低碳动态电—气最优能流的加速凸分散优化求解
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摘要
在综合能源系统背景下,提出一种计及碳交易机制的低碳动态电—气最优能流模型。考虑到气流传输的延迟特性,采用时空偏微分方程精确描述气流动态。此外,该模型引入一种碳交易机制以充分发挥电—气互联系统的经济与低碳效益。为实现电—气互联网络的分散优化并得到一个可靠的高质量解,提出两种内外层相协调的凸分散优化方法——罚凸凹过程(PCCP)-Benders和PCCP-交替方向乘子算法(ADMM)。在此凸分散优化框架下,外层优化基于一种PCCP将非凸气流动态凸化成一个迭代的二阶锥规划,而内层优化分别基于Benders分解和ADMM求解外层PCCP迭代的每一步。最后,通过算例仿真对比分析了上述两种凸分散优化算法的计算性能,并详细分析了碳交易成本对系统运行的影响,所得结果验证了文中模型及算法的有效性。
To adapt to the"Energy Internet",this paper proposes a low-carbon dynamic optimal gas-power flow model with carbon trading.However,the dynamic characteristics of gas flow are remarkably slower than those of power flow,the spacetime partial differential equations are used to accurately describe the dynamic gas flow.In addition,this model introduces a carbon trading mechanism for fully exploiting economic and low-carbon benefits of the integrated electricity and natural gas energy system.In order to achieve the decentralized optimization of gas-power interconnection network and obtain a high-quality solution,two kinds of inner and outer-coordinated convex decentralized optimization methods,named as penalty convexconcave procedure(PCCP)-Benders and PCCP-alternating direction method of multipliers(ADMM),are proposed.In this framework,the outer layer based on a PCCP transforms the non-convex dynamic gas flow into a second-order cone programming and the inner layer solves each step of the outer PCCP iteration with Benders decomposition and ADMM.Finally,a calculation example tests the optimization performance of PCCP-Benders and PCCP-ADMM,while the operation effect with different carbon trading prices is investigated in detail,the validity of model and algorithm is verified by the results.
To adapt to the"Energy Internet",this paper proposes a low-carbon dynamic optimal gas-power flow model with carbon trading.However,the dynamic characteristics of gas flow are remarkably slower than those of power flow,the spacetime partial differential equations are used to accurately describe the dynamic gas flow.In addition,this model introduces a carbon trading mechanism for fully exploiting economic and low-carbon benefits of the integrated electricity and natural gas energy system.In order to achieve the decentralized optimization of gas-power interconnection network and obtain a high-quality solution,two kinds of inner and outer-coordinated convex decentralized optimization methods,named as penalty convexconcave procedure(PCCP)-Benders and PCCP-alternating direction method of multipliers(ADMM),are proposed.In this framework,the outer layer based on a PCCP transforms the non-convex dynamic gas flow into a second-order cone programming and the inner layer solves each step of the outer PCCP iteration with Benders decomposition and ADMM.Finally,a calculation example tests the optimization performance of PCCP-Benders and PCCP-ADMM,while the operation effect with different carbon trading prices is investigated in detail,the validity of model and algorithm is verified by the results.
引文
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[10] 王伟亮,王丹,贾宏杰,等.考虑天然气网络状态的电力-天然气区域综合能源系统稳态分析[J].中国电机工程学报,2017,37(5):1293-1305.WANG Weiliang,WANG Dan,JIA Hongjie,et al.Steady state analysis of regional integrated energy system with consideration of NGS network status[J].Proceedings of the CSEE,2017,37(5):1293-1305.
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[12] 孙国强,陈霜,卫志农,等.计及相关性的电-气互联系统概率最优潮流[J].电力系统自动化,2015,39(21):11-17.SUN Guoqiang,CHEN Shuang,WEI Zhinong,et al.Probabilistic optimal power flow of combined natural gas and electric system considering correlation[J].Automation of Electric Power Systems,2015,39(21):11-17.
[13] YANG J,ZHANG N,KANG C,et al.Effect of natural gas flow dynamics in robust generation scheduling under wind uncertainty[J].IEEE Transactions on Power Systems,2018,33(2):2087-2097.
