Non-cooperative Game Optimization of Urban Energy Systems Based on Inner-outer Iterative Method

Chenxu Yin; Yonghui Sun; Dongliang Xie; Fan Sheng; Liang Zhao

doi:10.35833/MPCE.2025.000695

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Non-cooperative Game Optimization of Urban Energy Systems Based on Inner-outer Iterative Method

Original Paper | 更新时间：2026-09-28

- Non-cooperative Game Optimization of Urban Energy Systems Based on Inner-outer Iterative Method
- Journal of Modern Power Systems and Clean Energy Vol. 14, Issue 5, Pages: 1720-1731(2026)
- 作者机构：
  
  1.School of Electrical and Power Engineering, Hohai University, Nanjing 210098, China
  2.State Grid Electric Power Research Institute, Nanjing 211106, China
- 作者简介：
  
  Chenxu Yin is currently pursuing the Ph.D. degree in electrical engineering from Hohai University, Nanjing, China. His research interests include multi-energy system, collaborative optimization, game theory, and convex optimization. Email:chen_xu_yin@163.com
  Yonghui Sun received the Ph.D. degree from the City University of Hong Kong, Hong Kong, China, in 2010. He is currently a Professor with the School of Electrical and Power Engineering, Hohai University, Nanjing, China. His research interests include stability analysis and control of power systems, optimal planning and operation of integrated energy systems, optimization algorithm, and data analysis. Email:sunyonghui168@gmail.com
  Dongliang Xie received the Ph.D. degree in electrical engineering from Southeast University, Nanjing, China, in 2012. During 2011-2012, he was a Research Associate in Hong Kong Polytechnic University, Hong Kong, China. He is currently working for State Grid Electric Power Research Institute (SGEPRI), Nanjing, China. His research interests include digital-twin platform of complex systems, planning and operation optimization for high-renewable-penetration power systems, and resilience analysis under extreme cases. Email:xiedongliang@sgepri.sgcc.com.cn
  Fan Sheng is currently pursuing the M.S. degree in electrical engineering from Hohai University, Nanjing, China. His research interests include integrated energy system and robust optimization. Email:sf_011106@163.com
  Liang Zhao is currently pursuing the Ph.D. degree in electrical engineering from Hohai University, Nanjing, China. His research interests include analysis of power system adequacy, collaborative optimization, backup optimization, and deep reinforcement learning. Email:zhaoliang3626@163.com
- 基金信息：
- DOI：10.35833/MPCE.2025.000695
  CLC：
- Received：29 July 2025，
  
  Revised：2025-11-01，
  
  Accepted：13 February 2026，
  
  Online First：30 March 2026，
  
  Published：15 September 2026
- 稿件说明：
移动端阅览
Yin Chenxu,Sun Yonghui,Xie Dongliang,et al.Non-cooperative Game Optimization of Urban Energy Systems Based on Inner-outer Iterative Method[J].Journal of Modern Power Systems and Clean Energy,2026,14(05):1720-1731.
DOI：

Yin Chenxu,Sun Yonghui,Xie Dongliang,et al.Non-cooperative Game Optimization of Urban Energy Systems Based on Inner-outer Iterative Method[J].Journal of Modern Power Systems and Clean Energy,2026,14(05):1720-1731. DOI： 10.35833/MPCE.2025.000695.

摘要

Abstract

This paper addresses the increasingly tight energy coupling in urban energy systems

which are composed of the power distribution network (PDN)

the transportation network (TN)

and the gas distribution network (GDN). A non-cooperative game optimization model for the urban energy system is developed

to achieve coordinated optimization among these three different energy networks operated by independent stakeholders. To avoid excessive sharing of private information

an inner-outer iterative method is further proposed to obtain the Nash equilibrium and enhance solving efficiency. In the proposed method

each energy network is iteratively optimized by exchanging only the price and load information

and the network parameters are not disclosed. In the inner layer

the PDN-TN coupled subsystem and the PDN-GDN coupled subsystem are solved separately. In the outer layer

interactions between charging loads and gas prices are coordinated through the PDN

thereby enabling cross-network coordination of urban energy systems. Case studies demonstrate that the convergence speed of the PDN-TN coupled subsystem is significantly improved by dynamically adjusting the electricity price based on sensitivity coefficients. Balanced resource allocation of the urban energy system is achieved through the non-cooperative game

while autonomy of all stakeholders is preserved. Energy procurement costs are reduced by up to 25.56% compared with that of the PDN-TN coupled subsystem.

关键词

Keywords

references

L. Ge, B. Zhang, W. Huang et al. , “A review of hydrogen generation, storage, and applications in power system,” Journal of Energy Storage , vol. 75 , p. 109307 , Jan. 2024 .

W. Xu, Y. Guo, T. Meng et al. , “Coordinated dispatch based on distributed robust optimization for interconnected urban integrated energy and transmission systems,” Journal of Modern Power Systems and Clean Energy , vol. 12 , no. 3 , pp. 840 - 851 , May 2024.

Y. Tang, W. Liu, K. T. Chau et al. , “Stochastic behavior modeling and optimal bidirect ional charging station deployment in EV energy network,” IEEE Transactions on Intelligent Transportation Systems , vol. 26 , no. 5 , pp. 6231 - 6247 , May 2025.

