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Article(id=1241794071539290159, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241794070289387562, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2025.0505, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1734537600000, receivedDateStr=2024-12-19, revisedDate=1744041600000, revisedDateStr=2025-04-08, acceptedDate=null, acceptedDateStr=null, onlineDate=1773996378073, onlineDateStr=2026-03-20, pubDate=1761062400000, pubDateStr=2025-10-22, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773996378073, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773996378073, creator=13701087609, updateTime=1773996378073, updator=13701087609, issue=Issue{id=1241794070289387562, tenantId=1146029695717560320, journalId=1241701559352995854, year='2025', volume='45', issue='5', pageStart='1', pageEnd='227', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1773996377775, creator=13701087609, updateTime=1773996935444, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241796409465307627, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241794070289387562, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241796409465307628, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241794070289387562, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=38, endPage=51, ext={EN=ArticleExt(id=1241794071778365490, articleId=1241794071539290159, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Function-based seismic resilience assessment of urban power systems, columnId=1241794071602200899, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

The electric power system is the most critical component of urban infrastructure, serving as the foundation for the normal operation of a city. Earthquakes have a substantial impact on urban power systems. On one hand, it is reflected in the extensive damage to power infrastructure and the widespread power outages. On the other hand, it manifests in the long recovery times for power facilities and the significant impact on people’s livelihoods. Therefore, the performance analysis of the power system under seismic conditions and the post-earthquake restoration process urgently require attention. To more accurately assess and enhance the seismic resilience of urban power systems, a quantitative analysis framework for seismic resilience from a functional perspective has been established. The performance index of the power system is defined as the ratio of the population receiving power to the total population after an earthquake. The initial damage is determined through the seismic vulnerability modeling of power system components. The cascading failures of the power system following an earthquake are simulated using the DC power flow method to assess the power surplus in the city post-earthquake. The damaged components are then repaired, and the seismic resilience index is obtained by solving the system’s performance-time curve through an integral method. Based on functional analysis methods and component importance theory, the concept of post-earthquake restoration step length for the power system has been proposed. By adjusting the restoration step length, three restoration strategies have been developed including dynamic importance-based, static importance-based, and hybrid importance-based restoration strategies. A case study of a power grid in China has been conducted to validate the effectiveness of the resilience assessment framework and restoration strategies. The results show that the functional-based power system resilience assessment framework can effectively perform post-earthquake performance analysis and generate functional curves. The DC power flow analysis method accurately determines the state of each line and node in the power system, enabling a more realistic and reasonable simulation of cascading failures in the power system after an earthquake. Under 10,000 Monte Carlo simulations, the frequency distribution, average value, and the maximum value of the restoration strategy based on dynamic importance theory are significantly higher than those of the static importance-based strategy. The dynamic importance strategy yields the highest seismic resilience index, while the hybrid importance strategy provides intermediate results, and the static importance strategy results in the lowest seismic resilience index. The computational time required is inversely related to the resilience index, with the dynamic importance strategy taking 25 times longer than the static importance strategy. The hybrid importance strategy, which balances dynamic and static factors, has been shown to be the most efficient recovery strategy when dealing with large-scale computations and multiple scenarios, as it ensures higher resilience while maintaining computational efficiency.

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地震发生时,城市电力系统破坏严重且恢复时间较长,因此,地震作用下电力系统的功能分析及震后的恢复过程亟待研究。为了更准确地评估和更好地提升城市电力系统抗震韧性,该文建立了功能视角下的城市电力系统抗震韧性定量分析框架。基于电力潮流分析和震后电力系统破坏情况,求解震后城市的电力能力,将正常得到供电的人口与总人口的比率作为电力系统功能指标,通过积分法得到抗震韧性指标。同时,考虑恢复策略对韧性提升的影响,基于功能分析方法和元件重要度理论,提出了基于动态重要度、静态重要度和混合重要度的修复策略。以我国某电网为实例研究,验证了韧性评估框架和修复策略对韧性提升的有效性。结果表明：基于功能的电力系统韧性评估框架可较准确地完成震后电力系统的功能分析和级联失效模拟；基于动态重要度理论的修复策略得到的韧性指标高于静态重要度策略,混合重要度的结果介于两者之间；混合重要度兼顾了动态和静态的特点,保证较高韧性的同时兼顾了计算效率,在面对大型计算、多场景计算时是一种较好的恢复策略。

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周靖轩（1996—）,男,博士研究生,主要从事基础设施抗震韧性研究。E-mail：
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刘威（1976—）,男,副教授,博士,主要从事基础设施抗震韧性研究。E-mail：

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刘威（1976—）,男,副教授,博士,主要从事基础设施抗震韧性研究。E-mail：

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IEEE Transactions on Smart Grid, 2018, 9(2): 1442-1451., articleTitle=Resilience enhancement strategy for distribution systems under extreme weather events, refAbstract=null), Reference(id=1241802958455767689, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, doi=null, pmid=null, pmcid=null, year=2020, volume=203, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[36], rfOrder=44, authorNames=LIU W, SONG Z, OUYANG M, journalName=Reliability Engineering & System Safety, refType=null, unstructuredReference=LIU W, SONG Z, OUYANG M, et al. Recovery-based seismic resilience enhancement strategies of water distribution networks[J]. Reliability Engineering & System Safety, 2020, 203: 107088., articleTitle=Recovery-based seismic resilience enhancement strategies of water distribution networks, refAbstract=null), Reference(id=1241802958560625297, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, doi=null, pmid=null, pmcid=null, year=2010, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[37], rfOrder=45, authorNames=null, journalName=null, refType=null, unstructuredReference=GB 50545—2010 110 kV~750 kV架空输电线路设计规范[S]．北京：中国计划出版社, 2010., articleTitle=null, refAbstract=null), Reference(id=1241802958648705688, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, doi=null, pmid=null, pmcid=null, year=2010, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[37], rfOrder=46, authorNames=null, journalName=null, refType=null, unstructuredReference=GB 50545—2010 Code for design of 110 kV~750 kV overhead transmission line[S]. Beijing: China Planning Press, 2010. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1241802958740980385, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, doi=null, pmid=null, pmcid=null, year=2018, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[38], rfOrder=47, authorNames=null, journalName=null, refType=null, unstructuredReference=DL/T 599—2018城市配电网规划设计规范[S]．北京：中国电力出版社, 2018., articleTitle=null, refAbstract=null), Reference(id=1241802958879392428, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, doi=null, pmid=null, pmcid=null, year=2018, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[38], rfOrder=48, authorNames=null, journalName=null, refType=null, unstructuredReference=DL/T 599—2018 Code for design of urban distribution network planning[S]. Beijing: China Electric Power Press, 2018. 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articleId=1241794071539290159, language=CN, label=图8, caption=不同恢复策略电力系统功能时程曲线, figureFileSmall=LMhS6OtEcoMg6B5bauOUyw==, figureFileBig=S1UEBg34b9B6AK95h5pKLg==, tableContent=null), ArticleFig(id=1241802946611053291, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=EN, label=Table 1, caption=

