考虑随机性的主动配电网有功无功可行域计算方法

doi:10.11930/j.issn.1004-9649.202412008

中国电力 ›› 2025, Vol. 58 ›› Issue (4): 182-192.DOI: 10.11930/j.issn.1004-9649.202412008

• 面向新型电力系统的智慧用能优化与控制 • 上一篇下一篇

考虑随机性的主动配电网有功无功可行域计算方法

王宣元¹(), 张玮¹, 李长宇², 谢欢², 郭庆来³(), 王彬³, 张宇谦³

1. 国网冀北电力有限公司，北京　100052
2. 国网冀北电力有限公司电力科学研究院，北京　100045
3. 清华大学电机工程与应用电子技术系，北京　100084

收稿日期:2024-12-02 录用日期:2025-03-02 发布日期:2025-04-23 出版日期:2025-04-28
作者简介:
王宣元（1979），女，博士，高级工程师（教授级），从事电力系统、新能源电力电子设备运行控制及电力市场相关研究，E-mail：wang.xuanyuan@jibei.sgcc.com.cn
郭庆来（1979），男，通信作者，博士，教授，从事信息物理系统和无功电压优化控制研究，E-mail：guoqinglai@tsinghua.edu.cn
基金资助:
国网冀北电力有限公司科技项目（新能源集群主动支撑的“双高”送端电力系统无功电压调控关键技术及架构研究，B3018K23000Z）。

A Method for Calculating the Feasible Operation Region of Active and Reactive Power in Active Distribution Networks Considering Stochasticity

WANG Xuanyuan¹(), ZHANG Wei¹, LI Changyu², XIE Huan², GUO Qinglai³(), WANG Bin³, ZHANG Yuqian³

1. State Grid Jibei Electric Power Co., Ltd., Beijing 100052, China
2. State Grid Jibei Electric Co., Ltd. Research Institution, Beijing 100052, China
3. Department of Electrical Engineering, Tsinghua University, Beijing 100084, China

Received:2024-12-02 Accepted:2025-03-02 Online:2025-04-23 Published:2025-04-28
Supported by:
This work is supported by the Science and Technology Project of State Grid Jibei Electric Power Co., Ltd. (Research on Key Technologies and Architecture for Reactive Power Voltage Regulation in 'Dual High' Sending-end Power System Actively Supported by New Energy Clusters, No.B3018K23000Z).

摘要/Abstract

摘要：

随着可再生能源的大规模接入，电力系统面临灵活性资源短缺的挑战，而配电网中的分布式电源和电力电子设备具备提供灵活性的潜力。为此，综合了多种灵活性提供单元、网络运行约束及分布式电源和负荷的不确定性，提出一种考虑不确定性的配网灵活性提供潜力评估方法。首先，建立一种改进的确定性可行域计算方法；然后，通过基于抽样的方法建模负荷和分布式电源的不确定性；最后，通过算例结果验证该方法的准确性与有效性。算例结果表明，该方法能够提供可行域的概率分布及不同置信水平下的可行域，且在相同计算成本下具有更高的精度，避免了过于乐观的结果。

关键词: 可行域, 可再生能源, 灵活性资源, 输配协同, 随机性

Abstract:

The large-scale integration of renewable energy poses challenges to the power systems, such as the shortage of flexibility resources. However, renewable energy and power electronics connected to the distribution networks can provide flexibilities. This paper proposes a novel method to determine the stochastic feasible operation region of distribution networks, considering flexibility-providing units, network operational constraints, and uncertainties in renewable energy generation and loads. Firstly, an improved method for calculating the deterministic flexibility operation region is introduced. And then, a scenario-based approach is used to model the uncertainties of loads and distributed generations. Finally, a case study demonstrates the accuracy and effectiveness of the proposed method. The case study results show that the proposed method can provide both the probability distribution of the feasible operation region and the operation regions at different confidence levels, and achieves higher accuracy with the same computational cost and avoids overly optimistic results.

Key words: feasible operation region, renewable energy, flexibility resources, transmission-distribution coordination, stochasticity

王宣元, 张玮, 李长宇, 谢欢, 郭庆来, 王彬, 张宇谦. 考虑随机性的主动配电网有功无功可行域计算方法[J]. 中国电力, 2025, 58(4): 182-192.