H. Wang, C. Bai, Z. Wang et al. , “Resilient preparation and restoration strategy for integrated electric-gas distribution systems considering mobile energy storage,” IEEE Transactions on Smart Grid , vol. 16 , no. 2 , pp. 1127 - 1141 , Mar. 2025 .

J. Wang, Y. Sun, R. J. Mahfoud et al. , “Co-optimization of multi-stakeholders in multi-heterogeneous energy system considering gas flow dynamics,” Sustainable Energy, Grids and Networks , vol. 36 , p. 101175 , Dec. 2023 .

J. Xiong, Y. Sun, J. Wang et al. , “Multi-stage equipment optimal configuration of park-level integrated energy system considering flexible loads,” International Journal of Electrical Power and Energy Systems , vol. 140 , p. 108050 , Sept. 2022.

Y. Li, Y. Cai, T. Zhao et al. , “Multi-objective optimal operation of centralized battery swap charging system with photovoltaic,” Journal of Modern Power Systems and Clean Energy , vol. 10 , no. 1 , pp. 149 - 162 , Jan. 2022 .

Y. Wang, F. Lu, C. Gu et al. , “Multi-objective optimization for customer flexibility management to mitigate consecutive days of power supply shortages,” IEEE Transactions on Power Systems , vol. 40 , no. 4 , pp. 3306 - 3319 , Jul. 2025 .

J. Wang, Y. Sheng, H. Ge et al. , “Charging pricing for autonomous mobility-on-demand fleets based on game theory,” Journal of Modern Power Systems and Clean Energy , vol. 12 , no. 6 , pp. 2006 - 2018 , Nov. 2024 .

X. Ge, S. Cao, Y. Fu et al. , “Optimal scheduling of space-time dual-scale electric vehicles based on regional decoupling,” Proceedings of the CSEE , vol. 43 , no. 19 , pp. 7383 - 7396 , Oct. 2023 .

C. Lou, C. Li, L. Zhang et al. , “Two-stage bidding strategy with dispatch potential of electric vehicle aggregators for mitigating three-phase imbalance,” Journal of Modern Power Systems and Clean Energy , vol. 13 , no. 5 , pp. 1823 - 1835 , Sept. 2025.

X. Xu, Z. Qiu, T. Zhang et al. , “Distribut ed source-load-storage cooperative low-carbon scheduling strategy considering vehicle-to-grid aggregators,” Journal of Modern Power Systems and Clean Energy , vol. 12 , no. 2 , pp. 440 - 453 , Mar. 2024 .

K. Li, C. Shao, Z. Hu et al. , “A MILP method for optimal planning of electric vehicle charging stations in coordinated urban power and transportation networks,” IEEE Transactions on Power Systems , vol. 38 , no. 6 , pp. 5406 - 5419 , Nov. 2023 .

Y. Cui, Z. Hu, X. Duan et al. , “A multi-period charging service pricing game for public charging network operators considering the dynamics of coupled traffic-power systems,” IEEE Transactions on Intelligent Transportation Systems , vol. 24 , no. 9 , pp. 9355 - 9367 , Sept. 2023.

K. Li, C. Shao, Y. Wang et al. , “Optimal planning of urban integrated energy systems considering electricity-gas-transportation interactions,” Proceedings of the CSEE , vol. 43 , no. 6 , pp. 2263 - 2273 , Mar. 2023 .

S. Xie, J. Zheng, Z. Hu et al. , “Urban multi-energy network optimization: an enhanced model using a two-stage bound-tightening approach,” Applied Energy , vol. 277 , p. 115577 , Nov. 2020 .

Z. Zhang and K. S. Fedorovich, “Optimal operation of multi-integrated energy system based on multi-level Nash multi-stage robust,” Applied Energy , vol. 358 , p. 122557 , Mar. 2024 .

Y. Sun, B. Zhang, L. Ge et al. , “Day-ahead optimization schedule for gas-electric integrated energy system based on second-order cone programming,” CSEE Journal of Power and Energy Systems , vol. 6 , no. 1 , pp. 142 - 151 , Mar. 2020 .

Z. Tong, Z. Ren, J. Wu et al. , “Multi-agent game operation of electricity-hydrogen-transportation system considering HFCV hydrogen refueling uncertainty,” Automation of Electric Power Systems , vol. 49 , no. 2 , pp. 154 - 164 , Jan. 2025 .

Y. Si, L. Chen, X. Zhang et al. , “Capacity allocation of hybrid power system with hot dry rock geothermal energy, thermal storage, and PV based on game approaches,” Journal of Modern Power Systems and Clean Energy , vol. 11 , no. 1 , pp. 290 - 301 , Jan. 2023 .

C. Yin, Y. Sun, D. Xie et al. , “Multi-objective cooperative optimization of electricity-gas interconnected integrated energy system from game perspective,” Automation of Electric Power Systems , vol. 48 , no. 11 , pp. 173 - 183 , Jun. 2024 .

Z. Li, Q. Guo, H. Sun et al. , “A new LMP-sensitivity-based heterogeneous decomposition for transmission and distribution coordinated economic dispatch,” IEEE Transactions on Smart Grid , vol. 9 , no. 2 , pp. 931 - 941 , Mar. 2018 .

Power Quality – Deviation of Supply Voltage , GB/T 12325-2008, Jun. 2008 .

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