To address the rising demand for hydrogen energy and its reliance with the water sector, this study presents an optimal scheduling framework for a multi-energy microgrid (MEMG) that integrates electric, thermal, water, and hydrogen energy networks. To this end, a mixed-integer linear programming (MILP) model is formulated to minimize both operational costs and emissions. A bi-variate piecewise McCormick envelope technique is utilized to manage the non-linear constraints associated with the water network. The model also incorporates the transportation sector, including electric and hydrogen vehicles (EVs, HVs), with vehicle-to-grid (V2G) technology, and models their associated uncertainties using Monte Carlo simulation (MCS). Additionally, the sale of oxygen as a by-product of the hydrogenation process is also considered. The case study shows significant economic and environmental benefits, with a 29.66% cost reduction and 22.26% emissions decrease from water network integration. Oxygen sales further reduce costs by 14.19%, and V2G technology contributes an additional 2.35% cost and 6.01% emissions reduction. The proposed linear approximation method achieved superior performance, with a root mean square error (RMSE) of 0.72 and a relative error of 2.132%.
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