三相不平衡有源配电网鲁棒动态重构
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摘要
考虑配电网的三相不平衡运行和注入功率不确定性可以提高网络重构方案的优化效果和应用价值。首先,对考虑不确定性的分布式电源和负荷注入功率进行仿射数建模,划分重构时段,以有功网损最优为目标函数,基于三相Distflow潮流方程建立含不确定性预算的配电网两阶段鲁棒动态重构数学模型。为高效求解该模型,引入最佳等距分段线性逼近法对模型进行精度可控的线性松弛,并使用列约束生产算法迭代求解。采用标准化配电测试系统验证所提鲁棒动态重构模型的可行性和有效性,通过控制不确定性预算可进一步调节重构方案的保守性和鲁棒性。
The optimization effect and application value of network reconfiguration scheme can be improved considering the three-phase unbalanced operation of distribution network and the uncertainty of injection power. Firstly, the uncertainty of distributed generators and load injection power is modeled by the affine number, and the reconfiguration period is divided. The two-stage robust dynamic reconfiguration model of distribution network with uncertainty budget is established based on the three-phase Distflow power flow equation, which takes optimal active power of network loss as objective function. In order to efficiently solve the model, an optimal equidistant piecewise linear approximation algorithm is adopted for the precision-controlled linear relaxation of the model, and the column-and-constraint generation method is used to solve it iteratively. A standardized distribution test system is used to verify the feasibility and effectiveness of the proposed model, which shows that the conservatism and robustness of the reconfiguration scheme can be further adjusted by controlling the uncertainty budget.
The optimization effect and application value of network reconfiguration scheme can be improved considering the three-phase unbalanced operation of distribution network and the uncertainty of injection power. Firstly, the uncertainty of distributed generators and load injection power is modeled by the affine number, and the reconfiguration period is divided. The two-stage robust dynamic reconfiguration model of distribution network with uncertainty budget is established based on the three-phase Distflow power flow equation, which takes optimal active power of network loss as objective function. In order to efficiently solve the model, an optimal equidistant piecewise linear approximation algorithm is adopted for the precision-controlled linear relaxation of the model, and the column-and-constraint generation method is used to solve it iteratively. A standardized distribution test system is used to verify the feasibility and effectiveness of the proposed model, which shows that the conservatism and robustness of the reconfiguration scheme can be further adjusted by controlling the uncertainty budget.
引文
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[5] ZHANG Peng, LI Wenyuan, WANG Shouxiang.Reliability-oriented distribution network reconfiguration considering uncertainties of data by interval analysis[J].International Journal of Electrical Power & Energy Systems, 2012, 34(1): 138-144.
[6] BRUNO S, LAMONACA S, ROTONDO G, et al. Unbalanced three-phase optimal power flow for smart grids[J]. IEEE Transactions on Industrial Electronics, 2011, 58(10): 4504-4513.
[7] 李扬,韦钢,马钰,等.含电动汽车和分布式电源的主动配电网动态重构[J].电力系统自动化,2018,42(5):102-110.DOI:10.7500/AEPS20170926006.LI Yang, WEI Gang, MA Yu, et al. Dynamic reconfiguration of active distribution network considering electric vehicles and distributed generations[J]. Automation of Electric Power Systems, 2018, 42(5): 102-110. DOI: 10.7500/AEPS20170926006.
[8] 车仁飞,李仁俊.一种少环配电网三相潮流计算新方法[J].中国电机工程学报,2003,23(1):74-79.CHE Renfei, LI Renjun. A new three-phase power flow method for weakly meshed distribution systems[J]. Proceedings of the CSEE, 2003, 23(1): 74-79.
[9] DING Fei, LOPARO K A.Feeder reconfiguration for unbalanced distribution systems with distributed generation: a hierarchical decentralized approach[J]. IEEE Transactions on Power Systems, 2016, 31(2): 1633-1642.
[10] SOSIC D, STEFANOV P. Reconfiguration of the three phase unbalanced distribution network[C]// Mediterranean Conference on Power Generation, Transmission, Distribution and Energy Conversion, November 6-9, 2016, Belgrade, Serbia: 8p.
[11] 吴在军,成晟,朱承治.基于线性近似模型的三相不平衡有源配电网重构[J].电力系统自动化,2018,42(12):134-141.DOI:10.7500/AEPS20180108004.WU Zaijun, CHENG Sheng, ZHU Chengzhi.Reconfiguration of unbalanced active distribution network based on linear approximation model[J]. Automation of Electric Power Systems, 2018, 42(12): 134-141. DOI: 10.7500/AEPS 20180108004.
