A significant research effort has been dedicated in developing smartgrids in the form of interconnected microgrids. Their use is especially suitable for integration of solar generated electricity, due to the fact that by separating the electrical grid into smaller subsections, the fluctuations in the voltage and frequency that occur, can be to, a certain extent, isolated from the main grid. For the new topology, it is essential to optimize several important properties like the self-adequacy, reliability, supply-security and the potential for self-healing. These problems are frequently hard to solve, in the sense that they are hard combinatorial ones for which no polynomial time algorithm exists that can find the desired optimal solutions. Due to this fact research has been directed in finding approximate solutions, using different heuristic and metaheuristic methods. Another issue is that such systems are generally of a gigantic size. This resulted in two types of models, detailed ones that are applied to small systems and simplified ones for large ones. In the case of the former, graph models have shown to be very suitable especially ones that are based on graph partitioning problems[4]. One of the questions with the majority of previously developed graph models for large scales systems, is that they are deterministic. They are used for modeling an electrical grid which is in essence a stochastic system. In this work we focus on developing a stochastic graph model for including solar generated electricity to a system of interconnected microgrids. More precisely we focus on maximizing the self-adequacy of the individual microgrids, while trying to maximize the level of included solar generated energy, with a minimal amount of necessary energy storage. In our model we include the unpredictability of the generated electricity, and under such circumstances maintain a high probability that all demands in the system are satisfied. In practice we adapt and extend the concept of partitioning graphs with supply and demand for the problem of interest. This is done by having multiple values corresponding to the demand for one node in the graph. These values are used to represent energy usage in different time periods in one day. In a similar fashion we introduce a probability for the amount of electrical energy that will be produced by the generating nodes, and the maximal amount of storage in such nodes. Finally, we also include a heuristic approach to optimize this multi-objective optimization problem.


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