基于CVaR的风力发电效益分析
|
摘要
能源短缺与化石能源造成的环境污染和生态失衡等一系列问题已经严重影响到人类的生存发展。风能作为一种可持续利用、清洁的新能源，具有极大的节能环保效益。但在现有的电力市场体制下，电价机制并没有考虑电能生产过程中造成的环境污染和资源消耗等成本，风力发电潜在的节能环境效益没有得到体现。因此全面研究分析风力发电效益，是风电场规划及促进风电投资研发所必须解决的问题之一。
为了体现风力发电的节能环保效益，本文综合考虑风电生产成本、备用容量成本、上网发电收入及环境效益，建立了风力发电效益模型。由于模型中含有随机变量风速，因此采用CVaR数学方法来建立最大发电效益模型。与随机规划等传统方法不同，该方法不仅能把随机性问题定量化处理，还可有效处理“尾部风险”的影响。模型计算中，将难以解析的CVaR函数转化为概率密度函数的积分形式；并引入惩罚函数，将分段函数的非光滑部分光滑化处理；增加辅助变量，用离散点代替连续积分计算，将模型转换为线性优化问题。
以IEEE30节点系统为例，采用三种不同的方案求解风力发电效益。结果表明，考虑风速的影响，所求得风力发电效益更合理，验证了CVaR数学方法具有把非线性优化问题转化为线性优化问题的特点；将CVaR方法和机会约束规划方法相比较，计算了同等条件下的发电效益。结果表明，CVaR方法的计算不需要采用其他的智能算法，过程简便；并考虑了“尾部风险”的影响，计算结果更保守。
With the rapid development of global economy and the population continuesto increase, conventional oil, gas and coal-based energy demand is increasing, andincreasingly serious energy shortage. At the same time, fossil fuel caused byenvironmental pollution and ecological imbalance in a series of problems hasbegun to seriously affect human survival and development. The energy crisis hasbecome the subject of facing the world. Therefore, the human is an urgent need todevelop another new energy to solve these problems. And wind power as a clean,sustainable use of new energy, with a great deal of power generation efficiency andenvironmental values. To develop wind power is an effective way to alleviate theenergy crisis and environmental degradation
In recent years, under the encouragement and support of the Governments, thewind-based renewable energy power generation technology has developed rapidly,the wind energy utilization continuously improve the fan equipment costs and anoverall improvement in wind power generation efficiency. As in the existing systemof electricity market, the price mechanism does not consider the cost of theelectricity production process, resulting in environmental pollution and resourceconsumption, the potential benefits of wind-based energy generation does not get areasonable expression. Therefore, by considering the cost of wind power,generating income, environmental benefits and alternate costs, the establishment ofwind power generation efficiency model, in order to analyze the effectiveness ofwind power.
In the proposed model, the installed wind power capacity generation benefitsof the decision variables, generating effective optimization problem into thesolution of the installed capacity of the optimal value, then the benefit of powergeneration model to strike wind power generation efficiency. Because the windspeed of the installed capacity and the random variable, therefore, the trend oftransmission lines and the active power output of conventional units constraintconditions, using CVaR mathematical methods to solve the installed capacity.Different with the traditional method, the theory can not only take into accountwind speed randomness, but also to deal effectively with a confidence level otherthan the extreme cases. CVaR function in the integral calculation is relatively complicated, so the Monte Carlo simulation and analytical combining function ofCVaR transform and discrete computing discrete points instead of continuousintegration, and Computing for quick and easy to make.
Set the IEEE30 node simulation system for example, in order to solve theeconomic benefits of wind power under the three options. The results showed thatthe effectiveness and the size of the installed capacity of wind power and windspeed, CVaR confidence level has a direct relationship between the proposedtheoretical calculation method is novel and effective; CVaR method, andchance-constrained programming method compared to using the two methods werecalculated under the same conditions the benefit of power generation and installedcapacity. The results show that the CVaR calculation process is simple, and toconsider impacts outside the confidence, the result is more conservative. Therefore,the results obtained using CVaR function more in line with the actual situation.