[12] 黄红程,顾洁,方陈.基于无向生成树的并行遗传算法在配电网重构中的应用[J].电力系统自动化,2015,39(14):89-96.HUANG Hongcheng, GU Jie, FANG Chen. Application of undirected spanning tree-based parallel genetic algorithm in distributed network reconfiguration[J]. Automation of Electric Power Systems, 2015, 39(14): 89-96.
[13] POPOVIC D S, POPOVIC Z N. A risk management procedure for supply restoration in distribution networks[J].IEEE Transactions on Power Systems, 2004, 19(1): 221-228.
[14] 陈彬,王洪涛,曹曦.计及负荷模糊不确定性的网架重构后期负荷恢复优化[J].电力系统自动化,2016,40(20):6-12.CHEN Bin, WANG Hongtao, CAO Xi.Load restoration optimization during the last stage of network reconfiguration considering load fuzzy uncertainty[J].Automation of Electric Power Systems, 2016, 40(20): 6-12.
[15] HAGHIGHAT H, ZENG Bo. Distribution system reconfiguration under uncertain load and renewable generation[J]. IEEE Transactions on Power Systems, 2016, 31(4): 2666-2675.
[16] LEE C, LIU Cong, MEHROTRA S, et al. Robust distribution network reconfiguration[J]. IEEE Transactions on Smart Grid, 2015, 6(2): 836-842.
[17] 丁涛,郭庆来,柏瑞,等.考虑风电不确定性的区间经济调度模型及空间分支定界法[J].中国电机工程学报,2014,34(22):3707-3714.DING Tao, GUO Qinglai, BAI Rui, et al. Interval economic dispatch model with uncertain wind power injection and spatial branch and bound method[J]. Proceedings of the CSEE, 2014, 34(22): 3707-3714.
[18] 赵俊华,文福拴,薛禹胜,等.计及电动汽车和风电出力不确定性的随机经济调度[J].电力系统自动化,2010,34(20):22-29.ZHAO Junhua, WEN Fushuan, XUE Yusheng, et al. Power system stochastic economic dispatch considering uncertain outputs from plug-in electric vehicles and wind generators[J]. Automation of Electric Power Systems, 2010, 34(20): 22-29.
[19] 王守相,韩亮.DG出力不确定性对配电网影响力分析的复仿射数学方法[J].中国电机工程学报,2014,34(31):5507-5515.WANG Shouxiang, HAN Liang. Complex affine arithmetic based method for the analyses of DG’s uncertainty influence on distribution network[J]. Proceedings of the CSEE, 2014, 34(31): 5507-5515.
[20] 易海川,张彼德,王海颖,等.提高DG接纳能力的配电网动态重构方法[J].电网技术,2016,40(5):1431-1436.YI Haichuan, ZHANG Bide, WANG Haiying, et al.Distribution network dynamic reconfiguration method for improving distribution network’s ability of accepting DG[J].Power System Technology, 2016, 40(5): 1431-1436.
[21] 徐俊俊,戴桂木,吴在军,等.计及电动汽车和光伏不确定性的主动配电网量测优化配置[J].电力系统自动化,2017,41(1):57-64.DOI:10.7500/AEPS20160425009.XU Junjun, DAI Guimu, WU Zaijun, et al. Optimal meter placement for active distribution network considering uncertainties of plug-in electric vehicles and photovoltaic systems[J]. Automation of Electric Power Systems, 2017, 41(1): 57-64. DOI: 10.7500/AEPS20160425009.
[22] 朱俊澎,顾伟,张韩旦,等.考虑网络动态重构的分布式电源选址定容优化方法[J].电力系统自动化,2018,42(5):111-119.DOI:10.7500/AEPS20170605016.ZHU Junpeng, GU Wei, ZHANG Handan, et al. Optimal siting and sizing of distributed generators considering dynamic network reconfiguration[J]. Automation of Electric Power Systems, 2018, 42(5): 111-119.DOI: 10.7500/AEPS20170605016.
[23] BARAN M E, WU F F. Network reconfiguration in distribution systems for loss reduction and load balancing[J]. IEEE Transactions on Power Delivery, 1989, 4(2): 1401-1407.
