## 1 Introduction  
With the increasing penetration of renewable energy resources (RES) in distribution networks, how to utilize the random and volatile power has become a critical part of emerging smart grid designs [1]. In order to eliminate the negative impact of RES, the microgrid (MG) is considered to be a possible solution. Generally, the MG can be regarded as an integrated system with distributed energy resources (DERs) and loads, which can be operated both on grid-tied and isolated mode [2; 3]. With the increasing of MGs in community level, the interconnected multi-MG has shown greater advantages on lower the operation cost and enhance the reliability [4], by coordinated energy sharing [5; 6] and provision of urgent supply [7]. Until recently, a new type of direct current (DC)-link based on voltage source convertor (VSC) is proposed. DC-linkage is preferred over existing alternating current (AC)-linkage for the following two aspects. In isolated mode, DC-linked MGs can operate at different voltages and frequencies, if necessary, backup active power in an underloaded MG can be transferred to an overloaded MG to improve the supply reliability of the whole network [7]. Such DC-link can then be turned off to reduce its operating losses when both MGs do not need additional generation or do not have extra generating capacities for sharing [8]. In grid-connected mode, DC-link equipped at the end feeder, which is also named soft open points (SOP), improves the power handling capacity, voltage profile of AC distribution feeder and reduces the power loss [9; 10]. Furthermore, it can achieve rapid recovery of non-fault areas in the case of failure, and thus improve the reliability of the whole network [11]. Therefore, the DC-links can be deployed by the MG's owners between the adjacent MGs in community level, and then the energy trading within the multi-MG can be mutually decided by themselves, without paying network tariffs to the Distribution Network Operator (DNO). In this regard, the cooperative DC-linked multi-MG would change the power flows of the distribution system, and then make the reconfiguration decisions of distribution network less efficient, which is generally operated by DNO to minimize the power losses. Consequently, how to integrate the reconfiguration model with optimal operations of DC-linked MGs is an essential problem to be addressed. Many efforts have been devoted to solving the optimal operations of multi-MG, which can be roughly classified into two types by the operation goals: (1) reduce their operation cost (or increase the operation profit); (2) improve the system reliability. For the first type, the operation goal is generally set as minimize the overall operation cost of multi-MG [12; 13; 14]. The involving DERs may include diesel generations, microturbines, Photovoltaic (PV) panels, Wind Turbines (WT), and battery energy storages. Considering that the participated MGs may have different types of DERs, the operation cost could be reduced by maximizing the renewable energy sharing. During the operation, centralized or distributed optimization algorithms can be used, according to the different scenarios [15; 16]. The second type of multi-MG operation can be activated when the utility grid is outage (i.e., power system faults, unexpected disaster events, etc.). In this scenario, the operation goal could be maximize the load restore ability for important end users. The operation frameworks can be concluded as the hierarchical structure (i.e., DNO and MG operators) [17] and horizontal structure (i.e., only MG operators) [18]. In aforementioned studies, if the multi-MG is isolated from the utility grid, they only need to consider the energy trading between them. Otherwise, if the multi-MG is grid-connected, they still need to trade the energy with the AC distribution network.