基于混合信息的智能电网隐私保护分布式经济调度

张赟宁; 肖嵩航; 付文龙; 胡松林; 岳东

doi:10.16383/j.aas.c260244

基于混合信息的智能电网隐私保护分布式经济调度

doi: 10.16383/j.aas.c260244 cstr: 32138.14.j.aas.c260244

1.
三峡大学电气与新能源学院宜昌 443002
2.
南京邮电大学碳中和先进技术研究院南京 210023

基金项目: 国家自然科学基金(62573237)资助

详细信息

作者简介:
张赟宁：三峡大学电气与新能源学院副教授. 主要研究方向为电力系统分布式优化和电力信息安全. E-mail: zhangyunning@ctgu.edu.cn

肖嵩航：三峡大学电气与新能源学院硕士研究生. 主要研究方向为电力系统稳定与控制, 电力系统仿真分析, 智能电网的控制与优化运行和信息物理系统安全. E-mail: sean_xiao@ctgu.edu.cn

付文龙：三峡大学电气与新能源学院副教授. 主要研究方向为电力系统建模与控制. 本文通信作者. E-mail: fuwenlong@ctgu.edu.cn

胡松林：南京邮电大学碳中和先进技术研究院教授. 主要研究方向为网络控制系统, 多智能体系统和信息物理系统安全. E-mail: slhu621@njupt.edu.cn

岳东：南京邮电大学碳中和先进技术研究院教授. 主要研究方向为网络控制系统, 多智能体系统和电力系统最优控制. E-mail: yued@njupt.edu.cn

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出版历程
- 收稿日期: 2026-04-13
- 录用日期: 2026-07-01
- 网络出版日期: 2026-07-27

Privacy-preserving Distributed Economic Dispatch for Smart Grid Based on Hybrid Information

1.
College of Electrical Engineering and New Energy, China Three Gorges University, Yichang 443002
2.
Institute of Advanced Technology for Carbon Neutrality, Nanjing University of Posts and Telecommunications, Nanjing 210023

Funds: Supported by National Natural Science Foundation of China (62573237)

More Information

Author Bio:
ZHANG Yun-Ning　Associate professor at the College of Electrical Engineering and New Energy, China Three Gorges University. Her research interest covers distributed optimization of power systems and power information security

XIAO Song-Hang　Master student at the College of Electrical Engineering and New Energy, China Three Gorges University. His research interest covers power system stability and control, power system simulation and analysis, control and optimization for smart grid operation, and cyber-physical systems security

FU Wen-Long　Associate professor at the College of Electrical Engineering and New Energy, China Three Gorges University. His research interest covers power system modeling and control. Corresponding author of this paper

HU Song-Lin　Professor at the Institute of Advanced Technology for Carbon Neutrality, Nanjing University of Posts and Telecommunications. His research interest covers networked control systems, multi-agent systems and cyber-physical systems security

YUE Dong　Professor at the Institute of Advanced Technology for Carbon Neutrality, Nanjing University of Posts and Telecommunications. His research interest covers networked control systems, multi-agent systems and optimal control of power systems

