The combined cooling, heating, and power (CCHP) system, known for its outstanding compatibility performance, has been widely integrated with renewable energy sources such as hydrogen, wind, and photovoltaics, as well as decarbonization technologies in the energy field. However, the increased complexity of CCHP scheduling due to the high proportion of renewable energy sources and load fluctuations leads to negative returns if renewable energy sources are not scheduled reasonably and decarbonization technologies are not utilized. To address this challenge, this study introduced solid oxide electrolyzer cell (SOEC) and carbon capture system (CCS) into the CCHP system, and constructed a novel CCHP model considering hydrogen trading and decarbonization technologies. First, for the scheduling of SOEC and CCS, a game model was presented based on hydrogen sales and energy storage benefits. Second, a nudge and compel theory-based scheduling strategy and a duality operation strategy (DOS) considering sources-load fluctuation were proposed. Third, for the optimal energy scheduling problem of CCHP under new strategies and technologies, a novel multi-objective PID-based search algorithm with dynamic disturbance response was introduced. Finally, the proposed new strategies, methods, and models were verified through actual case studies on multiple typical days. The results revealed that, compared with the following electrical load strategy and following thermal load strategies, the DOS reduced costs by 3.03 % and 6.99 %, and emissions by 7.84 % and 1.39 %, respectively. The obtained outcomes contribute to the application and development of clean energy and decarbonization techniques.