{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:53:55Z","timestamp":1777510435917,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T00:00:00Z","timestamp":1762992000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"publisher","award":["2023YFB2407300"],"award-info":[{"award-number":["2023YFB2407300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["52477117"],"award-info":[{"award-number":["52477117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["52407135"],"award-info":[{"award-number":["52407135"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["U24B6008"],"award-info":[{"award-number":["U24B6008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Tianjin Natural Science Foundation Diversified Investment Key Program","award":["22JCZDJC00710"],"award-info":[{"award-number":["22JCZDJC00710"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the accelerating digital transformation of modern society, numerous data center (DC) agents are connected to the distribution power networks (DPNs) via microgrid and engaging in fierce market competition. To address the asymmetric operational risks faced by each data center agent, particularly those arising from market volatility and equipment failures, a novel cooperative game-theoretic approach is proposed in this paper. Firstly, a cooperative operation framework for the microgrid-integrated data centers (MDCs) system is established from two dimensions: joint task allocation across MDCs on the computing side and energy sharing among MDCs on the power side. Moreover, an optimal operating model for MDCs is established, which integrates the task allocation model that takes into account the task processing capacity of MDCs. Then, a cooperative operation model for the MDCs system based on Nash game theory is developed, and a joint solution framework for task allocation and the cooperative operation model is designed. Finally, the proposed cooperative game-theoretic approach is validated in a test system. The results show that the proposed approach ensures the reliable operation of the DPN while avoiding asymmetric operation risks among MDCs. It enhances the stability and security of distributed data processing. Furthermore, the Nash game-theoretic model achieves a symmetric distribution of profits and risks across MDCs, eliminating individual biases and maximizing the overall benefits of the cooperative alliance.<\/jats:p>","DOI":"10.3390\/sym17111950","type":"journal-article","created":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T12:57:13Z","timestamp":1763038633000},"page":"1950","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Novel Cooperative Game Approach for Microgrid Integrated with Data Centers in Distribution Power Networks"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-7944-2225","authenticated-orcid":false,"given":"Xi","family":"Zhang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Smart Power Distribution Equipment and System, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-7608-4339","authenticated-orcid":false,"given":"Tianxiang","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Smart Power Distribution Equipment and System, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Jin","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Smart Power Distribution Equipment and System, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4986-4438","authenticated-orcid":false,"given":"Qian","family":"Xiao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Smart Power Distribution Equipment and System, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-1566-1442","authenticated-orcid":false,"given":"Sen","family":"Tian","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Smart Power Distribution Equipment and System, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunfei","family":"Mu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Smart Power Distribution Equipment and System, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongjie","family":"Jia","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Smart Power Distribution Equipment and System, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1109\/TSG.2024.3478844","article-title":"Electrical circuit analogy-based maximum latency calculation method of internet data centers in power-communication network","volume":"16","author":"Xiao","year":"2025","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1109\/TSG.2024.3482390","article-title":"Privacy-preserving energy sharing among cloud service providers via collaborative job scheduling","volume":"16","author":"Sun","year":"2025","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Xiao, Q., Yu, H.L., Jin, Y., Jia, H.J., Mu, Y.F., Zhu, J.B., Liu, H.Q., Teodorescu, R., and Blaabjerg, F. (2025). Adaptive virtual inertia emulation and control scheme of cascaded multilevel converters to maximize its frequency support ability. IEEE Trans. Ind. Electron., early access.","DOI":"10.1109\/TIE.2025.3621665"},{"key":"ref_4","first-page":"1215","article-title":"Stochastic programming for cost optimization in geographically distributed internet data centers","volume":"8","author":"Wang","year":"2022","journal-title":"CSEE J. Power Energy Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3748","DOI":"10.1109\/TSG.2016.2640453","article-title":"Distributed real-time energy management in data center microgrids","volume":"9","author":"Yu","year":"2018","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"110032","DOI":"10.1016\/j.ijepes.2024.110032","article-title":"Energy-aware coordinated operation strategy of geographically distributed data centers","volume":"159","author":"Zhou","year":"2024","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"109466","DOI":"10.1016\/j.rser.2019.109466","article-title":"Internet data centers participating in demand response: A comprehensive review","volume":"117","author":"Chen","year":"2020","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1109\/TETCI.2023.3234545","article-title":"Safecool: Safe and energy-efficient cooling management in data centers with model-based reinforcement learning","volume":"7","author":"Wan","year":"2023","journal-title":"IEEE Trans. Emerg. Top. Comput. Intell."