基于不确定随机网络理论的主动配电网多目标规划模型及其求解方法
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摘要
提出一种基于不确定随机网络理论的主动配电网多目标规划模型。将线路的不可用度和稳定性指标作为权值,建立不确定随机主动配电网络。基于该网络,模型以投资总成本、维修、运行和管理费用最小为经济目标,以搜寻在不确定随机网络下的最小生成树为第二目标。规划的决策变量不仅包含系统线路的升级与扩建,且考虑主动配电网中分组投切电容器、静止无功补偿器、电压调节器和分布式电源等主动管理设备的投资与模拟运行,即主动网络管理措施。为求解复杂的混合整数非线性模型,该文采用二阶锥松弛技术将原模型转换为混合整数二阶锥规划问题,并构造了三维不确定机会空间以求解多目标规划问题。通过改进33节点系统的仿真结果,验证了模型的有效性。
A multi-objective planning model of active distribution network based on uncertain network theory was proposed innovatively in this paper. The unavailability and stability index of the feeders were taken as the weight value to model the uncertain random active distribution network. Based on this network, the model took the total costs of investment, maintenance, operation and management as the financial objective, and the second objective was to search the minimum spanning tree under uncertain random network. The planning decision variables not only included the upgrading and extension of distribution line, but also the investment and simulation operation of capacitor bank, static var compensator, voltage regulator and distribution generation were considered, which was namely active distribution management schemes. In order to solve the complex mixed integer nonlinear multiobjective model, the second order cone relaxation technique was used to transform the original model to the mixed integer second order cone programming problem, and the three-dimensional uncertain chance space was constructed to solve the multi-objective programming problem. The simulation results of the improved 33 node system verify the effectiveness of the model.
A multi-objective planning model of active distribution network based on uncertain network theory was proposed innovatively in this paper. The unavailability and stability index of the feeders were taken as the weight value to model the uncertain random active distribution network. Based on this network, the model took the total costs of investment, maintenance, operation and management as the financial objective, and the second objective was to search the minimum spanning tree under uncertain random network. The planning decision variables not only included the upgrading and extension of distribution line, but also the investment and simulation operation of capacitor bank, static var compensator, voltage regulator and distribution generation were considered, which was namely active distribution management schemes. In order to solve the complex mixed integer nonlinear multiobjective model, the second order cone relaxation technique was used to transform the original model to the mixed integer second order cone programming problem, and the three-dimensional uncertain chance space was constructed to solve the multi-objective programming problem. The simulation results of the improved 33 node system verify the effectiveness of the model.
引文
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[18]汪芳宗,王兆丰.基于混合整数二次锥规划方法的含分布式电源配电网优化重构方法[J].电力系统保护与控制,2016,44(24):24-30.Wang Fangzong,Wang Zhaofeng.An optimum reconfiguration method for distribution networks with DG based on mixed integer second-order cone programming[J].Power System Protection and Control,2016,44(24):24-30.
[19]Ravadanegh S N,Roshanagh R G.On optimal multistage electric power distribution networks expansion planning[J].International Journal of Electrical Power&Energy Systems,2014,54(1):487-497.
[20]Fang Xinli,Yang Qiang,Wang Jianhui,et al.Coordinated dispatch in multiple cooperative autonomous islanded microgrids[J].Applied Energy,2016,162:40-48.
[21]Liu Yuhan.Uncertain random variables:a mixture of uncertainty and randomness[J].Soft Computing,2013,17(4):625-634.
[22]Liu Baoding.Uncertain random graph and uncertain random network[J].Journal of Uncertain Systems,2014,8:3-12.
[23]Sheng Yuhong,Qin Zhongfeng,Shi Gang.Minimum spanning tree problem of uncertain random network[J].Journal of Intelligent Manufacturing,2017,28(3):565-574.
[24]Gao Xin,Jia Lifen,Kar S.Degree-constrained minimum spanning tree problem of uncertain random network[J].Journal of Ambient Intelligence&Humanized Computing,2017,8(5):747-757.
