基于图论及网络等值的配电网可靠性评估方法*

doi:10.11985/2021.03.013

电气工程学报 ›› 2021, Vol. 16 ›› Issue (3): 92-98.doi: 10.11985/2021.03.013

扫码分享

基于图论及网络等值的配电网可靠性评估方法^*

徐敬友¹(), 丁坚勇²(), 杨东俊¹(), 肖彦娟², 杨洁¹, 涂智福²

1.国网湖北省电力有限公司经济技术研究院武汉 430063
2.武汉大学电气与自动化学院武汉 430072

收稿日期:2021-02-18 修回日期:2021-08-06 出版日期:2021-09-25 发布日期:2021-10-29
通讯作者: 丁坚勇 E-mail:ccepri@163.com;jyding@whu.edu.cn;agcdydj@126.com
作者简介:* 丁坚勇,男,1957年生,博士,教授。主要研究方向为电力规划与可靠性、电力系统分析与控制。E-mail： jyding@whu.edu.cn
徐敬友,男,1974年生,硕士,高级工程师。主要研究方向为电网规划、电力系统分析。E-mail： ccepri@163.com
杨东俊,男,1975年生,博士,正高级工程师。主要研究方向为电网规划、电力经济技术分析及管理。E-mail： agcdydj@126.com
基金资助:
* 国网湖北省电力有限公司科技资助项目(52153818001F)

Distribution Network Reliability Evaluation Method Based on Graph Theory and Network Equivalence

XU Jingyou¹(), DING Jianyong²(), YANG Dongjun¹(), XIAO Yanjuan², YANG Jie¹, TU Zhifu²

1. State Grid Hubei Economic Research Institute, Wuhan 430063
2. School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072

Received:2021-02-18 Revised:2021-08-06 Online:2021-09-25 Published:2021-10-29
Contact: DING Jianyong E-mail:ccepri@163.com;jyding@whu.edu.cn;agcdydj@126.com

摘要/Abstract

摘要：

能源互联网的快速发展对电网形态、结构、功能提出了新的要求。针对配电网目标网架构建,提出基于图论的配电网可靠性评估方法,为配电网的规划和建设提供参考依据。提取配电网拓扑结构采用图的邻接矩阵表示,用加权邻接矩阵的边权代表配电网馈线上元件的可靠性参数,采用搜索树的方法找出复杂结构配电网的最小路,转化为最小割集矩阵得到网络的一二阶割集;运用图论的状态空间法推导出多元件系统可靠性指标等效合并计算公式,对于含分支馈线的复杂结构配电网,采用网络等值法将分支馈线对上级馈线的影响用等效元件的可靠性指标反映,通过网络等值有效降低配电网网架的空间复杂度,简化计算过程,具有良好的实际应用价值。最后在RBTS母线6系统的主馈线上验证了将图论和网络等值运用在配电网可靠性评估中的有效性。

关键词: 图论, 网络等值, 配电网可靠性, 搜索树, 状态空间法

Abstract:

The rapid development of energy internet has put forward new requirements for the shape, structure and function of the power grid. Aiming at the construction of the target grid structure of the distribution network, a method of evaluating the reliability of the distribution network based on graph theory is proposed. The structure is represented by the adjacency matrix of the graph, and the edge weights of the weighted adjacency matrix are used to represent the reliability parameters of the components in the feeder of the distribution network. The search tree method is used to find the minimum path of the distribution network with complex structure, which is transformed into the minimum cut set matrix to obtain the first and second order cut sets of the network. Secondly, the state-space method of graph theory is used to derive the equivalent combined calculation formula of multi-component system reliability index. For complex structure distribution networks with branch feeders, the network equivalent method is used to reflect the influence of the branch feeder on the upper feeder with the reliability index of the equivalent component. Network equivalents can effectively reduce the space complexity of the switching network frame, simplify the calculation process, and have good practical application value. Finally, the validity of applying graph theory and network equivalents to the reliability evaluation of distribution network is verified on the main feeder of RBTS bus 6 system.

