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

2026-01-20

AI Summary

This study addresses the challenges of dynamic pricing and demand management in electric vehicle charging stations, which arise from heterogeneous user behavior, spatiotemporal demand imbalances, and system uncertainty. The authors propose a highly scalable two-level Stackelberg game framework: the upper level optimizes time-varying electricity prices to maximize system utility, while the lower level models users’ decentralized decisions—accounting for price sensitivity, battery degradation, risk preferences, and travel costs—using a multinomial logit model. Departing from conventional network equilibrium assumptions, congestion is approximated via queueing theory. A rolling-horizon optimization approach, integrating a probability sensitivity analysis-guided cross-entropy method (PSA-CEM) and the method of successive averages (MSA), solves the resulting large-scale stochastic optimization problem. Empirical evaluation across 22 charging stations in Melbourne’s Clayton area demonstrates that the proposed mechanism significantly reduces queueing penalties and enhances user utility, outperforming both flat-rate and time-of-use pricing strategies.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Security and Privacy: Large-scale security measurements

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.

Problem

• stochastic dynamic pricing
• heterogeneous user behavior
• electric vehicle charging
• demand management
• system uncertainty

Innovation

• Stackelberg game
• behavioral heterogeneity
• stochastic dynamic pricing
• multinomial logit model
• queuing-theoretic approximation