[25]Liu Baoding.Uncertainty theory[J].Studies in Computational Intelligence,2010,154(3):1-79.
[26]Ishii H,Shiode S,Nishida T,et al.Stochastic spanning tree problem[J].Discrete Applied Mathematics,1981,3(4):263-273.
[27]Mohd A N Z,Musirin I,Mohamad H.Fast voltage stability index(FVSI)based technique for congestion management assessment[J].Applied Mechanics&Materials,2015,793:49-53.
[28]Li Wenyuan,Zhou Jiaqi,Xie Kaigui,et al.Power system risk assessment using a hybrid method of fuzzy set and monte carlo simulation[J].IEEE Transactions on Power Systems,2008,23(2):336-343.
[29]王建,熊小伏,李哲,等.气象环境相关的输电线路故障时间分布特征及模拟[J].电力自动化设备,2016,36(3):109-114.Wang Jian,Xiong Xiaofu,Li Zhe,et al.Modeling of generalized load steady-state characteristics based on affinity propagation clustering algorithm and its application[J].Electric Power Automation Equipment,2016,36(3):109-114.
[30]Jabr R A,Singh R,Pal B C.Minimum loss network reconfiguration using mixed-integer convex programming[J].IEEE Transactions on Power Systems,2012,27(2):1106-1115.
[31]肖浩,裴玮,邓卫,等.分布式电源对配电网电压的影响分析及其优化控制策略[J].电工技术学报,2016,31(增刊1):203-213.Xiao Hao,Pei Wei,Deng Wei,et al.Analysis of the impact of distributed generation on distribution network voltage and its optimal control strategy[J].Transactions of China Electrotechnical Society,2016,31(S1):203-213.
[32]马草原,孙展展,尹志超,等.基于双重混合粒子群算法的配电网重构[J].电工技术学报,2016,31(11):120-128.Ma Caoyuan,Sun Zhanzhan,Yin Zhichao,et al.Reconfiguration of distribution network based on double hybrid particle swarm algorithm[J].Transactions of China Electrotechnical Society,2016,31(11):120-128.
[33]韩禹歆,陈来军,王召健,等.基于自适应步长ADMM的直流配电网分布式最优潮流[J].电工技术学报,2017,32(11):26-37.Han Yuxin,Chen Laijun,Wang Zhaojian,et al.Distributed optimal power flow in direct current distribution network based on alternative direction method of multipliers with dynamic step size[J].Transactions of China Electrotechnical Society,2017,32(11):26-37.
[34]高红均,刘俊勇.考虑不同类型DG和负荷建模的主动配电网协同规划[J].中国电机工程学报,2016,36(18):4911-4922.Gao Hongjun,Liu Junyong.Coordinated planning considering different types of DG and load in active distribution network[J].Proceedings of the CSEE,2016,36(18):4911-4922.
[2]张建华,曾博,张玉莹,等.主动配电网规划关键问题与研究展望[J].电工技术学报,2014,29(2):13-23.Zhang Jianhua,Zeng Bo,Zhang Yuying,et al.Key issues and research prospects of active distribution network planning[J].Transactions of China Electrotechnical Society,2014,29(2):13-23.
[3]高红均,刘俊勇,魏震波,等.主动配电网分层鲁棒规划模型及其求解方法[J].中国电机工程学报,2017,37(5):1389-1400.Gao Hongjun,Liu Junyong,Wei Zhenbo,et al.A bilevel robust planning model of active distribution network and its solution method[J].Proceedings of the CSEE,2017,37(5):1389-1400.
[4]马瑞,金艳,刘鸣春.基于机会约束规划的主动配电网分布式风光双层优化配置[J].电工技术学报,2016,31(3):145-154.Ma Rui,Jin Yan,Liu Mingchun.Bi-level optimal configuration of distributed wind and photovoltaic generations in active distribution network based on chance constrained programming[J].Transactions of China Electrotechnical Society,2016,31(3):145-154.
