基于稀疏多项式混沌展开的孤岛微电网概率潮流计算
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摘要
考虑到可再生能源的不确定性对微电网运行的影响,传统确定性潮流计算难以全面描述系统运行状态与潮流分布情况。在计及微电网源荷随机性与相关性的情况下,文中建立了孤岛交流微电网的概率潮流模型。进一步,提出了一种稀疏多项式混沌展开方法用于快速准确得到孤岛微电网的输出响应,在含有高维输入随机变量时,有效提高了孤岛微电网的概率潮流计算效率。采用接入多台分布式电源的33节点孤岛微电网系统进行仿真,通过与传统方法的对比,验证了所提方法的高效性和准确性。
Considering the effect of uncertainty of renewable energy source(RES)on the operation of microgrid,it is hard to comprehensively describe operation states and power flow distribution through the traditional deterministic power flow calculation.Based on the randomness and dependency of generators and loads in microgrid,this paper develops a probabilistic power flow model of islanded AC microgrid.The sparse polynomial chaos expansion method is adopted to obtain output response of islanded microgrid quickly and accurately,also it can improve the efficiency of probabilistic power flow calculation of microgrid with high-dimensional input variables.Finally,a 33-node islanded microgrid with several distributed generators is simulated,and the effectiveness and accuracy of the proposed method are verified by comparing with traditional methods.
Considering the effect of uncertainty of renewable energy source(RES)on the operation of microgrid,it is hard to comprehensively describe operation states and power flow distribution through the traditional deterministic power flow calculation.Based on the randomness and dependency of generators and loads in microgrid,this paper develops a probabilistic power flow model of islanded AC microgrid.The sparse polynomial chaos expansion method is adopted to obtain output response of islanded microgrid quickly and accurately,also it can improve the efficiency of probabilistic power flow calculation of microgrid with high-dimensional input variables.Finally,a 33-node islanded microgrid with several distributed generators is simulated,and the effectiveness and accuracy of the proposed method are verified by comparing with traditional methods.
引文
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[3]ABDELAZIZ M M,FARAG H E,EL-SAADANY E F,et al.A novel and generalized three-phase power flow algorithm for islanded microgrids using a newton trust region method[J].IEEE Transactions on Power Systems,2013,28(1):190-201.
[4]彭寒梅,曹一家,黄小庆,等.无平衡节点孤岛运行微电网的连续潮流计算[J].中国电机工程学报,2016,36(8):2057-2067.PENG Hanmei,CAO Yijia,HUANG Xiaoqing,et al.Continuous power flow for islanding microgrid without balance nodes[J].Proceedings of the CSEE,2016,36(8):2057-2067.
[5]王成山,孙充勃,彭克,等.微电网交直流混合潮流算法研究[J].中国电机工程学报,2013,33(4):8-15.WANG Chengshan,SUN Chongbo,PENG Ke,et al.Study on AC-DC hybrid power flow algorithm for microgrid[J].Proceedings of the CSEE,2013,33(4):8-15.
[6]徐潇源,严正,冯冬涵,等.基于输入变量秩相关系数的概率潮流计算方法[J].电力系统自动化,2014,38(12):54-61.DOI:10.7500/AEPS20130429008.XU Xiaoyuan,YAN Zheng,FENG Donghan,et al.Probabilistic load flow calculation based on rank correlation coefficient of input random variables[J].Automation of Electric Power Systems,2014,38(12):54-61.DOI:10.7500/AEPS20130429008.
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[11]鲍海波,韦化.考虑风电的电压稳定概率评估的随机响应面法[J].中国电机工程学报,2012,32(13):77-85.BAO Haibo,WEI Hua.A stochastic response surface method for probabilistic evaluation of the voltage stability considering wind power[J].Proceedings of the CSEE,2012,32(13):77-85.
[12]张世达,孙永辉,赵景涛,等.基于随机响应面法的主动配电网无功优化[J].电力系统自动化,2017,41(13):30-38.DOI:10.7500/AEPS20161026003.ZHANG Shida,SUN Yonghui,ZHAO Jingtao,et al.Optimal reactive power flow in active distribution network based on stochastic response surface method[J].Automation of Electric Power Systems,2017,41(13):30-38.DOI:10.7500/AEPS20161026003.
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[14]汤雪松,殷明慧,邹云.考虑风速相关性的风电穿透功率极限的改进计算[J].电网技术,2015,39(2):420-425.TANG Xuesong,YIN Minghui,ZOU Yun.An improved method to calculate wind power penetration limit considering wind speed correlation[J].Power System Technology,2015,39(2):420-425.
[15]王晗,徐潇源,严正.基于改进信赖域算法的孤岛交直流混合微电网潮流计算[J].电力系统自动化,2017,41(20):38-46.DOI:10.7500/AEPS20170416002.WANG Han,XU Xiaoyuan,YAN Zheng.Power flow calculation of islanded AC-DC hybrid microgrid based on modified trust region method[J].Automation of Electric Power Systems,2017,41(20):38-46.DOI:10.7500/AEPS20170416002.
