Charging Pricing in Power-Traffic Systems With Price-Elastic Demand: A Quasi-Variational Inequality Approach

The rise of electric vehicles (EVs) fosters closer integration between the power and transportation sectors. While implementing a fair EV charging pricing strategy optimizes the system economic performance, modeling EV users' behaviors and their elastic demand in response to charging prices rem...

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Published in:	IEEE transactions on power systems Vol. 40; no. 6; pp. 5013 - 5026
Main Authors:	Xie, Shiwei, Xie, Longtao, Wu, Qiuwei, Shu, Shengwen, Chen, Yuanyi, Yang, Qiang, Shao, Zhenguo
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.11.2025 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Costs Elasticity Electric vehicle charging Electric vehicles EV user behavior Game theory Load shedding market regulation Optimization Price-elastic demand Pricing projection gradient algorithm quasi-variational inequality Reactive power Regulation Sensitivity analysis Transportation networks Transportation systems Upper bound
ISSN:	0885-8950, 1558-0679
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Abstract	The rise of electric vehicles (EVs) fosters closer integration between the power and transportation sectors. While implementing a fair EV charging pricing strategy optimizes the system economic performance, modeling EV users' behaviors and their elastic demand in response to charging prices remains a significant challenge. This paper proposes a novel pricing scheme for EV charging within power-transportation systems using a tri-level framework that considers the interactions among the power distribution network (PDN), charging network operator (CNO), and EVs. To capture the responsive behaviors of EVs, a user equilibrium (UE) model with price-elastic demand is formulated as a quasi-variational inequality (QVI). This approach reduces the tri-level pricing problem to a bi-level optimization problem by merging the middle and lower levels into an optimization problem with QVI constraints, thereby achieving mathematical tractability. The outer level optimizes energy dispatch in the PDN, while the inner level focuses on the CNO's pricing optimization in response to elastic EV demand. To solve the problem, a projection gradient algorithm and a tailored fixed-point algorithm are developed. Simulation results confirm the effectiveness and superiority of the proposed model and algorithms. Sensitivity analysis further shows that elasticity and regulation significantly affect system efficiency, demonstrating the model's robustness.
AbstractList	The rise of electric vehicles (EVs) fosters closer integration between the power and transportation sectors. While implementing a fair EV charging pricing strategy optimizes the system economic performance, modeling EV users' behaviors and their elastic demand in response to charging prices remains a significant challenge. This paper proposes a novel pricing scheme for EV charging within power-transportation systems using a tri-level framework that considers the interactions among the power distribution network (PDN), charging network operator (CNO), and EVs. To capture the responsive behaviors of EVs, a user equilibrium (UE) model with price-elastic demand is formulated as a quasi-variational inequality (QVI). This approach reduces the tri-level pricing problem to a bi-level optimization problem by merging the middle and lower levels into an optimization problem with QVI constraints, thereby achieving mathematical tractability. The outer level optimizes energy dispatch in the PDN, while the inner level focuses on the CNO's pricing optimization in response to elastic EV demand. To solve the problem, a projection gradient algorithm and a tailored fixed-point algorithm are developed. Simulation results confirm the effectiveness and superiority of the proposed model and algorithms. Sensitivity analysis further shows that elasticity and regulation significantly affect system efficiency, demonstrating the model's robustness.
Author	Shu, Shengwen Yang, Qiang Shao, Zhenguo Xie, Shiwei Chen, Yuanyi Xie, Longtao Wu, Qiuwei
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SubjectTerms	Algorithms Costs Elasticity Electric vehicle charging Electric vehicles EV user behavior Game theory Load shedding market regulation Optimization Price-elastic demand Pricing projection gradient algorithm quasi-variational inequality Reactive power Regulation Sensitivity analysis Transportation networks Transportation systems Upper bound
Title	Charging Pricing in Power-Traffic Systems With Price-Elastic Demand: A Quasi-Variational Inequality Approach
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