计及动态风光不确定性与需求响应的主动配电网有功-无功优化

doi:10.11930/j.issn.1004-9649.202501063

摘要/Abstract

摘要：

针对主动配电网中高峰值负荷对电压安全的影响，提出基于价格引导需求侧响应的有功-无功优化策略。首先，该策略结合多场景随机优化，提出基于非参数核密度估计和标准多元正态分布序列抽样的动态风光场景生成方法，得到典型日动态风光出力的概率集合。其次，考虑需求侧响应与电网互动以降低电网运行风险，提出基于分时电价引导用户负荷侧转移与无功补偿协同的优化策略。从多个场景概率出发，以配电网电压偏移和经济运行成本最小化构建优化目标。最后，针对该模型的复杂特征，提出多目标混合种群协同优化算法，得到最优无功补偿出力和用户侧负荷调度策略。验证结果表明，本文提出的策略能够有效降低电压越限风险，减小网损，实现配电网的安全经济运行。

关键词: 场景分析, 需求侧响应, 无功补偿, 多目标混合种群协同优化算法, 电压越限

Abstract:

To address the impact of peak loads on voltage security in active distribution networks, an active-reactive power optimization strategy is proposed based on price-guided demand-side response. Firstly, this strategy incorporates multi-scenario stochastic optimization and proposes a dynamic renewable scenario generation method based on nonparametric kernel density estimation and sequential sampling from standardized multivariate normal distributions, yielding a probabilistic set of typical daily wind-solar power profiles. Secondly, considering demand-side response and grid interaction to mitigate grid operational risks, this study proposes an optimization strategy coordinating time-of-use price-guided load shifting and reactive power compensation. The optimization objective is constructed based on multiple scenario probabilities to minimize voltage deviation and economic operation costs in the distribution networks. Finally, to address the complex characteristics of this model, a multi-objective hybrid multi-population collaborative optimization algorithm is proposed, yielding optimal reactive power compensation output and demand-side load scheduling strategy. Verification results show that the proposed strategy can effectively reduce the risk of voltage violations, minimize network losses, and achieve safe and economic operation of the distribution networks.

Key words: scenario analysis, demand-side response, reactive power compensation, multi-objective hybrid multi-population collaborative optimization algorithm, voltage violation

季红利, 徐雷, 杨佳卉, 窦春霞. 计及动态风光不确定性与需求响应的主动配电网有功-无功优化[J]. 中国电力, 2026, 59(2): 47-60.

JI Hongli, XU Lei, YANG Jiahui, DOU Chunxia. Active-reactive power optimization of active distribution networks considering dynamic wind-solar renewable uncertainty and demand response[J]. Electric Power, 2026, 59(2): 47-60.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202501063

https://www.electricpower.com.cn/CN/Y2026/V59/I2/47

图/表 23

图 1 动态风光场景生成方法

Fig.1 Method for generating dynamic wind-solar scenarios

图 2 主动配电网调度示意

Fig.2 Schematic of active distribution network dispatching

图 3 计及动态风光不确定性与需求响应的主动配电网有功-无功优化

Fig.3 Active-reactive power optimization of active distribution networks considering dynamic wind-solar uncertainty and demand response

表 1 配电网运行成本参数

Table 1 Distribution network operating cost parameters

运行成本	单价
主网购电/(元·(kW·h)^–1)	0.6
网损/(元·(kW·h)^–1)	0.9
CB/(元·组^–1)	25
SVC/(元·(kV·A)^–1)	0.5
IL/(元·(kW·h)^–1)	0.4

表 2 弹性电价矩阵参数

Table 2 Parameters of the elastic tariff matrix

自弹性系数$\varepsilon $	交叉弹性系数$\varepsilon $
自弹性系数$\varepsilon $	峰-平	峰-谷	平-谷
–0.1	0.01	0.01	0.01

