Toward less conservative distributed stability analysis of power systems via matrix-valued differential passivity indices

TL;DR

This paper introduces a matrix-valued differential passivity index to improve distributed stability analysis in power systems, reducing conservatism and enhancing accuracy.

Contribution

It extends scalar passivity indices to a matrix form for better capturing MIMO system interactions and develops new distributed stability criteria.

Findings

Matrix-valued passivity indices improve stability analysis accuracy.

Distributed criteria guarantee stability with passivity excess compensation.

Analytical expressions for system components facilitate compositional analysis.

Abstract

Passivity indices have been widely adopted to derive distributed stability certificates for power systems. Nevertheless, conventional passivity indices remain scalar-valued even for multi-input-multi-output (MIMO) systems, which can introduce excessive conservatism and compromise analysis accuracy. To overcome these limitations, this paper extends the differential passivity index to a matrix-valued formulation that captures both channel-wise passivity properties and inter-channel coupling effects in MIMO subsystems. On this basis, semi-distributed and fully distributed stability criteria are developed for power systems with heterogeneous nonlinear devices. It is shown that system stability is guaranteed when the aggregate passivity excess of devices compensates for the passivity shortage imposed by the network. Furthermore, analytical passivity matrix expressions for typical power system components are derived, facilitating compositional stability analysis. Case studies on a three-bus system and a modified IEEE 118-bus system validate the effectiveness of the proposed framework.