为了体现风力发电的节能环保效益，本文综合考虑风电生产成本、备用容量成本、上网发电收入及环境效益，建立了风力发电效益模型。由于模型中含有随机变量风速，因此采用CVaR数学方法来建立最大发电效益模型。与随机规划等传统方法不同，该方法不仅能把随机性问题定量化处理，还可有效处理“尾部风险”的影响。模型计算中，将难以解析的CVaR函数转化为概率密度函数的积分形式；并引入惩罚函数，将分段函数的非光滑部分光滑化处理；增加辅助变量，用离散点代替连续积分计算，将模型转换为线性优化问题。
以IEEE30节点系统为例，采用三种不同的方案求解风力发电效益。结果表明，考虑风速的影响，所求得风力发电效益更合理，验证了CVaR数学方法具有把非线性优化问题转化为线性优化问题的特点；将CVaR方法和机会约束规划方法相比较，计算了同等条件下的发电效益。结果表明，CVaR方法的计算不需要采用其他的智能算法，过程简便；并考虑了“尾部风险”的影响，计算结果更保守。
With the rapid development of global economy and the population continuesto increase, conventional oil, gas and coal-based energy demand is increasing, andincreasingly serious energy shortage. At the same time, fossil fuel caused byenvironmental pollution and ecological imbalance in a series of problems hasbegun to seriously affect human survival and development. The energy crisis hasbecome the subject of facing the world. Therefore, the human is an urgent need todevelop another new energy to solve these problems. And wind power as a clean,sustainable use of new energy, with a great deal of power generation efficiency andenvironmental values. To develop wind power is an effective way to alleviate theenergy crisis and environmental degradation
In recent years, under the encouragement and support of the Governments, thewind-based renewable energy power generation technology has developed rapidly,the wind energy utilization continuously improve the fan equipment costs and anoverall improvement in wind power generation efficiency. As in the existing systemof electricity market, the price mechanism does not consider the cost of theelectricity production process, resulting in environmental pollution and resourceconsumption, the potential benefits of wind-based energy generation does not get areasonable expression. Therefore, by considering the cost of wind power,generating income, environmental benefits and alternate costs, the establishment ofwind power generation efficiency model, in order to analyze the effectiveness ofwind power.
In the proposed model, the installed wind power capacity generation benefitsof the decision variables, generating effective optimization problem into thesolution of the installed capacity of the optimal value, then the benefit of powergeneration model to strike wind power generation efficiency. Because the windspeed of the installed capacity and the random variable, therefore, the trend oftransmission lines and the active power output of conventional units constraintconditions, using CVaR mathematical methods to solve the installed capacity.Different with the traditional method, the theory can not only take into accountwind speed randomness, but also to deal effectively with a confidence level otherthan the extreme cases. CVaR function in the integral calculation is relatively complicated, so the Monte Carlo simulation and analytical combining function ofCVaR transform and discrete computing discrete points instead of continuousintegration, and Computing for quick and easy to make.
Set the IEEE30 node simulation system for example, in order to solve theeconomic benefits of wind power under the three options. The results showed thatthe effectiveness and the size of the installed capacity of wind power and windspeed, CVaR confidence level has a direct relationship between the proposedtheoretical calculation method is novel and effective; CVaR method, andchance-constrained programming method compared to using the two methods werecalculated under the same conditions the benefit of power generation and installedcapacity. The results show that the CVaR calculation process is simple, and toconsider impacts outside the confidence, the result is more conservative. Therefore,the results obtained using CVaR function more in line with the actual situation.