图 4 IEEE 33节点拓扑结构

Fig.4 IEEE 33 node topology

图 5 2种场景生成方法对比

Fig.5 Comparison of two scenario-generation methods

图 6 SSE和SC指标

Fig.6 SSE and SC indicators

图 7 聚类后4组风光出力的场景概率

Fig.7 Scenario probability of 4 wind-solar power output clusters

图 8 负荷波动曲线

Fig.8 Load fluctuation curve

图 9 全局最低电压时序对比

Fig.9 Comparison of global minimum voltage time-series

图 10 有功网损时序对比

Fig.10 Comparison of active power network loss time-series

表 3 2种策略下的指标对比

Table 3 Comparison of metrics between two strategies

策略	平均电压偏移/(p.u.)	网损/MW	运行成本/万元
1	0.0160	2.630	5.553
2	0.0144	2.310	5.196

图 11 策略1无功补偿装置出力时序

Fig.11 Power output time-series of reactive power compensation device in strategy 1

图 12 策略2无功补偿元件出力时序

Fig.12 Power output time-series of reactive power compensation device in strategy 2

图 13 可转移负荷和分时电价曲线

Fig.13 Curves of shifting load and time-of-use price

图 14 可中断负荷响应量

Fig.14 Interruptible load response

表 4 分时电价划定

Table 4 Time-of-use tariff delineation

峰谷类型	时间段	电价/(元·(kW·h)^–1)
峰	18:00—24:00	0.89
平	08:00—12:00；17:00—18:00 00:00—12:00	0.61
谷	02:00—08:00；12:00—17:00	0.45

表 5 3种算法结果对比

Table 5 Comparison of three algorithms

案例	经济成本/万元	电压偏移/(p.u.)	运行时间/s
1	5.196	113.88	1233.84
2	5.485	107.38	1462.28
3	5.483	104.46	1373.36

图 15 3种算法下的最优Pareto前沿解

Fig.15 Optimal Pareto frontier solution for three algorithms

图 16 21时刻节点33的电压变化

Fig.16 Voltage variation of node 33 at time 21

表 6 2种场景生成方法结果对比

Table 6 Comparison of two scenario-generation methods

方法	SVC出力/(MV·A)	CB动作次数	用户舒适度/%
静态场景生成	5.503	12	94.02
动态场景生成	5.305	9	94.24

表 7 不同聚类数的调度结果

Table 7 Scheduling results for different numbers of clusters

聚类数	经济成本/万元	电压偏移/(p.u.)	运行时间/s
1	5.499	121.41	310.46
2	5.443	120.02	620.92
4	5.196	113.88	1233.84
6	5.125	110.33	1853.84
8	5.119	107.28	2478.58