Parameters for power plant susceptibility modeling

, figureFileSmall=null, figureFileBig=null, tableContent=
发电厂模型损坏情况（DSi）中位值（λi）/g对数标准差（βi）
小型发电厂轻微破坏0.100.55
中等破坏0.210.55
严重破坏0.480.50
毁坏0.780.50
中/大型发电厂轻微破坏0.100.60
中等破坏0.250.60
严重破坏0.520.55
毁坏0.920.55
), ArticleFig(id=1241802946791408379, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=CN, label=表1, caption=

发电厂易损性模型参数表

, figureFileSmall=null, figureFileBig=null, tableContent=
发电厂模型损坏情况（DSi）中位值（λi）/g对数标准差（βi）
小型发电厂轻微破坏0.100.55
中等破坏0.210.55
严重破坏0.480.50
毁坏0.780.50
中/大型发电厂轻微破坏0.100.60
中等破坏0.250.60
严重破坏0.520.55
毁坏0.920.55
), ArticleFig(id=1241802946929820424, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=EN, label=Table 2, caption=

Parameters for substation susceptibility modeling

, figureFileSmall=null, figureFileBig=null, tableContent=
变电站模型损伤情况（DSi）中位值（λi）/g对数标准差（βi）
低压变电站轻微破坏0.150.70
中等破坏0.290.55
严重破坏0.450.45
毁坏0.900.45
中压变电站轻微破坏0.150.60
中等破坏0.250.50
严重破坏0.350.40
毁坏0.700.40
高压变电站轻微破坏0.110.50
中等破坏0.150.45
严重破坏0.200.35
毁坏0.470.40
), ArticleFig(id=1241802947047260951, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=CN, label=表2, caption=

变电站易损性模型参数表

, figureFileSmall=null, figureFileBig=null, tableContent=
变电站模型损伤情况（DSi）中位值（λi）/g对数标准差（βi）
低压变电站轻微破坏0.150.70
中等破坏0.290.55
严重破坏0.450.45
毁坏0.900.45
中压变电站轻微破坏0.150.60
中等破坏0.250.50
严重破坏0.350.40
毁坏0.700.40
高压变电站轻微破坏0.110.50
中等破坏0.150.45
严重破坏0.200.35
毁坏0.470.40
), ArticleFig(id=1241802948578181926, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=EN, label=Table 3, caption=

Parameters for power distribution line susceptibility modeling

, figureFileSmall=null, figureFileBig=null, tableContent=
变电站模型损坏情况（DSi）中位值（λi）/g对数标准差（βi）
配电线路轻微破坏0.280.30
中等破坏0.400.20
严重破坏0.720.15
毁坏1.100.15
), ArticleFig(id=1241802948733371187, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=CN, label=表3, caption=

配电线路易损性模型参数表

, figureFileSmall=null, figureFileBig=null, tableContent=
变电站模型损坏情况（DSi）中位值（λi）/g对数标准差（βi）
配电线路轻微破坏0.280.30
中等破坏0.400.20
严重破坏0.720.15
毁坏1.100.15
), ArticleFig(id=1241802948846617405, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=EN, label=Table 4, caption=

Power system component repair time

, figureFileSmall=null, figureFileBig=null, tableContent=
种类受损状态时间/d
发电厂严重破坏22
毁坏65
变电站严重破坏7
毁坏30
线路严重破坏3
毁坏7
), ArticleFig(id=1241802948972446537, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=CN, label=表4, caption=

电力系统元件修复时间

, figureFileSmall=null, figureFileBig=null, tableContent=
种类受损状态时间/d
发电厂严重破坏22
毁坏65
变电站严重破坏7
毁坏30
线路严重破坏3
毁坏7
), ArticleFig(id=1241802949140218710, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=EN, label=Table 5, caption=

Type and number of grid components

, figureFileSmall=null, figureFileBig=null, tableContent=
电网元件类型区域电源/座变电站/座输电线路/条配电线路/条小型变电站/个
电网元件数量210114020
), ArticleFig(id=1241802949261853536, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=CN, label=表5, caption=

电网元件类型及数量

, figureFileSmall=null, figureFileBig=null, tableContent=
电网元件类型区域电源/座变电站/座输电线路/条配电线路/条小型变电站/个
电网元件数量210114020
), ArticleFig(id=1241802949396071278, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=EN, label=Table 6, caption=

Post-earthquake damage situation of the power network

, figureFileSmall=null, figureFileBig=null, tableContent=
破坏节点编号元件类型损坏状态元件修复天数/d破坏节点编号元件类型损坏状态元件修复天数/d
4小型变电站严重破坏717小型变电站严重破坏7
5中型变电站毁坏3021中型变电站严重破坏7
8中型变电站毁坏3022中型变电站毁坏30
10小型变电站毁坏3024中型变电站毁坏30
11小型变电站严重破坏726小型变电站严重破坏7
12小型变电站严重破坏727小型变电站严重破坏7
14中型变电站严重破坏729小型变电站严重破坏7
), ArticleFig(id=1241802949563843454, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=CN, label=表6, caption=

电力网络灾后破坏情况

, figureFileSmall=null, figureFileBig=null, tableContent=
破坏节点编号元件类型损坏状态元件修复天数/d破坏节点编号元件类型损坏状态元件修复天数/d
4小型变电站严重破坏717小型变电站严重破坏7
5中型变电站毁坏3021中型变电站严重破坏7
8中型变电站毁坏3022中型变电站毁坏30
10小型变电站毁坏3024中型变电站毁坏30
11小型变电站严重破坏726小型变电站严重破坏7
12小型变电站严重破坏727小型变电站严重破坏7
14中型变电站严重破坏729小型变电站严重破坏7
), ArticleFig(id=1241802949719032719, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=EN, label=Table 7, caption=

