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Overview on Theory Analysis and Application of Distributionally Robust OptimizationMethod in Power System
- Automation of Electric Power Systems Vol. 44, Issue 14, Pages: 179-191(2020)
- 作者机构：
四川大学电气工程学院，四川省 成都市 610065
- 作者简介：
- 基金信息：National Natural Science Foundation of China;the Fundamental Research Funds for the Central Universities
DOI：10.7500/AEPS20191022002
CLC：Received：22 October 2019，
Revised：2020-02-05，
Published Online：14 May 2020，
Published：25 July 2020
- 稿件说明：
移动端阅览
贺帅佳,阮贺彬,高红均等.分布鲁棒优化方法在电力系统中的理论分析与应用综述[J].电力系统自动化,2020,44(14):179-191.
HE Shuaijia,RUAN Hebin,GAO Hongjun,et al.Overview on Theory Analysis and Application of Distributionally Robust OptimizationMethod in Power System[J].Automation of Electric Power Systems,2020,44(14):179-191.
贺帅佳,阮贺彬,高红均等.分布鲁棒优化方法在电力系统中的理论分析与应用综述[J].电力系统自动化,2020,44(14):179-191. DOI： 10.7500/AEPS20191022002.
HE Shuaijia,RUAN Hebin,GAO Hongjun,et al.Overview on Theory Analysis and Application of Distributionally Robust OptimizationMethod in Power System[J].Automation of Electric Power Systems,2020,44(14):179-191. DOI： 10.7500/AEPS20191022002.
摘要
清洁能源、电价等不确定因素对电力系统的规划运行有着重要影响，而分布鲁棒优化(DRO)方法因结合了随机优化和鲁棒优化在处理不确定性方面的优点逐渐受到学者们的关注，文中对DRO方法在电力系统领域的应用情况进行综述。首先，阐述了DRO方法的特点，并与其他不确定性处理方法进行了对比分析。其次，介绍了不同类型的DRO方法在电力系统中的应用现状，并分析了各种DRO方法（包括概率密度、矩信息两大类及基于这两大类的分布鲁棒机会约束方法）的优缺点。最后，对DRO方法在电力系统领域待研究的方向进行了总结与展望。
Abstract
The uncertainty factors such as clean energy and electricity price have important influence on the planning and operation of power system. Distributionally robust optimization (DRO) method has received attention from researchers since it combines the advantages of stochastic optimization and robust optimization in dealing with uncertainties. This paper reviews the application of DRO method in power system. Firstly
the characteristics of DRO method are described
and it is compared and analyzed with other methods for coping with uncertainties. Secondly
the application status of different types of DRO methods in power system is introduced. Besides
advantages and disadvantages of various DRO methods are analyzed including two classes of probability density
moment information and distributed robust chance constrained method based on these two classes. Finally
the research directions of DRO method in the field of power system are summarized and prospected.
关键词
Keywords
references
李鹏 , 何帅 , 韩鹏飞 , 等 . 基于长短期记忆的实时电价条件下智能电网短期负荷预测 [J]. 电网技术 , 2018 ， 42 ( 12 ): 4045 - 4052 .
LI Peng , HE Shuai , HAN Pengfei , et al . Short-term load forecasting of smart grid based on long-short-term memory recurrent neural networks in condition of real-time electricity price [J]. Power System Technology , 2018 , 42 ( 12 ): 4045 - 4052 .
李博嵩 , 王旭 , 蒋传文 , 等 . 广泛负荷聚集商市场策略建模及风险效益分析 [J]. 电力系统自动化 , 2018 ， 42 ( 1 ): 119 - 126 .
LI Bosong , WANG Xu , JIANG Chuanwen , et al . Market strategy modeling and risk profit analysis of demand-side resource aggregator [J]. Automation of Electric Power Systems , 2018 , 42 ( 1 ): 119 - 126 .
李哲 , 王成福 , 梁军 , 等 . 计及风电不确定性的电-气-热综合能源系统扩展规划方法 [J]. 电网技术 , 2018 ， 42 ( 11 ): 3477 - 3485 .
