分位数拟合的点估计法随机潮流在输电网规划中的应用
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摘要
为了更全面地描述输电网规划中面临的负荷波动、风电出力这些不确定因素,以点估计法随机潮流为基础、年综合费用最小为目标函数,并计及网络损耗,建立输电网优化规划模型。引入多项式正态变换技术对非正态变量相关性进行处理。采用基于最小二乘的分位数拟合法求取多项式正态变换的系数,有效地避免了积分运算。以总体样本均值和样本方差均值为指标,量化相关性对风电出力的影响。采用改进的粒子群优化算法对修改的IEEE-RTS 24节点系统进行算例分析,结果表明,随着相关性的增强,负荷、风速出现极值的概率增加,电网需要投建更多线路以应对系统中的不确定因素。
In order to describe the uncertain factors,i.e. load fluctuation and wind power,faced in TNEP( Transmission Network Expansion Planning) more thoroughly,a transmission network optimization planning model is built based on stochastic power flow using PEM( Point Estimation Method),which takes the minimum annual comprehensive cost as its objective function and considers the network loss. The polynomial normal transformation technology is introduced to deal with the correlation of non-normal variables. The quantile fitting method based on least square is adopted to obtain the coefficients of polynomial normal transformation,effectively avoiding the integral operation. The impact of the correlation on wind power is quantified by the indexes of PM( Population Mean) and MSV( Mean of Sample Variance). The improved PSO( Particle Swarm Optimization) algorithm is used to analyze the modified IEEE-RTS 24-bus system,and results show that the probability of extreme values of load and wind speed is rising along with the increase of correlation,and power grid needs to build more lines to deal with the uncertain factors.
In order to describe the uncertain factors,i.e. load fluctuation and wind power,faced in TNEP( Transmission Network Expansion Planning) more thoroughly,a transmission network optimization planning model is built based on stochastic power flow using PEM( Point Estimation Method),which takes the minimum annual comprehensive cost as its objective function and considers the network loss. The polynomial normal transformation technology is introduced to deal with the correlation of non-normal variables. The quantile fitting method based on least square is adopted to obtain the coefficients of polynomial normal transformation,effectively avoiding the integral operation. The impact of the correlation on wind power is quantified by the indexes of PM( Population Mean) and MSV( Mean of Sample Variance). The improved PSO( Particle Swarm Optimization) algorithm is used to analyze the modified IEEE-RTS 24-bus system,and results show that the probability of extreme values of load and wind speed is rising along with the increase of correlation,and power grid needs to build more lines to deal with the uncertain factors.
引文
[1]AGHAEI J,AMJADY N,BAHARVANDI A,et al.Generation and transmission expansion planning:MILP-based probabilistic model[J].IEEE Transactions on Power Systems,2014,29(4):1592-1601.
[2]雷若冰,徐箭,孙辉,等.基于相关性分析的风电场群风速分布预测方法[J].电力自动化设备,2016,36(5):134-140.LEI Ruobing,XU Jian,SUN Hui,et al.Wind speed distribution forecasting based on correlation analysis for wind farm group[J].Electric Power Automation Equipment,2016,36(5):134-140.
[3]徐箭,洪敏,孙元章,等.基于经验Copula函数的多风电场出力动态场景生成方法及其在机组组合中的应用[J].电力自动化设备,2017,37(8):81-89.XU Jian,HONG Min,SUN Yuanzhang,et al.Dynamic scenario generation based on empirical Copula function for outputs of multiple wind farms and its application in unit commitment[J].Electric Power Automation Equipment,2017,37(8):81-89.
[4]洪绍云,程浩忠,曾平良,等.输电网扩展优化规划研究综述[J].电网技术,2016,40(10):3102-3107.HONG Shaoyun,CHENG Haozhong,ZENG Pingliang,et al.Review of transmission network expansion optimization planning[J].Power System Technology,2016,40(10):3102-3107.
[5]田书欣,程浩忠,曾平良,等.大型集群风电接入输电系统规划研究综述[J].中国电机工程学报,2014,34(10):1566-1574.TIAN Shuxin,CHENG Haozhong,ZENG Pingliang,et al.Review of transmission planning for integrating large clusters of wind power[J].Proceedings of the CSEE,2014,34(10):1566-1574.
[6]周金辉,余贻鑫,曾沅.大规模风电接入下输电网扩展规划的启发式优化算法[J].电力系统自动化,2011,35(22):66-70.ZHOU Jinhui,YU Yixin,ZENG Yuan.Heuristic optimization algorithm for transmission network expansion planning with large-scale wind power integration[J].Automation of Electric Power Systems,2011,35(22):66-70.
[7]袁越,吴博文,李振杰,等.基于多场景概率的含大型风电场的输电网柔性规划[J].电力自动化设备,2009,29(10):8-12.YUAN Yue,WU Bowen,LI Zhenjie,et al.Flexible planning of transmission system with large wind farm based on multi-scenario probability[J].Electric Power Automation Equipment,2009,29(10):8-12.
