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

doi:10.11930/j.issn.1004-9649.202412008

Abstract

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

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.

Add to citation manager EndNote|Ris|BibTeX

URL: https://www.electricpower.com.cn/EN/10.11930/j.issn.1004-9649.202412008

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

Figures/Tables 17

Fig.1 The FOR of different types of FPUs

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

Fig.3 Example of SFOR and CFOR of an FPU

Fig.4 Illustration of characterization error estimation

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

Fig.6 Flow of the proposed SFOR estimation method

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%）

Fig.7 Relative error of different methods

Fig.8 The actual error and the characterization error

Fig.9 Calculation time of the proposed method.

Fig.10 Relative error of SFOR with different parameters

Fig.11 Comparison of SFOR and CFOR results

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%）

Fig.12 Relative error of different methods

Fig.13 Calculation time of the proposed method

Fig.14 Relative error of SFOR with different parameters

Fig.15 Comparison of SFOR and CFOR results

References 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.

[1]	Lei ZHANG, Xiaowei MA, Manliang WANG, Li CHEN, Bingtuan GAO. Distributed Collaborative Control Strategy for Intra-regional AGC Units in Interconnected Power System with Renewable Energy [J]. Electric Power, 2025, 58(3): 8-19.
[2]	Tonghai JIANG, Feng WANG, Ziqi LIU, Shuaijie SHAN. A Joint Scenario Generation Method for Wind-Solar Meteorological Resources Based on Improved Generative Adversarial Network [J]. Electric Power, 2025, 58(3): 183-192.
[3]	Mingrun TANG, Ruoyang LI, Muran LIU, Xiaoyu CHENG, Yao LIU, Shuxia YANG. Prediction of Large-Scale Renewable Energy Access under Steady State of Electric Power System [J]. Electric Power, 2025, 58(2): 126-132.
[4]	Kun HUANG, Ming FU, Jiaxiang ZHAI, Haochen HUA. Distributed Coordination Optimization for Economic Operation of the Multi-Microgrid System Based on Improved Linearization ADMM [J]. Electric Power, 2025, 58(2): 193-202.
[5]	Ling LU, Tao YUAN, Bo YANG, Xin LI, Yang LU, Qiuping PU, Xin ZHANG. Two-Layer Optimization of Regional Integrated Energy System Considering Exergy Efficiency and Multiple Uncertainties [J]. Electric Power, 2025, 58(1): 128-140.
[6]	Xiaoyan ZOU, Ruihong ZHANG. Evolutionary Game Study of the Cooperation Mode Between Renewable Energy Generation Enterprises and Energy Storage Companies Considering Government Intervention [J]. Electric Power, 2025, 58(1): 153-163.
[7]	Yuqing WANG, Min ZHANG, Jiaxing WANG, Bohao LI, Tianyang YANG, Ming ZENG. Rental Price Decision of Shared Energy Storage Capacity Based on Supermodular Game [J]. Electric Power, 2025, 58(1): 164-173.
[8]	Chong SHAO, Rongyi HU, Jiao YU, Mingdian WANG. Dynamic Modeling and Control Strategy for Hybrid Energy Storage System Considering State of Charge and Storage State of Hydrogen [J]. Electric Power, 2024, 57(7): 109-124.
[9]	Xu HU, Ruijian AN, Yuchen DU, Xiaohan SHI, Yue WANG. Research on Europe-North Africa Hydrogen Coordinated Development [J]. Electric Power, 2024, 57(7): 151-162.
[10]	Zhengnan GAO, Nan JIANG, Qixin CHEN, Jiang XU, Haili WANG, Li XIN, Qinggui XU. Construction Experience of German Electricity Market Adapting to Energy Transition [J]. Electric Power, 2024, 57(6): 204-214.
[11]	Zimin ZHU, Jinfang ZHANG, Qing CHANG, Zhuan ZHOU, Xiaolin ZHANG. Adaptive VSG Control Strategy of Sending End for Large-Scale Renewable Energy Connected to Weakly-Synchronized Support VSC-HVDC System [J]. Electric Power, 2024, 57(5): 211-221.
[12]	Shuai WANG, Yuehui HUANG, Yuanhong NIE, Siyang LIU. Research on Development Scenario of Renewable Energy in Receiving-End Power Grid Based on Production Simulation [J]. Electric Power, 2024, 57(5): 240-250.
[13]	Zhiwei LIU, Yue MA, Zhicheng SHA, Yunshu SHAO, Yuanfang NIU, Xiaoming DONG, Chengfu WANG. Distributionally Robust Operation for Flexible Distribution Networks Considering Multi-correlation of Renewable Power Generation [J]. Electric Power, 2024, 57(12): 97-108.
[14]	Jing XU, Tiejun ZHAO, Xiaogang GAO, Ju YE, Lingling SUN. Risk Analysis of Insufficient Flexibility from Regulation Resources in High Proportion Renewable Energy Power Systems [J]. Electric Power, 2024, 57(11): 129-138.
[15]	Qixiang WANG, Zhentao HAN, Yi LIANG. Economic Dispatch Analysis of Risk Prevention and Control Based on Game Theory Equilibrium [J]. Electric Power, 2024, 57(10): 69-77.