LI Zhe , WANG Chengfu , LIANG Jun , et al . Expansion planning method of integrated energy system considering uncertainty of wind power [J]. Power System Technology , 2018 ， 42 ( 11 ): 3477 - 3485 .
王晗 , 严正 , 徐潇源 , 等 . 计及可再生能源不确定性的孤岛微电网概率潮流计算 [J]. 电力系统自动化 , 2018 ， 42 ( 1 ): 110 - 117 .
WANG Han , YAN Zheng , XU Xiaoyuan , et al . Probabilistic power flow calculation of islanded microgrid considering uncertainty of renewable energy [J]. Automation of Electric Power Systems , 2018 ， 42 ( 1 ): 110 - 117 .
马春艳 , 董春发 ， 吕志鹏 ， 等 . 计及随机因素的商业型虚拟发电厂短期交易与优化运行策略 [J]. 电网技术 , 2016 , 40 ( 5 ): 1543 - 1549 .
MA Chunyan , DONG Chunfa , LÜ Zhipeng , et al . Short-term trading and optimal operation strategy for commercial virtual power plant considering uncertainties [J]. Power System Technology , 2016 , 40 ( 5 ): 1543 - 1549 .
李健华 , 刘继春 , 陈雪 , 等 . 可再生能源的多能互补发电系统容量配置方法 [J]. 电网技术 , 2019 , 43 ( 12 ): 4387 - 4397 .
LI Jianhua , LIU Jichun , CHEN Xue , et al . Capacity allocation of multi-energy complementary system including renewable energy [J]. Power System Technology , 2019 , 43 ( 12 ): 4387 - 4397 .
AHMED H M A , ELTANTAWY A B , SALAMA M A . A planning approach for the network configuration of AC-DC hybrid distribution systems [J]. IEEE Transactions on Smart Grid , 2018 , 9 ( 3 ): 2203 - 2213 .
LI J , LI Z Y , LIU F , et al . Robust coordinated transmission and generation expansion planning considering ramping requirements and construction periods [J]. IEEE Transactions on Power Systems , 2018 , 33 ( 1 ): 268 - 280 .
AMJADY N , ATTARHA A , DEHGHAN S , et al . Adaptive robust expansion planning for a distribution network with DERs [J]. IEEE Transactions on Power Systems , 2018 , 33 ( 2 ): 1698 - 1715 .
孙国强 , 袁智 , 许晓慧 , 等 , 碳排放约束下虚拟电厂鲁棒优化竞标模型 [J]. 电力自动化设备 , 2017 , 37 ( 2 ): 97 - 103 .
SUN Guoqiang , YUAN Zhi , XU Xiaohui , et al . Bidding model based on robust optimization for virtual power plant under carbon emission constraint [J]. Electric Power Automation Equipment , 2017 , 37 ( 2 ): 97 - 103 .
张新松 ， 袁越 ， 茅靖峰 ， 等 . 基于蒙特卡洛模拟的电池储能系统容量优化配置 [J]. 电力自动化设备 , 2017 , 37 ( 4 ): 82 - 88 .
ZHANG Xinsong , YUAN Yue , MAO Jingfeng , et al . BESS capacity optimization based on Monte Carlo simulation [J]. Electric Power Automation Equipment , 2017 , 37 ( 4 ): 82 - 88 .
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 ( Supplement 1 ): 1 - 9 .
杨昕然 , 吕林 , 许立雄 , 等 . 考虑弹性裕度的城市输电网安全概率评估 [J]. 电网技术 , 2019 , 43 ( 2 ): 389 - 397 .
YANG Xinran , LÜ Lin , XU Lixiong , et al . Probabilistic security evaluation of urban transmission considering elastic margin [J]. Power System Technology , 2019 , 43 ( 2 ): 389 - 397 .
王高琴 , 沈炯 , 李益国 . 基于聚类和贝叶斯推断的市场出清电价离散概率分布预测 [J]. 中国电机工程学报 , 2007 , 27 ( 34 ): 90 - 95 .
WANG Gaoqin , SHEN Jiong , LI Yiguo . Forecasting of MCP’s discrete probability distribution based on clustering and Bayesian method [J]. Proceedings of the CSEE , 2007 , 27 ( 34 ): 90 - 95 .
