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The growing penetration of non-programmable renewable energy sources and the consequent fluctuations in energy prices and availability lead to the need to enhance energy system flexibility and synergies between different energy vectors. This can be reached through sector integration. Among the most relevant technologies used for this purpose, Power-to-Gas systems allow excess renewable electricity to be converted directly into fuels that can be then stored or used. A smart energy system, however, which includes these innovative solutions, requires intelligent management methods to optimize its operation. This work investigates the operational strategy of energy systems integrated with Power-to-Gas solutions for seasonal storage, by developing an optimization model for the system, formulated as Mixed-Integer Linear Programming problem. The algorithm tackles the uncertain nature of future disturbances, such as energy needs, generation and price using two-stage stochastic programming. The algorithm is tested on grid-connected and 100% renewable energy supply case studies. The novel stochastic algorithm allows a more robust optimization compared to a deterministic optimization, and system management is ensured under several future disturbances realization. Furthermore, the integration of Power-to-Gas solutions warrants the energy security of the energy systems and acts as a buffer to forestall unpredictable behavior of the disturbances.