Analysis of Modal Resonance Between PLL and DC-Link Voltage Control in Weak-Grid Tied VSCs

Weak ac grid operation is known to challenge the stability of voltage source converters (VSCs). This paper provides an interpretation for the cause of such instability in view of a particular modal resonance within VSC's control, i.e., the resonance between dc-link voltage control (DVC) and synchronizing control-phase-locked loop (PLL). To characterize this modal interaction, a two degrees-of-freedom mass-spring-damper model is first proposed. Subsequently, based on a multi-modal decomposition approach, the amount of interaction is quantified by the incremental damping and frequency drift superimposed on each individual mode. Analytical results indicate that when the natural frequencies of PLL and DVC mode are close, strong interaction will push the lower-frequency mode to move toward the decreased frequency and damping direction, while causing the higher-frequency mode to go the opposite. Moreover, weaker ac grid operation will amplify such frequency/damping excursion and, thus, will render the lower-frequency mode unstable. Further, when the ac voltage control (AVC) is disregarded, a dynamic stability margin is analytically derived, and operation beyond the margin will result in monotonic drift. With the inclusion of AVC, owing to its introduced additional negative damping, by contrast, instability will occur in the presence of oscillations. Both eigenvalue analysis and simulations are conducted to verify the results.