the simultaneous large-scale EV charging can disrupt the normal operation of the power grid in terms of frequency variation, voltage imbalance, voltage variation, power loss, etc [@impact1]-[@impact3]. In a conventional power grid, the generators will be incentivized to cooperatively control the output of real power and reactive power to maintain system stability, perform frequency regulation and voltage regulation. The charging service providers typically cannot participate in such market. Instead, we assume that they are fined in proportion to the “disturbance" they impose on the grid. Thus, the providers must optimally place the charging stations to mitigate the “disturbance" to the power grid. Accordingly, the overall utility function of service provider can be defined as:

$$\label{omega}
U_k=\Pi_k-wB_k,$$

where $\Pi_k$ is the total profits from EV charging. $B_k$ characterizes the penalty arising from large-scale EV charging. The variable $w$ is a weighting coefficient, reflecting the tolerance to the penalty. In the following section, we will further discuss how to develop a proper metric to evaluate the penalty $B_k$. We should note that the weighting factor $w$ in Equation (\[omega\]) offers a mechanism for the charging service providers to strike a balance between their own profit and the “stress" their charging adds to 