Weak Coupling Effects in the PLL Modes of Grid-Following PMSG Wind Power Systems

Abstract

Small-signal synchronisation stability is a critical issue of grid-connected permanent magnet synchronous generator (PMSG) wind power systems employing grid-following voltage source converters (VSCs). While most studies simplify the system by modelling multiple VSCs as a single unit to analyse oscillations caused by VSC-grid interactions, few have examined interactions among VSCs. This paper proposes the cross-synchronising coefficient to quantify these interactions and applies it to analyse small-signal synchronisation stability in multi-PMSG wind power systems. When considering only PLL, the cross-synchronising coefficient is analytically derived and generally small, or even zero, indicating weak coupling between the synchronisation dynamics of different grid-side converters. Unlike strong synchronising interactions among nearby synchronous generators, the interaction between the PLL dynamics of PMSG converters remains weak even at short electrical distances. When outer control loops are included, the interaction increases but remains moderate. These findings suggest that the weak coupling of PLL modes in PMSG wind power systems allow for independent stability analysis and control design. Simulation results validate the theoretical analysis, offering insights into the small-signal synchronisation stability of PMSG wind power systems.