First- and Second-Order Sensitivity Matrices (Differential Models) of Electric Power Systems: Applicability for Post-Emergency Steady-State Analysis

Reliability assessment of electric power systems necessitates an analysis of numerous operating states involving potential equipment outages and stochastic events within the minimal time. The sensitivity matrix method enables the calculation of post-emergency steady states. This paper describes the first- and second-order differential models for electric power system steady-state analysis, representing the dependence of bus voltage variations on power fluctuations. These models are applied to simulate generator outages and consumer load fluctuations. The proposed differential models are validated on a test electric power system. The first- and second-order sensitivity matrices applied to the model of electric power system steady states in power balance form demonstrate accurate qualitative and quantitative approximation of operating parameters. Furthermore, the second-order sensitivity matrices markedly improve the calculation accuracy of post-emergency steady-states.