[16]陈国恩,宗鹏鹏,朱伟,等.计及可再生能源与负荷互补特性的储能随机调度[J].电力建设,2015,36(6):27-33.CHEN Guoen,ZONG Pengpeng,ZHU Wei,et al.Stochastic dispatching of energy storage devices considering complementarity between renewable energy[J].Electric Power Construction,2015,36(6):27-33.
[17]吴巍,汪可友,李国杰.计及光伏发电相关性的多重积分法概率潮流计算[J].中国电机工程学报,2015,35(3):568-575.WU Wei,WANG Keyou,LI Guojie.Probabilistic load flow calculation method based on multiple integral method considering correlation of photovoltaic generation[J].Proceedings of the CSEE,2015,35(3):568-575.
[18]彭寒梅,李帅虎,李辉,等.孤岛运行交直流混合微电网的潮流计算[J].电网技术,2017,41(9):2887-2896.PENG Hanmei,LI Shuaihu,LI Hui,et al.Power flow calculation of islanded hybrid AC/DC microgrid[J].Power System Technology,2017,41(9):2887-2896.
[19]SUDRET B.Global sensitivity analysis using polynomial chaos expansions[J].Reliability Engineering&System Safety,2008,93(7):964-979.
[20]ISUKAPALLI S S,ROY A,GEORGOPOULOS P G.Stochastic response surface methods(SRSMs)for uncertainty propagation:application to environmental and biological systems[J].Risk Analysis,1998,18(3):351.
[21]HAESEN E,BASTIAENSEN C,DRIESEN J,et al.Aprobabilistic formulation of load margins in power systems with stochastic generation[J].IEEE Transactions on Power Systems,2009,24(2):951-958.
[22]MUKHERJEE S,NIYOGI P,POGGIO T,et al.Learning theory:stability is sufficient for generalization and necessary and sufficient for consistency of empirical risk minimization[J].Advances in Computational Mathematics,2006,25(1/2/3):161-193.
[23]WEI D L,CUI Z S,CHEN J.Uncertainty quantification using polynomial chaos expansion with points of monomial cubature rules[J].Computers&Structures,2008,86(23/24):2102-2108.
[24]BLATMAN G,SUDRET B.Adaptive sparse polynomial chaos expansion based on least angle regression[J].Journal of Computational Physics,2011,230(6):2345-2367.
[25]TIBSHIRANI R,JOHNSTONE I,EFRON B,et al.Least angle regression[J].Annals of Statistics,2004,32(2):407-451.
[26]MARELLI S,SUDRET B.UQLab:a framework for uncertainty quantification in MATLAB[C]//International Conference on Vulnerability,Risk Analysis and Management,July 13-16,2014,Liverpool,UK:2554-2563.
[2]LI Zhiyi,SHAHIDEHPOUR M,AMINIFAR F.Cybersecurity in distributed power systems[J].Proceedings of the IEEE,2017,105(7):1367-1388.
[3]ABDELAZIZ M M,FARAG H E,EL-SAADANY E F,et al.A novel and generalized three-phase power flow algorithm for islanded microgrids using a newton trust region method[J].IEEE Transactions on Power Systems,2013,28(1):190-201.
[4]彭寒梅,曹一家,黄小庆,等.无平衡节点孤岛运行微电网的连续潮流计算[J].中国电机工程学报,2016,36(8):2057-2067.PENG Hanmei,CAO Yijia,HUANG Xiaoqing,et al.Continuous power flow for islanding microgrid without balance nodes[J].Proceedings of the CSEE,2016,36(8):2057-2067.
[5]王成山,孙充勃,彭克,等.微电网交直流混合潮流算法研究[J].中国电机工程学报,2013,33(4):8-15.WANG Chengshan,SUN Chongbo,PENG Ke,et al.Study on AC-DC hybrid power flow algorithm for microgrid[J].Proceedings of the CSEE,2013,33(4):8-15.
[6]徐潇源,严正,冯冬涵,等.基于输入变量秩相关系数的概率潮流计算方法[J].电力系统自动化,2014,38(12):54-61.DOI:10.7500/AEPS20130429008.XU Xiaoyuan,YAN Zheng,FENG Donghan,et al.Probabilistic load flow calculation based on rank correlation coefficient of input random variables[J].Automation of Electric Power Systems,2014,38(12):54-61.DOI:10.7500/AEPS20130429008.
[7]崔雅莉,别朝红,王锡凡.输电系统可用输电能力的概率模型及计算[J].电力系统自动化,2003,27(14):36-40.CUI Yali,BIE Zhaohong,WANG Xifan.Study on probabilistic models and algorithms of available transfer capability[J].Automation of Electric Power Systems,2003,27(14):36-40.
[8]VILLANUEVA D,LUIS PAZOS J,FEIJOO A.Probabilistic load flow including wind power generation[J].IEEETransactions on Power Systems,2011,26(3):1659-1667.
