Optimization of a Solar–Biogas Hybrid Heating System for Typical Rural Buildings in Jiuquan, Hexi Corridor, Gansu Province

To improve renewable energy utilization and reduce fossil fuel consumption in building heating systems in Northwest China, this study proposes a solar–biogas hybrid heating system for the Jiuquan region. A dynamic simulation model was developed in TRNSYS, and multi-objective optimization was conducted using the NSGA-II algorithm. The optimization objectives were to maximize the solar fraction and minimize the initial system investment. The solar collector area, thermal storage tank volume, and biogas boiler start-up temperature were selected as decision variables. The results showed that the optimized solar fraction increased from 48.98% to 78.40% as the initial investment increased from 40,000 CNY to 80,000 CNY, although the marginal return gradually decreased. The NSGA-II algorithm generated a well-distributed Pareto front, revealing a clear trade-off between economic performance and solar energy utilization. Relative to the author-defined, proportionally scaled reference configurations, the optimized solutions increased the solar fraction by 18–21% across the examined investment levels. These improvement percentages are conditional on the adopted baseline definition. Considering both energy performance and economic feasibility, the scheme with a solar fraction of approximately 70% was identified as the compromise solution. Compared with the initial design, this scheme increased the initial investment by 15.52% and improved the solar fraction by 20.69%. These results indicate that appropriate configuration of key system parameters can substantially enhance renewable energy utilization. The proposed optimization method provides a useful reference for the design and operation of solar–biogas hybrid heating systems in Northwest China.