Key words: Graph theory, network equivalence, network reliability, search tree, state space method

中图分类号:

TM561

徐敬友, 丁坚勇, 杨东俊, 肖彦娟, 杨洁, 涂智福. 基于图论及网络等值的配电网可靠性评估方法^*[J]. 电气工程学报, 2021, 16(3): 92-98.

XU Jingyou, DING Jianyong, YANG Dongjun, XIAO Yanjuan, YANG Jie, TU Zhifu. Distribution Network Reliability Evaluation Method Based on Graph Theory and Network Equivalence[J]. Journal of Electrical Engineering, 2021, 16(3): 92-98.

图/表 9

图1

图2

图3

表1

图4

图5

图6

图7

表2

参考文献 19

[1]	周海京, 遇今. 故障模式、影响及危害性分析与故障树分析[M]. 北京: 航空工业出版社, 2003.
	ZHOU Haijing, YU Jin. Failure mode,impact and criticality analysis and fault tree analysis[M]. Beijing: Aviation Industry Press, 2003.
[2]	GUO H T, YANG X H. Automatic creation of Markov models for reliability assessment of safety instrumented systems[J]. Reliability Engineering & System Safety, 2008, 93(6):807-815.
[3]	孙志媛, 李海波, 鲁宗相. 考虑连锁故障的大电网可靠性评估[J]. 电力科学与技术学报, 2015, 30(1):67-72.
	SUN Zhiyuan, LI Haibo, LU Zongxiang. Power system reliability evaluation considering cascading failures[J]. Journal of Electric Power Science and Technology, 2015, 30(1):67-72.
[4]	NAESS A, LEIRA B J, BATSEVYCH O. System reliability analysis by enhanced Monte Carlo[J]. Structural Safety, 2009, 31(5):349-355. doi: 10.1016/j.strusafe.2009.02.004
[5]	冯雷, 朱林, 刘平. 考虑厂站主接线的电网暂态稳定概率评估方法[J]. 电力科学与技术学报, 2016, 31(4):123-128,142.
	FENG Lei, ZHU Lin, LIU Ping. Transient stability probability assessment of power system considering substation connection modes[J]. Journal of Electric Power Science and Technology, 2016, 31(4):123-128,142.
[6]	束洪春, 刘宗兵, 朱文涛. 基于图论的复杂配电网可靠性评估方法[J]. 电网技术, 2006(21):46-49.
	SHU Hongchun, LIU Zongbing, ZHU Wentao. A new method of reliability evaluation method for complex distribution network based on graph theory[J]. Power System Technology, 2006(21):46-49.
[7]	李响, 王宝巍, 欧阳卫年, 等. 分布式多电源开环接线的不同模式的可靠性分析[J]. 电气工程学报, 2020, 15(4):138-143.
	LI Xiang, WANG Baowei, OUYANG Weinian, et al. Reliability analysis of different modes of distributed multi-power open loop wiring[J]. Journal of Electrical Engineering, 2020, 15(4):138-143.
[8]	刘沛立, 石峰. 基于图论的故障影响遍历的配电网可靠性评估方法[J]. 低压电器, 2011(20):29-35.
	LIU Peili, SHI Feng. Power distribution network reliability evaluation method based on fault influence traverse of graph theory[J]. Electrical & Energy Management Technology, 2011(20):29-35.
[9]	王秀丽, 罗沙, 谢绍宇, 等. 基于最小割集的含环网配电系统可靠性评估[J]. 电力系统保护与控制, 2011, 39(9):52-58.
	WANG Xiuli, LUO Sha, XIE Shaoyu, et al. Reliability evaluation of distribution systems with meshed network based on the minimum-cut set[J]. Power System Protection and Control, 2011, 39(9):52-58.
[10]	肖彦娟, 丁坚勇. 基于故障树的电气主接线可靠性及薄弱环节分析[J]. 电测与仪表, 2020(16):12-16.
	XIAO Yanjuan, DING Jianyong. Reliability evaluation and weak part identification analysis of main electrical connection based on fault tree[J]. Electrical Measurement & Instrumentation, 2020(16):12-16.
[11]	羌丁建, 寿挺, 朱铁铭, 等. 高压配电网规划评价指标体系与综合评价模型[J]. 电力系统保护与控制, 2013, 41(21):52-57.
	QIANG Dingjian, SHOU Ting, ZHU Tieming, et al. An evaluation index system and comprehensive evaluation model on high-voltage distribution network planning[J]. Power System Protection and Control, 2013, 41(21):52-57.
[12]	冯雪平, 梁英, 郭炳庆. 基于图论的含分布式电源配电网供电恢复动态规划方法[J]. 电力系统保护与控制, 2012, 40(9):24-30.
	FENG Xueping, LIANG Ying, GUO Bingqing. A dynamic programming method based on graph theory for restoration of distribution system with DGs[J]. Power System Protection and Control, 2012, 40(9):24-30.
[13]	缪辉, 丁晓群. 基于图论和OBDD的含分布式电源配电网故障恢复算法[J]. 电工电能新技术, 2018, 37(9):59-66.
	MIAO Hui, DING Xiaoqun. Service restoration algorithm for distribution network with distributed generation based on graph theory and OBDD[J]. Advanced Technology of Electrical Engineering and Energy, 2018, 37(9):59-66.
[14]	胡福年, 孙守娟. 基于图论的矩阵算法在配电网故障定位中的应用[J]. 中国电力, 2016, 29(3):94-98.
	HU Funian, SUN Shoujuan. Fault location of distribution network by applying matrix algorithm based on graph theory[J]. China Electric Power, 2016, 29(3):94-98.
[15]	刘洪, 王博, 李梅菊, 等. 基于改进加权Voronoi图算法的有源配电网变电站规划[J]. 电力系统自动化, 2017, 41(13):45-52.
	LIU Hong, WANG Bo, LI Meiju, et al. Substation planning of active distribution network based on improved weighted Voronoi diagram method[J]. Automation of Electric Power Systems, 2017, 41(13):45-52.
[16]	周生海, 尹航, 顾颖, 等. 基于POP NSGA-Ⅱ的配电网故障恢复重构[J]. 电气工程学报, 2018, 13(6):28-35.
	ZHOU Shenghai, YIN Hang, GU Ying, et al. Service restoration reconfiguration in distribution systems based on pareto optimizing path NSGA-Ⅱ[J]. Journal of Electrical Engineering, 2018, 13(6):28-35.
[17]	郭永基. 可靠性工程原理[M]. 北京: 清华大学出版社, 2002.
	GUO Yongji. Principles of reliability engineering[M]. Beijing: Tsinghua University Press, 2002.
[18]	昝贵龙, 王主丁, 李秋燕, 等. 基于状态空间截断和隔离范围推导的高压配电网可靠性评估[J]. 电力系统自动化, 2017, 41(13):79-85.
	XI Guilong, WANG Zhuding, LI Qiuyan, et al. High voltage distribution network reliability evaluation based on state space truncation and isolation scope derivation[J]. Automation of Electric Power Systems, 2017, 41(13):79-85.
[19]	BILLINTON R, JOHNNAVITHULA S. A test system for teaching overall power system reliability assessment[J]. IEEE Trans. on Power System, 1996, 11(4):1670-1676. doi: 10.1109/59.544626

