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

TL;DR

This paper introduces a scalable, stochastic Stackelberg game framework for dynamic EV charging pricing that accounts for heterogeneous user behaviors and system uncertainties, improving demand management and user utility.

Contribution

It develops a novel bi-level stochastic pricing model incorporating behavioral heterogeneity and congestion effects, solved efficiently with a rolling-horizon PSA-CEM approach.

Findings

Reduces queuing penalties significantly.

Enhances user utility over fixed pricing.

Validated with real-world case study.

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.