Using inverse Lz-transform for obtaining compact stochastic model of complex power station for short-term risk evaluation

In this paper a short-term risk evaluation is performed for electric power stations, where each power generating unit is presented by a multi-state Markov model. Risk is treated as the probability of loss of load or in other words, as the probability of system entrance in the set of states, where demand cannot be satisfied. The main obstacle for risk evaluation in such cases is a "curse of dimensionality" – a great number of states of entire power station that should be analyzed. Usually when the number of system states is increasing drastically, enormous efforts are required for solving the problem by using classical Markov methods or simulation techniques. Well known universal generating function technique also cannot be directly applied because this technique is primarily oriented to steady-state reliability analysis. By using such extension of UGF techniques as Lz-transform, one can find for the short-term such reliability characteristics as loss of load probability, expected energy not supplied to consumers etc. However risk function still cannot be obtained by using these techniques. This problem in many practical cases is a challenge for reliability researchers and engineers. In this paper, a special method based on inverse Lz-transform (LZ−1 transform) is developed in order to calculate risk function for such multi-state power systems. In order to illustrate the proposed approach, the short-term risk evaluation for a power station with different coal-fired generating units is presented.