参考文献 26

1	鞠立伟, 吕硕硕, 李鹏. 新型电力系统需求侧灵活性资源时空协同优化与动态均衡机制研究综述[J]. 电力建设, 2024, 45 (9): 142- 163.
	JU Liwei, LVShuoshuo, LI Peng. Review of novel demand-side flexibility resource spatio-temporal co-optimization and dynamic equilibrium mechanism of power systems[J]. Electric Power Construction, 2024, 45 (9): 142- 163.
2	国家能源局. 国家能源局发布2024年1—8月份全国电力工业统计数据[EB/OL]. (2024-09-23)[2025-05-10]. https://www,nea.gov.cn/2024-09/23/c_1212399359.htm.
3	徐文韬, 米阳, 蔡鹏程, 等. 基于机会约束规划的含多微网主动配电网分布式优化管理[J]. 电力建设, 2024, 45 (11): 1- 13.
	XU Wentao, MI Yang, CAI Pengcheng, et al. Distributed optimization management for active distribution networks with multiple microgrids based on chance-constrained programming[J]. Electric Power Construction, 2024, 45 (11): 1- 13.
4	黎家明, 霍群海, 尹靖元, 等. 考虑柔性有载调压变压器的两阶段电压无功优化协调控制方法研究[J]. 电网技术, 2025, 49 (1): 272- 283.
	LI Jiaming, HUO Qunhai, YIN Jingyuan, et al. Research on two-stage voltage and reactive power optimization coordinated control method considering flexible on-load tap changer[J]. Power System Technology, 2025, 49 (1): 272- 283.
5	刘海涛, 陈彪, 朱林, 等. 考虑多种无功补偿装置协同优化的电压控制方法[J]. 中国电力, 2022, 55 (11): 97- 102.
	LIU Haitao, CHEN Biao, ZHU Lin, et al. A voltage control method considering the collaborative optimization of multiple reactive power compensation devices[J]. Electric Power, 2022, 55 (11): 97- 102.
6	袁桂丽, 丁宁, 杨彪, 等. 源网荷储协同优化的主动配电网日前调度[J]. 科学技术与工程, 2024, 24 (24): 10337- 10347.
	YUAN Guili, DING Ning, YANG Biao, et al. Daily dispatch of active distribution network with collaborative optimization of source-grid-load-storage[J]. Science Technology and Engineering, 2024, 24 (24): 10337- 10347.
7	任彦辉, 宋景龙, 余瑞, 等. 考虑需求侧响应的配电网无功补偿装置协调优化[J]. 智慧电力, 2024, 52 (1): 79- 86.
	REN Yanhui, SONG Jinglong, YU Rui, et al. Coordinated optimization of reactive power compensation device in distribution network considering on demand-side response[J]. Smart Power, 2024, 52 (1): 79- 86.
8	闫群民, 李召, 马永翔, 等. 考虑综合经济性的风光配电网储能优化配置[J]. 科学技术与工程, 2024, 24 (12): 5014- 5022.
	YAN Qunmin, LI Zhao, MA Yongxiang, et al. Consider the optimal configuration of energy storage in wind-solar distribution networks with comprehensive economy[J]. Science Technology and Engineering, 2024, 24 (12): 5014- 5022.
9	王金凤, 许梦雪. 基于改进鲸鱼算法的分布式电源双层规划[J]. 科学技术与工程, 2024, 24 (26): 11294- 11302.
	WANG Jinfeng, XU Mengxue. Bi-level planning for distributed power supply based on improved whale algorithm[J]. Science Technology and Engineering, 2024, 24 (26): 11294- 11302.
10	顾光荣, 杨鹏, 汤波, 等. 源-荷-储协同优化的配电网平衡能力提升方法[J]. 中国电机工程学报, 2024, 44 (13): 5097- 5109.
	GU Guangrong, YANG Peng, TANG Bo, et al. A method for improving the balance ability of distribution networks through source-load-storage collaborative optimization[J]. Proceedings of the CSEE, 2024, 44 (13): 5097- 5109.
11	葛磊蛟, 范延赫, 李小平, 等. 计及日前随机-日内滚动分布式的高比例光伏配电网无功优化方法[J/OL]. 电网技术, 1–15. (2024-10-21). https://doi.org/10.13335/j.1000-3673.pst.2024.1567.
	GE Leijiao, FAN Yanhe, LI Xiaoping, et al. A reactive power optimization method for high percentage of PV distribution networks taking into account day-ahead random and intraday rolling distributions[J/OL]. Power System Technology, 1–15. (2024-10-21). https://doi.org/10.13335/j.1000-3673.pst.2024.1567.
12	张磊, 姜贞强, 倪佳华, 等. 基于二阶锥凸松弛的海上风电场内部无功优化[J]. 电力建设, 2024, 45 (1): 92- 101.
	ZHANG Lei, JIANG Zhenqiang, NI Jiahua, et al. Internal reactive power optimization of offshore wind farms using second-order cone convex relaxation[J]. Electric Power Construction, 2024, 45 (1): 92- 101.
13	徐峰亮, 王克谦, 王文豪, 等. 计及激励型需求响应的低压配电网混合储能优化配置[J]. 中国电力, 2024, 57 (6): 90- 101.
