The operation strategy directly affects the design and operation of distributed energy systems (DESs). Following electrical load (FEL) and following thermal load (FTL) strategies, for example, cannot achieve the flexible scheduling of DESs. As a result, this paper proposes an optimized operation strategy with the minimum operation cost as the optimization objective. A system optimization model with the total system cost as the optimization objective is established based on the optimized operation strategy, and the proposed DES is optimized. The optimization outcomes are compared to those obtained using the FEL and FTL strategies. The results indicate that the optimized operation strategy can increase the capacity of the system’s CHP unit, absorption chiller, and energy storage devices. The carbon tax, operating cost, and total system cost are lower under the optimized operation strategy than under the FEL and FTL strategies, with reductions of 13.32%, 11.03%, and 0.36%, respectively, affected by the capacity of the equipment. Therefore, the optimized operation strategy can significantly improve the DES’s economic efficiency while lowering carbon emissions.