Post-earthquake state of the grid

, figureFileSmall=null, figureFileBig=null, tableContent=
震后电网状态节点线路
震后破坏4、5、8、11、12、14、17、21、22、24、26、27、29、32无
级联失效6、7、9、10、15、16、18、19、20、28、30、32线路5（节点2与节点6之间）、线路12（节点6和节点28之间）
最终失效4、5、6、7、8、9、10、11、12、14、15、16、17、18、19、20、21、22、24、26、27、28、29、30、31、32线路5（节点2与节点6之间）、线路12（节点6和节点28之间）
震后功能剩余0.375
), ArticleFig(id=1241802949857444765, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=CN, label=表7, caption=

震后电网状态

, figureFileSmall=null, figureFileBig=null, tableContent=
震后电网状态节点线路
震后破坏4、5、8、11、12、14、17、21、22、24、26、27、29、32无
级联失效6、7、9、10、15、16、18、19、20、28、30、32线路5（节点2与节点6之间）、线路12（节点6和节点28之间）
最终失效4、5、6、7、8、9、10、11、12、14、15、16、17、18、19、20、21、22、24、26、27、28、29、30、31、32线路5（节点2与节点6之间）、线路12（节点6和节点28之间）
震后功能剩余0.375
), ArticleFig(id=1241802950021022642, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241794071539290159, language=EN, label=Table 8, caption=

Results of different recovery strategies

, figureFileSmall=null, figureFileBig=null, tableContent=
计算结果动态重要度静态重要度混合重要度
步长3步长5
修复顺序26-12-27-4-11-14-17-21-29-32-5-8-10-22-2426-12-24-5-8-14-32-10-22-11-17-21-29-4-2726-12-24-27-29-4-11-14-32-17-21-5-8-10-2226-12-24-5-8-4-11-14-17-27-21-29-32-10-22
韧性指标0.78590.64380.74630.7038
计算时间/s1.99000.07900.65800.3850
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不同恢复策略结果

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计算结果动态重要度静态重要度混合重要度
步长3步长5
修复顺序26-12-27-4-11-14-17-21-29-32-5-8-10-22-2426-12-24-5-8-14-32-10-22-11-17-21-29-4-2726-12-24-27-29-4-11-14-32-17-21-5-8-10-2226-12-24-5-8-4-11-14-17-27-21-29-32-10-22
韧性指标0.78590.64380.74630.7038
计算时间/s1.99000.07900.65800.3850
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节点编号是否为电源节点负载/MW正常状态电压相位角节点编号是否为电源节点负载/MW正常状态电压相位角
1是—017是23.603.65×10-3
2否37.701.20×10-318否23.203.72×10-3
3否12.402.03×10-319否19.503.61×10-3
4否17.602.07×10-320否22.203.44×10-3
5否18.202.12×10-321否17.503.44×10-3
6否16.702.49×10-322否21.593.30×10-3
7否22.802.49×10-323否—0
8否30.003.20×10-324否18.702.63×10-3
9否17.202.53×10-325否32.704.99×10-4
10否15.803.49×10-326否15.222.63×10-3
11否15.602.26×10-327否14.913.20×10-3
12否11.202.84×10-328否16.112.83×10-3
13否27.002.37×10-329否17.292.96×10-3
14否16.203.13×10-330否17.603.27×10-3
15否18.203.16×10-331否11.203.29×10-3
16否22.503.30×10-332否19.703.63×10-3
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节点基本信息

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2否37.701.20×10-318否23.203.72×10-3
3否12.402.03×10-319否19.503.61×10-3
4否17.602.07×10-320否22.203.44×10-3
5否18.202.12×10-321否17.503.44×10-3
6否16.702.49×10-322否21.593.30×10-3
7否22.802.49×10-323否—0
8否30.003.20×10-324否18.702.63×10-3
9否17.202.53×10-325否32.704.99×10-4
10否15.803.49×10-326否15.222.63×10-3
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12否11.202.84×10-328否16.112.83×10-3
13否27.002.37×10-329否17.292.96×10-3
14否16.203.13×10-330否17.603.27×10-3
15否18.203.16×10-331否11.203.29×10-3
16否22.503.30×10-332否19.703.63×10-3
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2135.263250220135.009
3245.8821101068.277
4255.00025022055.398
5265.5561101086.175
63425.0001101020.209
731325.000250220102.400
841125.0001101051.386
9578.33325022037.198
106712.500110100.398
11694.762110103.412
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13781.78625022014.796
148285.0001101021.888
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169114.7621101010.548
1710204.762110105.710
18102114.286110106.983
1910226.6671101015.571
2010326.250110106.164
2111123.8461101026.588
2212137.1431101040.577
2312157.6921101031.137
2412165.0001101021.828
2513143.84625022034.823
2614155.000110103.373
2714214.76225022015.250
2815172.273110107.213
2915322.273110109.097
3016175.2631101015.200
3116283.0301101016.636
3216312.500110100.764
3317182.250110102.331
3417326.250110104.982
3518197.692110105.297
3618312.136110107.728
3718322.273110100.543
38192014.2861101024.797
3920245.5561101052.708
4021225.0002502209.234
4122245.55625022046.394
4223243.704250220117.802
43232516.667250220100.808
4425262.6321101068.108
4526298.3331101032.463
4626312.5001101020.425
4727282.5001101011.352
4827292.381110107.191
4927301.667110100.953
5027312.136110102.679
5129302.222110107.983
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线路基本信息

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基于功能的城市电力系统抗震韧性评估
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刘威 1, 2 , 周靖轩 1 , 林峰 1
地震工程与工程振动 | 研究论文 2025,45(5): 38-51
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地震工程与工程振动 | 研究论文 2025, 45(5): 38-51
基于功能的城市电力系统抗震韧性评估
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刘威1, 2 , 周靖轩1 , 林峰1
作者信息
  • 1.同济大学土木工程学院,上海200092
  • 2.同济大学土木工程防灾减灾全国重点实验室,上海200092