余爽 , 卫志农 , 孙国强 , 等 . 考虑不确定性因素的虚拟电厂竞标模型 [J]. 电力系统自动化 , 2014 , 38 ( 22 ): 43 - 49 .
YU Shuang , WEI Zhinong , SUN Guoqiang , et al . Analysis of dynamic reliability of transformer based on monitoring data of oil chromatography [J]. Automation of Electric Power Systems , 2014 , 38 ( 22 ): 43 - 49 .
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 ): 127 - 139 .
GAO Hongjun , LIU Junyong , WEI Zhenbo , et al . A bi-level robust planning model of active distribution network and its solution method [J]. Proceedings of the CSEE , 2017 , 37 ( 5 ): 127 - 139 .
杨楠 , 董邦天 , 黄禹 , 等 . 考虑不确定性和多主体博弈的增量配电网源网荷协同规划方法 [J]. 中国电机工程学报 , 2019 , 39 ( 9 ): 2689 - 2702 .
YANG Nan , DONG Bangtian , HUANG Yu , et al . Incremental distribution network source-load collaborative planning method considering uncertainty and multi-agent game [J]. Proceedings of the CSEE , 2019 , 39 ( 9 ): 2689 - 2702 .
张衡 , 程浩忠 , 曾平良 , 等 . 基于随机优化理论的输电网规划研究综述 [J]. 电网技术 , 2017 , 42 ( 10 ): 32 - 40 .
ZHANG Heng , CHENG Haozhong , ZENG Pingliang , et al . Overview of transmission network expansion planning based on stochastic optimization [J]. Power System Technology , 2017 , 42 ( 10 ): 32 - 40 .
朱光远 , 林济铿 , 罗治强 , 等 . 鲁棒优化在电力系统发电计划中的应用综述 [J]. 中国电机工程学报 , 2017 , 37 ( 20 ): 5881 - 5892 .
ZHU Guangyuan , LIN Jikeng , LUO Zhiqiang , et al . Robust optimization for generation scheduling in power systems: a review [J]. Proceedings of the CSEE , 2017 , 37 ( 20 ): 5881 - 5892 .
杨甲甲 , 赵俊华 , 文福拴 , 等 . 含电动汽车和风电机组的虚拟发电厂竞价策略 [J]. 电力系统自动化 , 2014 , 38 ( 13 ): 92 - 102 .
YANG Jiajia , ZHAO Junhua , WEN Fushuan , et al . Development of bidding strategies for virtual power plants considering uncertain outputs from plug-in electric vehicles and wind generators [J]. Automation of Electric Power Systems , 2014 , 38 ( 13 ): 92 - 102 .
贺帅佳 , 高红均 , 刘俊勇 , 等 . 计及需求响应柔性调节的分布鲁棒DG优化配置 [J]. 中国电机工程学报 , 2019 , 39 ( 8 ): 2253 - 2264 .
HE Shuaijia , GAO Hongjun , LIU Junyong , et al . Distributionally robust optimal DG allocation model considering flexible adjustment of demand response [J]. Proceedings of the CSEE , 2019 , 39 ( 8 ): 2253 - 2264 .
周任军 ， 任青青 ， 敏雄帮 ， 等 . 基于改进矩不确定分布鲁棒优化算法的多机调频比例决策 [J]. 电力自动化设备 ， 2019 , 39 ( 6 ): 1 - 8 .
ZHOU Renjun , REN Qingqing , MIN Xiongbang , et al . Frequency regulation ratio decision-making of multi-generator based on modified distributional robust optimization under moment uncertainty [J]. Electric Power Automation Equipment , 2019 , 39 ( 6 ): 1 - 8 .
XIONG P , JIRUTITIJAROEN P , SINGH C . A distributionally robust optimization model for unit commitment considering uncertain wind power generation [J]. IEEE Transactions on Power Systems , 2017 , 32 ( 1 ): 39 - 49 .
税月 , 刘俊勇 , 高红均 , 等 . 考虑风电不确定性的电气能源系统两阶段分布鲁棒协同调度 [J]. 电力系统自动化 , 2018 , 42 ( 13 ): 43 - 50 .
