基于随机优化理论的输电网规划研究综述Overview of Transmission Network Expansion Planning Based on Stochastic Optimization
张衡;程浩忠;曾平良;张建平;陆建忠;李聪;
摘要(Abstract):
以风、光、水为代表的可再生能源大规模并网环境下,负荷增长预测的误差以及输变电设备的随机故障等,使电力系统面临复杂的不确定性。如何在规划阶段模拟这些随机因素,提高规划方案的可操作性,是电网规划人员亟需解决的问题。从不确定因素的处理方式入手,系统地阐述了随机优化理论在输电网规划中的应用。以期望值、多场景及机会约束模型为代表,从其特征、处理方式等角度分析了各自的优缺点及研究方向。在此基础上,总结了输电网规划中2类重要的求解方法及常用的凸优化求解器。最后,结合当前电网规划的背景及发展趋势,展望了未来输电网规划模型中应该考虑及注意的问题。
关键词(KeyWords): 可再生能源;不确定因素;输电网规划;随机优化理论;凸优化
基金项目(Foundation): 国家重点基础研发项目(2016YFB0900102);; 国家自然科学基金重点项目(51337005)~~
作者(Author): 张衡;程浩忠;曾平良;张建平;陆建忠;李聪;
Email:
DOI: 10.13335/j.1000-3673.pst.2017.1176
参考文献(References):
- [1]Moreira A,Pozo D,Street A,et al.Reliable renewable generation and transmission expansion planning:co-optimizing system’s resources for meeting renewable targets[J].IEEE Transactions on Power Systems,2017,32(4):3246-3257.
- [2]U.S Department of Energy.20%wind energy by 2030:increasing wind energy’s contribution to U.S.electricity supply[EB/OL].[2008-07].http://www.nrel.gov/docs/fy08osti/41869.pdf.
- [3]国家发展和改革委员会能源研究所.中国2050高比例可再生能源发展情景暨路径研究[R].北京:国家发展和改革委员会能源研究所,2015.
- [4]刘振亚.全球能源互联网[M].北京:中国电力出版社,2015:1-24.
- [5]程浩忠.电力系统规划[M].北京:中国电力出版社,2014:6-13.
- [6]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(29):1592-1601.
- [7]曹一家,曹丽华,黎灿兵,等.考虑大停电风险的输电网扩展规划模型和算法[J].中国电机工程学报,2014,34(1):138-145.Cao Yijia,Cao Lihua,Li Canbing,et al.A model and algorithm for transmission expansion planning considering the blackout risk[J].Proceedings of the CSEE,2014,34(1):138-145(in Chinese).
- [8]Murugan P,Kannan S,Baskar S.Application of NSGA-II algorithm to single-objective transmission constrained generation expansion planning[J].IEEE Transactions on Power Systems,2009,24(4):1790-1797.
- [9]Qiu J,Dong Z Y,Zhao J H,et al.Multi-stage flexible expansion co-planning under uncertainties in a combined electricity and gas market[J].IEEE Transactions on Power Systems,2015,30(4):2119-2129.
- [10]Ugranli F,Karatepe E.Transmission expansion planning for wind turbine integrated power systems considering contingency[J].IEEE Transactions on Power Systems,2014,31(2):350-355.
- [11]Majidi-Qadikolai M,Baldick R.Stochastic transmission capacity expansion planning with special scenario selection for integrating N-1contingency analysis[J].IEEE Transactions on Power Systems,2016,31(6):4901-4912.
- [12]Majidi-Qadikolai M,Baldick R.Integration of contingency analysis with systematic transmission capacity expansion planning:ERCOT case study[J].IEEE Transactions on Power Systems,2016,31(3):2234-2245.
- [13]柳璐,程浩忠,马则良,等.考虑全寿命周期成本的输电网多目标规划[J].中国电机工程学报,2012,32(22):46-54.Liu Lu,Cheng Haozhong,Ma Zeliang,et al.Multi-objective transmission expansion planning considering life cycle cost[J].Proceedings of the CSEE,2012,32(22):46-54(in Chinese).
- [14]王一,程浩忠,胡泽春,等.计及过负荷风险的输电网多目标期望值规划[J].中国电机工程学报,2009,29(1):21-27.Wang Yi,Cheng Haozhong,Hu Zechun,et al.Multi-objective transmission expected value planning considering risk of overloading[J].Proceedings of the CSEE,2009,29(1):21-27(in Chinese).
