects of power electronic systems result from the nonholomorphic control units and the periodic operation trajectory. Finally, generalized eigenvalue and transfer function analysis methods are adopted to evaluate how the interaction between the advanced phase-locked loop (PLL), the current controller, and the network impacts the stability of a single VSC test system. Simulation results verify the proposed modeling and stability analysis method.
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