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This paper presents the solution of Markov chain reliability models with a large state-space. To specify a system reliability model, we use our previously proposed methodology, which is based on the Stochastic Automata Networks formalism. We model parts of the system by arrowhead matrices with functional transition rates. As a result, the infinitesimal generator matrix of the reliability model has a distinctive structure. In this paper, we demonstrate that a block Gauss–Seidel method can be applied very efficiently to such a structure. The application of the proposed methodology is illustrated by an example of a standard 3/2 substation configuration. Even though its Markov chain reliability model has almost two million states, its steady-state probabilities can be estimated in just a few seconds of CPU time. [ABSTRACT FROM AUTHOR]

In this paper, stochastic automata networks (SANs) formalism to model reliability of power systems substations is applied. The proposed strategy allows reducing the size of state space of Markov chain model and simplifying system specification. Two case studies of standard configurations of substations are considered in detail. SAN models with different assumptions were created. SAN approach is compared with exact reliability calculation by using a minimal path set method. Modeling results showed that total independence of automata can be assumed for relatively small power systems substations with reliable equipment. In this case, the implementation of Markov chain model by a using SAN method is a relatively easy task. [ABSTRACT FROM AUTHOR]