- [15]Mavalizadeh H,Ahmadi A,Heidari A.Probabilistic multi-objective generation and transmission expansion planning problem using normal boundary intersection[J].IET Generation Transmission&Distribution,2014,9(6):560-570.
- [16]Li C,Dong Z,Chen G,et al.Flexible transmission expansion planning associated with large-scale wind farms integration considering demand response[J].IET Generation Transmission&Distribution,2015,9(15):2276-2283.
- [17]路志英,葛少云,王成山.基于粒子群优化的加权伏罗诺伊图变电站规划[J].中国电机工程学报,2009,29(16):35-41.Lu Zhiying,Ge Shaoyun,Wang Chengshan.Substation location planning of the weighted voronoi diagram based on particle swarm optimization algorithm[J].Proceedings of the CSEE,2009,29(16):35-41(in Chinese).
- [18]欧阳武,程浩忠,张秀彬,等.考虑分布式电源调峰的配电网规划[J].电力系统自动化,2008,32(22):12-15.Ouyang Wu,Cheng Haozhong,Zhang Xiubin,et al.Distribution network planning considering DG for peak shaving[J].Automation of Electric Power Systems,2008,32(22):12-15(in Chinese).
- [19]Zhang X,Chen W,Dai C,et al.Dynamic multi-group self-adaptive differential evolution algorithm for reactive power optimization[J].International Journal of Electrical Power&Energy Systems,2010,32(5):351-357.
- [20]Luo F,Meng K,Dong Z Y,et al.Coordinated operational planning for wind farm with battery energy storage system[J].IEEE Transactions on Sustainable Energy,2015,6(1):253-262.
- [21]Bruninx K,Delarue E.Endogenous probabilistic reserve sizing and allocation in unit commitment models:cost-effective,reliable and fast[J].IEEE Transactions on Power Systems,2017,32(4):2593-2603.
- [22]Ziaee O,Choobineh F.Optimal location-allocation of TCSCS and transmission switch placement under high penetration of wind power[J].IEEE Transactions on Power Systems,2017,32(4):3006-3014.
- [23]Qiu T,Xu B,Wang Y,et al.Stochastic multi-stage co-planning of transmission expansion and energy storage[J].IEEE Transactions on Power Systems,2017,32(1):643-651.
- [24]Hong S,Cheng H,Zeng P,et al.Composite generation and transmission expansion planning with second order conic relaxation of AC power flow[C]//IEEE PES Asia-Pacific Power and Energy Engineering Conference.Xi’an,China:IEEE PES,2016:1688-1693.
- [25]Villumsen J C,Bronmo G,Philpott A B.Line capacity expansion and transmission switching in power systems with large-scale wind power[J].IEEE Transactions on Power Systems,2013,28(2):731-739.
- [26]Koltsaklis N E,Georgiadis M C,Yan J.A multi-period,multi-regional generation expansion planning model incorporating unit commitment constraints[J].Applied Energy,2015(158):310-331.
- [27]Tang L,Ferris M C.A hierarchical framework for long-term power planning models[J].IEEE Transactions on Power Systems,2015,30(1):46-56.
- [28]Ugranli F,Karatepe E,Nielsen A H.MILP approach for bilevel transmission and reactive power planning considering wind curtailment[J].IEEE Transactions on Power Systems,2017,32(1):652-660.
- [29]Garver L L.Transmission network estimation using linear programming[J].IEEE Transactions on Power Apparatus&Systems,1970,89(7):1688-1697.
- [30]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(in Chinese).
- [31]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):8-15.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):8-15(in Chinese).
- [32]Chatthaworn R,Chaitusaney S.Improving method of robust transmission network expansion planning considering intermittent renewable energy generation and loads[J].IET Generation Transmission&Distribution,2015,9(13):1621-1627.
- [33]Rahmani M,Romero R,Rider M J.Strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem[J].IEEE Transactions on Power Systems,2013,28(3):2164-2173.
- [34]Yu H,Chung C Y,Wong K P,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.
- [35]范松丽,艾芊,贺兴.基于机会约束规划的虚拟电厂调度风险分析[J].中国电机工程学报,2015,35(16):4025-4034.Fan Songli,Ai Qian,He Xing.Risk analysis on dispatch of virtual power plant based on chance constrained programming[J].Proceedings of the CSEE,2015,35(16):4025-4034(in Chinese).
