## 1 Introduction  
The distribution management system (DMS) [1; 2] is regarded as one of the most essential factors of the development of the smart grid. A new smart DMS with distributed energy resources (DERs) [3], increasing various loads [4], the amounts of data and devices, is facing more challenges. To reduce the complexity of a distribution system, a smart DMS can be considered as many coupled microgrids [5]. That is, conventional DMS can be transformed to a multi-microgrid (MMG) distribution system. In recent years, with the increment of the permeability of DERs [6], microgrids (MGs) [7] have grown rapidly worldwide due to flexible generation, environmentally-friendly characteristics, etc. In general, MGs can be operated by connecting to the utility grid, as well as in island mode [8]. The neighboring MGs can form an MG cluster, in which several MGs can exchange energy with one another [9]. On the one hand, forming a cluster can improve operation stability and reliability in power delivery [10], which is beneficial to realize the failure recovery of a distributed network. On the other hand, it is useful to reduce operation cost and realize the energy complementation of MGs [11]. Recently, the energy management of prosumer community groups [6; 12] has become an attractive issue in order to improve the operation efficiency and encourage local consumption of RESs. In addition, the development of integrated community groups [13; 14; 15] based on the combined heat and power (CHP) [16] system contributes to the cost reduction and energy conservation. In these cases, the energy management of the group including multiple MG prosumers considering the CHPsystem becomes an important problem to be addressed for cost reduction and energy sustainability. Therefore, the energy sharing management for interconnected MGs would be promising for application. In the existing literature, the optimal dispatch [17] of interconnected multi-microgrids in island mode is studied. A distributed convex optimization framework and a cost minimization model and algorithm based on the subgradient method are developed in [18] for energy trading between islanded MGs. Unlike the aforementioned studies, in this paper, an energy sharing framework is constructed at the distribution grid level. Until recently, numerous studies have worked on the energy management [6] of multi-microgrids, and there are different considerations for diverse purposes and specific problems. For the reduction of environmental pollution, an increasing number of distributed generation (DG) units has attracted more attention. The long-term DG placement and short-term DG placement are optimized in an MMG system considering the randomness of load demands and DG power generation [19]. Recently, renewable energy sources (RESs) have been exponentially growing to reduce carbon emissions and the operation cost of systems. However, it is difficult to control them due to their stochastic behavior. A bilevel optimal control scheme is proposed for stochastic optimal operation of interconnected microgrids characterized by renewable and traditional power production, bidirectional power flows, dynamic storage systems and stochastic modeling issues [20]. Moreover, the reliability is regarded as an important indicator for interconnection of MGs. The optimal planning in [21] takes into account various factors including the economics, reliability and variability of renewables, network and resource-based uncertainties. In addition, the battery energy storage system (BESS) [22; 23] is the key component to improve the utilization of RESs. A privacy-preserving distributed optimal scheduling method is proposed for the interconnected microgrids in [24]. In the optimization, the optimization objectives are commonly set as minimizing the operation cost or maximizing energy efficiency. Multi-objective optimization was used in [25] to solve operation optimization. In a distribution grid, the power loss should be further studied, which is rarely considered for simplicity.