A Cycle-Based Solvability Condition for Real Power Flow Equations

TL;DR

This paper introduces a cycle-based sufficient condition for the solvability of lossless real power flow equations, offering a less conservative and computationally efficient way to verify power flow solvability amid increasing renewable integration.

Contribution

It proposes a novel cycle-based solvability condition for lossless power flow equations, improving verification efficiency and accuracy over existing methods.

Findings

The condition is less conservative than previous criteria.

It effectively verifies solvability in tested systems.

Provides a foundation for extending to coupled power flow equations.

Abstract

The solvability condition of the power flow equation is important in operational planning and control as it guarantees the existence and uniqueness of a solution for a given set of power injections. As renewable generation becomes more prevalent, the steady-state operating point of the system changes more frequently, making it increasingly challenging to verify power flow solvability by running the AC power flow solver after each change in power injections. This process can be computationally intensive, and numerical solvers do not always converge reliably to an operational solution. In this paper, we propose a sufficient condition for the solvability of the lossless real power flow equation based on the cycle space of a meshed network. The proposed condition yields a less conservative solvability certificate than existing sufficient conditions on the tested systems and can serve as a useful foundation for developing solvability conditions for the fully coupled power flow equations.