计及分布式光伏出力不确定性的低压配电网仿射潮流计算方法

doi:10.11930/j.issn.1004-9649.202412047

摘要/Abstract

摘要：

源、荷不确定性增加了配电网实时态势感知的难度。为此，提出一种计及分布式光伏出力不确定性的低压配电网仿射潮流计算方法。考虑光伏出力及负荷的不确定性，建立低压配电网潮流模型。考虑中性点电压对潮流计算结果的影响，建立配电网状态变量的仿射表达式，从而减少区间运算的扩张效应，获得更紧凑的状态变量区间。基于标准配电网测试系统对所提方法进行验证。仿真结果表明，所提方法不仅能够提升计算精度，而且可以在电能质量分析中能给出更具参考价值的评估结果。

关键词: 分布式光伏, 不确定性, 配电网, 区间潮流

Abstract:

The uncertainty of the source and load increases the difficulty of real-time situation awareness of the distribution network. To this end, an affine power flow calculation for the low-voltage distribution network considering the uncertainty of distributed photovoltaic output is proposed. The power flow model of the low-voltage distribution network is established considering uncertainty of photovoltaic output and load. The influence of the neutral point voltage on the power flow calculation results is considered, and the affine expression of the distribution network state is established, thereby reducing the expansion effect of the interval operation and obtaining a more compact interval of the state variables. Based on the standard distribution network test system, the proposed method is. The simulation results show that the proposed method can not only improve the calculation accuracy but also give more valuable evaluation results in the analysis of power quality.

Key words: distributed photovoltaic, uncertainty, distribution systems, interval power flow

汪泽州, 毛琳明, 潘克勤, 储建新, 陈刚. 计及分布式光伏出力不确定性的低压配电网仿射潮流计算方法[J]. 中国电力, 2025, 58(10): 188-194.

WANG Zezhou, MAO Linming, PAN Keqin, CHU Jianxin, CHEN Gang. Affine Power Flow Calculation Method for Low-voltage Distribution Systems Considering the Uncertainty of Distributed Photovoltaic Output[J]. Electric Power, 2025, 58(10): 188-194.

导出引用管理器 EndNote|Ris|BibTeX

链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202412047

https://www.electricpower.com.cn/CN/Y2025/V58/I10/188

图/表 7

图 1 提出的配电系统仿射潮流计算方法流程

Fig.1 Flow chart of the proposed affine power flow calculation method of distribution systems

图 2 34节点配电网单线结构

Fig.2 The single line diagram of the 34 bus distribution system

图 3 4种方法计算的三相电压幅值范围

Fig.3 Ranges of three-phase voltage magnitudes calculated by the four methods

表 1 不同方法的保守性指标与仿真时间

Table 1 Conservative index and simulation time of different methods

方法	C_pv	C_pθ	时间/s
IA	51.31	30.14	30
AA	58.97	32.83	36
IM	76.01	60.18	44

图 4 不同功率波动范围下34节点a相电压幅值范围

Fig.4 Voltage magnitude ranges of phase a of bus 34 under different power disturbance ranges

图 5 不同功率波动范围下34节点b相电压幅值范围

Fig.5 Voltage magnitude ranges of phase b of bus 34 under different power disturbance ranges

图 6 不同功率波动范围下34节点c相电压幅值范围

Fig.6 Voltage magnitude ranges of phase c of bus 34 under different power disturbance ranges

