线性规划及其在节点电价分析中的应用
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摘要
随着电力工业市场化改革的进行,要求电力市场定价机制具有高效、透明、合理及准确等特征,但往往这些方面难以兼顾,故急需设计一种易于理解且能够减轻电力用户负担的电价制定方案。许多国家和地区(如新西兰、智利、美国加利福尼亚州等)都将节点电价作为电价定价机制的关键工具。节点电价反映了不同地区由于不同的电网物理特性而产生不同的发电及负荷电价。使用节点电价确定电力市场交易价格非常有效和精确,节点电价已成为引导电力市场高效、有序运行的重要经济信号。
本文首先讨论了电力工业市场化改革的进程,随着电力系统规模的不断扩大,垂直一体化模式下的管理成本日益增加,使引入竞争成为必要。而在竞争的电力市场中,现货价格是非常关键的信息,它可以影响合同价格,鼓励生产、消费和投资。因此,制定正确的价格是保证电力系统高效运行的关键。
在此基础上,介绍了线性规划的基础理论,主要是单纯形法、Karmarkar投影尺度算法以及原-对偶內点算法,并对他们之间的优缺点进行了比较与分析。
接着阐述了节点电价的概念与经济意义,并基于直流潮流在成本特性线性假设下,建立了节点电价的线型规划模型,并给出了模型的求解方法。
最后,针对上述模型和算法,以三节点系统和IEEE30节点系统为例,进行了节点电价的计算与分析,论证本文模型和算法的有效性。
总之,在线性规划基础上,进行节点电价的分析,模型简单、有效,并有机反应了节点电价的机理,对电力系统发展有指导作用。
As the power industry's market-oriented reform,the pricing mechanism of electricity market is required to be efficient,transparent, reasonable and accurate,but these features are often difficult to balance, so a pricing mechanism which is easy to understand and can reduce the burden of consumers is urgently needed.Many countries and regions(such as New Zealand,Chile,California,USA,etc.)make nodal price a key tool of the pricing mechanism of electricity market.Nodal price reflects the prices of different regions due to different physical characteristics of the power grid.Node price is very effective and accurate to identify the transaction price of electricity market.Node price has become an important economic signal which guided the electricity market to be efficient and order.
The marketization of the power industry in China and other countries is discussed firstly,but with the constantly development of power system, management costs is increasing under vertical integration mode,so the introduction of competition has been necessary.And in a competitive electricity market,the spot price is very important information,it could affect the contract price,and to encourage production, consumption and investment.Therefore,making a correct price is the key problem to ensure the power system efficient.
The basic theory of linear programming is given and the simplex method, Karmarkar' s projective algorithm and primal-dual interior-point method is proposed and analyzed.What is more,the short comings and advangtages of these three methods are also discussed.
The concept and economical meaning of nodal price are analyzed,based on DC power flow and the suppose that production curve is linear,the linear programming model of nodal price and the method to solve this modelis given.
finally a three-bus system and the IEEE thirty-bus system is calculated and analyzed in order to prove the validity of the model and the method.
The mechanism of nodal price has been discussed on the basis of linear programming,the model is simple and valid,it can give a direction for the development of power system.