引文
[1]包爱霞.大规模风电场容量可信度的分析及对华东电网备用的影响.中国电机工程学报，2009，29 (增刊).34-38苏鹏，刘天琪，李兴源.含风电的系统最优旋转备用的确定.电网技术，2010.34(12).158-162
[2]袁铁江，晁勤，李义岩，袁建党等.基于风电极限穿透功率的经济调度优化模型的研究.电力系统保护与控制，2011-01-11,39（1）.17-22
[3]赵海翔，关洪亮，范高峰等.基于静态安全和稳定约束的地区电网接入风电容量算法.中国电力，2007，40（3）78-83
[4]邓元昌，余志，流沙.基于尾流实验的风电场装机容量估算方法.中山大学报（自然版），2010，49(6).53-47
[5]袁玉琪.中国风力发电项目电价和激励机制研究[D].华北电力大学，2007
[6]安艳丽.风力发电运行价值分析与研究：[河北农业大学硕士学位论文].郑州：河北农业大学农业电气化与自动化专业，2011：23-26
[7]钱科军，袁越，石晓丹，ZHOU Chengke，分布式发电环境效益.鞠平.中国电机工程学报.2008-10-15,28（29）；11-15
[8]张希良.可再生能源促进法论证报告.2005
[9]任博强，彭鸣鸿，蒋传文等.记及风电成本的电力系统短期经济调度建模：电力系统保护与控制.2010，38（14）68-72
[10] B.Singh and L.B.Shilpkar.Steady state analysis of Single phase Self excitedInduction Generator. IEE Proc-Gener. Transm. Vol. 146, No. 5, September 1999, ,4821- 4829
[11] Mr.M.Senthilkumar. Optimal Capacitor for Maximum Output Power Tracking ofSelf Excited Induction Generator Using Fuzzy Logic Approach. (IJCSE)International Journal on Computer Science and Engineering. Vol. 02, No. 05,2010
[12] M.Senthil kumar, Dr.N.Kumaresan and Dr.M.Subbiah .Performance evaluation ofself excited induction generator using Fuzzy Logic. Power Electronics (IICPE),2010 India International Conference.
[13] M.H.Haque. Self-Excited Single-phase and Three-phase Induction Generators inRemote Areas. 5th International Conference on Electrical and ComputerEngineering. ICECE 2008
[14]张硕，李庚银，周明.考虑输电线路故障的风电场容量可信度计算.中国电机工程学报，2010,30（6）；19-25
[15]雷亚洲，王伟胜，印永华，等.一种静态安全约束下的确定电力系统风电准入功率极限的优化方法.中国电机工程学报，2001，21(6)：25-28
[16] Qianghua Fang, Le Ma, Xiangwu Yan, The Calculation of wind power penetrationlimit Based on DC power flow algorithm, Power and Energy EngineeringConference(APPEEC), 2010 Asia-Pacific
[17]郑国强，鲍海，陈树勇.基于近似线性规划的风电装机容量优化的改进算法.中国电机工程学报，2004，24(10)：68-71
[18]吴俊玲，周双喜，孙建锋，等.并网风力发电场的最大注入功率分析.电网技术，2004，28(2)：28232
[19]申洪，梁军，戴慧珠.基于电力系统暂态稳定分析的风电装机容量计算.电网技术，2002，26(8)：8-11
[20]雷亚洲，王伟胜，印永华，等.基于机会约束规划的风电风电装机容量计算.中国电机工程学报，2002，22(5)：32-35
[21] Xiaoqing Han, Yong Yan. Wind Power Penetration Limit Calculation Based onPower System Reliability, Sustainable Power Generation and Supply, 2009,SUPERGEN’09. International Conference on Page(s):1-4
[22]吴俊，李国杰，孙元章.基于随机规划的并网风电场最大注入功率计算.电网技术，2007，31(14)：15219
[23]乔嘉赓，徐飞，鲁宗相，等．基于相关机会规划的风电装机容量优化分析.电力系统自动化，2008，32(10)：84-87，103
[24] Schlueter. R.A, Park. G.L. A Modified Unit Commitment and Generation Controlfor Utilities with Large Wind Generation Penetrations. IEEE Transactions onPower Apparatus and Systems, Vol, PAS-104,No.7,July 1985
[25] Christensen J F , et al . Methods and models for evaluating the impact ofdecentralized generation. CIGRE Session, 1998
[26]王伟胜，冯双磊，张义斌.风电场最大装机容量和电网短路容量的关系，2005，9 (2)31-34.