[24] LORCA á, SUN X A. Adaptive robust optimization with dynamic uncertainty sets for multi-period economic dispatch under significant wind[J]. IEEE Transactions on Power Systems, 2015, 30(4): 1702-1713.
[25] TAYLOR J A, HOVER F S. Convex models of distribution system reconfiguration[J]. IEEE Transactions on Power Systems, 2012, 27(3): 1407-1413.
[26] ZENG Bo, ZHAO Long. Solving two-stage robust optimization problems using a column-and-constraint generation method[J]. Operations Research Letters, 2013, 41(5): 457-461.
[2] 裴玮,盛鹍,孔力,等.分布式电源对配网供电电压质量的影响与改善[J].中国电机工程学报,2008,28(13):152-157.PEI Wei, SHENG Kun, KONG Li, et al.Impact and improvement of distributed generation on distribution network voltage quality[J]. Proceedings of the CSEE, 2008, 28(13): 152-157.
[3] 张嘉堃,韦钢,朱兰,等.基于盲数模型的含分布式电源配电网供电能力评估[J].电力系统自动化,2016,40(8):64-70.ZHANG Jiakun, WEI Gang, ZHU Lan, et al. Blind-number model based power supply capability evaluation of distribution networks with distributed generators[J]. Automation of Electric Power Systems, 2016, 40(8): 64-70.
[4] 陶顺,陈鹏伟,肖湘宁,等.智能配电网不确定性建模与供电特征优化技术综述[J].电工技术学报,2017,32(10):77-91.TAO Shun, CHEN Pengwei, XIAO Xiangning, et al. Review on uncertainty modeling and power supply characteristics optimization technology in smart distribution network[J]. Transactions of China Electrotechnical Society, 2017, 32(10): 77-91.
[5] ZHANG Peng, LI Wenyuan, WANG Shouxiang.Reliability-oriented distribution network reconfiguration considering uncertainties of data by interval analysis[J].International Journal of Electrical Power & Energy Systems, 2012, 34(1): 138-144.
[6] BRUNO S, LAMONACA S, ROTONDO G, et al. Unbalanced three-phase optimal power flow for smart grids[J]. IEEE Transactions on Industrial Electronics, 2011, 58(10): 4504-4513.
[7] 李扬,韦钢,马钰,等.含电动汽车和分布式电源的主动配电网动态重构[J].电力系统自动化,2018,42(5):102-110.DOI:10.7500/AEPS20170926006.LI Yang, WEI Gang, MA Yu, et al. Dynamic reconfiguration of active distribution network considering electric vehicles and distributed generations[J]. Automation of Electric Power Systems, 2018, 42(5): 102-110. DOI: 10.7500/AEPS20170926006.
[8] 车仁飞,李仁俊.一种少环配电网三相潮流计算新方法[J].中国电机工程学报,2003,23(1):74-79.CHE Renfei, LI Renjun. A new three-phase power flow method for weakly meshed distribution systems[J]. Proceedings of the CSEE, 2003, 23(1): 74-79.
[9] DING Fei, LOPARO K A.Feeder reconfiguration for unbalanced distribution systems with distributed generation: a hierarchical decentralized approach[J]. IEEE Transactions on Power Systems, 2016, 31(2): 1633-1642.
[10] SOSIC D, STEFANOV P. Reconfiguration of the three phase unbalanced distribution network[C]// Mediterranean Conference on Power Generation, Transmission, Distribution and Energy Conversion, November 6-9, 2016, Belgrade, Serbia: 8p.
[11] 吴在军,成晟,朱承治.基于线性近似模型的三相不平衡有源配电网重构[J].电力系统自动化,2018,42(12):134-141.DOI:10.7500/AEPS20180108004.WU Zaijun, CHENG Sheng, ZHU Chengzhi.Reconfiguration of unbalanced active distribution network based on linear approximation model[J]. Automation of Electric Power Systems, 2018, 42(12): 134-141. DOI: 10.7500/AEPS 20180108004.
[12] 黄红程,顾洁,方陈.基于无向生成树的并行遗传算法在配电网重构中的应用[J].电力系统自动化,2015,39(14):89-96.HUANG Hongcheng, GU Jie, FANG Chen. Application of undirected spanning tree-based parallel genetic algorithm in distributed network reconfiguration[J]. Automation of Electric Power Systems, 2015, 39(14): 89-96.
