Optimal Computing Budget Allocation for Stochastic N–$k$ Problem in the Power Grid System

Abstract

The $N$ − $k$ problem is very well known in the power industry and it tries to answer the question whether there exists a set of $k$ lines in a power network with $N$ elements whose removal would cause the failure of the system. In practice, it is common to evaluate a system according to an $N$ −1 criterion, i.e., $k = 1$ . While this problem has traditionally been considered in a deterministic setting, stochastic behavior within the system is important especially in the context of extreme events. A number of stochastic Monte Carlo models have been proposed to estimate the probability of cascading failures. In this paper, we deal with simulation budget allocation of the stochastic $N$ –1 problem. More specifically, we assume that a simulation model is able to provide us an estimate of the system failure rate when any line is tripped. It is not difficult to see how simulation of all configurations to some certain accuracy can become computationally expensive with the growth of $N$ . Under such a setting, we transform the $N$ –1 problem into a stochastic selection process with optimal computing budget allocation (OCBA): given $N$ configurations, we would like to sequentially allocate a certain number of simulation replications in order to answer the question whether the system is reliable or not. We show through theoretical analysis and numerical experiments that the probability of correctly identifying the system reliability state can be increased by applying OCBA allocation rules in the simulation budget allocation process.