基于场景法的配电网有功–无功协调优化
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摘要
随着风电、光伏等可再生能源接入比例的升高,使得配电网运行和控制面临着巨大挑战。综合考虑风光储模型,并计及了风光荷的不确定性、风速与光照强度预测误差的相关性,结合多项式正态变换方法(three-order polynomial normal transform,TPNT)、拉丁超立方采样(Latin hypercube sampling,LHS)技术产生样本,并基于同步回代缩减法(synchronous back reduction,SBR)进行场景缩减,建立了基于场景法配电网有功–无功协调优化模型。利用二阶锥松弛(second order cone relaxation,SOCR)技术和大M等方法,将原始模型,即混合整数非线性非凸(mixed integer nonlinear programming,MINLP)模型,转换为混合整数二阶锥规划(mixed integer second-order cone programming,MISOCP)模型,可直接调用MOSEK求解器求解。在改进的IEEE 33配电系统上进行算例仿真,验证了所提方法的精确性、合理性。
Increase of proportion of renewable energy, such as wind power and photovoltaics, integrated into distribution network, brings large challenges to operation and control of distribution network. Considering wind power, photovoltaic generation and storage, and combining the three-order polynomial normal transform(TPNT) with Latin hypercube sampling(LHS) to consider uncertainty of random variables and relation with prediction error of wind speed and solar irradiance, synchronous back reduction(SBR) method is used to reduce scenarios to improve calculation efficiency, and a coordinated optimization model of active and reactive powers in distribution network is established based on scenario method. The second order cone relaxation(SOCR) and big M method are used to transform the mixed integer nonlinear programming model(MINLP) into a mixed integer secondorder cone programming(MISOCP) model, which can be solved with existing softwares such as MOSEK solver. The improved IEEE 33-node system is taken as an example for simulation with results confirming accuracy and rationality of the proposed algorithm.
Increase of proportion of renewable energy, such as wind power and photovoltaics, integrated into distribution network, brings large challenges to operation and control of distribution network. Considering wind power, photovoltaic generation and storage, and combining the three-order polynomial normal transform(TPNT) with Latin hypercube sampling(LHS) to consider uncertainty of random variables and relation with prediction error of wind speed and solar irradiance, synchronous back reduction(SBR) method is used to reduce scenarios to improve calculation efficiency, and a coordinated optimization model of active and reactive powers in distribution network is established based on scenario method. The second order cone relaxation(SOCR) and big M method are used to transform the mixed integer nonlinear programming model(MINLP) into a mixed integer secondorder cone programming(MISOCP) model, which can be solved with existing softwares such as MOSEK solver. The improved IEEE 33-node system is taken as an example for simulation with results confirming accuracy and rationality of the proposed algorithm.
引文
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[19]张璐,唐巍,丛鹏伟,等.含光伏发电的配电网有功无功资源综合优化配置[J].中国电机工程学报,2014,34(31):5525-5533.Zhang Lu,Tang Wei,Cong Pengwei,et al.Optimal configuration of active-reactive power sources in distribution network with photovoltaic generation[J].Proceedings of the CSEE,2014,34(31):5525-5533(in Chinese).
[20]王成山,王兴刚,孙玮.含大型风电场的电力系统概率最大输电能力快速计算[J].中国电机工程学报,2008,28(10):56-62.Wang Chengshan,Wang Xinggang,Sun Wei.Fast calculation and analysis of probabilistic total transfer capability in power system including large-scale wind farms[J].Proceedings of the CSEE,2008,28(10):56-62(in Chinese).
[21]Atwa Y M,El-Saadany E F,Salama M M A,et al.Optimal renewable resources mix for distribution system energy loss minimization[J].IEEE Transactions on Power Systems,2010,25(1):360-370.
[22]Dall’Anese E Dhople S V,Johnson B B,et al.Decentralized optimal dispatch of photovoltaic inverters in residential distribution systems[J].IEEE Transactions on Energy Conversion,2014,29(4):957-967.
[23]Dall’Anese E,Dhople S V,Johnson B B,et al.Optimal dispatch of residential photovoltaic inverters under forecasting uncertainties[J]IEEE Journal of Photovoltaics,2015,5(1):350-359.
[24]Gabash A,Li Pu.Active-reactive optimal power flow in distribution networks with embedded generation and battery storage[J].IEEETransactions on Power Systems,2012,27(4):2026-2035.
[25]李存斌,张建业,李鹏.考虑成本、排污及风险的微电网运营多目标优化模型[J].中国电机工程学报,2015,35(5):1051-1058.Li Cunbin,Zhang Jianye,Li Peng.Multi-objective optimization model of micro-grid operation considering cost,pollution discharge and risk[J].Proceedings of the CSEE,2015,35(5):1051-1058(in Chinese).
[26]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.
[2]刘一兵,吴文传,张伯明,等.基于混合整数二阶锥规划的三相有源配电网无功优化[J].电力系统自动化,2014,38(15):58-64.Liu Yibing,Wu Wenchuan,Zhang Boming,et al.Reactive power optimization for three-phase distribution networks with distributed generators based on mixed integer second-order cone programming[J].Automation of Electric Power Systems,2014,38(15):58-64(in Chinese).
[3]刘一兵,吴文传,张伯明,等.基于混合整数二阶锥规划的主动配电网有功-无功协调多时段优化运行[J].中国电机工程学报,2014,34(16):2575-2583.Liu Yibing,Wu Wenchuan,Zhang Boming,et al.A mixed integer second-order cone programming based active and reactive power coordinated multi-period optimization for active distribution network[J].Proceedings of the CSEE,2014,34(16):2575-2583(in Chinese).