本文首先讨论了电力工业市场化改革的进程,随着电力系统规模的不断扩大,垂直一体化模式下的管理成本日益增加,使引入竞争成为必要。而在竞争的电力市场中,现货价格是非常关键的信息,它可以影响合同价格,鼓励生产、消费和投资。因此,制定正确的价格是保证电力系统高效运行的关键。
在此基础上,介绍了线性规划的基础理论,主要是单纯形法、Karmarkar投影尺度算法以及原-对偶內点算法,并对他们之间的优缺点进行了比较与分析。
接着阐述了节点电价的概念与经济意义,并基于直流潮流在成本特性线性假设下,建立了节点电价的线型规划模型,并给出了模型的求解方法。
最后,针对上述模型和算法,以三节点系统和IEEE30节点系统为例,进行了节点电价的计算与分析,论证本文模型和算法的有效性。
总之,在线性规划基础上,进行节点电价的分析,模型简单、有效,并有机反应了节点电价的机理,对电力系统发展有指导作用。
As the power industry's market-oriented reform,the pricing mechanism of electricity market is required to be efficient,transparent, reasonable and accurate,but these features are often difficult to balance, so a pricing mechanism which is easy to understand and can reduce the burden of consumers is urgently needed.Many countries and regions(such as New Zealand,Chile,California,USA,etc.)make nodal price a key tool of the pricing mechanism of electricity market.Nodal price reflects the prices of different regions due to different physical characteristics of the power grid.Node price is very effective and accurate to identify the transaction price of electricity market.Node price has become an important economic signal which guided the electricity market to be efficient and order.
The marketization of the power industry in China and other countries is discussed firstly,but with the constantly development of power system, management costs is increasing under vertical integration mode,so the introduction of competition has been necessary.And in a competitive electricity market,the spot price is very important information,it could affect the contract price,and to encourage production, consumption and investment.Therefore,making a correct price is the key problem to ensure the power system efficient.
The basic theory of linear programming is given and the simplex method, Karmarkar' s projective algorithm and primal-dual interior-point method is proposed and analyzed.What is more,the short comings and advangtages of these three methods are also discussed.
The concept and economical meaning of nodal price are analyzed,based on DC power flow and the suppose that production curve is linear,the linear programming model of nodal price and the method to solve this modelis given.
finally a three-bus system and the IEEE thirty-bus system is calculated and analyzed in order to prove the validity of the model and the method.
The mechanism of nodal price has been discussed on the basis of linear programming,the model is simple and valid,it can give a direction for the development of power system.
引文
[1]王锡凡,王秀丽,陈皓勇.电力市场基础[M].西安:西安交通大学出
[2]于尔铿.电力市场.北京:中国电力出版社,1998.
[3]Hamoud G,Bradley I.Assessment ofTransmission Congestion Cost and Locational Marginal pricing in a Competitive Electricity Market fJ1.IEEE Transactions on Power Systems,2004,19(2):769-775.
[4]MUNASINGHE M,WARFORD J.Electricity pricing:theory and case studies[M].Baltimore,Maryland:Johns Hopkins University Press,1982.
[5]KINNUNEN K.Pricing of electricity distribution:an empirical eficiency study in Finland,Norway and Sweden[J].Utilities policy,2005,13(1):15-25.
[6]PAUL H,JONES STEVE.Eficient access transmission pricing[J].The Electricity Journal,1996,9(9):56-60.
[7]赵会茹,乞建勋,曾鸣,等.输配电价格管制模型研究[J].中国电机工程学报,2003(10):89-93.
[8]任震,吴国丙,黄雯莹 电力市场中输电定价问题研究[J].电力系统自动化,2003,27(1):81-86.
[9]SCHWEPPE F C,CARAMANIES M C,etal Spot pricing of electricity[M].Boston,MA:KluwerAcademic,1988.
[10]张永平,童小娇,倪以信,等.实时电力市场阻塞管理算法研究[J].电网技术,2004,28(15):6-10.
[11]袁智强,侯志俭,蒋传文,等.输电服务定价的研究进展[J].电力自动化设备,2003,23(10):81-86.