[8]范宏,程浩忠,唐永红,等.相关机会二层规划法在输电网扩展规划中的应用[J].电力自动化设备,2013,33(11):59-63.FAN Hong,CHENG Haozhong,TANG Yonghong,et al.Application of dependent-chance bilevel programming in transmission network expansion planning[J].Electric Power Automation Equipment,2013,33(11):59-63.
[9]YU H,CHUNG C,WONG K,et al.A chance constrained transmission network expansion planning method with consideration of load and wind farm uncertainties[J].IEEE Transactions on Power Systems,2009,24(3):1568-1576.
[10]杨欢,邹斌.含相关性随机变量的概率潮流三点估计法[J].电力系统自动化,2012,36(15):51-56.YANG Huan,ZOU Bin.A three-point estimate method for solving probabilistic power flow problems with correlated random variables[J].Automation of Electric Power Systems,2012,36(15):51-56.
[11]XIAO Q.Generating correlated random vector by polynomial normal transformation[EB/OL].[2016-12-10].http:∥arxiv.org/pdf/1508.06433v1.pdf.
[12]方斯顿,程浩忠,徐国栋,等.随机最优潮流及其应用的研究综述[J].电力自动化设备,2016,36(11):1-10.FANG Sidun,CHENG Haozhong,XU Guodong,et al.Reviews on stochastic optimal power flow and its application[J].Electric Power Automation Equipment,2016,36(11):1-10.
[13]雷加智,龚庆武.基于改进点估计法的输电线路过负荷风险评估[J].电力自动化设备,2017,37(4):67-72,81.LEI Jiazhi,GONG Qingwu.Transmission line overload risk assessment based on improved point estimation methods[J].Electric Power Automation Equipment,2017,37(4):67-72,81.
[14]芦晶晶,赵渊,赵勇帅,等.含分布式电源配电网可靠性评估的点估计法[J].电网技术,2013,37(8):2250-2257.LU Jingjing,ZHAO Yuan,ZHAO Yongshuai,et al.A point estimation method for reliability evaluation of distribution network with distributed generation[J].Power System Technology,2013,37(8):2250-2257.
[15]LI Y M,LI W Y,YAN W,et al.Probabilistic optimal power flow considering correlations of wind speeds following different distributions[J].IEEE Transactions on Power Systems,2014,29(4):1847-1854.
[16]MORALES J M,PREZ-RUIZ J.Point estimate schemes to solve the probabilistic power flow[J].IEEE Transactions on Power Systems,2007,22(4):1594-1601.
[17]EBERHART R C,KENNEDY J.A new optimizer using particle swarm theory[C]∥Proceedings of the Sixth International Symposium on Micro Machine and Human Science.MHS'95.Nagoya,Japan:IEEE,1995:39-43.
[18]SHI Y H,EBERHART R.A modified particle swarm optimizer[C]∥IEEE World Congress on Computational Intelligence.Anchorage,USA:IEEE,1998:69-73.
[19]李德毅,孟海军,史雪梅.隶属云和隶属云发生器[J].计算机研究与发展,1995,32(6):15-20.LI Deyi,MENG Haijun,SHI Xuemei.Membership clouds and membership cloud generators[J].Computer R&D,1995,32(6):15-20.
[20]戴朝华,朱云芳,陈维荣,等.云遗传算法及其应用[J].电子学报,2007,35(7):1419-1424.DAI Chaohua,ZHU Yunfang,CHEN Weirong,et al.Cloud model based genetic algorithm and its applications[J].Acta Eelctronica Sinica,2007,35(7):1419-1424.
[21]SHU Z,JIRUTITIJAROEN P.Latin hypercube sampling techniques for power systems reliability analysis with renewable energy sources[J].IEEE Transactions on Power Systems,2011,26(4):2066-2073.
[2]雷若冰,徐箭,孙辉,等.基于相关性分析的风电场群风速分布预测方法[J].电力自动化设备,2016,36(5):134-140.LEI Ruobing,XU Jian,SUN Hui,et al.Wind speed distribution forecasting based on correlation analysis for wind farm group[J].Electric Power Automation Equipment,2016,36(5):134-140.
[3]徐箭,洪敏,孙元章,等.基于经验Copula函数的多风电场出力动态场景生成方法及其在机组组合中的应用[J].电力自动化设备,2017,37(8):81-89.XU Jian,HONG Min,SUN Yuanzhang,et al.Dynamic scenario generation based on empirical Copula function for outputs of multiple wind farms and its application in unit commitment[J].Electric Power Automation Equipment,2017,37(8):81-89.
[4]洪绍云,程浩忠,曾平良,等.输电网扩展优化规划研究综述[J].电网技术,2016,40(10):3102-3107.HONG Shaoyun,CHENG Haozhong,ZENG Pingliang,et al.Review of transmission network expansion optimization planning[J].Power System Technology,2016,40(10):3102-3107.