[4]高红均,刘俊勇,沈晓东,等.主动配电网最优潮流研究及其应用实例[J].中国电机工程学报,2017,37(6):1634-1645.Gao Hongjun,Liu Junyong,Shen Xiaodong,et al.Optimal power flow research in active distribution network and its application examples[J].Proceedings of the CSEE,2017,37(6):1634-1645(in Chinese).
[5]Ding Tao,Liu Shiyu,Yuan Wei,et al.A two-stage robust reactive power optimization considering uncertain wind power integration in active distribution networks[J].IEEE Transactions on Sustainable Energy,2016,7(1):301-311.
[6]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,016,36(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(in Chinese).
[7]黄伟,刘斯亮,王武,等.长时间尺度下计及光伏不确定性的配电网无功优化调度[J].电力系统自动化,2018,42(5):154-162.Huang Wei,Liu Siliang,Wang Wu,et al.Optimal reactive power dispatch with long-time scale in distribution network considering uncertainty of photovoltaic[J].Automation of Electric Power Systems,2018,42(5):154-162(in Chinese).
[8]张世达,孙永辉,卫志农,等.考虑可控光伏系统概率模型的主动配电网日前优化调度[J].电网技术,2018,42(1):247-257.Zhang Shida,Sun Yonghui,Wei Zhinong,et al.Day-ahead optimal scheduling for active distribution network considering controllable photovltaic system via probability model[J].Power System Technology,2018,42(1):247-257(in Chinese).
[9]何禹清,彭建春,毛丽林,等.含多个风电机组的配电网无功优化[J].电力系统自动化,2010,34(19):37-41.He Yuqing,Peng Jianchun,Mao Lilin,et al.Reactive power optimization in distribution system with multiple wind power generators[J].Automation of Electric Power Systems,2010,34(19):37-41(in Chinese).
[10]Niknam T,Zare M,Aghaei J.Scenario-based multiobjective volt/var control in distribution networks including renewable energy sources[J].IEEE Transactions on Power Delivery,2012,27(4):2004-2019.
[11]郑能,丁晓群,管志成,等.考虑相关性的含风电的配电网无功优化[J].南方电网技术,2018,12(1):62-69.Zheng Neng,Ding Xiaoqun,Guan Zhicheng,et al.Reactive power optimization in distribution network with wind turbine generators considering the correlations[J].Southern Power System Technology,2018,12(1):62-69(in Chinese).
[12]Saunders C S.Point estimate method addressing correlated wind power for probabilistic optimal power flow[J].IEEE Transactions on Power Systems,2014,29(3):1045-1054.
[13]姜欣,陈红坤,熊虎,等.基于预测误差不确定性的规模化间歇式电源机组组合研究[J].电网技术,2014,38(9):2455-2460.Jiang Xin,Chen Hongkun,Xiong Hu,et al.A prediction error uncertainty based day-ahead unit commitment of large-scale intermittent power generation[J].Power System Technology,2014,38(9):2455-2460(in Chinese).
[14]Li Hongshuang,LüZhenzhou,Yuan Xiukai.Nataf transformation based point estimate method[J].Chinese Science Bulletin,2008,53(17):2586-2592.
[15]Chen Xingyuan,Tung Yeou-koung.Investigation of polynomial normal transform[J].Structural Safety,2003,25(4):423-445.
[16]Liu Peiling,Kiureghian A D.Multivariate distribution models with prescribed marginals and covariances[J].Probab Eng Mech,1986,1(2):105-112.
[17]蔡德福.计及相关性的概率潮流计算方法及应用研究[D].武汉:华中科技大学,2014.
[18]Gao Hongjun,Liu Junyong,Wang Lingfeng.Robust coordinated optimization of active and reactive power in active distribution systems[J].IEEE Transactions on Smart Grid,2018,9(5):4436-4447.
[19]张璐,唐巍,丛鹏伟,等.含光伏发电的配电网有功无功资源综合优化配置[J].中国电机工程学报,2014,34(31):5525-5533.Zhang Lu,Tang Wei,Cong Pengwei,et al.Optimal configuration of active-reactive power sources in distribution network with photovoltaic generation[J].Proceedings of the CSEE,2014,34(31):5525-5533(in Chinese).
[20]王成山,王兴刚,孙玮.含大型风电场的电力系统概率最大输电能力快速计算[J].中国电机工程学报,2008,28(10):56-62.Wang Chengshan,Wang Xinggang,Sun Wei.Fast calculation and analysis of probabilistic total transfer capability in power system including large-scale wind farms[J].Proceedings of the CSEE,2008,28(10):56-62(in Chinese).
[21]Atwa Y M,El-Saadany E F,Salama M M A,et al.Optimal renewable resources mix for distribution system energy loss minimization[J].IEEE Transactions on Power Systems,2010,25(1):360-370.
[22]Dall’Anese E Dhople S V,Johnson B B,et al.Decentralized optimal dispatch of photovoltaic inverters in residential distribution systems[J].IEEE Transactions on Energy Conversion,2014,29(4):957-967.
[23]Dall’Anese E,Dhople S V,Johnson B B,et al.Optimal dispatch of residential photovoltaic inverters under forecasting uncertainties[J]IEEE Journal of Photovoltaics,2015,5(1):350-359.
[24]Gabash A,Li Pu.Active-reactive optimal power flow in distribution networks with embedded generation and battery storage[J].IEEETransactions on Power Systems,2012,27(4):2026-2035.
[25]李存斌,张建业,李鹏.考虑成本、排污及风险的微电网运营多目标优化模型[J].中国电机工程学报,2015,35(5):1051-1058.Li Cunbin,Zhang Jianye,Li Peng.Multi-objective optimization model of micro-grid operation considering cost,pollution discharge and risk[J].Proceedings of the CSEE,2015,35(5):1051-1058(in Chinese).
[26]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.