[14] 王程,刘念.基于交替方向乘子法的互联微电网系统分布式优化调度[J].电网技术,2016,40(9):2675-2681.WANG Cheng,LIU Nian.Distributed optimal dispatching of interconnected microgrid system based on alternating direction method of multipliers[J].Power System Technology,2016,40(9):2675-2681.
[15] 瞿小斌,文云峰,叶希,等.基于串行和并行ADMM算法的电-气能量流分布式协同优化[J].电力系统自动化,2017,41(4):12-19.DOI:10.7500/AEPS20160805007.QU Xiaobin,WEN Yunfeng,YE Xi,et al.Distributed optimization of electric-gas integrated energy flow using serial and parallel iterative modes for alternating direction method of multipliers[J].Automation of Electric Power Systems,2017,41(4):12-19.DOI:10.7500/AEPS20160805007.
[16] 吕仁周,白晓清,李佩杰,等.基于交替方向乘子法的电动汽车分散式充电控制[J].电力系统自动化,2016,40(16):56-63.LYU Renzhou,BAI Xiaoqing,LI Peijie,et al.Decentralized charging control of electric vehicles based on alternate direction method of multiplier[J].Automation of Electric Power Systems,2016,40(16):56-63.
[17] COHEN G.Auxiliary problem principle and decomposition of optimization problems[J].Journal of Optimization Theory and Applications,1980,32(3):277-305.
[18] 刘宝英,杨仁刚.采用辅助问题原理的多分区并行无功优化算法[J].中国电机工程学报,2009,29(7):47-51.LIU Baoying,YANG Rengang.Multi-subarea parallel reactive power optimization based on APP[J].Proceedings of the CSEE,2009,29(7):47-51.
[19] 郑海艳.机组组合基于Benders分解与割平面的方法及约束优化SQP算法研究[D].南宁:广西大学,2015.ZHENG Haiyan.Study on methods based on Benders decomposition and cuts for unit commitment and SQP algorithm for constrained optimization[D].Nanning:Guangxi University,2015.
[20] 刘思夷,赵波,汪湘晋,等.基于Benders分解的独立型微电网鲁棒优化容量配置模型[J].电力系统自动化,2017,41(21):119-126.DOI:10.7500/AEPS20161228012.LIU Siyi,ZHAO Bo,WANG Xiangjin,et al.Capacity configuration model for robust optimization of stand-alone microgrid based on Benders decomposition[J].Automation of Electric Power Systems,2017,41(21):119-126.DOI:10.7500/AEPS20161228012.
[21] 晏鸣宇,张伊宁,艾小猛,等.采用Benders分解含机组禁止运行区间的安全约束最优潮流[J].电力系统自动化,2018,42(6):60-65.DOI:10.7500/AEPS20170528003.YAN Mingyu,ZHANG Yining,AI Xiaomeng,et al.Benders decomposition based security-constrained optimal power flow considering generator prohibited zones[J].Automation of Electric Power Systems,2018,42(6):60-65.DOI:10.7500/AEPS20170528003.
[22] CORREAPOSADA C M,S?NCHEZMART? N P S.Gas network optimization:a comparison of piecewise linear models[EB/OL].[2014-10-04].http://www.optimization-online.org/DB_HTML/2014/10/4580.html.
[23] 艾小猛,方家琨,徐沈智,等.一种考虑天然气系统动态过程的气电联合系统优化运行模型[J].电网技术,2018,42(2):409-416.AI Xiaomeng,FANG Jiakun,XU Shenzhi,et al.An optimal energy flow model in integrated gas-electric systems considering dynamics of natural gas system[J].Power System Technology,2018,42(2):409-416.
[24] FANG J,ZENG Q,AI X,et al.Dynamic optimal energy flow in the integrated natural gas and electrical power systems[J].IEEE Transactions on Sustainable Energy,2018,9(1):188-198.
[25] WANG C,WEI W,WANG J,et al.Convex optimization based distributed optimal gas-power flow calculation[J].IEEE Transactions on Sustainable Energy,2018,9(3):1145-1156.