    • 刘威（1976—）,男,副教授,博士,主要从事基础设施抗震韧性研究。E-mail：

通讯作者:

周靖轩（1996—）,男,博士研究生,主要从事基础设施抗震韧性研究。E-mail：
Function-based seismic resilience assessment of urban power systems
Wei LIU1, 2 , Jingxuan ZHOU1 , Feng LIN1
Affiliations
  • 1.Department of Structural Engineering, Tongji University, Shanghai 200092, China
  • 2.State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
出版时间: 2025-10-22 doi: 10.13197/j.eeed.2025.0505
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摘要
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地震发生时,城市电力系统破坏严重且恢复时间较长,因此,地震作用下电力系统的功能分析及震后的恢复过程亟待研究。为了更准确地评估和更好地提升城市电力系统抗震韧性,该文建立了功能视角下的城市电力系统抗震韧性定量分析框架。基于电力潮流分析和震后电力系统破坏情况,求解震后城市的电力能力,将正常得到供电的人口与总人口的比率作为电力系统功能指标,通过积分法得到抗震韧性指标。同时,考虑恢复策略对韧性提升的影响,基于功能分析方法和元件重要度理论,提出了基于动态重要度、静态重要度和混合重要度的修复策略。以我国某电网为实例研究,验证了韧性评估框架和修复策略对韧性提升的有效性。结果表明：基于功能的电力系统韧性评估框架可较准确地完成震后电力系统的功能分析和级联失效模拟；基于动态重要度理论的修复策略得到的韧性指标高于静态重要度策略,混合重要度的结果介于两者之间；混合重要度兼顾了动态和静态的特点,保证较高韧性的同时兼顾了计算效率,在面对大型计算、多场景计算时是一种较好的恢复策略。

电力系统  /  抗震韧性  /  潮流分析  /  级联失效  /  恢复策略

The electric power system is the most critical component of urban infrastructure, serving as the foundation for the normal operation of a city. Earthquakes have a substantial impact on urban power systems. On one hand, it is reflected in the extensive damage to power infrastructure and the widespread power outages. On the other hand, it manifests in the long recovery times for power facilities and the significant impact on people’s livelihoods. Therefore, the performance analysis of the power system under seismic conditions and the post-earthquake restoration process urgently require attention. To more accurately assess and enhance the seismic resilience of urban power systems, a quantitative analysis framework for seismic resilience from a functional perspective has been established. The performance index of the power system is defined as the ratio of the population receiving power to the total population after an earthquake. The initial damage is determined through the seismic vulnerability modeling of power system components. The cascading failures of the power system following an earthquake are simulated using the DC power flow method to assess the power surplus in the city post-earthquake. The damaged components are then repaired, and the seismic resilience index is obtained by solving the system’s performance-time curve through an integral method. Based on functional analysis methods and component importance theory, the concept of post-earthquake restoration step length for the power system has been proposed. By adjusting the restoration step length, three restoration strategies have been developed including dynamic importance-based, static importance-based, and hybrid importance-based restoration strategies. A case study of a power grid in China has been conducted to validate the effectiveness of the resilience assessment framework and restoration strategies. The results show that the functional-based power system resilience assessment framework can effectively perform post-earthquake performance analysis and generate functional curves. The DC power flow analysis method accurately determines the state of each line and node in the power system, enabling a more realistic and reasonable simulation of cascading failures in the power system after an earthquake. Under 10,000 Monte Carlo simulations, the frequency distribution, average value, and the maximum value of the restoration strategy based on dynamic importance theory are significantly higher than those of the static importance-based strategy. The dynamic importance strategy yields the highest seismic resilience index, while the hybrid importance strategy provides intermediate results, and the static importance strategy results in the lowest seismic resilience index. The computational time required is inversely related to the resilience index, with the dynamic importance strategy taking 25 times longer than the static importance strategy. The hybrid importance strategy, which balances dynamic and static factors, has been shown to be the most efficient recovery strategy when dealing with large-scale computations and multiple scenarios, as it ensures higher resilience while maintaining computational efficiency.

