Toward Calculation of High Quality Control Measures for Unsolvable Power Flows

This paper presents and discusses a new, robust approach for restoring the solvability of power flow equations in power systems. The degenerate stable equilibrium manifold of a non-hyperbolic dynamical system constructed from power system equations is introduced to measure the unsolvability of the power system. The sensitivity based on its energy function is then proposed to estimate mismatch reduction by each control in the power system. Further, a three-stage strategy, including the screening stage, ranking stage, and detailed analysis stage, is presented for power flow recovery. The proposed method can identify the globally optimal solution for a single control measure and a set of highquality solutions for multiple control measures. Additionally, the concept of a user preference control list is introduced, which allows users to directly specify their preference over each control measure. The numerical results for IEEE test systems are presented to analyze and test the performance of the proposed methodology.