Positive-Negative Sequence SRF-PLL Model for Accurate Stability Analysis in Grid-Tied Converters

Abstract

Current control loop, grid conditions, and phase-locked-loop (PLL) based synchronizing schemes play an important role in the stability of grid-connected converters. In order to asses the impact of the PLL to the impedance-based stability analysis, its contribution to the overall converter output impedance model must be included. In its model derivation, the synchronous reference frame-PLL (SRF-PLL) includes positive and negative sequences cross-coupling terms which contribute to the MIMO transfer function between the grid voltage and the current reference in αβ stationary reference frame. Simply neglecting these coupling terms results in a simplified SRF-PLL model which could lead to system stability misjudgments, especially in low frequency range and weak-grid condition. In this paper, a positive-negative sequence SRF-PLL (PN SRFPLL) model in αβ-frame is step-by-step derived and algebraically rearranged in order to deal with decoupled αβ-SISO systems. Moreover, to stabilize the system in weak-grids, the virtual impedance method is proven to be a valid solution. Stability analysis and simulations prove that the proposed PN SRF-PLL model can significantly improve the accuracy of the stability assessment and the design of the virtual impedance parameters.