Stackelberg game-based coordinated optimal operation method for multiple data centers and power grids

ZHANG Changlin; FAN Pengfei; HAN Jianpei

doi:10.3969/j.issn.2097-0706.2026.08.009

English Version Journal Login

您当前的位置：

首页 >

文章列表页 >

Stackelberg game-based coordinated optimal operation method for multiple data centers and power grids

System Scheduling & Low-Carbon Operation | 更新时间：2026-10-08

- Stackelberg game-based coordinated optimal operation method for multiple data centers and power grids
- BLASTING Vol. 48, Issue 8, Pages: 107-116(2026)
- 作者机构：
  
  1.辽宁工程技术大学电气与控制工程学院，辽宁葫芦岛 125105
  2.北方工业大学储能科学与工程学院，北京 100144
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(52507116);Beijing Natural Science Foundation(3254046)
- DOI：10.3969/j.issn.2097-0706.2026.08.009
  CLC： TK 01
- Received：06 July 2026，
  
  Revised：2026-07-22，
  
  Online First：06 August 2026，
  
  Published：25 August 2026
- 稿件说明：
移动端阅览
张昌林,范鹏飞,韩建沛.基于主从博弈的多数据中心与电网协同优化运行方法[J].综合智慧能源,2026,48(08):107-116.

ZHANG Changlin,FAN Pengfei,HAN Jianpei.Stackelberg game-based coordinated optimal operation method for multiple data centers and power grids[J].BLASTING,2026,48(08):107-116.
张昌林,范鹏飞,韩建沛.基于主从博弈的多数据中心与电网协同优化运行方法[J].综合智慧能源,2026,48(08):107-116. DOI： 10.3969/j.issn.2097-0706.2026.08.009.

ZHANG Changlin,FAN Pengfei,HAN Jianpei.Stackelberg game-based coordinated optimal operation method for multiple data centers and power grids[J].BLASTING,2026,48(08):107-116. DOI： 10.3969/j.issn.2097-0706.2026.08.009.

摘要

随着“东数西算”工程与新型电力系统建设的推进，数据中心已成为电力系统中快速增长的高耗能负荷，其灵活调节能力有望为电网提供低成本的柔性响应资源。然而，现有研究未能充分考虑电网运营商与多个数据中心间的利益博弈及多主体协同中的数据隐私保护问题，制约了理论成果的工程化应用。为此，提出了一种融合主从博弈与自适应交替方向乘子法（ADMM）的双层分布式优化方法。首先，构建了融合IT设备功耗、动态电能利用效率（PUE）冷却模型、排队论任务时延与跨中心迁移的多数据中心精细化灵活性模型，从时间与空间2个维度刻画数据中心的可调节潜力。其次，建立以配电系统运营商为上层领导者、各数据中心为下层跟随者的主从博弈双层优化模型——上层以系统总运行成本最小为目标制定分时激励电价，下层据此自主优化用电方案；利用KKT条件与互补松弛线性化，将双层问题转化为单层混合整数二次规划。在此基础上，设计了ADMM分布式求解框架，并采用基于原始/对偶残差比的自适应惩罚参数策略加速收敛；各主体仅需交换聚合响应量，无需共享任务队列、服务器配置等核心运营数据。基于改进IEEE 33节点系统的仿真结果表明：所提算法经34次迭代收敛，较固定惩罚参数方案提速74.40%，同时避免了对偶残差振荡风险；其系统总运行成本较基线方案降低18.3%，净负荷峰谷差缩小11.2%；与集中式优化相比，总成本仅增加约10.5%。灵敏度分析表明，当数据中心数量从3增至20时，单次迭代计算耗时从0.49 s增至14.46 s，呈近线性增长。所提方法在经济性、收敛性能与隐私保护之间实现了有效平衡：各数据中心仅需上报聚合响应量即可完成优化迭代，无需披露服务器配置、任务队列、储能SOC等内部运行数据，有效保护了各主体数据隐私。

