An integrated energy community with a distributed utilization of renewable energy and complementary electricity–gas–cold–heat integrated energy will play an important role in energy conservation and emission reduction. In addition, compared with traditional thermoelectric power equipment, solid oxide fuel cells have many advantages, such as a high energy utilization rate, good waste heat quality, and low carbon emissions. Therefore, the SOFC-based multi-energy and energy storage sharing operation model of an integrated energy community with an electricity–gas–cooling–heat integrated energy system is constructed, and a bi-objective optimal configuration model considering the carbon emission index is established. Considering the economic objective of the smallest annual total operating cost as the most important objective in optimizing the planning model, the ε-constraint method is used to transform the environmental objective function with the smallest annual total carbon emission into a constraint condition under the decision making of an economic single objective function, and then the planning model is linearized and solved by using the Big-M method and the McCormick relaxation method. By calculating and analyzing the energy allocation results in five scenarios, the effectiveness and rationality of the model built in this article are verified. At the same time, the calculation example analysis results show that as the ε value decreases, the energy configuration of the integrated energy community will shift from natural gas to clean energy. From this perspective, the energy equipment configuration and operating costs will increase. However, the heat storage system and power storage system sharing can effectively reduce the energy allocation capacity and costs.
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