Research On Calculation Method Of Importance Sampling Function In Monte Carlo Simulation For Power System Reliability Evaluation

Power system reliability assessment is an important work in planning and operation,because the reliability indexes can provide important information for them.When evaluate the reliability of complex and bulk system,the Monte Carlo simulation method is more useful than the analytical method,thus it received more attention in the reliability assessment of bulk power system.However,the Monte Carlo simulation method still convergence too slow due to the rarity of the failure events when evaluate the highly reliable systems.Therefore,it is great significance for the reliability assessment of bulk power system to do research on improving simulation speed of Monte Carlo simulation.Importance sampling is one of the effective methods to improve the convergence speed of Monte Carlo simulation.Its basic idea is to change the sampling distribution and highlight the important areas.In theory,there exists the optimal system state sampling probability density function,but it is impossible to obtain,and only an approximate important sampling density function can be constructed by some methods.The cross entropy method has achieved good effect and received widely recognized in improving the convergence speed of Monte Carlo simulation.In this paper,based on the deep understand of cross entropy method,two new methods of constructing the importance sampling density function is proposed for the non-sequential Monte Carlo simulation.The main contents of this paper are as follows:(1)Obtaining the importance sampling density function,in fact,is to obtain the system components' importance sampling distribution parameters.In the third chapter of this paper,an important sampling method based on the minimum cut set is proposed to construct the approximate optimal sampling density function.The method uses the minimum cut set to establish the nonlinear equations based on the original definition of the optimal sampling density function.The optimal components' unavailability is obtained by solving the equations after linearizing it.This method obtains the approximately sampling density function as same as the cross entropy method,but the method of obtaining the components' important sampling distribution parameters is different.The correctness and effectiveness of the method are verified by evaluating the RBTS and IEEE-RTS79 test system,and greatly improved the convergence speed of the non-sequential Monte Carlo simulation method.And the number of state samples processed in the preprocessing stage can be less than the cross entropy method.(2)The cross entropy method find the optimal components' importance sampling distribution parameters is based on the minimum KL distance.In the fourth chapter of this paper,some other distances are proposed to obtain the approximate optimal importance sampling density function,and their application in importance sampling are explored.One of the distances is the average squared logarithmic error distance formula from the concept of the squared error.The other distances f-divergence is introduced from the field of probability and statistical theory.The optimization problems are constructed by using these distances as the objective function,and then find the optimal components' importance sampling distribution parameters,so as to obtain the approximate optimal sampling density function.What's more,the f-divergence distance includes the KL distance,which is used in the cross entropy method.The assessment of RBTS and IEEE-RTS79 test systems shows that the distances proposed in this paper can also be used in importance sampling correctly and improve the convergence speed of non-sequential Monte Carlo simulation effectively.