Abstract
We consider mathematical models for analyzing the energy supply reliability of isolated systems and propose a three-level complex of nested models. The lower level represents the model of functioning of the energy supply system during the period under review. The second level is a model of the energy supply reliability analysis. This analysis is based on multiple simulations of functioning of the energy supply system in randomly formed conditions. The energy sources demand and supply, as well as the amount of carryover reserves of energy in storage, are assumed to be random values. To simulate functioning, the values of energy demand and production are formed using the Monto-Carlo method following their laws of probability. The random value of the carryover reserves is formed using the algorithm that generates the Markov sequence of these reserves. The upper level is represented by the model for selecting the optimal composition of the means ensuring reliability, i.e. energy reserves in the energy production and storage capacity. It was revealed that the algorithm for generating the random value of the energy sources carryover reserves yields the homogenous Markov sequence. Sufficient conditions for uniqueness of the stationary state were determined. Based on the experimental calculations, we estimated the number of iterations required to reach the stationary ergodic state.
Highlights
The issue of energy supply reliability for remote settlements is of particular importance and requires a special study
Fluctuations in the demand and production of energy resources depend on random factors, which stipulates development of special models adapted for research in random conditions
We have developed models for analyzing and optimizing energy supply reliability for remote locations: a simulation model for the functioning of energy supply system; a model for analyzing the energy supply reliability for a given set of stock facilities based on multiple use of the functioning simulation model and the model for optimizing the energy supply reliability based on the variation of stock facilities
Summary
The issue of energy supply reliability for remote settlements is of particular importance and requires a special study. Adverse conditions created by increased demand or reduced volume of energy production may result in shortages accompanied by economic damages that happen, for example, due to the need for expensive emergency supplies of additional energy from remote sources or the use of electricity from expensive sources (e.g. diesel power plants). In addition to these two random exogenous indicators, a third random factor should be taken into consideration – the amount of carryover reserves of energy. We consider the algorithm of forming carryover reserves of energy, which can be interpreted as an imitation of a long-term change in reserves as a result of random realizations of production and demand in each period
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