Accurate Stability Analysis of Three-Phase Converter System Connected to Weak Grid under Coordinate System Transformation

Abstract

This paper studies the simplified impedance criterion of the three-phase converter system in different coordinate systems. In addition, the influence of small signal stability of converter units under the weak grid is discussed in three-phase converter systems. Firstly, a small signal model of a three-phase grid-connected converter system is established based on the voltage and current double closed-loop control strategy in dq real coordinate system and the dynamic characteristics of SRF-PLL (Synchronous Reference Frame Phase-Locked Loop). Then, based on the coordinate transformation, the admittance models in the dq real coordinate system and the fb complex coordinate system are derived. Through the analysis of the admittance Bode diagram, the amplitude-frequency characteristics of the three-phase converter system have conjugate symmetry in the real coordinate system and diagonal conjugate symmetry in the complex coordinate system. Therefore, the three-phase symmetrical system can be stabilized only by drawing the Nyquist curve of the open-loop transfer function GHf or GHb. The three-phase asymmetric system can also be stabilized by drawing the Nyquist curve of the modified open-loop transfer function GHfM or GHbM . Finally, the simulation results show that the converter system loses stability when the transmission line impedance Lg = 0.6 pu. In this case, the three current decoupling terms will cause the system to lose stability, but the relative stability of the current reference value is the best, and the phase angle margin is −6.8°. Also, without considering the phase-locked loop dynamics, the system is in a steady state, otherwise, the system loses stability, and the system output current has a 39 Hz oscillation, which is consistent with the theoretical analysis results.