## 1 Introduction
Another study [18] presents a decentralized control strategy for the scheduling of the electrical energy activities of a microgrid composed of smart homes connected to a distributor, and the exchange of renewable energy produced by individually owned distributed energy resources. One study [19] presents a distributed power sharing framework among households in microgrids to improve the power reliability and reduce power demands and carbon emissions. Considering the mass connection of DG, it is necessary to address the uncertainty and fluctuation of DG with optimal planning and scheduling to improve the flexibility of the distribution network. Recent research works on the planning model considering the uncertainty of DG are mainly categorized into two types, namely, planning models based on scenario analysis [20] and models based on uncertainty theories, including robust theory [21; 22], stochastic theory [23], and credibility theory [24]. This paper uses the scenario analysis method to generate DG and load scenarios from historical data, which converts the uncertain planning model into the equivalent deterministic planning model. In order to deal with the randomness of DG, both the static and dynamic optimization methods are studied to solve the optimal scheduling problem. Other studies [2; 25; 26; 27] simulate the fluctuation of DG by subdividing the whole dispatch cycle into short-time-scale dispatch periods. Other studies [28; 29] use model predictive control (MPC) [30; 31] to realize optimal control of the distribution network with DG. However, the aforementioned research works mainly consider the impact of flexible resources on the flexibility of the distribution network, such as energy storage systems, demand side response, and superior grids. The evaluation of the distribution network flexibility considering the line capacity margin has been discussed for optimization of dispatching [12] and distribution reconfiguration [14]. It has not been considered in the optimal planning model for the accommodation of DG. Compared with previous studies, the main contributions of this paper are:  
1. A multi-objective optimal planning model for the accommodation of DG is proposed, which aims to maximize the daily energy supply, minimize the voltage amplitude deviation, and maximize the line capacity margin. The model effectively takes the distribution network flexibility into consideration while achieving multi-objective optimization under the secure operation constraints of the distribution network. 2. The optimal planning problem regarding high-dimensional variables and multi-peak objective functions is solved using the comprehensive learning particle swarm optimization (CLPSO) algorithm. The CLPSO algorithm can obtain the non-inferior solution set of the DG optimal planning problem, which is distributed across the whole Pareto optimal front and shows better diversity. 3. The mixed strategy Nash equilibrium strategy is first applied to decide the optimal planning solution from the non-inferior solutions, which handle the conflicts between multiple objective functions of the optimal planning model more effectively. Multi-Objective Optimization Model for Accommodation Capability of DG, Considering Distribution Network Flexibility