Simplified cross-entropy based approach for generating capacity reliability assessment

This paper presents a new algorithm to estimate the optimal importance sampling (IS) probability distribution in generating capacity reliability (GCR) problems. The proposed approach results from a combination of the cross-entropy (CE) concepts with the standard analytical GCR assessment. A mathematical analysis of the CE equations is carried out to demonstrate that the optimal change of measure or distortion can be obtained by simply dividing the annualized GCR indices for two different configurations of the generating system. Under these hypotheses, a straightforward algorithm based on fast Fourier transform is proposed to systematically obtain the optimal distorted unavailabilities for all generating units in the system. The accuracy and computational performance of the proposed approach are compared with the standard CE optimization process using different generating systems. The IEEE-RTS 79, IEEE-RTS 96, and two configurations of the Brazilian South-Southeastern system are all used for this purpose.