- [36]陈霜,孙国强,卫志农,等.计及碳排放的含风电场电力系统随机可用输电能力协调决策[J].电网技术,2016,40(2):405-411.Chen Shuang,Sun Guoqiang,Wei Zhinong,et al.Coordinated stochastic available transfer capability decision-making considering carbon emission with wind farm integration[J].Power System Technology,2016,40(2):405-411(in Chinese).
- [37]杨燕,文福拴,李力,等.计及风险控制策略的电力系统可用输电容量决策[J].电力系统自动化,2012,36(4):50-55.Yang Yan,Wen Fushuan,Li Li,et al.Available transfer capability decision-making with risk-control strategies[J].Automation of Electric Power Systems,2012,36(4):50-55(in Chinese).
- [38]孙国强,李逸驰,向育鹏,等.计及风速时空相关性的含风电场电力系统动态随机最优潮流计算[J].中国电机工程学报,2015,35(17):4308-4317.Sun Guoqiang,Li Yichi,Xiang Yupeng,et al.Dynamic stochastic optimal power flow of wind integrated power system considering temporal and spatial correlation of wind speed[J].Proceedings of the CSEE,2015,35(17):4308-4317(in Chinese).
- [39]Zhang Y,Shen S,Mathieu J.Distributionally robust chance-constrained optimal power flow with uncertain renewables and uncertain reserves provided by loads[J].IEEE Transactions on Power Systems,2017,32(2):1378-1388.
- [40]Wu Z,Zeng P,Zhang X P,et al.A solution to the chance-constrained two-stage stochastic program for unit commitment with wind energy integration[J].IEEE Transactions on Power Systems,2016,31(6):4185-4195.
- [41]Fang S,Cheng H,Xu G,et al.Stochastic optimal reactive power reserve dispatch considering voltage control areas[J].International Transactions on Electrical Energy Systems,2017,27(3):2269-2281.
- [42]Zou B,Xiao Q.Solving probabilistic optimal power flow problem using quasi Monte Carlo method and ninth-order polynomial normal transformation[J].IEEE Transactions on Power Systems,2014,29(1):300-306.
- [43]Hajian M,Rosehart W D,Zareipour H.Probabilistic power flow by monte carlo simulation with Latin supercube sampling[J].IEEE Transactions on Power Systems,2013,28(2):1550-1559.
- [44]Fan M,Vittal V,Heydt G T,et al.Probabilistic power flow analysis with generation dispatch including photovoltaic resources[J].IEEE Transactions on Power Systems,2013,28(2):1797-1805.
- [45]Su C L.Probabilistic load-flow computation using point estimate method[J].IEEE Transactions on Power Systems,2005,20(4):1843-1851.
- [46]Morales J M,Pérez-Ruiz J.Point estimate schemes to solve the probabilistic power flow[J].IEEE Transactions on Power Systems,2007,22(4):1594-1601.
- [47]石东源,蔡德福,陈金富,等.计及输入变量相关性的半不变量法概率潮流计算[J].中国电机工程学报,2012,32(28):104-113.Shi Dongyuan,Cai Defu,Chen Jinfu,et al.Probabilistic load flow calculation based on cumulant method considering correlation between input variables[J].Proceedings of the CSEE,2012,32(28):104-113(in Chinese).
- [48]甘磊,谷纪亭,钟宇军,等.考虑多形态间歇性电源集中接入的输电网随机双层规划方法[J].电网技术,2016,40(10):3125-3131.Gan Lei,Gu Jiting,Zhong Yujun,et al.Bi-level stochastic planning method of transmission networks with multiple centralized intermittent generations[J].Power System Technology,2016,40(10):3125-3131(in Chinese).
- [49]葛晓琳,张粒子,舒隽.风水火系统长期优化调度方法[J].中国电机工程学报,2013,33(34):153-161.Ge Xiaolin,Zhang Lizi,Shu Jun.A long-term optimal scheduling method for wind-hydro-thermal power systems[J].Proceedings of the CSEE,2013,33(34):153-161(in Chinese).
- [50]Dehghanian P,Kezunovic M.Probabilistic decision making for the bulk power system optimal topology control[J].IEEE Transactions on Smart Grid,2016,7(4):2071-2081.
- [51]梁浩,张沛,贾宏杰,等.基于概率潮流的未来输电线路经济评估[J].电网技术,2014,38(3):675-680.Liang Hao,Zhang Pei,Jia Hongjie,et al.Economic assessment of future transmission line base on probabilistic power flow[J].Power System Technology,2014,38(3):675-680(in Chinese).