逻辑关系	等效失效率λ/ (次/年)	等效修复率μ/ (次/年)	等效不可用率 (%)
串联	$\sum\limits_{i = {\text{1}}}^m {{\lambda _i}}$	${{\sum\limits_{i = {\rm{1}}}^m {{\lambda _i}} } \mathord{\left/ {\vphantom {{\sum\limits_{i = {\rm{1}}}^m {{\lambda _i}} } {\sum\limits_{i = {\rm{1}}}^m {\frac{{{\lambda _i}}}{{{\mu _i}}}} }}} \right. \kern-\nulldelimiterspace} {\sum\limits_{i = {\rm{1}}}^m {\frac{{{\lambda _i}}}{{{\mu _i}}}} }}$	$\sum\limits_{i = {\text{1}}}^m {{\lambda _i}} {r_i}$
并联	${{\prod\limits_{i = 1}^m {{\lambda _i}} } \mathord{\left/ {\vphantom {{\prod\limits_{i = 1}^m {{\lambda _i}} } {\sum\limits_{i = {\rm{1}}}^m {\frac{1}{{{\mu _i}}}} }}} \right. \kern-\nulldelimiterspace} {\sum\limits_{i = {\rm{1}}}^m {\frac{1}{{{\mu _i}}}} }}$	$\sum\limits_{i = {\text{1}}}^m {{\mu _i}}$	$\prod\limits_{i = 1}^m {{\lambda _i}{r_i}}$

