# A Second Order Cone Programming Model for Planning PEV Fast-Charging Stations

## TL;DR

This paper presents a stochastic SOCP model for planning PEV fast-charging stations, integrating transportation demand, heterogeneous vehicle ranges, and power network constraints to optimize siting and sizing.

## Contribution

It introduces a novel closed-form service rate model and a modified CFRLM for accurate demand capture, combined with a stochastic SOCP framework for integrated planning.

## Key findings

- Model effectively captures heterogeneous PEV demands.
- Incorporates power network AC power flow constraints.
- Demonstrates improved planning accuracy through numerical experiments.

## Abstract

This paper studies siting and sizing of plug-in electric vehicle (PEV) fast-charging stations on coupled transportation and power networks. We develop a closed-form service rate model of highway PEV charging stations' service abilities, which considers heterogeneous PEV driving ranges and charging demands.We utilize a modified capacitated flow refueling location model (CFRLM) to explicitly capture time-varying PEV charging demands on the transportation network under driving range constraints. We explore extra constraints of the CFRLM to enhance model accuracy and computational efficiency.We then propose a stochastic mixed-integer second order cone programming (SOCP) model for PEV fast-charging station planning. The model considers the transportation network constraints of CFRLM and the power network constraints with AC power flow. Numerical experiments are conducted to illustrate the effectiveness of the proposed method.