Abstract

With the advancement of the "East Data， West Computing" project and the accelerated construction of new power systems， data centers have become rapidly growing energy-intensive loads in power systems. Their flexible regulation capability is expected to provide low-cost flexible response resources for the power grid. However， existing research has not fully addressed two critical challenges： the game of interests between the grid operator and multiple data centers， and data privacy protection in multi-agent collaboration， thereby hindering the engineering application of relevant theoretical results. To address these challenges， a bi-level distributed optimization method integrating Stackelberg game theory with an adaptive alternating direction method of multipliers （ADMM） was proposed. A high-fidelity multi-data-center flexibility model was established by integrating IT equipment power consumption， dynamic power usage effectiveness （PUE） cooling models， queueing-theoretic task delay， and cross-data-center workload migration， thereby characterizing the adjustable potential of data centers across both spatial and temporal dimensions. A Stackelberg game-based bi-level optimization model was established， with the distribution system operator （DSO） as the upper-level leader and each data center as the lower-level follower. The upper level aimed to minimize the total system operating cost by setting time-of-use incentive electricity prices， while the lower level autonomously optimized electricity consumption strategies accordingly. The bi-level model was transformed into a single-level mixed-integer quadratic programming by applying Karush-Kuhn-Tucker （KKT） conditions and complementary slackness linearization. On this basis， an ADMM-based distributed solution framework was designed. An adaptive penalty parameter strategy based on the primal to dual residual ratio was adopted to accelerate convergence. Each agent was required only to exchange aggregated response quantities， without sharing task queues， server configurations， or other core operational data. Simulation results based on a modified IEEE 33-bus distribution test system demonstrated that the proposed algorithm converged after 34 iterations， accelerating convergence by 74.40% compared with a fixed penalty parameter scheme， while avoiding the risk of dual residual oscillations. The proposed method reduced total system operating cost by 18.3% and narrowed the net load peak-valley difference by 11.2% compared with the baseline scheme. Compared with the centralized optimization， the proposed method incurred a cost increase of only approximately 10.5%. Sensitivity analysis showed that as the number of data centers increased from 3 to 20， the computation time per iteration increased from 0.49 s to14.46 s， exhibiting a near-linear growth trend. The proposed method achieves an effective balance among economic efficiency， convergence performance， and data privacy protection. Each data center needs to report only aggregated regulation response quantities to complete the optimization iterations， thereby effectively preserving the data privacy of each agent.

关键词

Keywords

references

国家能源局 . 2025年全国电力工业统计数据［R］. 北京， 2026 .

中国电力企业联合会 . 中国电力行业年度发展报告2025 ［R］. 北京， 2025 .

国网能源研究院 . 中国电力供需分析报告2025 ［R］. 北京， 2025 .

FAN X B ， WEBER W D ， BARROSO L A . Power provisioning for a warehouse-sized computer ［J］. Computer Architecture News ， 2007 ， 35 （ 2 ）： 13 - 23 .

QURESHI A ， WEBER R ， BALAKRISHNAN H ， et al . Cutting the electric bill for Internet-scale systems ［C］// Proceedings of the ACM SIGCOMM 2009 Conference on Data Communication . 2009 ： 123 - 134 .

GOIRI I ， LE K ， NGUYEN T D ， et al . GreenHadoop： Leveraging green energy in data-processing frameworks ［C］// Proceedings of the 7th ACM European Conference on Computer Systems . 2012 ： 57 - 70 .

CAO Y J ， ZHANG S F . Facilitating the provision of load flexibility to the power system by data centers： A hybrid research method applied to China ［J］. Utilities Policy ， 2023 ， 84 ： 101636 .

曹雨洁，丁肇豪，王鹏，等 . 能源互联网背景下数据中心与电力系统协同优化（二）：机遇与挑战［J］. 中国电机工程学报， 2022 ， 42 （ 10 ）： 3512 - 3526 .

