Stochastic Dynamic Pricing of Electric Vehicle Charging with Heterogeneous User Behavior: A Stackelberg Game Framework

TL;DR

The paper addresses dynamic pricing for EV charging networks under stochastic, heterogeneous user behavior by formulating a bi-level Stackelberg game where prices are set by a leader to maximize a system performance index and EVs respond via a probabilistic MNL choice model incorporating travel, waiting, and charging costs. It introduces a rolling-horizon solution that blends a dynamic PSA-guided Cross-Entropy Method with the Method of Successive Averages to efficiently solve large-scale, time-varying pricing problems without relying on network equilibrium constraints. The methodology explicitly models station and vehicle heterogeneity, queuing dynamics, reachability, and nonlinear charging curves, providing a robust framework that reduces queuing penalties while improving user utility compared to fixed or ToU pricing. Real-world validation in Clayton, Melbourne demonstrates significant welfare improvements and scalability, offering a practical tool for strategic EV charging management that balances operator revenue and user experience. The work highlights the importance of integrating behavioral stochasticity and multi-level heterogeneity into pricing decisions for effective congestion management in urban charging networks.

Abstract

The rapid adoption of electric vehicles (EVs) introduces complex spatiotemporal demand management challenges for charging station operators (CSOs), exacerbated by demand imbalances, behavioral heterogeneity, and system uncertainty. Traditional dynamic pricing models, often relying on deterministic EV-CS pairings and network equilibrium assumptions, frequently oversimplify user behavior and lack scalability. This study proposes a stochastic, behaviorally heterogeneous dynamic pricing framework formulated as a bi-level Stackelberg game. The upper level optimizes time-varying pricing to maximize system-wide utility, while the lower level models decentralized EV users via a multinomial logit (MNL) choice model incorporating price sensitivity, battery aging, risk attitudes, and network travel costs. Crucially, the model avoids network equilibrium constraints to enhance scalability, with congestion effects represented via queuing-theoretic approximations. To efficiently solve the resulting large-scale optimization problem, a rolling-horizon approach combining the Dynamic Probabilistic Sensitivity Analysis-guided Cross-Entropy Method (PSA-CEM) with the Method of Successive Averages (MSA) is implemented. A real-world case study in Clayton, Melbourne, validates the framework using 22 charging stations. Simulation results demonstrate that the proposed mechanism substantially reduces queuing penalties and improves user utility compared to fixed and time-of-use pricing. The framework provides a robust, scalable tool for strategic EV charging management, balancing realism with computational efficiency.

Figures (12)

• Figure 1: Overall framework of the proposed bi-level Stackelberg optimization for stochastic EV charging station selection and dynamic pricing.
• Figure 2: The overall algorithmic structure of the proposed bi-level optimization framework.
• Figure 3: Spatial and temporal overview of the study area: (Left) Spatial distribution of Level 2 and Fast-Charging Stations (FCS) with EV demand hotspots in Melbourne; (Right) Hourly EV charging demand profile.
• Figure 4: Convergence analysis of the CEM algorithm. (a) System utility bounds across 24 time windows, highlighting algorithmic robustness. (b) Detailed evolution of utility and standard deviation ($\sigma$), illustrating search space contraction.
• Figure 5: 3D PDF evolution of price distributions for Station 8 across a 24-hour horizon, illustrating the convergence of price density over optimization iterations.