Combined cooling, heating, and power systems present a promising solution for enhancing energy efficiency, reducing costs, and lowering emissions. This study focuses on improving operational stability by optimizing system design using the GA + BP neural network algorithm. By integrating phase change energy storage, specifically a box-type heat bank, the system effectively addresses load imbalance issues by aligning building thermoelectric demand with system output. This approach increases energy storage density, improves space utilization efficiency, and streamlines maintenance. The study evaluates the system's implementation in residential buildings across five climate zones, leveraging the GA + BP neural network algorithm to optimize energy, economic, and environmental aspects. The proposed full-load operation strategy, rather than the traditional hybrid operation strategy, reduces the need for frequent system adjustments, enhancing stability and efficiency. Results show a significant reduction in primary energy consumption, ranging from 7.74 × 103 to 2.08 × 106 kWh across the five cities studied. Energy optimization indexes improve by 0.27 %–3.78 % compared to electricity load operation and 1.94 %–8.58 % compared to thermal load operation. Comprehensive optimization indexes also demonstrate enhancements ranging from 5.78 % to 27.68 % and 2.67 % to 28.22 %, respectively. The full-load operation strategy proves highly effective for energy savings in residential buildings, offering innovative contributions to optimizing combined cooling, heating, and power systems, developing distributed energy systems, and promoting sustainable building development.