[12]赵连生.电力价格设计[M].北京:水利电力出版杜,1992年
[13]于尔铿 谢开 韩放 曹昉 杨以涵:电力市场概述[J].电网技术,1995,19(3):58-62
[14]徐解宪 范斌Ashok M&nglick博士Peter mmer李凡:区域电力市场的十大障碍及其对策[J].中国电力企业管理,2003,(1):23-25
[15]Wood A J,Wo llenberg B F.Power Generation Operation and Control.Second Edition.Wiley Interscience,1996
[16]Arbel Ami.Exploring Interior Point Linear Programming Algorithms and Software.Combridge:TheM IT Press,1993
[17]Ross D W,Kim S.Dynamic Economic Dispatch of Generation.IEEE T ransactions on Power Apparatus and Systems,1980,PA S-99(6)
[18]Wood W G.Spinning Reserve Constrained Static and Dynamic Economic Dispatch.IEEE Trans on Power Apparatus andSystems,1982,PA S- 101(2)
[19]Lee F N,L emonidis L,L iu K C.P rice2based Ramp2rateModel for Dynamic Dispatch and Unit Commitment.IEEE T rans on Power Systems,1994,9(3)
[20]T ravers D L,Kaye R J.Dynamic Dispatch by Constructive Dynamic Programming.IEEE T rans on Power System s,1993,13(1)
[21]Somuah C B,Khunaizi N.App lication of L inear Programming Redispatch Technique to Dynam ic Generation A llocation.IEEE Trans on Power Systems,1990,5(1)
[22]Schweppe F,Caramanis M,Tablors R.Spot Pricing of Electricity[M].Boston:Kluwer Academic Publisher,1988.
[23]Christie R.D,Wollenberg B.F,Wangensteen I.Transmission management in thederegulated environment.Proceedings of the IEEE,2000,88(2):170-195.
[24]David A.K,Fang R.S.Congestion management of electric power systems underopen transmission access.International Conference on APSCOM-97,vol.2,11-14,Nov 1997,pp.469-474.
[25]Robert Dahlgren,Chen-Ching Liu,Jacques Lawarree.Risk assessment in energy trading.IEEE Trans on Power Systems,2003,18(2):503-511.
[26]刘皓明,李卫星,倪以信.计及静态安全约束的跨区域双边交易最大交易量实用计算方法.电网技术,2003,27(9):1-5.
[27]刘振亚.特高压电网.北京:中国经济出版社,2005.
[28]Landgren G.L,Terhune H.L,Angel R.K,Transmission interchange capability analysis by computer.IEEE Trans on Power Apparatus and Systems,1972,91(6):2405-2414.
[29]Landgren G.L,Anderson S.W.Simultaneous power interchange capability analysis.IEEE Trans on Power Apparatus and Systems, 1973, 92(6): 1973-1986.
[30] Heydt G.T, Katz B.M. A stochastic model in simultaneous interchange capacitycalculations. IEEE Trans on Power Apparatus and Systems, 1975, 94(2): 350-359.
[31] Landgren G.L, Anderson S.W. Maximized transmission grid loading using linearprogramming. IEEE Tutorial Course, 1976, 76CHI107-2-PWR.
[32] Garver L.L, Can Home P.R, Wirgau K.A. Load supplying capability of generation-transmission networks. IEEE Trans on Power Apparatus and Systems,1979, 98(3): 957-962.
[33] PJM Transmission Reliability Task Force. Bulk power area reliability evaluationconsidering probabilistic transfer capability. IEEE Trans on Power Apparatus andSystems, 1982, 101(9): 3551-3562.
[34] Yan Ou, Chanan Singh. Assessment of available transfer capability and margins.IEEE Trans on Power Systems, 2002, 17(2): 463-468.
[35] R. Gnanadass, Narayana Prasad Padhy, K. Manivannan. Assessment of availabletransfer capability for practical power systems with combined economic emission dispatch. Electric Power Systems Research 69 (2004): 267-276.
[36] Mark H. Gravener, Chika Nwankpa, Tai-sim Yeoh. ATC computational issues.Proceedings of the 32nd Hawaii International Conference on System Sciences, 1999.
[37] Mark H. Gravener, Chika Nwankpa. Available transfer capability and first ordersensitivity. IEEE Trans on Power Systems, 1999, 14(2): 512-518.
