Limit Cycle and Large Signal Stability Boundary Induced by Outer Controller of Grid-Connected VSC

This paper illustrates the phenomenon of the limit cycle surrounding the stable equilibrium point (SEP) induced by outer controller of grid-connected voltage source converter (VSC). The limit cycle is one of the oscillation mechanisms of a grid-connected VSC where its existence constitutes the large signal stability boundary. A third-order differential-algebraic equations (DAEs) studied model with DC and AC voltage outer controller is first developed. It is found that as the active power increases, DC voltage controller bandwidth increases or DC voltage controller damping ratio decreases, the system is prone to existing a limit cycle. Simulation reveals that the existence of a limit cycle reduces the region of attraction (ROA) under large signal. Furthermore, based on the Demidowitsch criterion, the paper proposes an analytical sufficient condition for non-existence of a limit cycle, so the system can be relieved from it and thus expand the ROA. The proposed condition can be effectively utilized without numerical simulations. Both the electromagnetic transient simulations and experimental results have verified the theoretical analysis.