them. Instead, we employ Mento Carlo method to estimate those two values.

Multi-stage Charging Station Planning Scheme
--------------------------------------------

At each planning stage, the service providers aim at solving the following fundamental problem to obtain the optimal placement policy subjected to the QoS constraints.

$$\label{obj}
\begin{aligned}
&[S_k^T|S_1^{T-1},S_2^{T-1},S_3^{T-1}]=\\
&\operatorname*{argmax}_{\substack{{s_{1,k},\cdots,s_{L,k}}\\{s_{j,k}\in\{0,1\}}}}\left\{\mathbb{E}_{S_{-k}}[U_k]|S_1^{T-1},
S_2^{T-1},S_3^{T-1}\right\},
\end{aligned}$$

subject to $$\Upsilon_k\leq\Upsilon^0,$$ $$\Xi_k\leq\Xi^0,$$ where $\mathbb{E}_{S_{-k}}[.]$ denotes the expectation over $S_{-k}$, and $S_k^T$ is the placement policy at stage $T$. The variables $\Upsilon^0$ and $\Xi^0$ are the predetermined QoS constraints.

To solve this problem, we are confronted with three principal questions: (1) How to predict the aggregated charging demand $\psi_{j,k}$ at each charging station candidate? (2) How to find an appropriate metric to characterize the impacts of EV charging on the power grid? (3) How to derive the optimal placement policy in a tractable way? For the first question, we assume that the service providers estimate the charging demand using a nested logit model. In Section [slowromancap3@]{}, we will describe the nested logit model and elaborate on how to use this model to analyze consumer behavior and estimate the charging demand. In Section [slowromancap4@]{}, we will discuss how the EV charging may impact the power grid, and propose a metric to 