Assessment and Improvement for Ensuring Power Flow Solution Existence in Multi-Infeed Renewable Energy Systems

This paper presents an analytical methodology to complement the drawbacks of existing theories in utilizing the generalized short circuit ratio (gSCR) in ensuring power flow solution existence for power systems dominated by renewable energy sources (RESs). Based on the theorem of implicit function, a general analytical model considering distinct RES control modes and system operating conditions is derived to characterize the existence of power flow solution in multi-infeed renewable energy systems (MIRESs). Based on that, the classical assumptions of gSCR-based theories, namely the uniform power factor angles of RESs and negligible voltage angle differences among points of common coupling (PCCs), have been revisited and then rigorously removed to obtain a sufficient condition for power flow solution existence under normal operating conditions where RESs are not engaged in low-voltage ride-through (LVRT) control. Furthermore, a gSCR-based sufficient condition for solution existence under low-voltage conditions, where RESs are in LVRT control, is derived, along with an improved LVRT control for RESs based on the sufficient condition to avoid loss-of-solution. Based on the proposed sufficient conditions and improved control, a comprehensive methodology is presented to ensure solution existence under complex operating conditions where LVRT-enabled and non-LVRT RESs coexist. Finally, case studies are conducted on practical MIRES using power flow calculations and time-domain simulations, while extensive Monte Carlo tests (10⁶ samples per scenario) are performed across normal, low-voltage, and complex operating conditions, to confirm that the proposed methodology consistently ensures power flow solution existence in all tested cases.