[5]李斌,吕林,刘友波,等.考虑光伏接入不确定性的主动配电网有功-无功可控资源优化配置[J].电网技术,2017,41(2):355-362.Li Bin,LüLin,Liu Youbo,et al.Optimal configuration of controllable active-reactive power resources in active distribution network considering photovoltaic access uncertainty[J].Power System Technology,2017,41(2):355-362.
[6]刘佳,徐谦,程浩忠,等.计及主动配电网转供能力的可再生电源双层优化规划[J].电工技术学报,2017,32(9):179-188.Liu Jia,Xu Qian,Cheng Haozhong,et al.Bi-level optimal renewable energy sources planning considering active distribution network Power Transfer capability[J].Transactions of China Electrotechnical Society,2017,32(9):179-188.
[7]李秀磊,耿光飞,季玉琦,等.主动配电网中储能和需求侧响应的联合优化规划[J].电网技术,2016,40(12):3803-3810.Li Xiulei,Geng Guangfei,Ji Yuqi,et al.Integrated optimal planning of energy storage and demand side response in active power distribution network[J].Power System Technology,2016,40(12):3803-3810.
[8]Jadidoleslam M,Ebrahimi A,Latify M A.Probabilistic transmission expansion planning to maximize the integration of wind power[J].Renewable Energy,2017,114:866-878.
[9]Shen Xinwei,Shahidehpour M,Zhu Shouzhen,et al.Multi-stage planning of active distribution networks considering the co-optimization of operation strategies[J].IEEE Transactions on Smart Grid,2018,9(2):1425-1433.
[10]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.Amixed 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.
[11]常垚,程林,李洪涛,等.基于半正定松弛最优潮流的主动配电网多源协调优化控制[J].电网技术,2016,40(8):2416-2422.Chang Yao,Cheng Lin,Li Hongtao,et al.Distribution system optimal power flow with various controllable sources based on semi-definite relaxation[J].Power System Technology,2016,40(8):2416-2422.
[12]Gao Hongjun,Liu Junyong,Wang Lingfeng.Robust coordinated optimization of active and reactive power in active distribution systems[J].IEEE Transactions on Smart Grid,2017,DOI:10.1109/TSG.2017.2657782.
[13]季玉琦,耿光飞,温渤婴,等.基于最优分割法的含DG配电网动态无功优化[J].电网技术,2017,41(8):2585-2592.Ji Yuqi,Geng Guangfei,Wen Boying,et al.Dynamic reactive power optimization in distribution network with DG based on optimal partition[J].Power System Technology,2017,41(8):2585-2592.
[14]邢海军,程浩忠,杨镜非,等.考虑多种主动管理策略的配电网扩展规划[J].电力系统自动化,2016,40(23):70-76.Xing Haijun,Cheng Haozhong,Yang Jingfei,et al.Distribution network expansion planning considering multiple active management strategies[J].Automation of Electric Power Systems,2016,40(23):70-76.
[15]张沈习,袁加妍,程浩忠,等.主动配电网中考虑需求侧管理和网络重构的分布式电源规划方法[J].中国电机工程学报,2016,36(增刊1):1-9.Zhang Shenxi,Yuan Jiayan,Cheng Haozhong,et al.Optimal distributed generation planning in active distribution network considering demand side management and network reconfiguration[J].Proceedings of the CSEE,2016,36(S1):1-9.
[16]张旭升,李瑞生,黄利军,等.基于分层储能的主动配电网需求响应控制策略研究及实现[J].电力系统保护与控制,2017,45(15):40-49.Zhang Xusheng,Li Ruisheng,Huang Lijun,et al.Research and application on demand response based on hierarchical power storage[J].Power System Protection and Control,2017,45(15):40-49
[17]高艺文,刘俊勇,雷成,等.考虑配电网结构变化的DG规划[J].电力系统保护与控制,2014,42(4):40-46.Gao Yiwen,Liu Junyong,Lei Cheng,et al.DGplanning considering the variation of the distribution network structure[J].Power System Protection and Control,2014,42(4):40-46.
[18]汪芳宗,王兆丰.基于混合整数二次锥规划方法的含分布式电源配电网优化重构方法[J].电力系统保护与控制,2016,44(24):24-30.Wang Fangzong,Wang Zhaofeng.An optimum reconfiguration method for distribution networks with DG based on mixed integer second-order cone programming[J].Power System Protection and Control,2016,44(24):24-30.