WANG Xuanyuan, ZHANG Wei, LI Changyu, XIE Huan, GUO Qinglai, WANG Bin, ZHANG Yuqian. A Method for Calculating the Feasible Operation Region of Active and Reactive Power in Active Distribution Networks Considering Stochasticity[J]. Electric Power, 2025, 58(4): 182-192.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202412008

https://www.electricpower.com.cn/CN/Y2025/V58/I4/182

图/表 17

图 1 不同种类FPU的FOR

Fig.1 The FOR of different types of FPUs

图 2 非凸FOR的凸分解

Fig.2 Division of non-convex FOR into convex sub-FORs

图 3 单个FPU的SFOR和CFOR示例

Fig.3 Example of SFOR and CFOR of an FPU

图 4 刻画误差的估算方法示意

Fig.4 Illustration of characterization error estimation

图 5 FOR切线的估算方法示意

Fig.5 Determination of the tangent of FOR at a vertex

图 6 本文SFOR计算方法的流程

Fig.6 Flow of the proposed SFOR estimation method

表 1 算例I研究中的FPU

Table 1 The FPUs in the case study I

FPU 类型	数量	容量/kW	备注
PV	8	12.5×8=100	位于节点1、2、12、13、14、15、23、24
DFIG	4	100+150×3=550	位于节点9、10、11、17（100 kW）
ESS	2	25×2=50	位于节点3、4
OLTC	1	/	配电变压器（±2×2.5%）

图 7 不同方法在不同定点数下的相对误差

Fig.7 Relative error of different methods

图 8 实际误差与刻画误差

Fig.8 The actual error and the characterization error

图 9 不同参数下所提方法的计算时间

Fig.9 Calculation time of the proposed method.

图 10 不同参数下的SFOR误差

Fig.10 Relative error of SFOR with different parameters

图 11 SFOR与CFOR结果对比

Fig.11 Comparison of SFOR and CFOR results

表 2 算例II研究中的FPU

Table 2 The FPUs in the case study II

FPU 类型	数量	容量/MW	备注
PV	14	10×2+4× 2.5=30	位于节点4（2.5 MW）、5（2.5 MW）、6、7、8、9、10、28（2.5 MW）、29（2.5 MW）、30、31、32、33、34
DG	1	20	位于节点80
ESS	5	1×5=5	位于节点75、77、85、110、112
CL	16	14×1.5+ 2×2=25	位于节点4、6、8、10、28、30、32、34（2 MW）、36（2 MW）、70、72、74、76、106、108、110、112
OLTC	1	/	配电变压器（±2×2.5%）

