to characterize the competition among service providers, and the optimal station placement policy is obtained. Section [slowromancap6@]{} shows the architecture and applications of the simulation software and discusses a case study in San Pedro District. Conclusions are given in Section [slowromancap7@]{}. Table [slowromancap1@]{} provides a full description of parameters and symbols used in the paper.

Problem Formulation
===================

  Parameter                                   Description                          Unit
  ------------------------------------------- ------------------------------------ --------
  $L$                                         Total Candidate Locations            -
  $N$                                         Total EVs                            -
  $\psi_{j,k}^n$                              Charging Demand                      kWh
  $s_{j,k}$                                   Placement Indicator                  -
  $F_{j,k}$                                   Setup Cost                           \$
  $R_k$                                       Total Revenue                        \$
  $c_{j,k}$                                   Locational Marginal Price            \$
  $\Pi_k$                                     Total Profit                         \$
  $U_k$                                       Overall utility                      \$
  w                                           Coef. of EV Charging Penalty         -
  $\Upsilon_k$                                Average Service Probability          -
  $\Xi_k$                                     Average Service Coverage             -
  $t_k$                                       Average Charging Time                min
  $p_k$                                       Retail Charging Price                \$/kWh
  $i_n$                                       Income of the $n$th EV owner         \$
  $d_{j,k}^n$                                 Deviating distance                   km
  $z_{j,k}^n$                                 Indicator of Destination             -
  $d_{th}$                                    Distance threshold                   km
  $r_{j,k}$                                   Indicator of Restaurant              -
  $g_{j,k}$                                   Indicator of Shopcenter              -
  $m_{j,k}$                                   Indicator of Supermarket             -
  $\mathbf{P}_{\textrm{g}}^{\textrm{base}}$   Active power vector without EV       -
  $\mathbf{P}_{\textrm{g}}^{\textrm{EV}}$     Active power vector with EV          -
  $\mathbf{Q}_{\textrm{g}}^{\textrm{base}}$   Reactive power vector without EV     -
  $\mathbf{Q}_{\textrm{g}}^{\textrm{EV}}$     Reactive power vector with EV        -
  $v_i$                                       Voltage at bus $i$                   Volts
  $\phi_{ik}$                                 