[19]Ravadanegh S N,Roshanagh R G.On optimal multistage electric power distribution networks expansion planning[J].International Journal of Electrical Power&Energy Systems,2014,54(1):487-497.
[20]Fang Xinli,Yang Qiang,Wang Jianhui,et al.Coordinated dispatch in multiple cooperative autonomous islanded microgrids[J].Applied Energy,2016,162:40-48.
[21]Liu Yuhan.Uncertain random variables:a mixture of uncertainty and randomness[J].Soft Computing,2013,17(4):625-634.
[22]Liu Baoding.Uncertain random graph and uncertain random network[J].Journal of Uncertain Systems,2014,8:3-12.
[23]Sheng Yuhong,Qin Zhongfeng,Shi Gang.Minimum spanning tree problem of uncertain random network[J].Journal of Intelligent Manufacturing,2017,28(3):565-574.
[24]Gao Xin,Jia Lifen,Kar S.Degree-constrained minimum spanning tree problem of uncertain random network[J].Journal of Ambient Intelligence&Humanized Computing,2017,8(5):747-757.
[25]Liu Baoding.Uncertainty theory[J].Studies in Computational Intelligence,2010,154(3):1-79.
[26]Ishii H,Shiode S,Nishida T,et al.Stochastic spanning tree problem[J].Discrete Applied Mathematics,1981,3(4):263-273.
[27]Mohd A N Z,Musirin I,Mohamad H.Fast voltage stability index(FVSI)based technique for congestion management assessment[J].Applied Mechanics&Materials,2015,793:49-53.
[28]Li Wenyuan,Zhou Jiaqi,Xie Kaigui,et al.Power system risk assessment using a hybrid method of fuzzy set and monte carlo simulation[J].IEEE Transactions on Power Systems,2008,23(2):336-343.
[29]王建,熊小伏,李哲,等.气象环境相关的输电线路故障时间分布特征及模拟[J].电力自动化设备,2016,36(3):109-114.Wang Jian,Xiong Xiaofu,Li Zhe,et al.Modeling of generalized load steady-state characteristics based on affinity propagation clustering algorithm and its application[J].Electric Power Automation Equipment,2016,36(3):109-114.
[30]Jabr R A,Singh R,Pal B C.Minimum loss network reconfiguration using mixed-integer convex programming[J].IEEE Transactions on Power Systems,2012,27(2):1106-1115.
[31]肖浩,裴玮,邓卫,等.分布式电源对配电网电压的影响分析及其优化控制策略[J].电工技术学报,2016,31(增刊1):203-213.Xiao Hao,Pei Wei,Deng Wei,et al.Analysis of the impact of distributed generation on distribution network voltage and its optimal control strategy[J].Transactions of China Electrotechnical Society,2016,31(S1):203-213.
[32]马草原,孙展展,尹志超,等.基于双重混合粒子群算法的配电网重构[J].电工技术学报,2016,31(11):120-128.Ma Caoyuan,Sun Zhanzhan,Yin Zhichao,et al.Reconfiguration of distribution network based on double hybrid particle swarm algorithm[J].Transactions of China Electrotechnical Society,2016,31(11):120-128.
[33]韩禹歆,陈来军,王召健,等.基于自适应步长ADMM的直流配电网分布式最优潮流[J].电工技术学报,2017,32(11):26-37.Han Yuxin,Chen Laijun,Wang Zhaojian,et al.Distributed optimal power flow in direct current distribution network based on alternative direction method of multipliers with dynamic step size[J].Transactions of China Electrotechnical Society,2017,32(11):26-37.
[34]高红均,刘俊勇.考虑不同类型DG和负荷建模的主动配电网协同规划[J].中国电机工程学报,2016,36(18):4911-4922.Gao Hongjun,Liu Junyong.Coordinated planning considering different types of DG and load in active distribution network[J].Proceedings of the CSEE,2016,36(18):4911-4922.