Analytical parameter optimization based on importance sampling for power-system reliability evaluation
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Abstract:
Importance sampling (IS) can effectively speed up the Monte Carlo simulation (MCS) of power-system reliability evaluation. As a promising IS method, the cross-entropy method (CEM) can estimate the parameters of the IS probability density function (IS-PDF) by using an iterative parameter optimization procedure; nevertheless the iterative parameter optimization incurs high computation burden. A novel analytical approach for IS-PDF parameters optimization is proposed in this paper to reduce the computation cost. Firstly, the theoretically optimal IS-PDF for failure system states is formulated by a set of nonlinear equations where the PDF parameters, i.e. the optimal component unavailabilities, are to be solved. Because these equations are too many to be solved, the concept of minimum cut set identification is introduced to reduce the number of equations significantly while keeping the equality constraint for the theoretically optimal IS-PDF. Finally, to derive the optimal component unavailabilities, the least square estimation is used to solve these equations. The effectiveness and efficiency of the proposed method are verified by MRBTS and IEEE-RTS79.
