A PLL-Equivalent Model for Low Frequency Dynamic Analysis of Weak-Grid connected VSC

Low-frequency dynamic (LFD) (around 1~10Hz) of PLL-synchronized weak grid linked voltage source converter (WG-VSC) has been observed and dominated by the "outer loop-PLL-weak grid" interaction. To provide a clear insight to LFD of WG-VSC, a PLL-equivalent model is proposed in this paper. Firstly, a generic LFD analysis model is derived, which contains PLL and a ‘outer loop-WG' part which integrating outer loop dynamics, grid strength and VSC operation point. Then, this complicated ‘outer loop-WG' part is divided into two parallel loops, representing the influence of active side outer loop and reactive side control on LFD of WG-VSC respectively. Furthermore, a reduced PLL-equivalent model which can maintain sufficient accuracy for LFD analysis of WG-VSC is derived by simplifying the ‘outer loop-WG' part into a firstorder loop and combining original PI controller of PLL. With this model, comprehensive theoretical analysis for LFD instability mechanism has been carried out. The effectiveness of PLL-equivalent model and accuracy of analysis results are verified by time-domain simulations in PSCAD/EMTDC.