[13] POPOVIC D S, POPOVIC Z N. A risk management procedure for supply restoration in distribution networks[J].IEEE Transactions on Power Systems, 2004, 19(1): 221-228.
[14] 陈彬,王洪涛,曹曦.计及负荷模糊不确定性的网架重构后期负荷恢复优化[J].电力系统自动化,2016,40(20):6-12.CHEN Bin, WANG Hongtao, CAO Xi.Load restoration optimization during the last stage of network reconfiguration considering load fuzzy uncertainty[J].Automation of Electric Power Systems, 2016, 40(20): 6-12.
[15] HAGHIGHAT H, ZENG Bo. Distribution system reconfiguration under uncertain load and renewable generation[J]. IEEE Transactions on Power Systems, 2016, 31(4): 2666-2675.
[16] LEE C, LIU Cong, MEHROTRA S, et al. Robust distribution network reconfiguration[J]. IEEE Transactions on Smart Grid, 2015, 6(2): 836-842.
[17] 丁涛,郭庆来,柏瑞,等.考虑风电不确定性的区间经济调度模型及空间分支定界法[J].中国电机工程学报,2014,34(22):3707-3714.DING Tao, GUO Qinglai, BAI Rui, et al. Interval economic dispatch model with uncertain wind power injection and spatial branch and bound method[J]. Proceedings of the CSEE, 2014, 34(22): 3707-3714.
[18] 赵俊华,文福拴,薛禹胜,等.计及电动汽车和风电出力不确定性的随机经济调度[J].电力系统自动化,2010,34(20):22-29.ZHAO Junhua, WEN Fushuan, XUE Yusheng, et al. Power system stochastic economic dispatch considering uncertain outputs from plug-in electric vehicles and wind generators[J]. Automation of Electric Power Systems, 2010, 34(20): 22-29.
[19] 王守相,韩亮.DG出力不确定性对配电网影响力分析的复仿射数学方法[J].中国电机工程学报,2014,34(31):5507-5515.WANG Shouxiang, HAN Liang. Complex affine arithmetic based method for the analyses of DG’s uncertainty influence on distribution network[J]. Proceedings of the CSEE, 2014, 34(31): 5507-5515.
[20] 易海川,张彼德,王海颖,等.提高DG接纳能力的配电网动态重构方法[J].电网技术,2016,40(5):1431-1436.YI Haichuan, ZHANG Bide, WANG Haiying, et al.Distribution network dynamic reconfiguration method for improving distribution network’s ability of accepting DG[J].Power System Technology, 2016, 40(5): 1431-1436.
[21] 徐俊俊,戴桂木,吴在军,等.计及电动汽车和光伏不确定性的主动配电网量测优化配置[J].电力系统自动化,2017,41(1):57-64.DOI:10.7500/AEPS20160425009.XU Junjun, DAI Guimu, WU Zaijun, et al. Optimal meter placement for active distribution network considering uncertainties of plug-in electric vehicles and photovoltaic systems[J]. Automation of Electric Power Systems, 2017, 41(1): 57-64. DOI: 10.7500/AEPS20160425009.
[22] 朱俊澎,顾伟,张韩旦,等.考虑网络动态重构的分布式电源选址定容优化方法[J].电力系统自动化,2018,42(5):111-119.DOI:10.7500/AEPS20170605016.ZHU Junpeng, GU Wei, ZHANG Handan, et al. Optimal siting and sizing of distributed generators considering dynamic network reconfiguration[J]. Automation of Electric Power Systems, 2018, 42(5): 111-119.DOI: 10.7500/AEPS20170605016.
[23] BARAN M E, WU F F. Network reconfiguration in distribution systems for loss reduction and load balancing[J]. IEEE Transactions on Power Delivery, 1989, 4(2): 1401-1407.
[24] LORCA á, SUN X A. Adaptive robust optimization with dynamic uncertainty sets for multi-period economic dispatch under significant wind[J]. IEEE Transactions on Power Systems, 2015, 30(4): 1702-1713.
[25] TAYLOR J A, HOVER F S. Convex models of distribution system reconfiguration[J]. IEEE Transactions on Power Systems, 2012, 27(3): 1407-1413.
[26] ZENG Bo, ZHAO Long. Solving two-stage robust optimization problems using a column-and-constraint generation method[J]. Operations Research Letters, 2013, 41(5): 457-461.