[9]HONG H P.An efficient point estimate method for probabilistic analysis[J].Reliability Engineering&System Safety,1998,59(3):261-267.
[10]韩冬,马进,贺仁睦,等.基于随机响应面法的电力系统仿真不确定性分析[J].电力系统自动化,2011,35(24):12-16.HAN Dong,MA Jin,HE Renmu,et al.Uncertainty analysis based on stochastic response surface method in power system simulation[J].Automation of Electric Power Systems,2011,35(24):12-16.
[11]鲍海波,韦化.考虑风电的电压稳定概率评估的随机响应面法[J].中国电机工程学报,2012,32(13):77-85.BAO Haibo,WEI Hua.A stochastic response surface method for probabilistic evaluation of the voltage stability considering wind power[J].Proceedings of the CSEE,2012,32(13):77-85.
[12]张世达,孙永辉,赵景涛,等.基于随机响应面法的主动配电网无功优化[J].电力系统自动化,2017,41(13):30-38.DOI:10.7500/AEPS20161026003.ZHANG Shida,SUN Yonghui,ZHAO Jingtao,et al.Optimal reactive power flow in active distribution network based on stochastic response surface method[J].Automation of Electric Power Systems,2017,41(13):30-38.DOI:10.7500/AEPS20161026003.
[13]NI Fei,NGUYEN P H,COBBEN J F.Basis-adaptive sparse polynomial chaos expansion for probabilistic power flow[J].IEEE Transactions on Power Systems,2017,32(1):694-704.
[14]汤雪松,殷明慧,邹云.考虑风速相关性的风电穿透功率极限的改进计算[J].电网技术,2015,39(2):420-425.TANG Xuesong,YIN Minghui,ZOU Yun.An improved method to calculate wind power penetration limit considering wind speed correlation[J].Power System Technology,2015,39(2):420-425.
[15]王晗,徐潇源,严正.基于改进信赖域算法的孤岛交直流混合微电网潮流计算[J].电力系统自动化,2017,41(20):38-46.DOI:10.7500/AEPS20170416002.WANG Han,XU Xiaoyuan,YAN Zheng.Power flow calculation of islanded AC-DC hybrid microgrid based on modified trust region method[J].Automation of Electric Power Systems,2017,41(20):38-46.DOI:10.7500/AEPS20170416002.
[16]陈国恩,宗鹏鹏,朱伟,等.计及可再生能源与负荷互补特性的储能随机调度[J].电力建设,2015,36(6):27-33.CHEN Guoen,ZONG Pengpeng,ZHU Wei,et al.Stochastic dispatching of energy storage devices considering complementarity between renewable energy[J].Electric Power Construction,2015,36(6):27-33.
[17]吴巍,汪可友,李国杰.计及光伏发电相关性的多重积分法概率潮流计算[J].中国电机工程学报,2015,35(3):568-575.WU Wei,WANG Keyou,LI Guojie.Probabilistic load flow calculation method based on multiple integral method considering correlation of photovoltaic generation[J].Proceedings of the CSEE,2015,35(3):568-575.
[18]彭寒梅,李帅虎,李辉,等.孤岛运行交直流混合微电网的潮流计算[J].电网技术,2017,41(9):2887-2896.PENG Hanmei,LI Shuaihu,LI Hui,et al.Power flow calculation of islanded hybrid AC/DC microgrid[J].Power System Technology,2017,41(9):2887-2896.
[19]SUDRET B.Global sensitivity analysis using polynomial chaos expansions[J].Reliability Engineering&System Safety,2008,93(7):964-979.
[20]ISUKAPALLI S S,ROY A,GEORGOPOULOS P G.Stochastic response surface methods(SRSMs)for uncertainty propagation:application to environmental and biological systems[J].Risk Analysis,1998,18(3):351.
[21]HAESEN E,BASTIAENSEN C,DRIESEN J,et al.Aprobabilistic formulation of load margins in power systems with stochastic generation[J].IEEE Transactions on Power Systems,2009,24(2):951-958.
[22]MUKHERJEE S,NIYOGI P,POGGIO T,et al.Learning theory:stability is sufficient for generalization and necessary and sufficient for consistency of empirical risk minimization[J].Advances in Computational Mathematics,2006,25(1/2/3):161-193.
[23]WEI D L,CUI Z S,CHEN J.Uncertainty quantification using polynomial chaos expansion with points of monomial cubature rules[J].Computers&Structures,2008,86(23/24):2102-2108.
[24]BLATMAN G,SUDRET B.Adaptive sparse polynomial chaos expansion based on least angle regression[J].Journal of Computational Physics,2011,230(6):2345-2367.
[25]TIBSHIRANI R,JOHNSTONE I,EFRON B,et al.Least angle regression[J].Annals of Statistics,2004,32(2):407-451.
[26]MARELLI S,SUDRET B.UQLab:a framework for uncertainty quantification in MATLAB[C]//International Conference on Vulnerability,Risk Analysis and Management,July 13-16,2014,Liverpool,UK:2554-2563.