图 12 不同方法在不同定点数下的相对误差

Fig.12 Relative error of different methods

图 13 不同参数下所提方法的计算时间

Fig.13 Calculation time of the proposed method

图 14 不同参数下的SFOR误差

Fig.14 Relative error of SFOR with different parameters

图 15 SFOR与CFOR结果对比

Fig.15 Comparison of SFOR and CFOR results

参考文献 37

1	朱法华, 徐静馨. 双碳背景下中国与主要发达国家电力低碳转型比较[J]. 电力科技与环保, 2024, 40 (6): 561- 571.
	ZHU Fahua, XU Jingxin. Comparison of low-carbon transformation in electricity between China and major developed countries under the background of carbon peaking and carbon neutrality[J]. Electric Power Technology and Environmental Protection, 2024, 40 (6): 561- 571.
2	谭显东, 刘俊, 徐志成, 等. “双碳” 目标下“十四五” 电力供需形势[J]. 中国电力, 2021, 54 (5): 1- 6.
	TAN Xiandong, LIU Jun, XU Zhicheng, et al. Power supply and demand balance during the 14th Five-Year Plan period under the goal of carbon emission peak and carbon neutrality[J]. Electric Power, 2021, 54 (5): 1- 6.
3	卓振宇, 张宁, 谢小荣, 等. 高比例可再生能源电力系统关键技术及发展挑战[J]. 电力系统自动化, 2021, 45 (9): 171- 191.
	ZHUO Zhenyu, ZHANG Ning, XIE Xiaorong, et al. Key technologies and developing challenges of power system with high proportion of renewable energy[J]. Automation of Electric Power Systems, 2021, 45 (9): 171- 191.
4	金晨, 任大伟, 肖晋宇, 等. 支撑碳中和目标的电力系统源-网-储灵活性资源优化规划[J]. 中国电力, 2021, 54 (8): 164- 174.
	JIN Chen, REN Dawei, XIAO Jinyu, et al. Optimization planning on power system supply-grid-storage flexibility resource for supporting the "carbon neutrality" target of China[J]. Electric Power, 2021, 54 (8): 164- 174.
5	HUANG P X, VANFRETTI L. Adaptive damping control of MMC to suppress high-frequency resonance[J]. IEEE Transactions on Industry Applications, 2023, 59 (6): 7224- 7237.
6	周海浪, 刘一畔, 陈雨果, 等. 考虑灵活性收益的需求侧资源可行域聚合方法[J]. 中国电力, 2022, 55 (9): 56- 63, 155.
	ZHOU Hailang, LIU Yipan, CHEN Yuguo, et al. Demand side feasible region aggregation considering flexibility revenue[J]. Electric Power, 2022, 55 (9): 56- 63, 155.
7	ZHOU Y, LI Z S, YANG M. A framework of utilizing distribution power systems as reactive power prosumers for transmission power systems[J]. International Journal of Electrical Power & Energy Systems, 2020, 121, 106139.
8	JIN X L, MU Y F, JIA H J, et al. Alleviation of overloads in transmission network: a multi-level framework using the capability from active distribution network[J]. International Journal of Electrical Power & Energy Systems, 2019, 112, 232- 251.
9	尚博文, 徐铭铭, 张金帅, 等. 高比例分布式光伏接入背景下配电网电压调控方法研究综述[J]. 智慧电力, 2024, 52 (12): 1- 11.
	SHANG Bowen, XU Mingming, ZHANG Jinshuai, et al. A review of voltage regulation methods for distribution networks in the context of high proportion of distributed photovoltaic integration[J]. Smart Power, 2024, 52 (12): 1- 11.
10	季湛洋, 胡阳, 孔令行, 等. 考虑多领域耦合特性的风电机组一次调频动态建模与仿真[J/OL]. 中国电力: 1–13 [2025-2-27]. http://kns.cnki.net/kcms/detail/11.3265.tm.20250226.1553.017.html.
	JI Zhanyang, HU Yang, KONG Lingxing, et al. Dynamic modeling and simulation of wind turbine unit frequency regulation considering multi-domain coupling characteristics[J/OL]. Electric Power: 1–13 [2025-2-27]. http://kns.cnki.net/kcms/detail/11.3265.tm.20250226.1553.017.html.
11	鲁宗相, 李海波, 乔颖. 高比例可再生能源并网的电力系统灵活性评价与平衡机理[J]. 中国电机工程学报, 2017, 37 (1): 9- 20.
	LU Zongxiang, LI Haibo, QIAO Ying. Flexibility evaluation and supply/demand balance principle of power system with high-penetration renewable electricity[J]. Proceedings of the CSEE, 2017, 37 (1): 9- 20.
12	齐军, 马鹏, 周生存, 等. 基于深度强化学习的新型终端配电网源荷储协同控制[J/OL]. 内蒙古电力技术: 1–12 [2025-2-19]. http://kns.cnki.net/kcms/detail/15.1200.tm.20250218.1641.004.html.
	Qi Jun, MA Peng, ZHOU Shengcun, et al. New terminal distribution network source load storage collaborative control based on deep reinforcement learning[J/OL]. Inner Mongolia Electric Power: 1–12 [2025-2-19]. http://kns.cnki.net/kcms/detail/15.1200.tm.20250218.1641.004.html.
13	YU M K, WANG J X, YAN J, et al. Pricing information in smart grids: a quality-based data valuation paradigm[J]. IEEE Transactions on Smart Grid, 2022, 13 (5): 3735- 3747.
14	王琦, 董洪达, 贺子谦, 等. 考虑灵活性资源互济的虚拟电厂集群优化调度策略[J]. 东北电力大学学报, 2024, 44 (5): 101- 111.
	WANG Qi, DONG Hongda, HE Ziqian, et al. Optimization and scheduling strategy for virtual power plant clusters considering flexibility and resource complementarity[J]. Journal of Northeast Electric Power University, 2024, 44 (5): 101- 111.
15	王佳莹, 檀鑫鑫, 吴玉鑫, 等. 多形态灵活资源调控下的可再生能源配额多主体博弈研究[J]. 智慧电力, 2025, 53 (2): 9- 15, 40.
	WANG Jiaying, TAN Xinxin, WU Yuxin, et al. Multi-agent game of renewable energy quotas under polymorphic flexible resource regulation[J]. Smart Power, 2025, 53 (2): 9- 15, 40.