[38] LuonanChen, Hidekisuzllki, Tsunehisawachi, Yukihimshimura .Components of Nodal Prices for ElectricPower Systems [J]Transaction onPower systems. 2002, 17 (1 ):41-49
[39] R.A.S.K.Ranatunga,U.D.Annakkage, C.S.Kumble. Implications of Reactive Power on Nodal Pricing and Dispatch [C]. IEEE Power Engineering Society Winter Meeting.Singapore 2000, 885-890.
[40]G.Hamoud,I.Bradley.Assessment of Transmission Congestion Cost and Locational Marginal Pricing in a Competitive Electricity Market[J].Transaction on Power Systems.2004,19(2):769-775
[41]Thomas J.Overbye,Xu Cheng,Yan Sun.A Comparison of the AC and DC Power Flow Models for LMP Calculations[C].37th Annal Hawaii International Conference on System Sciences,2004.
[42]J.Toyoda,H.Saitoh,H.Sato.Basic Properties of Nodal Pricing Mechanism in the Weakly Tied Network[C].PowerCon,2002,Kunming(China)Volume:3,928-932.
[43]Richard D.Tabors forward Markets for Transmission that Clear at LMP:A Hybrid Proposal[C].The 34th Annal Hawaii International Conference on System Sciences,2001,Maui,Hawaii(USA):839-846
[44]Peng wang,Hua Cai.Impact of Transmission Reliability on Nodal Price in Electric Power Market[C].Transmission and Distribution Conference and Exhibition 2002.Yokohama(Japan):1966-1969
[45]Y.-Y.Hong,C.-Y.Hsiao.Locational Marginal Price Forecasting in Deregulated Electricity Markets Using Artificial Intelligence[J].IEE proceedings.Part C 2002,149(5):621-626
[46]Eugene Litvinov,Tongxin Zheng,Gary Rosenwald,Payman Shamsollahi.Marginal loss Modeling in LMP Calculation[J].Transaction on Power Systems.2004,19(2):880-888
[47]Koeunyi Bae,KyungSoo Han,James S.Thorp.Nodal Price Dependent,Dual-Mode Transmission Line Protection Strategy[J].The 33rd Annual Hawaii International Conference on System Sciences.2000Maui,Hawaii(USA):1330-1337
[48]诸骏伟.电力系统分析 上册.北京:中国电力出版社,1998.
[49]G.C.Ejebe,J.G.Waight,M.Santos-nieto,et al.Fast calculation of linear availabletransfer capability.IEEE Trans on Power Systems,2000,15(3):1112-1116.
[50]Santiago Grijalva,Peter W.Sauer,James D.Weber.Enhancement of linear ATCcalculations by the incorporation of reactive power flows. IEEE Trans on PowerSystems, 2003, 18(2): 619-624.
[51] H. Chiang, A. J. Flueck, K. S. Shah, et al. CPFLOW: A practical tool for tracingpower system steady-state stationary behavior due to load and generation variations.IEEE Trans. On Power System, 1995, 10: 623-634.
[2]于尔铿.电力市场.北京:中国电力出版社,1998.
[3]Hamoud G,Bradley I.Assessment ofTransmission Congestion Cost and Locational Marginal pricing in a Competitive Electricity Market fJ1.IEEE Transactions on Power Systems,2004,19(2):769-775.
[4]MUNASINGHE M,WARFORD J.Electricity pricing:theory and case studies[M].Baltimore,Maryland:Johns Hopkins University Press,1982.
[5]KINNUNEN K.Pricing of electricity distribution:an empirical eficiency study in Finland,Norway and Sweden[J].Utilities policy,2005,13(1):15-25.
[6]PAUL H,JONES STEVE.Eficient access transmission pricing[J].The Electricity Journal,1996,9(9):56-60.
[7]赵会茹,乞建勋,曾鸣,等.输配电价格管制模型研究[J].中国电机工程学报,2003(10):89-93.
[8]任震,吴国丙,黄雯莹 电力市场中输电定价问题研究[J].电力系统自动化,2003,27(1):81-86.