SHUI Yue , LIU Junyong , GAO Hongjun , et al . Two-stage distributed robust cooperative dispatch for integrated electricity and natural gas energy systems considering uncertainty of wind power [J]. Automation of Electric Power Systems , 2018 , 42 ( 13 ): 43 - 50 .
阮贺彬 , 高红均 , 刘俊勇 , 等 . 考虑DG无功支撑和开关重构的主动配电网分布鲁棒无功优化模型 [J]. 中国电机工程学报 , 2019 , 39 ( 3 ): 685 - 695 .
RUAN Hebin , GAO Hongjun , LIU Junyong , et al . A distributionally robust reactive power optimization model for active distribution network considering reactive power support of DG and switch reconfiguration [J]. Proceedings of the CSEE , 2019 , 39 ( 3 ): 685 - 695 .
SCARF H . A min-max solution of an inventory problem [J]. Studies in the Mathematical Theory of Inventory and Production , 1958 , 25 ( 2 ): 201 - 209 .
BERTSIMAS D , POPESCU I . Optimal inequalities in probability theory: a convex optimization approach [J]. SIAM Journal on Optimization , 2005 , 15 ( 3 ): 780 - 804 .
KLABJANl D , SIMCHI-LEVI D , SONG M . Robust stochastic lot-sizing by means of histograms [J]. Production and Operations Management , 2013 , 22 ( 3 ): 691 - 710 .
LANDAU H . Moments in mathematics [EB/OL]. [ 2020-02-01 ]. http://www.ams.org/books/psapm/037/ http://www.ams.org/books/psapm/037/ .
DELAGE E , YE Y . Distributionally robust optimization under moment uncertainty with application to data-driven problems [J]. Operations Research , 2010 , 58 ( 3 ): 595 - 612 .
BERTSIMAS D , NATARAJAN K , TEO C . Probabilistic combinatorial optimization: moments, semidefinite programming, and asymptotic bounds [J]. SIAM Journal on Optimization , 2004 , 15 ( 1 ): 185 - 209 .
BERTSIMAS D , NATARAJAN K , TEO C . Persistence in discrete optimization under data uncertainty [J]. Math Program , 2006 , 108 ( 2 ): 251 - 274
BERTSIMAS D , DOAN X , NATARAJAN K , et al . Models for minimax stochastic linear optimization problems with risk aversion [J]. Mathematics of Operation Research , 2010 , 35 ( 3 ): 580 - 602 .
GALLEGO G , MOON I . The distribution-free newsboy problem—review and extensions [J]. Journal of the Operational Research Society , 1993 , 44 ( 8 ): 825 - 834 .
NATARAJAN K , SIM M , UICHANCO J . Asymmetry and ambiguity in newsvendor models [J]. Management Science , 2018 , 64 ( 7 ): 3146 - 3167 .
ROSS S , BARMISH B . Distributionally robust gain analysis for systems containing complex uncertainty [C]// IEEE Conference on Decision and Control, December 4-7 , 2001 , Orlando , USA .
HE X , WU Y C . Probabilistic QoS constrained robust downlink multiuser MIMO transceiver design with arbitrarily distributed channel uncertainty [J]. IEEE Transactions on Wireless Communications , 2013 , 12 ( 12 ): 6292 - 6302 .
BAI M , YANG Z . Distributionally robust self-scheduling optimization with CO 2 emissions constraints under uncertainty of prices [J]. Journal of Applied Mathematics , 2014 ( 12 ): 1 - 7 .
YANG Y , WU W C . A distributionally robust optimization model for real-time power dispatch in distribution networks [J]. IEEE Transactions on Smart Grid , 2019 , 10 ( 4 ): 3743 - 3752 .
王海冰 , 戚永志 , 王承民 , 等 . 考虑柔性负荷的两阶段随机优化调度模型 [J]. 电网技术 , 2018 , 42 ( 11 ): 3669 - 3675 .
WANG Haibing , QI Yongzhi , WANG Chengmin , et al . Two-stage stochastic optimal scheduling model considering flexible load [J]. Power System Technology , 2018 , 42 ( 11 ): 3669 - 3675 .