参考文献 36

1	赵琳, 郭尚民, 商文颖, 等. 基于FDOA的可再生能源系统配置优化[J]. 中国电力, 2025, 58 (7): 168- 176. DOI
	ZHAO Lin, GUO Shangmin, SHANG Wenying, et al. Configuration optimization of renewable energy systems based on FDOA[J]. Electric Power, 2025, 58 (7): 168- 176. DOI
2	周才期, 刘静利, 孙鹏凯, 等. 分布式光伏波动事件多级区间滚动预警方法[J]. 中国电力, 2024, 57 (8): 96- 107. DOI
	ZHOU Caiqi, LIU Jingli, SUN Pengkai, et al. Multi-level interval rolling warning method for distributed photovoltaic fluctuation events[J]. Electric Power, 2024, 57 (8): 96- 107. DOI
3	杨军, 王楠楠, 王江, 等. 基于潮流追踪的有源配电网碳排放流分析方法[J]. 浙江电力, 2024, 43 (6): 80- 87.
	YANG Jun, WANG Nannan, WANG Jiang, et al. A method for carbon emission flow analysis in active distribution networks based on power flow tracking[J]. Zhejiang Electric Power, 2024, 43 (6): 80- 87.
4	周洋, 黄德志, 李培栋, 等. 考虑平衡端点相位不对称及光伏接入的低压配电网三相潮流模型[J]. 中国电力, 2024, 57 (10): 190- 198.
	ZHOU Yang, HUANG Dezhi, LI Peidong, et al. A three-phase power flow model for low-voltage distribution networks considering balanced bus phase asymmetry and photovoltaic access[J]. Electric Power, 2024, 57 (10): 190- 198.
5	张亚健, 陈茨, 薛飞, 等. 电制氢协同的含高比例光伏配电网两阶段电压随机优化控制[J]. 中国电力, 2024, 57 (8): 23- 35. DOI
	ZHANG Yajian, CHEN Ci, XUE Fei, et al. Two-stage stochastic optimal voltage control of high-proportional photovoltaic distribution networks considering auxiliary power to hydrogen[J]. Electric Power, 2024, 57 (8): 23- 35. DOI
6	杨康, 李蓝青, 李艺丰, 等. 一种新型分布式光伏出力区间预测方法[J]. 发电技术, 2024, 45 (4): 684- 695. DOI
	YANG Kang, LI Lanqing, LI Yifeng, et al. A novel distributed photovoltaic output interval prediction method[J]. Power Generation Technology, 2024, 45 (4): 684- 695. DOI
7	张海涛, 李文娟, 李雪峰, 等. 基于变分模态分解和时间注意力机制TCN网络的光伏发电功率预测[J]. 电测与仪表, 2024, 61 (12): 156- 163.
	ZHANG Haitao, LI Wenjuan, LI Xuefeng, et al. Photovoltaic power forecasting based on TPA-TCN model and variational modal decomposition[J]. Electrical Measurement & Instrumentation, 2024, 61 (12): 156- 163.
8	周忠玉, 孔小民, 郝沛, 等. 面向云储能差异化调控的有源配电网多区域分布式光伏高效消纳方法[J]. 湖南电力, 2024, 44 (3): 136- 144.
	ZHOU Zhongyu, KONG Xiaomin, HAO Pei, et al. Efficient consumption methods of multi-area distributed photovoltaic energy for active distribution network with differentiated scheduling for cloud energy storage[J]. Hunan Electric Power, 2024, 44 (3): 136- 144.
9	冯侃, 魏立保, 吴兆彬, 等. 基于集群划分的含高比例户用光伏配电网电压控制研究[J]. 综合智慧能源, 2025, 47 (2): 60- 70.
	FENG Kan, WEI Libao, WU Zhaobin, et al. Research on voltage control of distribution networks with high-proportion household photovoltaics based on cluster division[J]. Integrated Intelligent Energy, 2025, 47 (2): 60- 70.
10	呼斯乐, 于源, 王渊, 等. 考虑灵活性分析的典型光伏日出力率曲线提取方法[J]. 内蒙古电力技术, 2024, 42 (3): 20- 27.
	HU Sile, YU Yuan, WANG Yuan, et al. Method for extracting typical PV daily output curves considering flexibility analysis[J]. Inner Mongolia Electric Power, 2024, 42 (3): 20- 27.
11	陈晓华, 吴杰康. 基于北方苍鹰优化算法优化长短期记忆神经网络的光伏发电功率短期预测[J]. 山东电力技术, 2024, 51 (10): 10- 17.
	CHEN Xiaohua, WU Jiekang. Photovoltaic power short-term prediction based on long short-term memory neural network optimized by northern goshawk optimization algorithm[J]. Shandong Electric Power, 2024, 51 (10): 10- 17.