CAO Yujie ， DING Zhaohao ， WANG Peng ， et al . Coordinated operation for data center and power system in the context of energy Internet （Ⅱ）： Opportunities and challenges ［J］. Proceedings of the CSEE ， 2022 ， 42 （ 10 ）： 3512 - 3526 .

BELADY C ， RAWSON A ， PFLEUGER J ， et al . Green grid data center power efficiency metrics： PUE and DCiE： White paper ［R］. The Green Grid ， 2008 .

DAYARATHNA M ， WEN Y G ， FAN R . Data center energy consumption modeling： A survey ［J］. IEEE Communications Surveys & Tutorials ， 2016 ， 18 （ 1 ）： 732 - 794 .

LE K ， BIANCHINI R ， ZHANG J R ， et al . Reducing electricity cost through virtual machine placement in high performance computing clouds ［C］// Proceedings of 2011 International Conference for High Performance Computing， Networking， Storage and Analysis （SC' 11）. 2011 .

LI Y L ， WEN Y G ， TAO D C ， et al . Transforming cooling optimization for green data center via deep reinforcement learning ［J］. IEEE Transactions on Cybernetics ， 2019 ， 50 （ 5 ）： 1 - 12 .

GOIRI Í ， KATSAK W ， LE K ， et al . Parasol and greenswitch： Managing datacenters powered by renewable energy ［J］. ACM SIGPLAN Notices ， 2013 ， 48 （ 4 ）： 51 - 64 .

ALBADI M H ， EL-SAADANY E F . A summary of demand response in electricity markets ［J］. Electric Power Systems Research ， 2008 ， 78 （ 11 ）： 1989 - 1996 .

MOGHADDAM M P ， ABDOLLAHI A ， RASHIDINEJAD M . Flexible demand response programs modeling in competitive electricity markets ［J］. Applied Energy ， 2011 ， 88 （ 9 ）： 3257 - 3269 .

MAHARJAN S ， ZHU Q Y ， ZHANG Y ， et al . Dependable demand response management in the smart grid： A Stackelberg game approach ［J］. IEEE Transactions on Smart Grid ， 2013 ， 4 （ 1 ）： 120 - 132 .

CHEN J T ， ZHU Q Y . A Stackelberg game approach for two-level distributed energy management in smart grids ［J］. IEEE Transactions on Smart Grid ， 2018 ， 9 （ 6 ）： 6554 - 6565 .

芮涛，李国丽，胡存刚，等 . 考虑电价机制的微电网群主从博弈优化方法［J］. 中国电机工程学报， 2020 ， 40 （ 8 ）： 2535 - 2545 .

RUI Tao ， LI Guoli ， HU Cungang ， et al . Stackelberg game optimization method for microgrid cluster considering electricity price mechanism ［J］. Proceedings of the CSEE ， 2020 ， 40 （ 8 ）： 2535 - 2545 .

郭昆健，高赐威，林国营，等 . 现货市场环境下售电商激励型需求响应优化策略［J］. 电力系统自动化， 2020 ， 44 （ 15 ）： 28 - 35 .

GUO Kunjian ， GAO Ciwei ， LIN Guoying ， et al . Optimization strategy of incentive based demand response for electricity retailer in spot market environment ［J］. Automation of Electric Power Systems ， 2020 ， 44 （ 15 ）： 28 - 35 .

BOYD S ， PARIKH N ， CHU E ， et al . Distributed optimization and statistical learning via the alternating direction method of multipliers ［J］. Foundations & Trends in Machine Learning ， 2011 ， 3 （ 1 ）： 1 - 122 .

KRANING M ， CHU E ， LAVAEI J ， et al . Dynamic network energy management via proximal message passing ［J］. Foundations and Trends in Optimization ， 2014 ， 1 （ 2 ）： 73 - 126 .