[9]SCHWEPPE F C,CARAMANIES M C,etal Spot pricing of electricity[M].Boston,MA:KluwerAcademic,1988.
[10]张永平,童小娇,倪以信,等.实时电力市场阻塞管理算法研究[J].电网技术,2004,28(15):6-10.
[11]袁智强,侯志俭,蒋传文,等.输电服务定价的研究进展[J].电力自动化设备,2003,23(10):81-86.
[12]赵连生.电力价格设计[M].北京:水利电力出版杜,1992年
[13]于尔铿 谢开 韩放 曹昉 杨以涵:电力市场概述[J].电网技术,1995,19(3):58-62
[14]徐解宪 范斌Ashok M&nglick博士Peter mmer李凡:区域电力市场的十大障碍及其对策[J].中国电力企业管理,2003,(1):23-25
[15]Wood A J,Wo llenberg B F.Power Generation Operation and Control.Second Edition.Wiley Interscience,1996
[16]Arbel Ami.Exploring Interior Point Linear Programming Algorithms and Software.Combridge:TheM IT Press,1993
[17]Ross D W,Kim S.Dynamic Economic Dispatch of Generation.IEEE T ransactions on Power Apparatus and Systems,1980,PA S-99(6)
[18]Wood W G.Spinning Reserve Constrained Static and Dynamic Economic Dispatch.IEEE Trans on Power Apparatus andSystems,1982,PA S- 101(2)
[19]Lee F N,L emonidis L,L iu K C.P rice2based Ramp2rateModel for Dynamic Dispatch and Unit Commitment.IEEE T rans on Power Systems,1994,9(3)
[20]T ravers D L,Kaye R J.Dynamic Dispatch by Constructive Dynamic Programming.IEEE T rans on Power System s,1993,13(1)
[21]Somuah C B,Khunaizi N.App lication of L inear Programming Redispatch Technique to Dynam ic Generation A llocation.IEEE Trans on Power Systems,1990,5(1)
[22]Schweppe F,Caramanis M,Tablors R.Spot Pricing of Electricity[M].Boston:Kluwer Academic Publisher,1988.
[23]Christie R.D,Wollenberg B.F,Wangensteen I.Transmission management in thederegulated environment.Proceedings of the IEEE,2000,88(2):170-195.
[24]David A.K,Fang R.S.Congestion management of electric power systems underopen transmission access.International Conference on APSCOM-97,vol.2,11-14,Nov 1997,pp.469-474.
[25]Robert Dahlgren,Chen-Ching Liu,Jacques Lawarree.Risk assessment in energy trading.IEEE Trans on Power Systems,2003,18(2):503-511.
[26]刘皓明,李卫星,倪以信.计及静态安全约束的跨区域双边交易最大交易量实用计算方法.电网技术,2003,27(9):1-5.
[27]刘振亚.特高压电网.北京:中国经济出版社,2005.
[28]Landgren G.L,Terhune H.L,Angel R.K,Transmission interchange capability analysis by computer.IEEE Trans on Power Apparatus and Systems,1972,91(6):2405-2414.
[29]Landgren G.L,Anderson S.W.Simultaneous power interchange capability analysis.IEEE Trans on Power Apparatus and Systems, 1973, 92(6): 1973-1986.
[30] Heydt G.T, Katz B.M. A stochastic model in simultaneous interchange capacitycalculations. IEEE Trans on Power Apparatus and Systems, 1975, 94(2): 350-359.
[31] Landgren G.L, Anderson S.W. Maximized transmission grid loading using linearprogramming. IEEE Tutorial Course, 1976, 76CHI107-2-PWR.
[32] Garver L.L, Can Home P.R, Wirgau K.A. Load supplying capability of generation-transmission networks. IEEE Trans on Power Apparatus and Systems,1979, 98(3): 957-962.
