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Sequential Charging Station Location Optimization under Uncertain Charging Behavior and User Growth

Wenjia Shen, Bo Zhou, Ruiwei Jiang, Siqian Shen

Abstract

Charging station availability is crucial for a thriving electric vehicle market. Due to budget constraints, locating these stations usually proceeds in phases, which calls for careful consideration of the (random) charging demand growth throughout the planning horizon. This paper integrates user choice behavior into two-stage and multi-stage stochastic programming models for intracity charging station planning under demand uncertainty. We derive a second-order conic representation for the nonlinear, nonconvex formulation by taking advantage of the binary nature of location variables and propose subgradient inequalities to accelerate computation. Numerical results demonstrate the value of employing multi-stage models, particularly in scenarios of high demand fluctuations, increased demand dispersion, and high user sensitivity to the distance-to-recharge.

Sequential Charging Station Location Optimization under Uncertain Charging Behavior and User Growth

Abstract

Charging station availability is crucial for a thriving electric vehicle market. Due to budget constraints, locating these stations usually proceeds in phases, which calls for careful consideration of the (random) charging demand growth throughout the planning horizon. This paper integrates user choice behavior into two-stage and multi-stage stochastic programming models for intracity charging station planning under demand uncertainty. We derive a second-order conic representation for the nonlinear, nonconvex formulation by taking advantage of the binary nature of location variables and propose subgradient inequalities to accelerate computation. Numerical results demonstrate the value of employing multi-stage models, particularly in scenarios of high demand fluctuations, increased demand dispersion, and high user sensitivity to the distance-to-recharge.

Paper Structure

This paper contains 18 sections, 2 theorems, 10 equations, 4 figures, 5 tables.

Table of Contents

  1. INTRODUCTION
  2. LITERATURE REVIEW
  3. Long-term Charging Station Location
  4. EV User Choice Behavior
  5. PROBLEM FORMULATIONS
  6. Deterministic Multi-period Model
  7. Multi-stage Stochastic Programming Model
  8. SOLUTION APPROACH
  9. Second-Order Conic Representation
  10. COMPUTATIONAL RESULTS
  11. Experiment Settings
  12. Comparison of Solving Time
  13. Comparison of \ref{['2_objective']} and \ref{['m_objective']} Results
  14. Sensitivity Analysis
  15. Variability of demand growth
  16. ...and 3 more sections

Key Result

Theorem 1

The (nonlinear and nonconvex) constraints q-def admit the following second-order conic representation: where $\overline{d}^{ts}_i := \max_{h \in H}\{d^{ts}_{ih}\}$.

Figures (4)

  • Figure 1: User demand nodes and candidate sites in Trois-Rivières.
  • Figure 2: Decision dynamics in year 3 of scenario A and B, with A showing more demand in the south and B in the center.
  • Figure 3: Planning under scenario C and D, with C showing a new urban center in the northwest and D in the southeast.
  • Figure 4: Planning of two-stage model when new urban centers may emerge.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof