Fuzzy Autoregressive Modeling and Parameter Estimation for Electrical Power Distribution Systems

Abstract

In this article, we analyzed the operating voltage of a substation in Kinshasa by transforming its classical distribution into a fuzzy distribution. This approach allowed us to estimate fuzzy stochastic parameters, which we classified as total and partial parameters. Total parameters, such as fuzzy expectation and variance, have a maximum membership degree of 1. Partial parameters, such as fuzzy autocovariance and autocorrelation, have membership degrees less than 1. This study formalized a fuzzy distribution approach based on Zadeh arithmetic, providing a rigorous framework for imprecision modeling. The integration of fuzzy numbers into the estimation methods led to a more robust evaluation of the model parameters. Furthermore, the stationarity criteria were re-examined in this fuzzy context, highlighting their theoretical consistency and practical applicability. The results obtained confirm the relevance of this approach for the analysis of random phenomena tainted by epistemic uncertainty. The results show that the fuzzy expectation and variance have a maximum degree of membership equal to 1, while the autocorrelation functions reach a maximum degree of 0.332, confirming the partial nature of the estimated model.