Generation of random states of electric power systems at assessment of their reliability by the Monte Carlo method

Abstract

In this paper we deal with the problem related to effective assessment of reliability of electric power systems, particularly, the efficiency of pseudorandom number generators while using the Monte Carlo method for generation of random states of electric power systems. We consider the efficiency of four pseudorandom number generators: linear congruential generator, lagged Fibonacci generator, Mersenne Twister and Sobol sequence. The Kolmogorov-Smirnov test for analysis of randomness of sequences was used to analyze the above pseudorandom generators. Based on this analysis, it has been determined that the most random sequence may be obtained while using the Sobol sequences generator. Next, visual analysis of these pseudorandom number sequences was conducted. It showed that 2d points gained from the Sobol sequence filled the surface more evenly than other generators, where as the linear congruential generator and the lagged Fibonacci generator would form voids. In the final part of the research, the analyzed pseudo random generators were used in a model for reliability assessment using the Monte Carlo method. We modeled a three-node electric power system test scheme. As a result, the linear congruential generator and the lagged Fibonacci generator did not stabilize even after ten thousand random states of the system. These results correlate with the Kolmogorov-Smirnov test and show that these generators are barely random and unsuitable for reliability assessment using the Monte Carlo method. The Mersenne Twister and the Sobol sequence results were much better. The expected value of power shortage stabilized by the 4000th rando state with the Sobol sequence. In conclusion, we can say that the Sobol sequence is the most suitable pseudorandom generator for reliability assessment using the Monte-Carlo method than the other generators considered above.