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This research aims to analyze and enhance a tri-generation energy system that utilizes geothermal energy for producing power from heat extracted from the geothermal source, along with freshwater and heating. To achieve this, the study employed the central composite design method from response surface methodology. The system comprises a double-flash geothermal configuration, a desalination component, and a transcritical carbon dioxide Rankine cycle. A Pareto analysis was performed to pinpoint and rank the most critical factors affecting the system s performance, while residual analysis assessed the precision of the central composite design approach. The analysis of variance offered a numerical evaluation of how processing parameters influenced power generation, heating output, freshwater yield, and overall system efficiency. In the end, the central composite design method facilitated the optimization of system performance. Findings from the Pareto analysis indicated that the geothermal source temperature had the greatest influence on power production, hot water output, and overall efficiency, while the mass flow rate of the geothermal source primarily affected freshwater generation. Under optimal operating conditions, the system was able to generate a power output of 1191.8 kW, produce 64.89 kg/s of hot water, generate 4.94 kg/s of freshwater, and achieve an efficiency of 59.96 %. This study illustrates the significance of transforming heat extracted from the geothermal source into valuable energy and emphasizes the advantages of integrated systems for converting heat extracted from the geothermal source into power, heating, and freshwater. https://www.sciencedirect.com/science/article/abs/pii/ S0960148124023346