[5]田书欣,程浩忠,曾平良,等.大型集群风电接入输电系统规划研究综述[J].中国电机工程学报,2014,34(10):1566-1574.TIAN Shuxin,CHENG Haozhong,ZENG Pingliang,et al.Review of transmission planning for integrating large clusters of wind power[J].Proceedings of the CSEE,2014,34(10):1566-1574.
[6]周金辉,余贻鑫,曾沅.大规模风电接入下输电网扩展规划的启发式优化算法[J].电力系统自动化,2011,35(22):66-70.ZHOU Jinhui,YU Yixin,ZENG Yuan.Heuristic optimization algorithm for transmission network expansion planning with large-scale wind power integration[J].Automation of Electric Power Systems,2011,35(22):66-70.
[7]袁越,吴博文,李振杰,等.基于多场景概率的含大型风电场的输电网柔性规划[J].电力自动化设备,2009,29(10):8-12.YUAN Yue,WU Bowen,LI Zhenjie,et al.Flexible planning of transmission system with large wind farm based on multi-scenario probability[J].Electric Power Automation Equipment,2009,29(10):8-12.
[8]范宏,程浩忠,唐永红,等.相关机会二层规划法在输电网扩展规划中的应用[J].电力自动化设备,2013,33(11):59-63.FAN Hong,CHENG Haozhong,TANG Yonghong,et al.Application of dependent-chance bilevel programming in transmission network expansion planning[J].Electric Power Automation Equipment,2013,33(11):59-63.
[9]YU H,CHUNG C,WONG K,et al.A chance constrained transmission network expansion planning method with consideration of load and wind farm uncertainties[J].IEEE Transactions on Power Systems,2009,24(3):1568-1576.
[10]杨欢,邹斌.含相关性随机变量的概率潮流三点估计法[J].电力系统自动化,2012,36(15):51-56.YANG Huan,ZOU Bin.A three-point estimate method for solving probabilistic power flow problems with correlated random variables[J].Automation of Electric Power Systems,2012,36(15):51-56.
[11]XIAO Q.Generating correlated random vector by polynomial normal transformation[EB/OL].[2016-12-10].http:∥arxiv.org/pdf/1508.06433v1.pdf.
[12]方斯顿,程浩忠,徐国栋,等.随机最优潮流及其应用的研究综述[J].电力自动化设备,2016,36(11):1-10.FANG Sidun,CHENG Haozhong,XU Guodong,et al.Reviews on stochastic optimal power flow and its application[J].Electric Power Automation Equipment,2016,36(11):1-10.
[13]雷加智,龚庆武.基于改进点估计法的输电线路过负荷风险评估[J].电力自动化设备,2017,37(4):67-72,81.LEI Jiazhi,GONG Qingwu.Transmission line overload risk assessment based on improved point estimation methods[J].Electric Power Automation Equipment,2017,37(4):67-72,81.
[14]芦晶晶,赵渊,赵勇帅,等.含分布式电源配电网可靠性评估的点估计法[J].电网技术,2013,37(8):2250-2257.LU Jingjing,ZHAO Yuan,ZHAO Yongshuai,et al.A point estimation method for reliability evaluation of distribution network with distributed generation[J].Power System Technology,2013,37(8):2250-2257.
[15]LI Y M,LI W Y,YAN W,et al.Probabilistic optimal power flow considering correlations of wind speeds following different distributions[J].IEEE Transactions on Power Systems,2014,29(4):1847-1854.
[16]MORALES J M,PREZ-RUIZ J.Point estimate schemes to solve the probabilistic power flow[J].IEEE Transactions on Power Systems,2007,22(4):1594-1601.
[17]EBERHART R C,KENNEDY J.A new optimizer using particle swarm theory[C]∥Proceedings of the Sixth International Symposium on Micro Machine and Human Science.MHS'95.Nagoya,Japan:IEEE,1995:39-43.
[18]SHI Y H,EBERHART R.A modified particle swarm optimizer[C]∥IEEE World Congress on Computational Intelligence.Anchorage,USA:IEEE,1998:69-73.
[19]李德毅,孟海军,史雪梅.隶属云和隶属云发生器[J].计算机研究与发展,1995,32(6):15-20.LI Deyi,MENG Haijun,SHI Xuemei.Membership clouds and membership cloud generators[J].Computer R&D,1995,32(6):15-20.
[20]戴朝华,朱云芳,陈维荣,等.云遗传算法及其应用[J].电子学报,2007,35(7):1419-1424.DAI Chaohua,ZHU Yunfang,CHEN Weirong,et al.Cloud model based genetic algorithm and its applications[J].Acta Eelctronica Sinica,2007,35(7):1419-1424.
[21]SHU Z,JIRUTITIJAROEN P.Latin hypercube sampling techniques for power systems reliability analysis with renewable energy sources[J].IEEE Transactions on Power Systems,2011,26(4):2066-2073.