[33] PJM Transmission Reliability Task Force. Bulk power area reliability evaluationconsidering probabilistic transfer capability. IEEE Trans on Power Apparatus andSystems, 1982, 101(9): 3551-3562.
[34] Yan Ou, Chanan Singh. Assessment of available transfer capability and margins.IEEE Trans on Power Systems, 2002, 17(2): 463-468.
[35] R. Gnanadass, Narayana Prasad Padhy, K. Manivannan. Assessment of availabletransfer capability for practical power systems with combined economic emission dispatch. Electric Power Systems Research 69 (2004): 267-276.
[36] Mark H. Gravener, Chika Nwankpa, Tai-sim Yeoh. ATC computational issues.Proceedings of the 32nd Hawaii International Conference on System Sciences, 1999.
[37] Mark H. Gravener, Chika Nwankpa. Available transfer capability and first ordersensitivity. IEEE Trans on Power Systems, 1999, 14(2): 512-518.
[38] LuonanChen, Hidekisuzllki, Tsunehisawachi, Yukihimshimura .Components of Nodal Prices for ElectricPower Systems [J]Transaction onPower systems. 2002, 17 (1 ):41-49
[39] R.A.S.K.Ranatunga,U.D.Annakkage, C.S.Kumble. Implications of Reactive Power on Nodal Pricing and Dispatch [C]. IEEE Power Engineering Society Winter Meeting.Singapore 2000, 885-890.
[40]G.Hamoud,I.Bradley.Assessment of Transmission Congestion Cost and Locational Marginal Pricing in a Competitive Electricity Market[J].Transaction on Power Systems.2004,19(2):769-775
[41]Thomas J.Overbye,Xu Cheng,Yan Sun.A Comparison of the AC and DC Power Flow Models for LMP Calculations[C].37th Annal Hawaii International Conference on System Sciences,2004.
[42]J.Toyoda,H.Saitoh,H.Sato.Basic Properties of Nodal Pricing Mechanism in the Weakly Tied Network[C].PowerCon,2002,Kunming(China)Volume:3,928-932.
[43]Richard D.Tabors forward Markets for Transmission that Clear at LMP:A Hybrid Proposal[C].The 34th Annal Hawaii International Conference on System Sciences,2001,Maui,Hawaii(USA):839-846
[44]Peng wang,Hua Cai.Impact of Transmission Reliability on Nodal Price in Electric Power Market[C].Transmission and Distribution Conference and Exhibition 2002.Yokohama(Japan):1966-1969
[45]Y.-Y.Hong,C.-Y.Hsiao.Locational Marginal Price Forecasting in Deregulated Electricity Markets Using Artificial Intelligence[J].IEE proceedings.Part C 2002,149(5):621-626
[46]Eugene Litvinov,Tongxin Zheng,Gary Rosenwald,Payman Shamsollahi.Marginal loss Modeling in LMP Calculation[J].Transaction on Power Systems.2004,19(2):880-888
[47]Koeunyi Bae,KyungSoo Han,James S.Thorp.Nodal Price Dependent,Dual-Mode Transmission Line Protection Strategy[J].The 33rd Annual Hawaii International Conference on System Sciences.2000Maui,Hawaii(USA):1330-1337
[48]诸骏伟.电力系统分析 上册.北京:中国电力出版社,1998.
[49]G.C.Ejebe,J.G.Waight,M.Santos-nieto,et al.Fast calculation of linear availabletransfer capability.IEEE Trans on Power Systems,2000,15(3):1112-1116.
[50]Santiago Grijalva,Peter W.Sauer,James D.Weber.Enhancement of linear ATCcalculations by the incorporation of reactive power flows. IEEE Trans on PowerSystems, 2003, 18(2): 619-624.
[51] H. Chiang, A. J. Flueck, K. S. Shah, et al. CPFLOW: A practical tool for tracingpower system steady-state stationary behavior due to load and generation variations.IEEE Trans. On Power System, 1995, 10: 623-634.