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Hierarchical Game for Coupled Power System with Energy Sharing and Transportation System

Dongxiang Yan, Tongxin Li, Changhong Zhao, Han Wang, Yue Chen

TL;DR

The paper addresses the problem of coordinating coupled power and transportation networks under energy sharing and EV charging by formulating a hierarchical game that couples a generalized Nash equilibrium for energy sharing with Wardrop routing. It introduces an energy sharing market under AC network constraints that yields a socially optimal equilibrium and derives a MILP by applying polyhedral SOC approximation, primal-dual reformulation, and piecewise McCormick envelopes. The approach is validated on IEEE test networks, showing mutual influence between sharing prices, charging demand, and traffic patterns, while achieving favorable computation times and robustness against convergence issues compared to benchmarks. The work demonstrates the feasibility and benefits of integrating energy sharing with EV charging in a coupled infrastructure context and points to future extensions to multi-period dynamics and ride sharing.

Abstract

The wide deployment of distributed renewable energy sources and electric vehicles can help mitigate climate crisis. This necessitates new business models in the power sector to hedge against uncertainties while imposing a strong coupling between the connected power and transportation networks. To address these challenges, this paper first proposes an energy sharing mechanism considering AC power network constraints to encourage local energy exchange in the power system. Under the proposed mechanism, all prosumers play a generalized Nash game. We prove that the energy sharing equilibrium exists and is socially optimal. Furthermore, a hierarchical game is built to characterize the interactions both inside and between the power and transportation systems. Externally, the two systems are engaged in a generalized Nash game because traffic flows serve as electric demands by charging behaviors, and each driver pays the energy sharing price for charging. The hierarchical game is then converted into a mixed-integer linear program (MILP) with the help of optimality conditions and linearization techniques. Numerical experiments validate the theoretical results and show the mutual impact between the two systems.

Hierarchical Game for Coupled Power System with Energy Sharing and Transportation System

TL;DR

The paper addresses the problem of coordinating coupled power and transportation networks under energy sharing and EV charging by formulating a hierarchical game that couples a generalized Nash equilibrium for energy sharing with Wardrop routing. It introduces an energy sharing market under AC network constraints that yields a socially optimal equilibrium and derives a MILP by applying polyhedral SOC approximation, primal-dual reformulation, and piecewise McCormick envelopes. The approach is validated on IEEE test networks, showing mutual influence between sharing prices, charging demand, and traffic patterns, while achieving favorable computation times and robustness against convergence issues compared to benchmarks. The work demonstrates the feasibility and benefits of integrating energy sharing with EV charging in a coupled infrastructure context and points to future extensions to multi-period dynamics and ride sharing.

Abstract

The wide deployment of distributed renewable energy sources and electric vehicles can help mitigate climate crisis. This necessitates new business models in the power sector to hedge against uncertainties while imposing a strong coupling between the connected power and transportation networks. To address these challenges, this paper first proposes an energy sharing mechanism considering AC power network constraints to encourage local energy exchange in the power system. Under the proposed mechanism, all prosumers play a generalized Nash game. We prove that the energy sharing equilibrium exists and is socially optimal. Furthermore, a hierarchical game is built to characterize the interactions both inside and between the power and transportation systems. Externally, the two systems are engaged in a generalized Nash game because traffic flows serve as electric demands by charging behaviors, and each driver pays the energy sharing price for charging. The hierarchical game is then converted into a mixed-integer linear program (MILP) with the help of optimality conditions and linearization techniques. Numerical experiments validate the theoretical results and show the mutual impact between the two systems.
Paper Structure (36 sections, 2 theorems, 38 equations, 17 figures, 5 tables, 1 algorithm)

This paper contains 36 sections, 2 theorems, 38 equations, 17 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Acronyms
  2. Indices and Sets
  3. Parameters
  4. Decision Variables
  5. Introduction
  6. Mathematical Formulation
  7. Energy Sharing Equilibrium in Power System
  8. Wardrop User Equilibrium in Transportation System
  9. Hierarchical Game of Coupled Systems
  10. Solution Methodology
  11. Optimization Models For Computing the Equilibrium
  12. Transformation and Linearization
  13. Primal-dual Optimality Condition of Problem \ref{['eq:share-eq']}
  14. KKT Condition of Problem \ref{['eq:traffic-eq']}
  15. Linearization of the Bilinear Term and Travel Time
  16. ...and 21 more sections

Key Result

Proposition 1

The generalized Nash equilibrium $(b^*,d^*,\lambda^*)$ of the energy sharing game eq:market and eq:eachnode can be obtained by where $d_i^*,\forall i \in \mathcal{E}_N$ is unique with $\lambda_i^*=\xi^*_i$.

Figures (17)

  • Figure 1: Structure of the coupled power and transportation systems.
  • Figure 2: Illustration of three types of links.
  • Figure 3: Hierarchical game of transportation and power systems.
  • Figure 4: Modified IEEE 33-bus test system with 4 prosumers.
  • Figure 5: Left: Original transportation network with 12 nodes and 20 links. Right: Expanded transportation network with 28 nodes and 44 links.
  • ...and 12 more figures

Theorems & Definitions (4)

  • Definition 1
  • Definition 2
  • Proposition 1
  • Proposition 2