16	SARSTEDT M, HOFMANN L. Monetarization of the feasible operation region of active distribution grids based on a cost-optimal flexibility disaggregation[J]. IEEE Access, 2022, 10, 5402- 5415.
17	SUN H B, GUO Q L, SHEN X W, et al. Energy Internet: redefinition and categories[J]. Energy Internet, 2024, 1 (1): 3- 8.
18	刘军会, 龚健, 佟炳绅, 等. 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/OL]. 中国电力: 1–9 [2025-2-26]. http://kns.cnki.net/kcms/detail/11.3265.TM.20250226.0812.004.html.
	LIU Junhui, GONG Jian, TONG Bingshen, et al. Coordinated optimization method for virtual power plants considering distributed energy storage and photovoltaics with distribution networks[J/OL]. Electric Power: 1–9 [2025-2-26]. http://kns.cnki.net/kcms/detail/11.3265.TM.20250226.0812.004.html.
19	ZHAO L, ZHANG W, HAO H, et al. A geometric approach to aggregate flexibility modeling of thermostatically controlled loads[J]. IEEE Transactions on Power Systems, 2017, 32 (6): 4721- 4731.
20	HELENO M, SOARES R, SUMAILI J, et al. Estimation of the flexibility range in the transmission-distribution boundary[C]//2015 IEEE Eindhoven PowerTech. Eindhoven, Netherlands. IEEE, 2015: 1–6.
21	MOKHTARIAN K, JACOBSEN H A. Coordinated caching in planet-scale CDNs: analysis of feasibility and benefits[C]//IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications. San Francisco, CA, USA. IEEE, 2016: 1–9.
22	SILVA J, SUMAILI J, BESSA R J, et al. Estimating the active and reactive power flexibility area at the TSO-DSO interface[J]. IEEE Transactions on Power Systems, 2018, 33 (5): 4741- 4750.
23	GIACOMO V, ROSSI M , MONETA D . Effects of Distribution System Characteristics on TSO-DSO Ancillary Services Exchange[C]//CIRED 2019.
24	STANKOVIĆ S, SÖDER L, HAGEMANN Z, et al. Reactive power support adequacy at the DSO/TSO interface[J]. Electric Power Systems Research, 2021, 190, 106661. DOI
25	DING T, ZENG Z Y, QU M, et al. Two-stage chance-constrained stochastic thermal unit commitment for optimal provision of virtual inertia in wind-storage systems[J]. IEEE Transactions on Power Systems, 2021, 36 (4): 3520- 3530. DOI
26	CHEN X, LI N. Leveraging two-stage adaptive robust optimization for power flexibility aggregation[J]. IEEE Transactions on Smart Grid, 2021, 12 (5): 3954- 3965.
27	张天策, 李庚银, 王剑晓, 等. 基于可行域投影理论的新能源电力系统协同运行方法[J]. 电工技术学报, 2024, 39 (9): 2784- 2796.
	ZHANG Tiance, LI Gengyin, WANG Jianxiao, et al. Coordinated operation method of renewable energy power systems based on feasible region projection theory[J]. Transactions of China Electrotechnical Society, 2024, 39 (9): 2784- 2796.
28	SAVVOPOULOS N, HATZIARGYRIOU N. An effective method to estimate the aggregated flexibility at distribution level[J]. IEEE Access, 2023, 11, 31373- 31383. DOI
29	ZHOU M Y, CHEN S, HUANG K, et al. Coordination of medium-voltage distribution networks and microgrids based on an aggregate flexibility region approach[J]. Sustainable Energy, Grids and Networks, 2024, 39, 101485.
30	KUNDU S, KALSI K, BACKHAUS S. Approximating flexibility in distributed energy resources: a geometric approach[C]//2018 Power Systems Computation Conference (PSCC). Dublin, Ireland. IEEE, 2018: 1–7.
31	LIEN J M, AMATO N M. Approximate convex decomposition of polygons[J]. Computational Geometry, 2006, 35 (1/2): 100- 123.
32	GEOFFRION A M. Generalized benders decomposition[J]. Journal of Optimization Theory and Applications, 1972, 10 (4): 237- 260.
33	MCKAY M D, BECKMAN R J, CONOVER W J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code[J]. Technometrics, 2000, 42 (1): 55.
34	BARAN M E, WU F F. Network reconfiguration in distribution systems for loss reduction and load balancing[J]. IEEE Transactions on Power Delivery, 2002, 4 (2): 1401- 1407.
35	RIAZ S, MANCARELLA P. On feasibility and flexibility operating regions of virtual power plants and TSO/DSO interfaces[C]//2019 IEEE Milan PowerTech. Milan, Italy. IEEE, 2019: 1–6.
36	LOPEZ L, GONZALEZ-CASTELLANOS A, POZO D, et al. QuickFlex: a fast algorithm for flexible region construction for the TSO-DSO coordination[C]//2021 International Conference on Smart Energy Systems and Technologies (SEST). Vaasa, Finland. IEEE, 2021: 1–6.
37	ZHANG D, FU Z C, ZHANG L C. An improved TS algorithm for loss-minimum reconfiguration in large-scale distribution systems[J]. Electric Power Systems Research, 2007, 77 (5/6): 685- 694.

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考虑随机性的主动配电网有功无功可行域计算方法

A Method for Calculating the Feasible Operation Region of Active and Reactive Power in Active Distribution Networks Considering Stochasticity

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