12	VACCARO A, CAÑIZARES C A, BHATTACHARYA K. A range arithmetic-based optimization model for power flow analysis under interval uncertainty[J]. IEEE Transactions on Power Systems, 2013, 28 (2): 1179- 1186. DOI
13	DING T, BO R, LI F X, et al. Interval power flow analysis using linear relaxation and optimality-based bounds tightening (OBBT) methods[J]. IEEE Transactions on Power Systems, 2015, 30 (1): 177- 188. DOI
14	DUAN C, JIANG L, FANG W L, et al. Moment-SOS approach to interval power flow[J]. IEEE Transactions on Power Systems, 2017, 32 (1): 522- 530. DOI
15	DING T, LI F X, LI X, et al. Interval radial power flow using extended DistFlow formulation and Krawczyk iteration method with sparse approximate inverse preconditioner[J]. IET Generation, Transmission & Distribution, 2015, 9(14): 1998–2006.
16	DAS B. Radial distribution system power flow using interval arithmetic[J]. International Journal of Electrical Power & Energy Systems, 2002, 24 (10): 827- 836.
17	裴爱华, 刘明波, 张弛. 考虑负荷不确定性的区间潮流计算方法[J]. 电力系统及其自动化学报, 2004, 16 (6): 24- 27, 43.
	PEI Aihua, LIU Mingbo, ZHANG Chi. Interval algorithm for power flow calculation with uncertain load[J]. Proceedings of Electric Power System and Automation, 2004, 16 (6): 24- 27, 43.
18	邵振国, 李壹民, 颜熙颖, 等. 基于全纯嵌入的电力系统不确定性仿射潮流方法[J]. 中国电机工程学报, 2024, 44 (1): 105- 117.
	SHAO Zhenguo, LI Yimin, YAN Xiying, et al. Affine power flow algorithm for power system based on holomorphic embedding method[J]. Proceedings of the CSEE, 2024, 44 (1): 105- 117.
19	杜萍静, 杨明, 曹良晶, 等. 含电压源换流器交直流系统的仿射潮流算法[J]. 电工技术学报, 2020, 35 (5): 1106- 1117.
	DU Pingjing, YANG Ming, CAO Liangjing, et al. Affine power flow algorithm for AC/DC systems with voltage source converter[J]. Transactions of China Electrotechnical Society, 2020, 35 (5): 1106- 1117.
20	GU W, LUO L Z, DING T, et al. An affine arithmetic-based algorithm for radial distribution system power flow with uncertainties[J]. International Journal of Electrical Power & Energy Systems, 2014, 58, 242- 245.
21	WANG S X, HAN L, WU L. Uncertainty tracing of distributed generations via complex affine arithmetic based unbalanced three-phase power flow[J]. IEEE Transactions on Power Systems, 2015, 30 (6): 3053- 3062. DOI
22	邵振国, 黄耿业, 张嫣, 等. 固定噪声元的预测–校正型仿射潮流迭代算法[J]. 中国电机工程学报, 2021, 41 (7): 2331- 2341.
	SHAO Zhenguo, HUANG Gengye, ZHANG Yan, et al. A predictor-corrector affine power flow iteration algorithm based on fixed noise element[J]. Proceedings of the CSEE, 2021, 41 (7): 2331- 2341.
23	VACCARO A, CANIZARES C A, VILLACCI D. An affine arithmetic-based methodology for reliable power flow analysis in the presence of data uncertainty[J]. IEEE Transactions on Power Systems, 2010, 25 (2): 624- 632. DOI
24	VACCARO A, CAÑIZARES C A. An affine arithmetic-based framework for uncertain power flow and optimal power flow studies[J]. IEEE Transactions on Power Systems, 2017, 32 (1): 274- 288. DOI
25	卢新星, 瞿振宇, 黄际元, 等. 考虑多种实时气象因素的分布式光伏出力预测模型构建与优化[J]. 湖南电力, 2024, 44 (6): 128- 133.
