## 1 Introduction
This paper focuses on a distributed coordinated method for optimal energy management and operation of RMGs integrated with ADN by considering the power flow and operational constraints. In recent years, various distributed optimization methods such as, auxiliary problem principle, benders and optimality condition decomposition and alternating direction method of multipliers considering; energy management, dynamic economic dispatch and optimal power flow (OPF) problems have been studied extensively [16; 17; 18]. The distributed optimization methods are essentially iterative approaches based on decomposition-coordination. Compared with the traditional centralized method, the distributed method effectively decreases the model complexity and improves computational efficiency. Recently, the analytical target cascading (ATC) method (relatively new distributed algorithm) has been used and achieved satisfactory result in; unit commitment for multi-regional power systems [19], optimal operation problems of power system encompassing active distribution networks [20], collaborative optimal power flow (OPF) among the transmission system and active distribution grids [21]. Comparing with other distributed methods mentioned above, ATC method has more flexible coordination strategies with improved convergence properties [22]. However, the application of ATC method is fairly little in coordinating the operation of the distribution system and end-user level. In this paper, ATC method is extended to solve the optimally coordinated operation problems between the RMGs and ADN. Moreover, residential demand response (DR) becomes increasingly attractive due to its great potential [23]. In [24], a residential DR management model is proposed to manage DR provided by flexible household loads, and it has been shown that the residential DR can reduce energy expense of individual households as well as flatten the total load profile of DN. However, EVs with DR potential were not taken into account. Emerging plug-in EVs in household prosumers and the associated Vehicle-to-Home (V2H) capability offer new residential DR resources for the RMG. Therefore, residential DR provided by EVs and V2H capability is incorporated in the modeling in this paper. To the best of the authors' knowledge, there is no report about ATC-based distributed method applied to optimally coordinated operation problems between the RMGs and ADN that take into account residential DR and the underlying power flow and operational constraints on the ADN simultaneously. In this paper, the cluster of household prosumers in the close spatial distance (e.g., residential district) is treated as an RMG and a hierarchical structure of ADN integration of multi-RMGs is presented. The RMGOs and DSO are regarded as two different entities with their autonomous objectives, ATC method is used to represent the collaboration and cooperation relationship between the RMGs and ADN. The energy management problem in RMG and optimal operation problem in ADN are modeled individually according to their own load demand and available energy sources The associated residential demand response and power flow balance is solved independently in a distributed coordination manner, and then the optimal coordinated operating point and economic benefit of each entity are achieved. A case study is conducted based on the modified IEEE-33 bus distribution system to verify the feasibility and effectiveness of the proposed method. The remaining paper is organized as follows. The hierarchical structure of ADN integration of multi-RMGs is illustrated in Section 2. ATC-based distributed optimization modeling for RMGs and ADN is presented in Section 3. Section 3 illustrates the solving procedure. Section 4 shows the case studies and numerical results. Conclusions are drawn in Section 5.