[2] 余晓丹,徐宪东,陈硕翼,等.综合能源系统与能源互联网简述[J].电工技术学报,2016,31(1):1-13.YU Xiaodan,XU Xiandong,CHEN Shuoyi,et al.A brief review to integrated energy system and energy internet[J].Transactions of China Electrotechnical Society,2016,31(1):1-13.
[3] 艾芊,郝然.多能互补、集成优化能源系统关键技术及挑战[J].电力系统自动化,2018,42(4):2-10.DOI:10.7500/AEPS 20170927008.AI Qian,HAO Ran.Key technologies and challenges for multi-energy complementarity and optimization of integrated energy system[J].Automation of Electric Power Systems,2018,42(4):2-10.DOI:10.7500/AEPS20170927008.
[4] CAO Y,QIANG L I,TAN Y,et al.A comprehensive review of energy internet:basic concept,operation and planning methods,and research prospects[J].Journal of Modern Power Systems and Clean Energy,2018,6(3):1-13.
[5] WEI Z,ZHANG S,SUN G,et al.Power-to-gas considered peak load shifting research for integrated electricity and natural-gas energy systems[J].Proceedings of the CSEE,2017,37(16):4601-4609.
[6] NASTASI B,BASSO G L.Power-to-gas integration in the transition towards future urban energy systems[J].International Journal of Hydrogen Energy,2017,42(38):23933-23951.
[7] 董帅,王成福,梁军,等.计及电转气运行成本的综合能源系统多目标日前优化调度[J].电力系统自动化,2018,42(11):8-15.DOI:10.7500/AEPS20170721003.DONG Shuai,WANG Chengfu,LIANG Jun,et al.Multi-objective optimal day-ahead dispatch of integrated energy system considering power-to-gas operation cost[J].Automation of Electric Power Systems,2018,42(11):8-15.DOI:10.7500/AEPS20170721003.
[8] LIU W,WEN F,XUE Y.Power-to-gas technology in energy systems:current status and prospects of potential operation strategies[J].Journal of Modern Power Systems and Clean Energy,2017,5(3):439-450.
[9] 徐宪东,贾宏杰,靳小龙,等.区域综合能源系统电/气/热混合潮流算法研究[J].中国电机工程学报,2015,35(14):3634-3642.XU Xiandong,JIA Hongjie,JIN Xiaolong,et al.Study on hybrid heat-gas-power flow algorithm for integrated community energy system[J].Proceedings of the CSEE,2015,35(14):3634-3642.
[10] 王伟亮,王丹,贾宏杰,等.考虑天然气网络状态的电力-天然气区域综合能源系统稳态分析[J].中国电机工程学报,2017,37(5):1293-1305.WANG Weiliang,WANG Dan,JIA Hongjie,et al.Steady state analysis of regional integrated energy system with consideration of NGS network status[J].Proceedings of the CSEE,2017,37(5):1293-1305.
[11] 秦婷,刘怀东,王锦桥,等.基于碳交易的电-热-气综合能源系统低碳经济调度[J].电力系统自动化,2018,42(14):8-13.DOI:10.7500/AEPS20171220005.QIN Ting,LIU Huaidong,WANG Jinqiao,et al.Carbon trading based low-carbon economic dispatch for integrated electricity-heat-gas energy system[J].Automation of Electric Power Systems,2018,42(14):8-13.DOI:10.7500/AEPS 20171220005.
[12] 孙国强,陈霜,卫志农,等.计及相关性的电-气互联系统概率最优潮流[J].电力系统自动化,2015,39(21):11-17.SUN Guoqiang,CHEN Shuang,WEI Zhinong,et al.Probabilistic optimal power flow of combined natural gas and electric system considering correlation[J].Automation of Electric Power Systems,2015,39(21):11-17.
[13] YANG J,ZHANG N,KANG C,et al.Effect of natural gas flow dynamics in robust generation scheduling under wind uncertainty[J].IEEE Transactions on Power Systems,2018,33(2):2087-2097.