摘要

摘要: 为满足供电可靠性、经济性和安全性等运行要求, 智能电网通常涉及微电网孤岛运行、并网运行以及两种运行模式之间的动态切换. 本文提出了一种考虑不同运行模式下系统数据隐私保护需求的智能电网分布式经济调度算法. 首先将微-主网通信机制融入所提算法中, 实现了微电网与主网之间信息的双向交互. 进一步地, 为克服现有隐私保护方法存在的收敛精度不足以及需收集全局信息等问题, 引入基于混合信息的隐私保护机制, 其中混合信息由节点状态及其功率信息构成, 各节点通过接收混合信息完成自身状态更新. 利用Perron-Frobenius定理、矩阵扰动理论以及Karush-Kuhn-Tucker条件证明了所提算法无需收集全局信息即可使系统状态精确收敛至全局最优解. 同时, 考虑两种典型的窃听者模型, 对所提算法在孤岛与并网两种运行模式下经济调度的隐私性进行了分析. 最后, 通过不同运行条件下的仿真实验, 验证了所提算法的可行性和优越性.
- 智能电网 /
- 分布式经济调度 /
- 隐私保护 /
- 一致性算法 /
- 混合信息
Abstract: To meet the operational requirements of power supply reliability, economy, and security, smart grids typically involve microgrid islanded operation, grid-connected operation, and dynamic switching between these two operating modes. This paper proposes a distributed economic dispatch algorithm for smart grids that considers the data privacy protection requirements of the system under different operating modes. First, the micro-main grid communication mechanism is integrated into the proposed algorithm, realizing bidirectional information interaction between the microgrid and the main grid. Furthermore, to overcome the shortcomings of existing privacy-preserving methods, such as insufficient convergence accuracy and the need to collect global information, a privacy-preserving mechanism based on hybrid information is introduced, where the hybrid information consists of the node states and their power information, and each node updates its own state by receiving hybrid information. By utilizing the Perron-Frobenius theorem, matrix perturbation theory, and Karush-Kuhn-Tucker conditions, it is proven that the proposed algorithm enables the system state to converge exactly to the global optimal solution without requiring the collection of global information. Meanwhile, considering two typical eavesdropper models, the privacy of economic dispatch under both islanded and grid-connected operating modes is analyzed for the proposed algorithm. Finally, the feasibility and superiority of the proposed algorithm are validated through simulation experiments under different operating conditions.
- smart grid /
- distributed economic dispatch /
- privacy-preserving /
- consensus algorithm /
- hybrid information

HTML全文

图 1 SG的局部结构

Fig. 1 Partial structure of SG

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图 2 两种典型的窃听者模型((a) 诚实但好奇节点; (b) 外部窃听者节点)

Fig. 2 Two typical eavesdropper models ((a) Honest-but-curious node; (b) External eavesdropper node)

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图 3 融入微-主网通信机制后的实验结果((a)增量成本/增量效益; (b)功率量; (c)局部功率偏差; (d)全局功率偏差)

Fig. 3 Experimental results after incorporating micro-main grid communication mechanism ((a) Incremental cost/ incremental benefit; (b) Power quantity; (c) Local power deviation; (d) Global power deviation)

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图 4 PPDEDA的实验结果((a)增量成本/增量效益; (b)功率量; (c)局部功率偏差; (d)全局功率偏差)

Fig. 4 Experimental results of PPDEDA ((a) Incremental cost/ incremental benefit; (b) Power quantity; (c) Local power deviation; (d) Global power deviation)

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图 5 PPDEDA的即插即用特性((a)增量成本/增量效益; (b)功率量; (c)局部功率偏差; (d) 全局功率偏差)

Fig. 5 The plug-and-play feature of PPDEDA ((a) Incremental cost/ incremental benefit; (b) Power quantity; (c) Local power deviation; (d) Global power deviation)

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图 6 不同初始状态信息下PPDEDA的仿真结果(增量成本/增量效益; (b)局部功率偏差; (c)3号节点获取的信息$ n_{ij}(k)$; (d)3号节点获取的信息$e_{ij}(k) $)

Fig. 6 Simulation results of PPDEDA under different initial state information ((a) Incremental cost/incremental benefit; (b) Local power deviation; (c) Information $n_{ij}(k) $ obtained by node 3; (d) Information $ e_{ij}(k)$ obtained by node 3)

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图 7 不同初始状态信息下PPDEDA的仿真结果((a)增量成本/增量效益; (b)局部功率偏差; (c) 外部窃听者获取的信息$n_{ij}(k) $; (d)外部窃听者获取的信息$e_{ij}(k) $)

Fig. 7 Simulation results of PPDEDA under different initial state information ((a) Incremental cost/incremental benefit; (b) Local power deviation; (c) Information $n_{ij}(k) $ obtained by eavesdropper; (d) Information $e_{ij}(k) $ obtained by eavesdropper)