	XU Fengliang, WANG Keqian, WANG Wenhao, et al. Optimal allocation of hybrid energy storage in low-voltage distribution networks with incentive-based demand response[J]. Electric Power, 2024, 57 (6): 90- 101.
14	陈倩, 王维庆, 王海云. 基于含分布式电源的配电网优化运行研究[J]. 电测与仪表, 2023, 60 (11): 19- 28.
	CHEN Qian, WANG Weiqing, WANG Haiyun. Research on optimal operation of distribution network with distributed generation integration[J]. Electrical Measurement & Instrumentation, 2023, 60 (11): 19- 28.
15	JAMEEL M, ABOUHAWWASH M. Multi-objective Mantis Search Algorithm (MOMSA): a novel approach for engineering design problems and validation[J]. Computer Methods in Applied Mechanics and Engineering, 2024, 422, 116840.
16	车兵, 李轩, 郑建勇, 等. 基于LHS与BR的风电出力场景分析研究[J]. 电力工程技术, 2020, 39 (6): 213- 219.
	CHE Bing, LI Xuan, ZHENG Jianyong, et al. Scenario analysis of wind power output based on LHS and BR[J]. Electric Power Engineering Technology, 2020, 39 (6): 213- 219.
17	杨宏, 闫玉杰, 王瑜. Beta分布在风电预测误差模型中的适用性[J]. 电测与仪表, 2020, 57 (11): 37- 41, 48.
	YANG Hong, YAN Yujie, WANG Yu. Applicability of Beta distribution on wind power forecast error modeling[J]. Electrical Measurement & Instrumentation, 2020, 57 (11): 37- 41, 48.
18	高帆, 包道日娜, 狄彦强, 等. 考虑风光出力动态相关性的场景生成方法[J]. 太阳能学报, 2024, 45 (8): 256- 264.
	GAO Fan, BAO Daorina, DI Yanqiang, et al. Scene generation method considering dynamic correlation of wind and photovoltaic outputs[J]. Acta Energiae Solaris Sinica, 2024, 45 (8): 256- 264.
19	张辰毓, 许刚. 分布式多元随机动态场景生成及快速精准场景降维算法[J]. 电网技术, 2022, 46 (2): 671- 681.
	ZHANG Chenyu, XU Gang. Distributed multivariate random dynamic scenario generation and fast & accurate scenario simplified algorithm[J]. Power System Technology, 2022, 46 (2): 671- 681.
20	赵书强, 金天然, 李志伟, 等. 考虑时空相关性的多风电场出力场景生成方法[J]. 电网技术, 2019, 43 (11): 3997- 4004.
	ZHAO Shuqiang, JIN Tianran, LI Zhiwei, et al. Wind power scenario generation for multiple wind farms considering temporal and spatial correlations[J]. Power System Technology, 2019, 43 (11): 3997- 4004.
21	胡恒, 秦建茹, 李海波, 等. 考虑极限场景的电力系统分布鲁棒低碳经济调度[J]. 电力建设, 2025, 46 (4): 160- 172.
	HU Heng, QIN Jianru, LI Haibo, et al. Distributed robust low-carbon economic dispatch of power systems considering extreme scenarios[J]. Electric Power Construction, 2025, 46 (4): 160- 172.
22	张家美, 孙凯, 孙沛. 基于对抗神经网络和K-means++的配电网光伏接入能力评估方法[J]. 电工电能新技术, 2025, 44 (2): 65- 73.
	ZHANG Jiamei, SUN Kai, SUN Pei. Photovoltaic access capability evaluation of distribution networks based on adversarial neural networks and K-means++ clustering[J]. Advanced Technology of Electrical Engineering and Energy, 2025, 44 (2): 65- 73.
23	易锦桂, 朱自伟, 谢青. 基于改进场景聚类算法的海上风电储能优化配置研究[J]. 中国电力, 2022, 55 (12): 2- 10.
	YI Jingui, ZHU Ziwei, XIE Qing. Research on optimal configuration of offshore wind power energy storage based on improved scene clustering algorithm[J]. Electric Power, 2022, 55 (12): 2- 10.
24	唐文升, 王阳, 张煜, 等. 基于多维价格弹性系数的分时电价对负荷特性影响机理[J]. 中国电力, 2024, 57 (02): 202- 211.
	TANG Wensheng, WANG Yang, ZHANG Yu, et al. Influence mechanism of time-of-use electricity prices on industry load characteristics based on multi-dimensional price elasticity coefficient matrix[J]. Electric Power, 2024, 57 (02): 202- 211.
25	朱显辉, 胡旭, 师楠, 等. 考虑价格和激励/补偿耦合机制的微网容量多层内嵌优化[J]. 中国电力, 2023, 56 (3): 173- 186.
	ZHU Xianhui, HU Xu, SHI Nan, et al. Multi-layer embedded optimization of microgrid capacity considering price and incentive/compensation coupling mechanism[J]. Electric Power, 2023, 56 (3): 173- 186.
26	UNIVERSITY H P, AI Y L. The optimization of reactive power for distribution network with PV generation based on NSGA-III[J]. CPSS Transactions on Power Electronics and Applications, 2021, 6 (3): 193- 200.

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