Partitioned Mixed Small Gain-Phase Decentralized Stability Criterion for Power Systems

Abstract

The increasing penetration of converter-interfaced resources is making power-system stability assessment more challenging, particularly in heterogeneous grids containing both grid-forming and grid-following converters. Existing decentralized mixed small-gain and small-phase criteria provide scalable stability certificates, but they require all converters to satisfy the same type of condition at a given frequency. As a result, they cannot simultaneously exploit the low gain of grid-following converters and the favorable phase properties of grid-forming converters, leading to unnecessary conservatism. This paper proposes a partitioned mixed gain-phase decentralized stability criterion that allows distinct subsets of converters to satisfy different local requirements at the same frequency. Specifically, one subset can be certified through small-gain bounds, while the complementary subset is certified through small-phase bounds. The admissible trade-off between gain and phase margins is determined by a network-dependent quadratic constraint, yielding a technology-aware stability certificate that remains local at the converter level. The paper characterizes the admissible set of gain and phase bounds, establishes useful convexity and boundedness properties, and develops a practical procedure for selecting these bounds. The proposed method is demonstrated on heterogeneous systems containing grid-forming and grid-following converters, including a two-converter system and the IEEE 39-bus system, outperforming the standard decentralized small-gain and small-phase conditions.