power system  /  seismic resilience  /  current analysis  /  cascade failure  /  recovery strategy
刘威, 周靖轩, 林峰. 基于功能的城市电力系统抗震韧性评估. 地震工程与工程振动, 2025 , 45 (5) : 38 -51 . DOI: 10.13197/j.eeed.2025.0505
Wei LIU, Jingxuan ZHOU, Feng LIN. Function-based seismic resilience assessment of urban power systems[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (5) : 38 -51 . DOI: 10.13197/j.eeed.2025.0505
正文
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0　引言
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城市基础设施是保障城市正常运行和健康发展的物质基础[1]。电力系统作为城市基础设施系统中最重要的部分,发挥着维系城市正常运转、保障其他基础设施系统正常运行的作用。城市电力系统因受灾而发生的破坏将对居民生活和企业运营造成比以往更严重的直接和间接损失。城市灾害中造成后果最严重、波及范围最广、最为典型的是地震,我国历史上的强震都导致了大范围、长时间的停电。2008年5月12日,我国四川汶川县发生里氏8.0级地震,映秀镇电力受到严重破坏。四川省电力公司组织100多人的小分队,经过连夜抢修,5月21日20时才基本恢复供电能力,全镇停电达到9 d[2]。2013年4月20日,我国四川省雅安市芦山县发生了里氏7.0级地震,灾区的变电站、高压电气设备、输电线路及杆塔等电力设施遭受严重破坏,造成大量输电线路断路、跳闸和设备损坏,导致约18.66万用户停电[3]。通过以上实例得知,地震对城市电力系统的破坏是巨大的,主要体现在两方面：一方面是电力基础设施的破坏程度大、停电面积广；另一方面是在震后对电力设施的修复时间长、对民生影响大。因此,地震作用下电力系统的功能演变及震后的功能恢复亟待研究。
近年来“韧性”逐渐成为指导城市基础设施防灾减灾的新导向。“韧性”一词最早源于1973年加拿大学者Holling一篇生态系统研究的文章[4]。BRUNEAU等[5]提出了社区抗震韧性分析框架,这标志着“韧性”正式被引入工程学领域。各行业的学者在引用韧性定义时也对其概念进行了相应的修改。不同学者在面对韧性问题时侧重的重点不尽相同,因此在研究韧性的方法也各有区别,定性[5-7]和定量[8-10]共存,目前研究范式已达成初步共识。在传统抗震防震工作“以防为主”的概念的基础上,韧性综合了震后应急和修复过程形成了防灾—减灾—救灾—重建全链条,指导未来抗震工作以全链条视角为基础设施建设提供防灾技术方向、减灾救灾架构和恢复重建策略,抗震韧性设计的理念代表着当前结构抗震和城市防灾减灾领域的前沿方向[11-12]。在技术和概念均已革新的前提下,抗震工作对电力系统功能运行的模拟精准度和灾后修复策略研究都提出了更高要求。
对于电力系统运行模拟,以往已有比较完善的研究。目前,电力系统的韧性评估方法主要分为复杂网络分析方法[13-17]和潮流分析方法[18-20]两大类。复杂网络分析方法将电力系统抽象为网络,将发电机、变电站和用户简化为节点[13],将输、配电线路简化为连接节点的边,以组件失效的形式来模拟元件发生物理破坏或者与网络连接断开的情况[17]。复杂网络研究方法能够较快地将实际问题抽象化,形成合理有效的结论,但忽略了电力系统运行的物理特性,对于电力系统的级联失效模拟不深刻。潮流分析方法通过计算电力系统运行过程中功率或者潮流的稳态解进行故障模拟,可以较为精确地模拟灾后各节点和线路的运行状态[18-20],适用于大规模模拟和多场景分析,对于城市尺度下的抗震韧性评估模拟较准确。基于潮流分析方法的模型很好地还原了电力系统的物理本质和运行规律,同时对灾后的电力系统响应的模拟也更精准。但是,目前将潮流分析方法用于电力系统灾后分析的研究较少。
震后电力系统的韧性包括震后初始破坏、功能潮流级联失效和功能曲线恢复这3个阶段,具有时间属性。除了提升电力系统的自身抗震能力,提高电力系统的功能恢复速率也是提升电力系统抗震韧性的有效手段。灾后恢复过程中,修复灾后物理破坏的元件会提升系统功能,在既定修复资源下,不同的修复顺序将产生不同的恢复曲线[22-23],因此更好的修复策略可有效提升系统韧性。针对灾后电力系统的恢复策略,学者们已经开展了广泛的研究。例如CHEN等[24]就建立了混合整数线性规划模型（mixed-integer linear programming, MILP）,以该模型为基础研究电力系统灾后通过一系列如控制动作、协调开关等操作来恢复电力系统功能的问题,并且通过IEEE 123节点验证了模型的有效性。WANG等[25]在Chen等的研究基础上进一步提出了三相网络模型（three-phase network model）,采用三相输出功率对微电网进行了更深层次的研究,利用IEEE 123节点和IEEE 34节点验证了科学的微电网组建方法更有利于提升电力系统的韧性。
此外,一些学者采用启发式算法[26-27]解决修复次序问题,例如XU等[28]就利用启发式算法将恢复过程中的动态约束纳入考虑范围之内,从最大覆盖范围的角度对电力系统修复策略进行了制定。宋朝阳[29]基于用户需求,提出了基于重要度理论的恢复策略,避免了迭代求解过程,在系统功能的视角下进行元件重要度排序。武千翔[30]在此基础上提出混合重要度算法。重要度理论在优化恢复策略和提升供水系统抗震韧性方面起到积极作用,但在电力系统抗震韧性分析和提升方面还有待发展。
综上,针对电力系统震后功能模拟和韧性提升,本文采用潮流方法建立基于功能的韧性评估框架对城市电力系统进行抗震韧性评估,并根据重要度理论采用动态、静态和混合重要度修复策略进行灾后功能恢复和韧性提升研究。以我国某市电力网络为例对本框架进行验证,得到电力系统在地震下的级联失效响应和恢复策略,为电力系统抗震工作提供理论指导。
1　基于功能的电力系统韧性评估框架
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1.1　电力系统功能指标
本文以城市用户能否获得电力供应为系统功能指标（power system performance degree index, PDI）,如式（1）所示：
式中：n（t）为t时刻时能够得到电力供应的人口数量；N为电力系统中人口的总数。
