Research On Optimal F-divergence Importance Sampling Method For Monte Carlo Simulation Of Composite Power System Reliability Evaluation

The reliability evaluation of composite power system can effectively identify system risk and weak points,and its evaluation results can provide important decision-making reference for power system planning and operation.However,with the continuous development of social economy and the large-scale interconnection of renewable energy,the structure and scale of the power system become increasingly complex,and the uncertain factors in system operation increase,which makes the reliability evaluation problem highly complicated.Therefore,it is of great engineering practical value and academic significance to carry out research on the rapid evaluation method of composite power system reliability evaluation.Monte Carlo simulation(MCS)method can realize the simulation of complex random operation characteristics,especially suitable for the reliability evaluation of large-scale complex power system.However,since the simulation efficiency of MCS is sensitive to the probability of fault events,the convergence speed is slow in high reliability system.To solve this problem,the importance sampling method replaces the original probability density function of random variables with the importance sampling probability density function(IS-PDF),which significantly improves the simulation efficiency of MCS.The key point of whether the importance sampling method can achieve the acceleration performance is how to optimize the parameters of IS-PDF.Therefore,this paper discusses the influence of parameter selection method on the reliability evaluation of composite power system,and the research shows that the unreasonable parameter selection even leads to the opposite effect,that is,slower simulation efficiency.Aiming at the parameter optimization estimation problem of IS-PDF,the traditional cross-entropy based importance sampling method realizes effective estimation of IS-PDF parameters based on KL distance.However,KL distance is actually only a form of generalized f-divergence family,which is effective but not unique.Therefore,starting with the generalized distance measure,this paper proposes the f-divergence importance sampling method,discusses the implementation of the typical distance measure of f-divergence family in the importance sampling method,and gives the unified iterative update expression of IS-PDF parameters,so as to extend the traditional cross-entropy based importance sampling method to a more general method.Through reliability evaluation of IEEE-RTS79 system and MRTS79 system with reduced peak load,the validity and high efficiency of f-divergence important sampling method in different reliability level systems are verified.Different IS-PDF parameters can be obtained by using different distance measures in f-divergence family,which leads to different importance sampling efficiency.Therefore,this paper further proposes the optimal f-divergence importance sampling method.Based on the principle that reducing the variance can improve the simulation efficiency,the iterative optimization determination of the optimal distance measure form in the f-divergence family is realized by minimizing the variance of the product of the reliability index test function and the likelihood ratio function,which further excavates the efficiency improvement potential of the important sampling method.IEEE-RTS79 system,MRTS79 system and IEEE-RTS 96 system are used for reliability evaluation.Compared with the traditional cross-entropy based importance sampling method,the optimal f-divergence importance sampling method has better convergence performance and higher simulation efficiency,which further improves the efficiency of importance sampling method.