范刘洋 , 汪可友 , 李国杰 , 等 . 计及风电时间相关性的鲁棒机组组合 [J]. 电力系统自动化 , 2018 , 42 ( 1 ): 91 - 97 .
FAN Liuyang , WANG Keyou , LI Guojie , et al . Robust unit commitment considering temporal correlation of wind power [J]. Automation of Electric Power Systems , 2018 , 42 ( 1 ): 91 - 97 .
蔡霁霖 , 徐青山 , 王旭东 . 基于加速时序蒙特卡洛法的风电场置信容量评估 [J]. 电力系统自动化 , 2018 , 42 ( 5 ): 86 - 93 .
CAI Qilin , XU Qingshan , WANG Xudong . Evaluation of credit capacity for wind farms based on accelerated sequential Monte Carlo method [J]. Automation of Electric Power Systems , 2018 , 42 ( 5 ): 86 - 93 .
吴玮坪 , 胡泽春 , 宋永华 . 结合随机规划和序贯蒙特卡洛模拟的风电场储能优化配置方法 [J]. 电网技术 , 2018 , 42 ( 4 ): 1055 - 1062 .
WU Weiping , HU Zechun , SONG Yonghua . Optimal sizing of energy storage system for wind farms combining stochastic programming and sequential Monte Carlo simulation [J]. Power System Technology , 2018 , 42 ( 4 ): 1055 - 1062 .
张衡 , 程浩忠 , 柳璐 , 等 . 基于点估计法随机潮流的输电网多阶段规划研究 [J]. 电网技术 , 2018 , 42 ( 10 ): 3204 - 3211 .
ZHANG Heng , CHENG Haozhong , LIU Lu , et al . Research on multistage transmission network expansion planning using point estimation method based on stochastic power flow [J]. Power System Technology , 2018 , 42 ( 10 ): 3204 - 3211 .
范婷婷 , 杜松怀 , 刘科研 , 等 . 计及输入变量相关性的有源配电网可靠性概率评估三点估计法 [J]. 电网技术 , 2017 , 41 ( 7 ): 289 - 296 .
FAN Tingting , DU Songhuai , LIU Keyan , et al . Probabilistic reliability evaluation of active distribution network based on three-point estimate method considering correlation of input variables [J]. Power System Technology , 2017 , 41 ( 7 ): 289 - 296 .
GAO H J , LIU J Y , WANG L F , et al . Decentralized energy management for networked microgrids in future distribution systems [J]. IEEE Transactions on Power Systems , 2018 , 33 ( 4 ): 3599 - 3610 .
朱嘉远 , 刘洋 , 许立雄 , 等 . 风电全消纳下的配电网储能可调鲁棒优化配置 [J]. 电网技术 , 2018 , 42 ( 6 ): 1875 - 1883 .
ZHU Jiayuan , LIU Yang , XU Lixiong , et al . Adjustable robust optimization for energy storage system in distribution network based on wind power full accommodation [J]. Power System Technology , 2018 , 42 ( 6 ): 1875 - 1883 .
WANG C , GAO R , WEI W , et al . Risk-based distributionally robust optimal gas-power flow with Wasserstein distance [J]. IEEE Transactions on Power Systems , 2019 , 34 ( 3 ): 2190 - 2204 .
CHEN Y W , GUO Q L , SUN H B , et al . A distributionally robust optimization model for unit commitment based on Kullback-Leibler divergence [J]. IEEE Transactions on Power Systems , 2019 , 34 ( 3 ): 2190 - 2204 .
CHEN Y , WEI W , LIU F , et al . Distributionally robust hydro-thermal-wind economic dispatch [J]. Applied Energy , 2016 , 173 : 511 - 519 .
WEI W , LIU F , MEI S W . Distributionally robust co-optimization of energy and reserve dispatch [J]. IEEE Transactions on Sustainable Energy , 2016 , 7 ( 1 ): 289 - 300 .
WANG Z , BIAN Q Y , XIN H H , et al . A distributionally robust coordinated reserve scheduling model considering CVaR-based wind power reserve requirements [J]. IEEE Transactions on Sustainable Energy , 2016 , 7 ( 2 ): 625 - 636 .
