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Hybrid Petri nets have been extended to include general transitions that fire after a randomly distributed amount of time. With a single general one-shot transition the state space and evolution over time can be represented either as a Parametric Location Tree or as a Stochastic Time Diagram. Recent work has shown that both representations can be combined and then allow multiple stochastic firings. This work presents an algorithm for building the Parametric Location Tree with multiple general transition firings and shows how its transient probability distribution can be computed using multi-dimensional integration. We discuss the (dis-)advantages of an interval arithmetic and a geometric approach to compute the areas of integration. Furthermore, we provide details on how to perform a Monte Carlo integration either directly on these intervals or convex polytopes, or after transformation to standard simplices. A case study on a battery-backup system shows the feasibility of the approach and discusses the performance of the different integration approaches.

Domestic renewable energy systems, including photovoltaic energy generation, as well as local storage, are becoming increasingly popular and economically feasible, but do come with a wide range of options. Hence, it can be difficult to match their specification to specific customer's needs. Next to the usage-specific demand profiles and location-specific production profiles, local energy storage through the use of batteries is becoming increasingly important, since it allows one to balance variations in production and demand, either locally or via the grid. Moreover, local storage can also help to ensure a continuous energy supply in the presence of grid outages, at least for a while. Hybrid Petri net (HPN) models allow one to analyze the effect of different battery management strategies on the continuity of such energy systems in the case of grid outages. The current paper focuses on one of these strategies, the so-called smart strategy, that reserves a certain percentage of the battery capacity to be only used in case of grid outages. Additionally, we introduce a new strategy that makes better use of the reserved backup capacity, by reducing the demand in the presence of a grid outage through a prioritization mechanism. This new strategy, called power-save, only allows the essential (high-priority) demand to draw from the battery during power outages. We show that this new strategy outperforms previously-proposed strategies through a careful analysis of a number of scenarios and for a selection of survivability measures, such as minimum survivability per day, number of survivable hours per day, minimum survivability per year and various survivability quantiles.

Hybrid Petri Nets with general transitions (HPnG) include general transitions that fire after a randomly distributed amount of time. Stochastic Time Logic (STL) expresses properties that can be model checked using a symbolic representation for sets of states as convex polytopes. Model checking then performs geometric operations on convex polytopes. The implementation of previous approaches was restricted to two stochastic firings. This paper instead proposes model checking algorithms for HPnGs with an arbitrary but finite number of stochastic firings and features an implementation based on the library HyPro.

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