可靠性指标	计算值	参考值
SAIFI/[次/(户·年)]	1.014 3	1.006 7
SAIDI/[h/(户·年)]	6.723 1	6.668 8
CAIDI/[h/(户·年)]	6.628 3	6.624 7
ASAI(%)	99.923 2	99.923 9
AENS/(MW·h/年)	73.026 5	72.815 3

基于图论及网络等值的配电网可靠性评估方法^*

Distribution Network Reliability Evaluation Method Based on Graph Theory and Network Equivalence

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 9

参考文献 19

相关文章 15

编辑推荐

Metrics

本文评价

[1]	罗晓祎, 张凤阁. 一种分数槽永磁同步电机的转矩计算方法^*[J]. 电气工程学报, 2021, 16(3): 1-8.
[2]	王恒宜, 汪飞. 小电容应用下的三角形联结级联H桥STATCOM建模和最优控制器设计^*[J]. 电气工程学报, 2021, 16(3): 25-32.
[3]	徐攀腾, 朱博, 喻文翔, 宋述波, 李建勋, 樊友平. 多类型元件混合直流电网机电暂态建模仿真^*[J]. 电气工程学报, 2021, 16(3): 54-61.
[4]	马涛, 侯磊, 许杨勇, 祁天星, 杨天阔, 齐庆峰, 刘学识, 娄博威. 电极旋转情况下真空电弧阳极熔蚀过程的数值仿真与分析^*[J]. 电气工程学报, 2021, 16(2): 108-114.
[5]	伍文俊, 王思佳, 蔡嘉齐. 含网电变压器保护的电动修井机超级电容储能控制^*[J]. 电气工程学报, 2021, 16(2): 122-130.
[6]	霍陆昱, 陈怡霖, 杜海忠, 章治国. 基于多周期离散迭代模型的移相全桥倍流同步整流变换器及其稳定性分析[J]. 电气工程学报, 2021, 16(2): 131-140.
[7]	克帕依吐·吐尔逊, 李明, 汪齐, 廖凯. 石榴石型直流光学电流互感器及其稳定性研究^*[J]. 电气工程学报, 2021, 16(2): 149-158.
[8]	赵振喜, 李洪丰, 侯伟, 李兴, 屈国际, 肖洪波. 国网吉林电力基建电力物联网研究与实践[J]. 电气工程学报, 2021, 16(2): 166-173.
[9]	党存禄, 李旭鹏, 孙海斌, 武文成. 双馈风电机组次同步控制相互作用的抑制方法 ^*[J]. 电气工程学报, 2021, 16(1): 119-126.
[10]	刘鑫, 原熙博, 韩东旭, 赵凯, 由蕤. 一种基于矩阵变换器的海上风力机中压电能变换系统 ^*[J]. 电气工程学报, 2021, 16(1): 127-133.
[11]	李志坚, 邢继文, 杜伯学, 肖萌, 孔晓晓, 李进. 高储能聚合物材料复配体系研究进展 ^*[J]. 电气工程学报, 2021, 16(1): 134-140.
[12]	李存贺, 赵博, 刘剑, 鲁炳林. 开关磁阻电动机小样本磁链特性精确建模方法 ^*[J]. 电气工程学报, 2021, 16(1): 16-25.
[13]	李金, 张喜铭, 谢型浪, 李恒. 变电站安全运维装置技术方案 ^*[J]. 电气工程学报, 2020, 15(4): 114-120.
[14]	李兴, 侯伟, 杨宇, 王鹏, 苏海军, 付铭明. 论电力基建业务中边缘计算的应用与实践[J]. 电气工程学报, 2020, 15(4): 153-160.
[15]	李清波, 林佳壕. 基于混合型柔性限流器直流配网故障暂态特性研究 ^*[J]. 电气工程学报, 2020, 15(4): 65-74.