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图 8 39节点系统下PPDEDA的仿真结果((a)增量成本/增量效益; (b)功率量; (c)局部功率偏差; (d)全局功率偏差)

Fig. 8 Simulation results of PPDEDA on the 39-node system ((a) Incremental cost/incremental benefit; (b) Power quantity; (c) Local power deviation; (d) Global power deviation)

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图 9 $|P_{{\rm{sum}}}| $的曲线图

Fig. 9 $|P_{{\rm{sum}}}| $ curve

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图 10 $|P_{{\rm{sum}}}| $的曲线图

Fig. 10 $|P_{{\rm{sum}}}| $ curve

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B1 微-主网通信拓扑图

B1 Micro-main grid communication topology diagram

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表 1 数学符号说明

Table 1 Explanation of mathematical symbols

数学符号	符号说明
$ P_i(k) $	时刻$ k $节点$ i $功率
$ \vartheta_i $、$ \beta_i $、$ \phi_i $	成本函数的固定参数
$ \omega_i $、$ \alpha_i $	效用函数的固定参数
$ \lambda_0 $	主网的电价
$ P^{\rm{ms}}(k) $	主网在时刻$ k $输出的功率
$ \lambda_i(k) $	时刻$ k $节点$ i $的增量成本/增量效益
$ \psi_i(k) $	时刻$ k $节点$ i $的局部功率偏差
$ \eta $	固定步长
$ \Delta P^{\rm{m}}_i(k) $	节点$ i $于时刻$ k $与主网的交换功率增量
$ P^{\rm{m}}_i(k) $	节点$ i $于时刻$ k $与主网的交换功率
$ n_{ij}(k) $、$ e_{ij}(k) $	节点$ j $于时刻$ k $向节点$ i $传输的混合信息
$ n_{i0}(k) $、$ e_{i0}(k) $	主网于时刻$ k $对节点$ i $的状态修正量
$ \hat{\lambda}_i(0) $、$ \hat{\psi}_i(0) $	窃听者对节点$ i $初始状态的估计值

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表 2 孤岛模式下不同隐私保护方法的仿真时间对比

Table 2 Comparison of simulation time for different privacy-preserving methods in islanded mode

方法	总运行时间(s)	平均运行时间(s)
文献[31]	1.3594	0.0136
文献[20]	8.1359	0.0814
文献[25]	1.7061	0.0171
PPDEDA	1.6562	0.0166

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表 3 并网模式下不同隐私保护方法的仿真时间对比

Table 3 Comparison of simulation time for different privacy-preserving methods in grid-connected mode

方法	总运行时间(s)	平均运行时间(s)
文献[25]	2.1908	0.0219
PPDEDA	2.0873	0.0209

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B1 发电机运行参数以及其初始值

B1 Generator operating parameters and their initial values

节点编号	$ \vartheta_i $	$ \beta_i $	$ \phi_i $	$ P_i^{{\rm{Min}}} $ (kW)	$ P_i^{{\rm{Max}}} $ (kW)	$ P_i(0) $ (kW)	$ \psi_i(0) $ (kW)
1	0.528	0.346	0.0627	15	110	20	-20
2	0.643	0.834	0.0189	10	135	30	-30
3	0.497	0.527	0.0853	20	169	40	-40

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B2 柔性负荷运行参数以及其初始值

B2 Load operating parameters and their initial values

节点编号	$ \alpha_i $	$ \omega_i $	$ P_i^{{\rm{Min}}} $ (kW)	$ P_i^{{\rm{Max}}} $ (kW)	$ P_i(0) $ (kW)	$ \psi_i(0) $ (kW)
1	0.0564	17.264	17	149	20	20
2	0.0917	19.646	20	137	30	30
3	0.0346	16.431	16	176	20	20
3	0.0823	18.563	18	84	20	20

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