式中：ni为第i个变电站辖区内的人口数；si（t）为t时刻变电站的状态,本文选择两态模型（0/1）,正常供电取1,不正常供电取0,在震后供电能力受限的情况下,变电站实际能否继续承担负荷仍受其他因素（如潮流约束、线路损伤等）影响,因此采用二元状态近似建模有助于简化计算；k为变电站总数。
1.2　电力系统抗震韧性
本文采用OUYANG等[15]提出的“三阶段”韧性分析模型,计算系统功能在时间轴上的积分来计算系统韧性。电力系统在地震作用下的响应曲线见图1。图中t0时刻前电力系统处于正常工作阶段,能满足服务区域内所有用户的电力需求,此时系统的功能值为1；t0时刻发生地震,电力系统部分元件破坏,部分用户供电需求无法得到满足,此时电力系统的功能值降低至PDI0；t1时刻修复工作开始,系统功能值逐渐回升至震前水平。
根据图1的系统功能时程曲线求解可得出电力系统抗震韧性（resilience, R）计算公式为
式中：R为系统的韧性值；t1为系统震后功能初始值的时刻；t2为系统完全修复的时刻。
1.3　城市电力系统元件地震易损性模型
城市电力系统中的常见元件包括发电厂、变电站、输/配电线路等,目前的研究对于上述几类元件在地震作用下的易损性模型较成熟,国内外较为常用的模型包括Hazard United States-Multi-Hazard（HAZUS）模型[31]和我国RISN-TG041—2022《城市工程系统抗震韧性评价导则标准规范》[32]（以下简称《导则》）。本文采用《导则》中的电力元件地震易损性模型。
1）发电厂
发电厂受到地震影响的破坏程度分为5个等级,分别为基本完好、轻微破坏、中等破坏、严重破坏和毁坏。《导则》中认为元件在地震下发生中等及以下破坏时仍可以发挥原有功能,当元件在地震下发生严重破坏和毁坏时则失去原有功能。
发电厂在地震作用下发生指定破坏的超越概率服从对数正态分布,发电厂达到某个破坏等级的超越概率可以按照式（4）进行计算[32]：
式中：Φ[•]为标准正态分布函数；DSi为发电厂的破坏等级（轻微破坏i=1,中等破坏i=2,严重破坏i=3,毁坏i=4）；PGA为发电厂所处场地的峰值地面加速度；λi为发电厂破坏等级DSi对应的易损性曲线的中位值,取值见表1；βi为发电厂破坏等级DSi对应的易损性曲线的对数标准差,取值见表1。本文采用的易损性参数,一方面被用于计算元件的物理破坏概率以判定元件是否失效（仅严重破坏和毁坏状态会导致功能丧失,轻微破坏和中等破坏认为功能正常）,不直接参与功能状态计算；另一方面,除状态的判断外,由易损性参数计算出的不同状态可决定元件的修复时间。
2）变电站
变电站分为低压、中压和高压变电站。类似于发电厂,变电站受到地震影响的破坏程度也分为5个等级,同样只有发生严重破坏和毁坏情况才认为其失去了原有功能[32]。
变电站在地震作用下发生指定破坏的超越概率服从对数正态分布,达到某个破坏等级的超越概率可以按照式（4）计算,对应的参数则按表2进行选取。
3）输/配电线路
输电线路一般进行长距离输送高压电能,高压输电线路通常架设输电塔上；配电线路则经过变电站将电力输送至城市用户,通常架设在电线杆上。《导则》[32]认为输电塔和输电线路抗震性能较高,因而不考虑其受地震的影响。高压输电线路（如220 kV）通常设计抗震等级较高,实际震害案例（如汶川地震）中输电塔倒塌概率极低（小于1%）,同时输电线路的主要脆弱环节在于塔架倒塌,而导线损伤概率较低,因此本文假设仅配电线路可能受损。
对于配电线路而言,同样认为发生严重破坏和毁坏情况才失去原有功能。
配电线路达到某个破坏等级的超越概率同样按式（4）计算,参数取值见表3。
1.4　电力系统直流潮流分析方法
本文的直流潮流分析是基于交流潮流方法开展的,参考文献[16-17]给出了交流潮流分析的基本方程,如方程（5）所示：
式中：Ui、Uj分别为节点i、j的电压；Yij为两节点之间的支路的导纳；Pi为注入节点的有功功率；Qi为注入节点i的无功功率；Yij为复数,为Yij的共轭,为的共轭；G和B为Y的实部和虚部。
使用牛顿-拉夫逊法迭代求解可以得到每个节点的有功功率、无功功率、电压和相位角,以及每条线路的功率损耗、电流。
部分学者根据实际需要,进行了一些合理假设,对潮流分析方法进行了简化,称之为直流潮流分析方法[20,21]。有以下假设：①高压电网中电抗X远大于电阻R,对地电导可以忽略,故假设Gij=0；②电网各个节点电压与额定电压差别不大,电压可以按标幺值计算,认为Ui=Uj=1；③假设每条线路两端的相位差值很小,则有sinθij=sin（θi-θj）=θi-θj；④模型中只重点关注有功功率传输与节点电压相位角的关系,因此不考虑无功功率的计算。
基于上述假设,公式中的功率计算便简化成式（6）,即
如果将式中各个物理量用矩阵表示的话,式（6）可改写成式（7）,即
式中：P为电力系统线路的功率潮流矩阵；B为线路的导纳矩阵；θ为线路两端相位角差的矩阵。
可以看出,这是一个线性方程,避免了不收敛,可以得到各节点电压、各节点相位角和各支路功率分布。
1.5　失效判定
根据直流潮流分析方法可得出电力系统网络中各条线路的功率分布,则可以按式（8）判断线路是否发生潮流越限,
式中：Pi为电力系统网络中第i条线路的实际负载值,其具体数值依据电力系统网络整体潮流分析计算结果确定；Pi,max为电力系统网络中第i条线路的容许最大负载值,具体数值依据该断线缆的额定电压值以及线缆的相关物理参数确定,本文参考国标GB 50061—2010《66 kV及以下架空电力线路设计规范》[33]对电线负载的电流值进行判断。根据线路功率的潮流判断后将失去功能的线路带入电网信息,判断在物理破坏后是否发生了功能失效。
1.6　修复模型
1）修复资源
本文的修复资源包括修复物资和修复人员,其中修复物资指震后修复受损的电力系统元件所需要的一切物资的统称,包括操作工具、使用设备以及更换元件等；修复人员指在震后对电力系统网络进行修复的所有人员,包括检测人员、技术人员和交通驾驶人员等。
按照研究需求,本文作出以下假设：①每处破坏需要一个单位的资源进行修复；②资源充足,地震引发的额外运输时间不考虑；③震后电力系统大面积失去功能,备用电源无法满足需求,不考虑备用电源的供能。
2）修复时间
本文的修复时间指地震下物理破坏的元件恢复功能所需要的时间。修复时间的主要由元件的破坏状态及元件的破坏数量决定,参照2.3节介绍的易损性模型。《导则》[32]建议：当发电厂、变电站和配电线路处于基本完好、轻微破坏或中等破坏状态时,这些单元正常工作,其功能不受影响。因此系统的功能时程曲线不受其修复进度限制,从系统功能视角出发,可合理忽略其修复时间对整体韧性指标的影响,因此本文不考虑轻微和中等破坏的修复时间。不同元件在严重破坏和毁坏状态下的修复时间根据《导则》[32]建议,见表4。在对于恢复时间的建模中,为了便于对比不同恢复策略对系统韧性指标的影响,本文采用固定恢复时间以简化模型计算,并确保各策略之间的对比结果具有一致性。
