Fuzzy Autoregressive Modeling and Parameter Estimation for Electrical Power Distribution Systems
Christian Mpeti Benimi
Faculty of Science and Technology, Department of Mathematics and Computer Science, National Pedagogical University (UPN), Kinshasa, Democratic Republic of the Congo.
Emilien Loranu Londjiringa
Sciences Section, Department of Mathematics and Physics, ISP BUNIA, Ituri, Democratic Republic of the Congo.
Grace Nkwese Mazoni
Faculty of Science and Technology, Department of Mathematics and Computer Science, National Pedagogical University (UPN), Kinshasa, Democratic Republic of the Congo.
Camile Likotelo Binene *
Faculty of Science and Technology, Department of Mathematics and Computer Science, National Pedagogical University (UPN), Kinshasa, Democratic Republic of the Congo.
Fernand Mamanya Tapasa
Faculty of Science and Technology, Department of Mathematics and Computer Science, National Pedagogical University (UPN), Kinshasa, Democratic Republic of the Congo.
Jean-Marie Kapenga Kazadi
Faculty of Science and Technology, Department of Mathematics and Computer Science, National Pedagogical University (UPN), Kinshasa, Democratic Republic of the Congo.
Rostin Mabela Makengo
Faculty of Science and Technology, Department of Mathematics and Computer Science, University of Kinshasa, Kinshasa, Democratic Republic of the Congo.
*Author to whom correspondence should be addressed.
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.
Keywords: Fuzzy autoregressive process (\(\widetilde{AR}\)), Expected value \(\mathbb{E}\)[x(\(\tilde{e_t}\))], variance \(\tilde{\gamma_o}\), autocorrelation \(\tilde{\varphi}\), autocovariance \(\tilde{\gamma_i}\)