	LU Xinxing, QU Zhenyu, HUANG Jiyuan, et al. Construction and optimization of distributed photovoltaic output forecast model considering multiple real-time meteorological factors[J]. Hunan Electric Power, 2024, 44 (6): 128- 133.
26	赵高帅, 罗涛, 闫大威, 等. 考虑源荷相关性及不确定性的配电网网架规划方法[J]. 浙江电力, 2024, 43 (10): 65- 74.
	ZHAO Gaoshuai, LUO Tao, YAN Dawei et al. A framework planning method for distribution networks considering the source-load correlation and uncertainty[J]. 浙江电力, 2024, 43 (10): 65- 74.
27	曹宏宇, 梁言贺, 刘惠颖, 等. 考虑风-光-储不确定性的新型电力系统概率潮流计算[J]. 电测与仪表, 2024, 61 (6): 87- 93.
	CAO Hongyu, LIANG Yanhe, LIU Huiying, et al. Probabilistic power flow calculation of novel power system considering uncertainty of wind-light-storage[J]. Electrical Measurement & Instrumentation, 2024, 61 (6): 87- 93.
28	LU Z M, YAN W, HUANG D Z, et al. State estimation for medium- and low-voltage distribution systems considering measurement characteristics and grounded slack bus[J]. IEEE Transactions on Instrumentation and Measurement, 2022, 71, 1008112.
29	穆怀天, 廉洪亮, 刘娟, 等. 基于数据物理融合驱动配电网三相线性化潮流及线损分析应用[J]. 中国电力, 2024, 57 (10): 46- 56. DOI
	MU Huaitian, LIAN Hongliang, LIU Juan, et al. Application of three-phase linearized power flow and line loss analysis of distribution network driven by data and physics fusion[J]. Electric Power, 2024, 57 (10): 46- 56. DOI
30	陆文甜. 基于增量交换的主动配电网分布式多目标最优潮流[J]. 综合智慧能源, 2024, 46 (2): 43- 48.
	LU Wentian. Increment-exchange-based decentralized multi-objective optimal power flow algorithm for active distribution grids[J]. Integrated Intelligent Energy, 2024, 46 (2): 43- 48.
31	杨剑锋, 李婷, 杨爱民, 等. 含电能路由器的光伏配电网电压越限问题潮流优化研究[J]. 发电技术, 2025, 46 (1): 113- 125. DOI
	YANG Jianfeng, LI Ting, YANG Aimin, et al. Research on tidal optimization of voltage overrun problem in photovoltaic distribution network with electrical energy router[J]. Power Generation Technology, 2025, 46 (1): 113- 125. DOI
32	LENG S P, LIU K P, RAN X H, et al. An affine arithmetic-based model of interval power flow with the correlated uncertainties in distribution system[J]. IEEE Access, 2020, 8, 60293- 60304. DOI
33	胡真, 汪盼. 计及可再生能源不确定性的实时需求响应策略研究[J]. 湖南电力, 2023, 43 (1): 30- 34, 40.
	HU Zhen, WANG Pan. Research on real-time demand response strategy considering renewable energy uncertainty[J]. Hunan Electric Power, 2023, 43 (1): 30- 34, 40.
34	杨彪, 李佳蓉, 魏子轲. 美国分布式能源发展对我国的启示[J]. 中国电力企业管理, 2024, (25): 94- 96.
35	张静忠, 蒙飞, 孙阳, 等. 考虑有功不确定性的配电网新能源无功优化控制[J]. 中国电力, 2024, 57 (3): 51- 59.
	ZHANG Jingzhong, MENG Fei, SUN Yang, et al. Reactive power optimization control for renewable energy in distribution networks considering active power uncertainties[J]. Electric Power, 2024, 57 (3): 51- 59.
36	贾晓强, 杨永标, 杜姣, 等. 气候变化条件下基于智能预测模型的虚拟电厂不确定性运行优化研究[J]. 发电技术, 2023, 44 (6): 790- 799.
	JIA Xiaoqiang, YANG Yongbiao, DU Jiao, et al. Study on uncertainty operation optimization of virtual power plant based on intelligent prediction model under climate change[J]. Power Generation Technology, 2023, 44 (6): 790- 799.