周任军 , 闵雄帮 , 童小娇 , 等 . 电力环保经济调度矩不确定分布鲁棒优化方法 [J]. 中国电机工程学报 , 2015 , 35 ( 13 ): 3248 - 3255 .
ZHOU Renjun , MIN Xiongbang , TONG Xiaojiao , et al . Distributional robust optimization under moment uncertainty of environmental and economic dispatch for power system [J]. Proceedings of the CSEE , 2015 , 35 ( 13 ): 3248 - 3255 .
BIENSTOCK D , CHERTKOV M , HARNET S . Chance-constrained optimal power flow: risk-aware network control under uncertainty [J]. Siam Review , 2014 , 56 ( 3 ): 461 - 495 .
SHI Z C , LIANG H , HUANG S J , et al . Distributionally robust chance-constrained energy management for islanded microgrids [J]. IEEE Transactions on Smart Grid , 2019 , 10 ( 2 ): 2234 - 2244 .
税月 , 刘俊勇 , 高红均 , 等 . 考虑风电不确定性的电热综合系统分布鲁棒协调优化调度模型 [J]. 中国电机工程学报 , 2018 , 38 ( 24 ): 7235 - 7247 .
SHUI Yue , LIU Junyong , GAO Hongjun , et al . A distributionally robust coordinated dispatch model for integrated electricity and heating systems considering uncertainty of wind power [J]. Proceedings of the CSEE , 2018 , 38 ( 24 ): 7235 - 7247 .
DING T , YANG Q R , YANG Y H , et al . A data-driven stochastic reactive power optimization considering uncertainties in active distribution networks and decomposition method [J]. IEEE Transactions on Smart Grid , 2018 , 9 ( 5 ): 4994 - 5004 .
ZHAO C Y , GUAN Y P . data-driven stochastic unit commitment for integrating wind generation [J]. IEEE Transactions on Power Systems , 2016 , 31 ( 4 ): 2587 - 2596 .
DING T , YANG Q R , LIU X Y , et al . Duality-free decomposition based data-driven stochastic security-constrained unit commitment [J]. IEEE Transactions on Sustainable Energy , 2019 , 10 ( 1 ): 82 - 93 .
王皓 , 艾芊 , 甘霖 , 等 . 基于多场景随机规划和MPC的冷热电联合系统协同优化 [J]. 电力系统自动化 , 2018 , 42 ( 13 ): 51 - 58 .
WANG Hao , AI Qian , GAN Lin , et al . Collaborative optimization of combined heating and power system based on multi-scenario stochastic programming and model predictive control [J]. Automation of Electric Power Systems , 2018 , 42 ( 13 ): 51 - 58 .
ZHU R J , WEI H , BAI X Q . Wasserstein metric based distributionally robust approximate framework for unit commitment [J]. IEEE Transactions on Power Systems , 2019 , 34 ( 4 ): 2991 - 3001 .
WANG C , GAO R , QIU F , et al . Risk-based distributionally robust optimal power flow with dynamic line rating [J]. IEEE Transactions on Power Systems , 2018 , 33 ( 6 ): 6074 - 6086 .
ZHANG Y L , SHEN S Q , MATHIEU J L . 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 .
GAO R , KLEYWEGT A J . Distributionally robust stochastic optimization with Wasserste in distance [EB/OL]. [ 2020-02-01 ]. https://arxiv.org/abs/1604.02199 https://arxiv.org/abs/1604.02199 .
GAO R , KLEYWEGT A J . Distributionally robust stochastic optimization with dependence structure [EB/OL]. [ 2020-02-01 ]. https://arxiv.org/abs/1701. 04200 https://arxiv.org/abs/1701.04200 .
ALVARADO D , MOREIRA A , MORENO R , et al . Transmission network investment with distributed energy resources and distributionally robust security [J]. IEEE Transactions on Power Systems , 2018 , 34 ( 6 ): 5157 - 5168 .
ZHAO C Y , JIANG R W . Distributionally robust contingency-constrained unit commitment [J]. IEEE Transactions on Power Systems , 2018 , 33 ( 1 ): 94 - 102 .
BABAEI S , ZHAO C Y , FAN L . A data-driven model of virtual power plants in day-ahead unit commitment [J]. IEEE Transactions on Power Systems , 2019 , 34 ( 6 ): 5125 - 5135 .