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"114806","DOI":"10.1016\/j.apenergy.2020.114806","article-title":"A review of power consumption models of servers in data centers","volume":"265","author":"Jin","year":"2020","journal-title":"Appl. Energy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"126031","DOI":"10.1016\/j.apenergy.2025.126031","article-title":"Green optimization for micro data centers: Task scheduling for a combined energy consumption strategy","volume":"393","author":"Hu","year":"2025","journal-title":"Appl. Energy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1109\/TSG.2022.3197613","article-title":"Exploiting internet data centers as energy prosumers in integrated electricity-heat system","volume":"14","author":"Yin","year":"2023","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1109\/TSTE.2023.3306529","article-title":"Combined heat and power dispatch against cold waves utilizing responsive internet data centers","volume":"15","author":"Yin","year":"2024","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"122769","DOI":"10.1016\/j.apenergy.2024.122769","article-title":"Managing data center cluster as non-wire alternative: A case in balancing market","volume":"360","author":"Cao","year":"2024","journal-title":"Appl. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1109\/TCC.2021.3130644","article-title":"Carbon management of multi-datacenter based on spatio-temporal task migration","volume":"11","author":"Yang","year":"2023","journal-title":"IEEE Trans. Cloud Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"986","DOI":"10.1109\/TSTE.2023.3321591","article-title":"Collaborative response of data center coupled with hydrogen storage system for renewable energy absorption","volume":"15","author":"Long","year":"2024","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"133991","DOI":"10.1016\/j.energy.2024.133991","article-title":"A novel two-stage energy sharing method for data center cluster considering \u2018Carbon-Green Certificate\u2019 coupling mechanism","volume":"313","author":"Bian","year":"2024","journal-title":"Energy"},{"key":"ref_17","first-page":"778","article-title":"Distributed resource allocation for data center networks: A hierarchical game approach","volume":"8","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Cloud Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1109\/JSYST.2019.2921592","article-title":"An adaptive grid frequency support mechanism for energy management in cloud data centers","volume":"14","author":"Kaur","year":"2020","journal-title":"IEEE Syst. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1109\/TIA.2022.3214186","article-title":"Joint workload scheduling in geo-distributed data centers considering UPS power losses","volume":"59","author":"Ye","year":"2023","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1109\/TSG.2020.3037556","article-title":"Bi-level robust optimization for distribution system with multiple microgrids considering uncertainty distribution locational marginal price","volume":"12","author":"Wang","year":"2021","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6760","DOI":"10.1109\/TII.2020.2974023","article-title":"Peer-to-peer energy sharing in distribution networks with multiple sharing regions","volume":"16","author":"Chen","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Tian, S., Xiao, Q., Li, T.X., Jin, Y., Mu, Y.F., Jia, H.J., Li, W., Teodorescu, R., and Guerrero, J.M. (2024). An Optimization Strategy for EV-Integrated Microgrids Considering Peer-to-Peer Transactions. Sustainability, 16.","DOI":"10.3390\/su16208955"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1109\/TSG.2024.3471611","article-title":"Asymmetric bargaining-based SOP planning considering peer-to-peer electricity trading","volume":"16","author":"Ji","year":"2025","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5232","DOI":"10.1109\/TSG.2024.3382810","article-title":"Computation offloading for cloud-edge collaborative virtual power plant frequency regulation service","volume":"15","author":"Lin","year":"2024","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1454","DOI":"10.1109\/TSG.2022.3168150","article-title":"Peer-to-peer energy trading using prediction intervals of renewable energy generation","volume":"14","author":"Jia","year":"2023","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"133991","DOI":"10.1016\/j.apenergy.2018.05.095","article-title":"Bargaining-based cooperative energy trading for distribution company and demand response","volume":"226","author":"Fan","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1109\/TSG.2023.3309405","article-title":"A fully distributed privacy-preserving energy management system for networked microgrid cluster based on homomorphic encryption","volume":"15","author":"Yuan","year":"2024","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_28","first-page":"119","article-title":"Coordinated operations of highly renewable power systems and distributed data centers","volume":"54","author":"Li","year":"2023","journal-title":"Sci. Sin. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1109\/TCC.2024.3396476","article-title":"Low-carbon operation of data centers with joint workload sharing and carbon allowance trading","volume":"12","author":"Yan","year":"2024","journal-title":"IEEE Trans. Cloud Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3914","DOI":"10.1109\/TPWRS.2025.3532208","article-title":"Unlocking spatio-temporal flexibility of data centers in multiple regional peer-to-peer energy transaction markets","volume":"40","author":"Jin","year":"2025","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/TSG.2024.3452064","article-title":"Optimal planning of multi-microgrid system with shared energy storage based on capacity leasing and energy sharing","volume":"16","author":"Han","year":"2025","journal-title":"IEEE Trans. Smart Grid"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1950\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T05:30:12Z","timestamp":1763184612000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1950"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,13]]},"references-count":31,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111950"],"URL":"https:\/\/doi.org\/10.3390\/sym17111950","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,13]]}}}