[1]	刘晗, 刘金东, 李贺, 李彦立, 于起媛, 赵远, 耿亚男. 基于CEEMDAN与NRBO-XGBoost的含光伏配电网漏电故障辨识[J]. 中国电力, 2025, 58(9): 23-32.
[2]	吉兴全, 张祥星, 张玉敏, 叶平峰, 王德龙, 黄心月. 基于LSD算法的多分支配电网故障定位[J]. 中国电力, 2025, 58(9): 54-67.
[3]	赵珊珊, 高菲, 李雅洁, 李建芳, 张瑜, 段祥骏, 董伟杰. 基于改进模因算法的含微网群的柔性配电网多目标优化控制[J]. 中国电力, 2025, 58(9): 97-104.
[4]	王世谦, 韩丁, 王楠, 白宏坤, 宋大为, 胡彩红. 基于双层主从博弈的主动配电网协同调度[J]. 中国电力, 2025, 58(9): 105-114.
[5]	林济铿, 石涛. 基于模型预测控制的区域电网频率控制方法[J]. 中国电力, 2025, 58(9): 124-137.
[6]	栗志鹏, 刘少博, 杨浩, 董蕊, 祁琛峰, 沈硕, 赵鹏. 基于PSO的配电网谐波抑制与降损增效协同优化[J]. 中国电力, 2025, 58(8): 50-59.
[7]	高芳杰, 孙玉杰, 李忆, 乐鹰, 张继广, 许传博, 刘敦楠. 计及海上风电制氢的海岛多能微网鲁棒优化调度[J]. 中国电力, 2025, 58(7): 68-79.
[8]	孔令国, 田杨进, 康建东, 方磊, 刘闯, 蔡国伟. 考虑多电解槽协同的海上独立能源岛不确定性双层优化配置[J]. 中国电力, 2025, 58(7): 80-90, 104.
[9]	刘军会, 龚健, 佟炳绅, 李松杰, 张艺涵, 崔世常, 田春筝, 张永斌. 基于分布式储能与光伏的虚拟电厂与配电网协同优化方法[J]. 中国电力, 2025, 58(6): 1-9.
[10]	王方敏, 顼佳宇, 苏宁, 牛焕娜, 袁嘉兴, 门盼龙. 新型电力系统风险抑制下分布式光伏承载力概率评估方法[J]. 中国电力, 2025, 58(6): 33-44.
[11]	翟哲, 陈梓煜, 刘起兴, 梁彦杰, 李智勇. 计及风险管理的分布式资源聚合商电力市场交易模型[J]. 中国电力, 2025, 58(6): 56-66, 155.
[12]	秦昆, 渠志江, 韩建伟, 许涛, 高峰, 迟晓莉. 基于可调虚拟阻抗的“柔-储-充”装置电池优化运行策略[J]. 中国电力, 2025, 58(6): 145-155.
[13]	李鹏, 祖文静, 刘一欣, 田春筝, 郝元钊, 李慧璇. 基于不完全量测数据的配电网状态估计方法[J]. 中国电力, 2025, 58(5): 1-10.
[14]	檀勤良, 贺嘉明, 吕函谕, 丁毅宏. 考虑成本不确定性的发电企业低碳技术采纳决策优化研究[J]. 中国电力, 2025, 58(5): 62-73.
[15]	汪进锋, 李金鹏, 许银亮, 刘海涛, 何锦雄, 许建远. 考虑不确定性和绿证交易的虚拟电厂与配电网分布式优化[J]. 中国电力, 2025, 58(4): 21-30, 192.