HE C , ZHANG X P , LIU T Q , et al . Distributionally robust scheduling of integrated gas-electricity systems with demand response [J]. IEEE Transactions on Power Systems , 2019 , 34 ( 5 ): 3791 - 3803 .
XI L , WING C K , SHIWEI X , et al . Security-constrained multi-period economic dispatch with renewable energy utilizing distributionally robust optimization [J]. IEEE Transactions on Sustainable Energy , 2019 , 10 ( 2 ): 768 - 779 .
戴蕾思 , 叶承晋 , 傅旭华 , 等 . 考虑概率分布约束的含高渗透率风电电力系统储能鲁棒优化方法 [J]. 电网技术 , 2017 , 41 ( 3 ): 94 - 102 .
DAI Leisi , YE Chengjin , FU Xuhua , et al . Distributional robust joint chance constrained optimal capacity installment of energy storage in power system with high penetration of wind power [J]. Power System Technology , 2017 , 41 ( 3 ): 94 - 102 .
ALISMAIL F , XIONG P , SINGH C . Optimal wind farm allocation in multi-area power systems using distributionally robust optimization approach [J]. IEEE Transactions on Power Systems , 2018 , 33 ( 1 ): 536 - 554 .
李志伟 , 赵书强 , 刘金山 . 基于相关机会目标规划的电力系统日内滚动调度 [J]. 电力系统自动化 , 2019 , 43 ( 11 ): 77 - 88 .
LI Zhiwei , ZHAO Shuqiang , LIU Jinshan . Intraday rolling dispatching of power system based on dependent chance goal programming [J]. Automation of Electric Power Systems , 2019 , 43 ( 11 ): 77 - 88 .
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 .
ZARE A , CHUNG C Y , ZHAN J , et al . A distributionally robust chance-constrained MILP model for multistage distribution system planning with uncertain renewables and loads [J]. IEEE Transactions on Power Systems , 2018 , 33 ( 5 ): 5248 - 5262 .
XIE W J , AHMED S . Distributionally robust chance constrained optimal power flow with renewables: a conic reformulation [J]. IEEE Transactions on Power Systems , 2018 , 33 ( 2 ): 1860 - 1867 .
ZHOU A , YANG M , WANG Z . A linear solution method of generalized robust chance constrained real-time dispatch [J]. IEEE Transactions on Power Systems , 2018 , 33 ( 6 ): 7313 - 7316 .
YANG H M , ZHANG S M , QIU D , et al . Distributionally robust optimal bidding of controllable load aggregators in the electricity market [J]. IEEE Transactions on Power Systems , 2018 , 33 ( 1 ): 1089 - 1091 .
QIU F , WANG J H . Distributionally robust congestion management with dynamic line ratings [J]. IEEE Transactions on Power Systems , 2015 , 30 ( 4 ): 2198 - 2199 .
GUO Y , BAKER K , DALL’ANESE E , et al . Data-based distributionally robust stochastic optimal power flow: Part Ⅰ methodologies [J]. IEEE Transactions on Power Systems , 2019 , 34 ( 2 ): 1483 - 1492 .
GUO Y , BAKER K , DALL’ANESE E , et al . Data-based distributionally robust stochastic optimal power flow: Part Ⅱ case studies [J]. IEEE Transactions on Power Systems , 2019 , 34 ( 2 ): 1493 - 1503 .
ESFAHANI P M , KUHN D . Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations [J]. Math Program , 2018 , 171 ( 1/2 ): 115 - 166 .
GIVENS C R , SHORTT R M . A class of Wasserstein metrics for probability distributions [J]. Michigan Math , 1984 , 31 ( 2 ): 231 - 240 .
CHEN X , WU W C , ZHANG B M , et al . Data-driven DG capacity assessment method for active distribution networks [J]. IEEE Transactions on Power Systems , 2017 , 32 ( 5 ): 3946 - 3957 .
MIETH R , DVORKIN Y . Data-driven distributionally robust optimal power flow for distribution systems [J]. IEEE Control Systems Letters , 2018 , 2 ( 3 ): 363 - 368 .
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