1.7　技术路线图
本文评估框架和技术路线图见图2。本文所采用基于重要度的3种修复策略详见第2节介绍。
2　基于重要度的修复策略
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本文通过求解功能时程曲线的积分,得到系统的韧性指标。显然不同的修复策略导致不同的震后恢复曲线,进而得到的韧性指标也不相同。因此,优化修复顺序对于提高韧性至关重要,震后恢复策略是韧性提升的重要手段,也是韧性研究的重要部分。为此,本文提出了基于重要度的修复策略,该策略通过评估各元件的功能重要度,优化修复顺序,从而提升电力系统的抗震韧性。
本文假设电力系统元件具有两态破坏准则,即元件未完全修复前无法发挥功能。因此对于受损元件本文采用非抢占式修复方式：确定某元件需要修复后必须将该元件上所有的受损部件修复后才进行下一个元件的修复作业。在电力系统韧性分析中,非抢占式修复的假设可以更方便地研究修复策略[34-35]。本文基于LIU等[36]和武千翔[30]的研究给出了3种有助于提升系统韧性的修复策略。
2.1　基于功能的重要度指标
震后电力系统PDI从1降低至PDI0,PDI随着元件修复而逐渐提升,不同的元件修复对于电力系统的功能提升不同,即每个元件的重要度不同。若多个元件重要度相同,按照元件编号由小到大的顺序进行修复。重要度为0的元件（修复后系统性能无提升）在排序中自动后置。在静态重要度修复策略中,若出现多个重要度为0的元件,则按照元件编号由小到大的顺序修复。综合修复元件提升的系统功能以及修复所需时间,元件重要度指标的定义如式（9）所示：
式中：Is,i为元件i的重要度指标；PDI0为灾后该电力系统网络的功能指标；PDI,i为修复元件i后系统的功能指标；Ti为修复元件i所需要的时间（d）。
2.2　基于功能的修复步长
每种破坏情景对应一种电力系统功能值,在同一种破坏下,经过特定天数将系统功能由震后初始值提升至1。在这个过程中,修复时间、初始功能和最终功能是相同的,区别在于不同的元件修复顺序。根据2.1节的重要度指标,在开始修复前对元件进行重要度排序,则可以得到一个固定序列。随着元件的修复,电力系统网络也在变化,在修复了某些元件之后,剩余元件的重要度可能会发生变化。倘若修复若干个元件后对剩余元件再进行重要度排序,基于潮流分析和新的电网拓扑结构这个排序会更新。本文对基于功能的修复步长的定义是：当按照重要度排序进行修复时,在修复一定数量元件后再运行潮流分析计算得到新的排序,那么此时这里的元件修复数量便为该修复工作的修复步长。可以看出,每次的修复步长不必一致,且选择范围为1至待修复元件的总数量。
2.3　静态重要度和动态重要度修复策略
1）静态重要度策略
当修复步长为待修复元件总数,即按照式（9）只进行一次重要度排序计算,在电力网络变化后不改变修复顺序,此时得到基于静态重要度的修复策略。
2）动态重要度策略
当修复步长为1时,即每修复一个元件都运行一次重要度排序计算得到新的修复顺序,此时得到基于动态重要度的修复策略。设待修复元件为集合H,设当修复工作进行到第t天时已经修复的元件构成集合S,则剩余某个尚未修复的元件i的动态重要度指标为
式中：Id,i（t）为i元件在t时刻时的动态重要度；PDI,H（S）为在t时刻考虑已经修复的元件集合H（s）后计算得到的系统功能指标；PDI,H（S,i）（t）为在PDI,H（S）的基础上进一步修复元件i之后计算得到的系统功能指标；Ti为修复元件i所需要的时间（d）。
2.4　基于混合重要度顺序的修复策略
显然动态重要度的效果要好于静态重要度,更符合功能潮流分析的运行规律,但计算耗时较长。
当计算步长得介于1和待修复元件数之间时,就得到混合重要度策略。混合重要度策略相比于静态和动态重要度策略,通过步长的变化,兼顾了计算效果与计算效率。3种重要度策略的示意图见图3。
3　算例分析
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3.1　电网概况
由于电力系统信息数据保密,本文基于我国东部某城市基础路网和电力网络通用布局规则[33,37]生成了一个虚拟电网,其具体布局规则如下：①发电厂设置在城市边郊,由2座小型发电厂供电,对于无本地发电厂的实际区域电网,可将远距离输入的国家骨干电网变电站视为区域电源节点,其功能等效于发电厂；②输电线路为220 kV的高压输电线,最大承载250 MW,沿城际高速公路分布；③根据DL/T 599—2018《城市配电网规划设计规范》[38],案例电网的10 kV配电线路采用11回并联设计,单回线路额定容量为10 MW。此外按照规范,城市配电网的设计应满足N-1安全准则的要求,故总负载核定为100 MW。为简化计算并体现冗余设计,案例中将配电线路为10 kV的中低压配电线的总负载近似设为110 MW,沿城区的主干路分布；④变电站位于电压转换的位置,主要布置在输配电线路相交处以及配电线路和用户终端相交处；⑤通过中型变电站将220 kV的配电线电压降至10 kV,再通过小型变电站连接至用户终端。
本文以发电厂元件作为电源节点,变电站元件和用户终端作为负载节点,以输电线路和配电线路作为各节点之间的线路。将电力系统网络拓扑结构绘制成图,得到电力系统网络布局图,见图4。假设每个变电站的辖区人口相等,旨在演示工程案例的计算方法以及计算效果。
根据以上规则,各类电网元件的具体数量见表5。电力系统线路、节点的基本信息和正常状态数据见附录A和附录B。
3.2　Monte Carlo模拟
本文采用Monte Carlo计算方法来对元件损坏情况进行多次模拟。在模拟过程中,假设各个元件损坏情况之间相互独立,城市设防烈度为9度,工况考虑为罕遇地震（PGA为0.62 g）。模拟的具体步骤是：①对每一个元件都随机取一个概率参数P,P服从0~1之间的均匀分布；②根据各元件各损坏状态的超越概率得到该元件的震后损坏状态；③电力系统韧性评估；④记录静态重要度和静态重要度策略下电力系统抗震韧性结果；⑤重复步骤①~步骤④,直到进行指定次数的模拟。
本文基于Monte Carlo模拟对算例电网生成了10000次破坏场景,对每次场景对比了动态和静态策略下的韧性评估结果。2种策略下韧性指标的频率分布直方图（纵坐标为频数, Monte Carlo模拟的次数）,见图5,其统计特征（包括平均值、变异系数、最大值和最小值等统计量值）的对比则见图6。由图5、图6可知,动态重要度策略在韧性的均值和最值上都显著大于静态重要度策略,动态重要度理论策略有更优秀的效果,对震后电力系统的韧性提升更高；同时动态重要度有更小的变异系数,多次Monte Carlo模拟下结果更稳定,数据分布集中程度高,均值反映的结论更有代表性。