[14] 王程,刘念.基于交替方向乘子法的互联微电网系统分布式优化调度[J].电网技术,2016,40(9):2675-2681.WANG Cheng,LIU Nian.Distributed optimal dispatching of interconnected microgrid system based on alternating direction method of multipliers[J].Power System Technology,2016,40(9):2675-2681.
[15] 瞿小斌,文云峰,叶希,等.基于串行和并行ADMM算法的电-气能量流分布式协同优化[J].电力系统自动化,2017,41(4):12-19.DOI:10.7500/AEPS20160805007.QU Xiaobin,WEN Yunfeng,YE Xi,et al.Distributed optimization of electric-gas integrated energy flow using serial and parallel iterative modes for alternating direction method of multipliers[J].Automation of Electric Power Systems,2017,41(4):12-19.DOI:10.7500/AEPS20160805007.
[16] 吕仁周,白晓清,李佩杰,等.基于交替方向乘子法的电动汽车分散式充电控制[J].电力系统自动化,2016,40(16):56-63.LYU Renzhou,BAI Xiaoqing,LI Peijie,et al.Decentralized charging control of electric vehicles based on alternate direction method of multiplier[J].Automation of Electric Power Systems,2016,40(16):56-63.
[17] COHEN G.Auxiliary problem principle and decomposition of optimization problems[J].Journal of Optimization Theory and Applications,1980,32(3):277-305.
[18] 刘宝英,杨仁刚.采用辅助问题原理的多分区并行无功优化算法[J].中国电机工程学报,2009,29(7):47-51.LIU Baoying,YANG Rengang.Multi-subarea parallel reactive power optimization based on APP[J].Proceedings of the CSEE,2009,29(7):47-51.
[19] 郑海艳.机组组合基于Benders分解与割平面的方法及约束优化SQP算法研究[D].南宁:广西大学,2015.ZHENG Haiyan.Study on methods based on Benders decomposition and cuts for unit commitment and SQP algorithm for constrained optimization[D].Nanning:Guangxi University,2015.
[20] 刘思夷,赵波,汪湘晋,等.基于Benders分解的独立型微电网鲁棒优化容量配置模型[J].电力系统自动化,2017,41(21):119-126.DOI:10.7500/AEPS20161228012.LIU Siyi,ZHAO Bo,WANG Xiangjin,et al.Capacity configuration model for robust optimization of stand-alone microgrid based on Benders decomposition[J].Automation of Electric Power Systems,2017,41(21):119-126.DOI:10.7500/AEPS20161228012.
[21] 晏鸣宇,张伊宁,艾小猛,等.采用Benders分解含机组禁止运行区间的安全约束最优潮流[J].电力系统自动化,2018,42(6):60-65.DOI:10.7500/AEPS20170528003.YAN Mingyu,ZHANG Yining,AI Xiaomeng,et al.Benders decomposition based security-constrained optimal power flow considering generator prohibited zones[J].Automation of Electric Power Systems,2018,42(6):60-65.DOI:10.7500/AEPS20170528003.
[22] CORREAPOSADA C M,S?NCHEZMART? N P S.Gas network optimization:a comparison of piecewise linear models[EB/OL].[2014-10-04].http://www.optimization-online.org/DB_HTML/2014/10/4580.html.
[23] 艾小猛,方家琨,徐沈智,等.一种考虑天然气系统动态过程的气电联合系统优化运行模型[J].电网技术,2018,42(2):409-416.AI Xiaomeng,FANG Jiakun,XU Shenzhi,et al.An optimal energy flow model in integrated gas-electric systems considering dynamics of natural gas system[J].Power System Technology,2018,42(2):409-416.
[24] FANG J,ZENG Q,AI X,et al.Dynamic optimal energy flow in the integrated natural gas and electrical power systems[J].IEEE Transactions on Sustainable Energy,2018,9(1):188-198.
[25] WANG C,WEI W,WANG J,et al.Convex optimization based distributed optimal gas-power flow calculation[J].IEEE Transactions on Sustainable Energy,2018,9(3):1145-1156.
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