ERSEGHE T . Distributed optimal power flow using ADMM ［J］. IEEE Transactions on Power Systems ， 2014 ， 29 （ 5 ）： 2370 - 2380 .

ZHANG T ， ZHU Q Y . Dynamic differential privacy for ADMM-based distributed classification learning ［J］. IEEE Transactions on Information Forensics and Security ， 2017 ， 12 （ 1 ）： 172 - 187 .

WANG Y M ， WU L ， WANG S X . A fully-decentralized consensus-based ADMM approach for DC-OPF with demand response ［J］. IEEE Transactions on Smart Grid ， 2017 ， 8 （ 6 ）： 2637 - 2647 .

陈敏，高赐威，郭庆来，等 . 互联网数据中心负荷时空可转移特性建模与协同优化：驱动力与研究架构［J］. 中国电机工程学报， 2022 ， 42 （ 19 ）： 6945 - 6958 .

CHEN Min ， GAO Ciwei ， GUO Qinglai ， et al . Modeling and coordinated optimization for spatiotemporal load regulation potentials of Internet data centers： Mtivation and architecture ［J］. Proceedings of the CSEE ， 2022 ， 42 （ 19 ）： 6945 - 6958 .

HAN O Z ， DING T ， MU C G ， et al . Coordinative optimization between multiple data center operators and a system operator based on two-level distributed scheduling algorithm ［J］. IEEE Internet of Things Journal ， 2023 ， 10 （ 9 ）： 7517 - 7527 .

张文博，秦文萍，刘佳昕，等 . 绿证-电-碳耦合市场下计及需求响应与租赁共享储能的VPP鲁棒优化调度策略［J］. 综合智慧能源， 2025 ， 47 （ 5 ）： 31 - 40 .

ZHANG Wenbo ， QIN Wenping ， LIU Jiaxin ， et al . Robust optimization scheduling strategy for virtual power plants considering demand response and leasing shared energy storage under the green certificate-electricity-carbon coupled market ［J］. Integrated Intelligent Energy ， 2025 ， 47 （ 5 ）： 31 - 40 .

王宇轩，郝宁，赵峰，等 . 面向微网的源网荷储一体化功率分配策略研究［J］. 综合智慧能源， 2025 ， 47 （ 8 ）： 58 - 67 .

WANG Yuxuan ， HAO Ning ， ZHAO Feng ， et al . Research on integrated power allocation strategy of source-network-load-storage for microgrids ［J］. Integrated Intelligent Energy ， 2025 ， 47 （ 8 ）： 58 - 67 .

BARAN M E ， WU F F . Optimal sizing of capacitors placed on a radial distribution system ［J］. IEEE Transactions on Power Delivery ， 1989 ， 4 （ 1 ）： 735 - 743 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Optimal operation of computing-electricity coordination considering differentiated demand response

Deep reinforcement learning method for energy-computing coordinated scheduling in integrated energy systems considering flexible data center tasks

Technical pathways and applicability of direct nuclear power supply for data centers

Economic analysis of wind-photovoltaic-storage-driven data centers under green power direct connection mode

Optimal scheduling of integrated computation-electricity-thermal systems considering the spatiotemporal characteristics of computing workload

Related Author

ZHANG Dongdong

LIU Yining

CHEN Tuoyu

WU Xiaodong

JIANG Meihui

ZHU Hongyu

ZHANG Jie

QU Xinmei

Related Institution

School of New Energy， Inner Mongolia University of Technology

College of Integrated Circuits， Beijing University of Posts and Telecommunications

College of Electrical and Information Engineering， Hunan University

Engineering Research Center of Large, Energy Storage Technology， Ministry of Education， Inner Mongolia University of Technology

Inner Mongolia Autonomous Region Key Laboratory of New Energy and Energy Storage Technology, Energy Storage Technology， Ministry of Education， Inner Mongolia University of Technology

AI问答

⁰