Toward less conservative distributed stability analysis of power systems via matrix-valued differential passivity indices
For power system engineers, this provides less conservative distributed stability certificates by capturing inter-channel coupling, though the improvement is incremental.
The paper extends differential passivity indices to a matrix-valued formulation for MIMO subsystems, reducing conservatism in distributed stability analysis of power systems. Case studies on three-bus and IEEE 118-bus systems validate the approach.
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.