The developed model is a mathematical algorithm that manages different energy sources for the water–energy nexus. The work comprises the definition of the model and the mathematical algorithm that executes the system's simulation. Subsequently, the optimization algorithm is defined for Excel Solver (single-objective) and Python (multi-objective). The model is designed to be applicable to a diverse range of hybrid energy systems, particularly in conjunction with pumped hydropower storage. It focuses on the energy and water balance between subsystems to manage and simulate the performance throughout time. To conclude the algorithm development, the model was tested on a case study. The experiment was conducted on a 24-hour consumption irrigation field. The model was used to explore a variety of scenarios involving different energy sources, including photovoltaic, wind, PHS, grid, and battery (off-grid) technologies. The results demonstrated that a system integrating photovoltaic, wind, PHS, and the grid is the most economically and environmentally viable option, exhibiting the lowest grid consumption compared to a scenario solely relying on PV and PHS. A third scenario was tested, in which the grid was replaced with a battery energy storage system (BESS), thus providing an off-grid solution. Despite reducing carbon emissions, the system encountered challenges in meeting the full demand for water and energy. The scenarios that envisage the implementation of the electric grid permit the sale of surplus renewable energy, including photovoltaic (PV) and wind, during periods of low demand. This contributes to a reduction in costs. It is the scenario with both solar and wind that benefits the most from these conditions, as it can reproduce a positive grid cash flow throughout the year for higher water allocations.