Model of Supply Restoration of Energy Consumers by Markov State Space Models

For the application of Markov state space models in modelling substations and switching procedures, i.e. a supply restoration procedure, it is crucial to determine all parameters that influence the supply interruption duration. The Markov model is chosen due to a possibility to clearly model all procedures and states during disturbances, which result in the supply interruption, according to [1, 2, 3]. In order to determine all the relevant parameters, the transmission network supply interruption reports from the year 2006 until the year 2010, as well as the supply interruption data in the transmission area Osijek from the year 2000 until the year 2010, were analysed. Based on this analysis, the supply restoration processes in the Croatian Transmission System Operator (TSO) and transmission area Osijek were determined. The Markov state space models application is possible only if probability density of failure and restoration is exponentially distributed [1-5]. Use of the Markov models for the power system networks reliability analysis is appropriate due to the possibility to keep track of all the processes that happen during the disturbances, which result in the supply interruption of final customers. The TSO collects the data about the network under its jurisdiction and makes the reports about the supply interruptions annually. In order to be able to model the power network by using the Markov models, the density function of the supply restoration duration has to be determined. An initial assumption is that the supply interruption frequency, as a random variable, has is the exponential density function, so it would not be considered in this paper [3, 7]. If the supply interruption and the duration do not have the exponential density function, then fake states should be introduced in the model, which are combined to form the exponential density function [3-5]. Based on analyses of the data from [6] and