- [52]Roh J H,Shahidehpour M,Wu L.Market-based generation and transmission planning with uncertainties[J].IEEE Transactions on Power Systems,2009,24(3):1587-1598.
- [53]Park J B,Park Y M,Won J R,et al.An improved genetic algorithm for generation expansion planning[J].IEEE Transactions on Power Systems,2000,15(3):916-922.
- [54]Hemmati R,Hooshmand R A,Khodabakhshian A.Coordinated generation and transmission expansion planning in deregulated electricity market considering wind farms[J].Renewable Energy,2016(85):620-630.
- [55]Maghouli P,Hosseini S H,Buygi M O,et al.A multi-objective framework for transmission expansion planning in deregulated environments[J].IEEE Transactions on Power Systems,2009,24(2):1051-1061.
- [56]Karimi E,Ebrahimi A.Inclusion of blackouts risk in probabilistic transmission expansion planning by a multi-objective framework[J].IEEE Transactions on Power Systems,2015,30(5):2810-2817.
- [57]Barati F,Seifi H,Sadegh Sepasian M,et al.Multi-period integrated framework of generation,transmission and natural gas grid expansion planning for large-scale systems[J].IEEE Transactions on Power Systems,2014,30(5):2527-2537.
- [58]Hui Z,Heydt G T,Vittal V,et al.An improved network model for transmission expansion planning considering reactive power and network losses[J].IEEE Transactions on Power Systems,2013,28(3):3471-3479.
- [59]Choi J,El-Keib A A,Tran T.A fuzzy branch and bound-based transmission system expansion planning for the highest satisfaction level of the decision maker[J].IEEE Transactions on Power Systems,2005,20(1):476-484.
- [60]Romero R,Asada E N,Carreno E,et al.Constructive heuristic algorithm in branch-and-bound structure applied to transmission network expansion planning[J].IET Generation Transmission&Distribution,2007,1(2):318-323.
- [61]Zhang X,Shahidehpour M,Alabdulwahab A S,et al.Security-constrained co-optimization planning of electricity and natural gas transportation infrastructures[J].IEEE Transactions on Power Systems,2015,30(6):2984-2993.
- [62]Binato S,Pereira M V F,Granville S.A new benders decomposition approach to solve transmission network design problems[Power Point presentation][J].IEEE Transactions on Power Systems,2001,16(2):235-240.
- [63]Street A,Brigatto A,Valladao D M.Co-optimization of energy and ancillary services for hydrothermal operation planning under a general security criterion[J/OL].IEEE Transactions on Power Systems,http://ieeexplore.ieee.org/document/7862252/.[2017-02-22].DOI:10.1109/TPWRS.2017.2672555.
- [64]Gao H,Liu J,Wang L.Robust coordinated optimization of active and reactive power in active distribution systems[J/OL].IEEE Transactions on Smart Grid,http://ieeexplore.ieee.org/document/7833212/.[2017-01-25].DOI:10.1109/TSG.2017.2657782.
- [65]Teimourzadeh S,Aminifar F.MILP formulation for transmission expansion planning with short-circuit level constraints[J].IEEE Transactions on Power Systems,2015,31(4):1-10.
- [66]Pozo D,Sauma E E,Contreras J.A three-level static MILP model for generation and transmission expansion planning[J].IEEE Transactions on Power Systems,2013,28(1):202-210.
- [67]?zdemir?,Munoz F D,Ho J L,et al.Economic analysis of transmission expansion planning with price-responsive demand and quadratic losses by successive LP[J].IEEE Transactions on Power Systems,2016,31(2):1096-1107.
- [68]Camponogara E,Campos d A K,Hardt R.Piecewise-linear approximations for a non-linear transmission expansion planning problem[J].IET Generation Transmission&Distribution,2015,9(12):1235-1244.
- [69]Lei J,An T,Du Z,et al.A general unified AC/DC power flow algorithm with MTDC[J].IEEE Transactions on Power Systems,2017,32(4):2837-2846.
- [70]Beerten J,Cole S,Belmans R.Generalized steady-state VSC MTDC model for sequential AC/DC power flow algorithms[J].IEEE Transactions on Power Systems,2012,27(2):821-829.
- [71]鲁宗相,李海波,乔颖.含高比例可再生能源电力系统灵活性规划及挑战[J].电力系统自动化,2016,40(13):147-158.Lu Zongxiang,Li Haibo,Qiao Ying.Power system flexibility planning and challenges considering high proportion of renewable energy[J].Automation of Electric Power Systems,2016,40(13):147-158(in Chinese).