Sensitivity models for steady-state and dynamic state probabilities and its application to protection system reliability evaluation

The electric equipments in power systems are composed of multiple components with different functions and transition rates. The stochastic nature given by Markov process decides the availability of the equipment. To include the uncertainty of reliability parameter, and set the optimal interval of preventive maintenance, state probabilities with changing transition rates are compared in the existing literatures. It is time-consuming, therefore inefficient to quantify impact of several parameters of large systems. It is incompetent when there is correlation among the transition rates. Based on the state transition matrix, sensitivity models of steady-state and dynamic state probabilities to the transition rates are proposed in this paper. In the steady-state evaluation, the sensitivities are given by the inverse and the derivative of the transition matrix. In dynamic evaluation, the sensitivities are given by the Taylor expansion of the dynamic state probability. The proposed model is validated by the reliability analysis to a typical protection system. The numerical results show that the evaluation period, initial state, and transition rates, especially those transiting out from the initial state, have notable influence on the steady-state and dynamic reliability of multiple-state systems.