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We propose a state space model for electrical power systems made by independent semi-Markov components, in which restoration times can have a nonexponential distribution, thus obtaining a more realistic reliability characterization, especially regarding the outage duration distribution. We also propose a model for an energy storage unit, assuming that the storage is fully charged when it begins to deliver power. An approximate analytical evaluation based on the minimal cut sets for the outage allows to surmount the shortcomings of the Monte Carlo approach. The application of the model for an uninterruptible power supply (UPS) system shows that the autonomy of the storage plays a key role, not only for the frequency of the load point voltage failures, but also for their duration distribution.