3.3　功能失效
本节于上述模拟中选取一组进行震后功能失效模拟,选取的电力系统震后破坏情况见表6。根据表6的电力系统元件破坏状态,利用潮流分析对震后受损电力系统进行计算,得到震后的电网状态,见表7。在震后初始破坏基础上,线路5（节点2与节点6之间）、线路12（节点6和节点28之间）新电力系统拓扑结构进行再次计算得到级联失效的供电节点,进而得到最终失效的节点和线路,以及震后功能剩余0.375。震后电力系统级联失效示意图见图7。
震后电力系统初始状态分析结果表明,基于电力直流潮流分析的方法很好地还原了该地区的电力系统在罕遇地震作用下的破坏以及级联失效结果。地震下在元件物理破坏失去功能的同时,电力网络的功能也发生了变化；电力系统潮流重新分布过程中出现了线路潮流越限,导致该线路在未发生物理破坏的情况下失去功能,进而导致级联失效；最终的失效节点多于物理破坏线路,系统的功能也进一步降低。
3.4　恢复策略
针对3.3节中的破坏工况,本节对比了4种恢复策略,包括：动态重要度策略、静态重要度策略、步长为3（简称“混合3”）和步长为5的混合重要度（简称“混合5”）策略。不同恢复策略电力系统功能时程曲线见图8,不同恢复策略的恢复顺序、对应的韧性指标和计算所需时间见表8。
由图8可知,该破坏状态下电力系统的震后初始功能仅存0.375,若只考虑物理破坏则系统残余功能为0.50,这显示出功能潮流分析相对更准确；随着时间推移,功能时程曲线也在逐渐上升,直到220 d修复完毕,系统功能达到1。4种策略中,动态重要度的时程功能恢复最快,混合3和混合5次之,最后是静态重要度。
由表8可知,动态、静态、混合3和混合5的韧性指标分别为0.7859、0.6438、0.7463、0.7038,同样符合图8的结论。在计算用时上,静态重要度仅有0.079 s,而动态重要度则需要1.99 s,是静态重要度时长的25倍；混合3和混合5分别用时0.658、0.385 s,介于二者中间。总的来说,混合重要度兼顾了动态和静态的特点,在保证较高韧性的时候又兼顾了计算效率,在面对大型计算、多场景计算时是一种较好的恢复策略。由此可见,不同恢复策略下的系统韧性存在较大差别,因此选择计算效率高、系统韧性高的恢复策略对于提升系统的韧性非常重要。在修复顺序上,4种策略的前2个修复元件都为26、12,一方面修复26和12号节点后能完成拓扑上的成环形；另一方面根据重要度理论,通过较短时间（14 d）能够对系统进行显著提升（由0.375到0.500）,两者的重要度排序最高。剩下的破坏元件中,按照重要度算法,除了静态重要度,考虑修复时间后发现修复时长较短（7 d）的元件优先级更高,比如动态重要度策略将修复时长7 d的元件排在前面,将修复时长30 d的元件放置于后面；混合3和混合5则在修复步长内将修复时长7 d的元件排在前面。
由图8和表8可知,动态重要度以较快的功能提升速率从而得到较高韧性,原因体现在两方面：一方面依据重要度算法,动态重要度在每一次计算后都选择能够迅速提升功能的节点进行修复；另一方面提前将功能值恢复到一定高度也是提升韧性的好方法。若只看前5个待修复元件,动态重要度优先选择只修复7 d的元件,而其他策略则可能选择破坏较严重需要修30 d的元件,这造成曲线上升斜率较低,与此同时动态重要度则将修复时间为30 d的元件尽可能后置；换而言之,“抢先”将韧性提升到较高值的思路通过体现韧性的“快速恢复性”特点而得到更高的韧性。混合3和混合5策略则通过缩小步长增加每步的曲线上升斜率而获得,在计算速度允许下再缩小步长可获得更高韧性结果。
4　结论
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本文以地震作用下城市电力系统的韧性评估为研究主题,采用了电力直流潮流分析方法建立了基于功能的电力系统定量化抗震韧性评估框架,并结合基于重要度的三类恢复策略以提升电力系统抗震韧性,以我国某电网为实例展开案例研究用以验证提出框架和方法的有效性,得出以下结论：
1）基于功能的电力系统韧性评估框架可合理完成震后电力系统的功能分析和功能曲线求解；利用直流潮流分析方法能够准确得到电力系统中各线路和各节点的状态,进而更真实、合理地模拟出电力系统震后级联失效现象。
2）在10 000次Monte Carlo模拟下,基于动态重要度理论的修复策略求解的频率分布、平均值和最值明显高于静态重要度策略的结果,同时动态重要度策略有更低的方差,求解结论更稳定、可靠。
3）在4种修复策略（动态、静态、混合3和混合5）中,动态重要度的时程功能和韧性指标最大,混合3和混合5次之,最后是静态重要度；计算所用时间与时程功能相反,动态重要度的计算时长是静态重要度的25倍；混合重要度兼顾了动态和静态的特点,在保证计算效率的前提下有效提升了韧性,在面对大型计算、多场景计算时是一种非常好的恢复策略。
基金
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  • 国家重点研发计划(2022YFC3803000)
  • 同济大学2022年度学科交叉联合攻关项目计划任务书(C2_3_3_ZD_03)
文献
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2025年第45卷第5期
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doi: 10.13197/j.eeed.2025.0505
  • 接收时间：2024-12-19
  • 首发时间：2026-03-20
  • 出版时间：2025-10-22
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  • 收稿日期：2024-12-19
  • 修回日期：2025-04-08
基金
国家重点研发计划(2022YFC3803000)
同济大学2022年度学科交叉联合攻关项目计划任务书(C2_3_3_ZD_03)
作者信息
    1.同济大学土木工程学院,上海200092
    2.同济大学土木工程防灾减灾全国重点实验室,上海200092

通讯作者:

周靖轩（1996—）,男,博士研究生,主要从事基础设施抗震韧性研究。E-mail：
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2种不同金属材料的力学参数
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Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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