denote the $j$-th charging outlet in the $i$-th station, where $\textbf{J}_i$ is the set of charging outlets belonging to the $i$-th charging station. In this distribution network, different charging stations are connected to different transformers/lines, represented by different nodes later for consistency. Therefore, the matrix $\textbf{X}_{(L\times I)}$ is used to indicate the relationship between different nodes and charing stations, where $X_{li}\!=\!1$ means that the $i$-th station is downstream of the $l$-th node, otherwise $X_{li}\!=\!0$. It should be noted that the network constraint is not explicitly modelled here as in generic AC networks. We only use the matrix $\mathbf{X}_{\!\left(L\times I\!\right)}$ to reflect the DC power flow relationship between different nodes and charging stations to present the problem clearly. Meanwhile, other non-EV loads, such as factories, households, and shopping malls, are also fed by this distribution network. The amount of uncontrollable loads connected to the $l$-th node is $N_l(t)$ in time slot $t$.

To alleviate the burden imposed by charging stations on the distribution networks, every charging station is equipped with a renewable energy generator, whose production rate is $U_i(t)\!\in\![0,U_{max}]$ for the $i$-th station, and the cost to use its own renewable energy is neglected in this scenario. We do not consider 