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— This paper introduces a comprehensive modeling approach for optimizing the capacities of various energy converters and storage systems within a residential Energy Hub (EH). The model focuses on minimizing energy supply costs to customers while maximizing the utilization of renewable and hydrogen-based technologies. Through the optimization process, we determined that implementing CHP units in the EH could reduce total costs by approximately 78% with green tax incentives and by 46.7% without them. Additionally, the inclusion of an incentive to the EH resulted in a 27.2% reduction in total costs imposed on subscribers. The study also evaluates the impact of uncertainties in photovoltaic (PV) electricity generation, demonstrating the benefits of using stochastic optimization over deterministic methods. The results indicate that the economic advantage of this approach over deterministic methods is 86.75%–95.74% greater, depending on the scenario. Sensitivity analysis further reveals that the investment costs of fuel cells significantly influence the optimal capacity design and economic viability of the EH model. • Proposing a modeling procedure for hydrogen within renewable-based energy hub studies. • Extracting a probabilistic model for solar radiation and ambient temperature. • Presenting various operating strategies in planning studies of residential energy hubs. • Developing a stochastic optimization algorithm for running the proposed model. [ABSTRACT FROM AUTHOR]