Stochastic model of the smart power grid section functioning

Abstract

A feature of large systems, in particular electric power systems, is that the entire system physical state of the is affected by a large number of interacting elements that are randomly in different states. The work relevance is caused by to the fact that construction of mathematical models taking into account the structure and features of the power grid functioning allows us to solve important problems of the energy intellectualization. The goal of the study is due to the desire to show the advantages that arise when using the apparatus of the hidden Markov models theory to semi-Markov models of intelligent electrical systems. To do this, we build a semi-Markov model of a section of a distribution power grid (intelligent electrical grid). Using the theory of semi-Markov processes with a common phase space of states, it is possible to determine the temporal characteristics of the system reliability and obtain a more adequate model. However, territorial dispersion, inaccessibility of some sections of electrical networks and the widespread introduction of automation tools give rise to new problems. For a timely response to various factors, it becomes necessary to as-sess and forecast the states of the system (sections of the system) depending on the signals received in the course of its operation. This can be achieved by applying the hidden Markov models theory. Reliability characteristics are determined and, using the algorithm of stationary phase enlargement, an enlarged semi-Markov model of the section of the intelligent distribution grid is built, which allows passing to the finite state space of the model. Using the merged model, the parameters are determined and a hidden Markov model is developed, for which the most probable states corresponding to a given signal vector are found, the elements subsequent states of the modeled system and signals are predicted. The final part of the article provides an example of finding the reliability characteristics of the system and solving a number of problems in hidden Markov models theory.