Parameter Design Oriented Analysis of the Current Control Stability of the Weak-Grid-Tied VSC

This paper studies the dynamic behaviors of weak-grid-tied VSCs with simplified transfer functions, which provides an accurate stability analysis and useful indications for tuning system parameters. A reduced-order multi-input multi-output (MIMO) transfer function that contains four single-input single-output (SISO) transfer functions for the weak-grid-tied VSC is first presented. It is found that the four SISO transfer functions share the same equivalent open-loop transfer function, i.e., the same stability conclusion. The Bode plots of the equivalent open-loop transfer function show that the inner current loop behaves as a band-pass filter whose maximum gain is approximately at the frequency of the PLL's bandwidth. By stability criterion, the harmonic amplification and instability occur when its maximum gain exceeds 0 dB caused by high PLL's bandwidth, large grid impedance or high active power. It is also found that the target system is less stable when it works as an inverter than as a rectifier, due to the risk of the local positive feedback in the inverter mode. An effective criterion is further proposed to guide the selection of a proper PLL's bandwidth to ensure the stability of the VSC system. Simulation results validate the correctness of the analysis and the efficacy of the criterion.