## 1 Introduction  
Present energy demands and greenhouse gas emissions have been promoting the rapid development of renewable-energy-based distributed generation and electric vehicles (EVs) [1]. With recent technological advancements, there has been a significant increment in integrating renewables and EVs into the end-user level. For instance, the presence of renewable distributed generation (e.g., PV generation at rooftops) and EVs in a residence or vill makes it function to supply its domestic loads by using the distributed energy resources (DERs). In this regard, residential end-users are facing the transition from consumers to prosumers, and the residential prosumers can be able to generate and consume energy internally looking for an autonomous operation [2]. The residential prosumers or prosumer clusters can be seen as residential microgrids (RMGs) with the capability to manage their distributed energy resources, e.g., renewable distributed generation units, EVs, flexible loads and their participation in demand response. As residential energy consumption occupies a considerable proportion of energy in the demand side [3; 4], RMGs have attracted increasing concerns. In the near future, large numbers of RMGs may emerge prominently in active distribution networks (ADNs). Considerable work has been undertaken concerning home/residential microgrid energy management for the integration of renewables and EVs into residential loads and optimization of energy consumption for end-users [5; 6; 7; 8; 9; 10; 11; 12]. However, most of the existing literature is only directed toward a single residential microgrid system, the interaction relationship between RMGs and active distribution network (ADN) were not taken into account. In [5], an energy service decision-support tool is presented to schedule the available distributed energy resources integrated into the household to optimize home energy consumption and even provides energy services. In [6], an optimal management system is proposed for the energy management of a residential microgrid, this optimization model considered the renewable energy sources, integration of electric vehicles, vehicle to the grid system, and the energy consumption of a household with the day-ahead electricity price. The researchers in [9; 10; 11; 12] studied the designing of home energy management systems for coordinated optimal control between the behavior of energy use of a household and the operation of distributed energy resources. In [13], optimal management problem of an RMG is formulated as a mixed integer linear programming model aiming for a minimum operating cost of the RMG, and its economic value is assessed from the perspective of a homeowner. In [14], an optimal energy management model for an RMG with various types of distributed energy sources is proposed; load scheduling potential of household appliances is taken into account. Optimal operation problems of RMGs in a given area are investigated in [15], based on local electricity prices and building characteristics, an optimization model is developed to minimize the electrical costs of all residential households in the RMG with associated constraints. While the RMG and ADN are two different entities, they are actually also interconnected. The operating point of one entity impacts the operating point of the other. The energy management models presented in the literature mentioned above only considered supply-demand balance in single RMGs while ignoring the underlying ADN and the associated system operational and power flow constraints. The energy scheduling decisions are although beneficial for individual RMGs but they can threaten the distribution system efficiency. Therefore, coordination between RMGs and ADN is necessary and is of great importance. How to effectively coordinate the energy management and optimal operation between RMGs and ADN bring challenges for the residential microgrid owners (RMGOs) and distribution system operator (DSO).