[27] Wen-Tsuan Lai, Wei-Tzer Huang, Shiuan-Tai Chen, et al. Development of theShort-Circuit Capacities Curves for Distribution Systems Planning Using Matlab.Cybernetics and Intelligent Systems, 2006 IEEE Conference
[28]周双喜，王海超，陈寿孙.风力发电运行价值分析.电网技术，2006-7，30（14）；98-102
[29]刘振伟.风电并网影响及最大装机容量研究：[华中科技大学硕士学位论文] .武汉：华中科技大学电力系统及其自动化专业，2007，41-42
[30]万航羽.风电场模型研究及应用：[北京交通大学硕士学位论文].北京：北京交通大学电力系统及其自动化专业，2008：7-9
[31]魏学好，周浩.中国火力发电行业减排污染的环境价值标准估算[J].环境科学研究，2003,16(1)：53-57.
[32] IEC 61400-21：Wind Turbine Generator Systems.part 21：Measurement andAssessment of Power Quality Characteristics of Grid Connected WindTurbines[S].2001
[33] GRUBB M, JAMASB T, POLLITT M G. Delivering a low-carbon electricitysystem. Cambridge, UK：Cambridge, University Press,2008
[34]尹炼，刘文洲.风力发电[M].北京：中国电力出版社，2002.
[35]彭虎，郭玉峰，王松岩等.风电场分布特性的模式分析.电网技术，2010，34(9)：206-210
[36]徐玉琴，李学冬.基于改进免疫克隆算法的含分布式电源配电网规划方法.电网技术，2010，34(8)：96-101
[37] Artzner P, Delbaen F, Eber J, Heath D. Thinking Coherently. RISK, 1997, 10(11).68-71
[38]梁有为，胡志坚，陈友平.分布式发电及其在电力系统中的应用研究综述.电网技术，2003，12（2）；83-88
[39] Ion Boldea Syed A.Nasar. The Induction Machine Handbook.CRC Press,2002
[40]任博强，蒋传文，彭鸣鸿等.基于改进遗传算法的含风电场的电力系统短期经济调度及其风险管理.现代电力电，2010，27(1)；76-80
[41] Rockafellar R T, Uryasev S. Conditional Value-at-Risk for General LossDistributions. Journal of Banking and Finance. 2002, (26): 1443－1471
[42]胡军.电力资产分配的WCVaR的最优组合：[长沙理工大学硕士学位论文].长沙：长沙理工大学电力系统及其自动化专业，2009：25-29
[43]彭莎.CVaR理论在风电场穿透功率极限计算中的应用研究：[长沙理工大学硕士学位论文].长沙：长沙理工大学电力系统及其自动化专业，2011：23-26
[44]周任军，胡军，罗萧，胡敏，叶佳明.发电资产最优组合分配的WCVaR风险度量方法.长沙理工大学学报（自然版）.2009，6（3）38-42
[45] IPCC.Special report on carbon dioxide capture and storage . Cambridge：Cambridge [M] University Press,2005：2-4.
[46]甜春筝，李琼林，宋晓凯，风电场建模及其对接入电网稳定性的影响分析[J]．电力系统保护与控制，2009，1(10)：46-51．
[47]王壬，尚金成等.基于条件风险价值的购电组合优化及风险管理，电网技术，2006，30(20)：72-75
[48]张伯明，陈寿孙，严正.高等电力网络分析.清华大学出版社，2007，326－328
[49]风电场并网对系统影响分析及穿透功率极限优化算法：[华北电力大学硕士学位论文].北京：华北电力大学电力系统及其自动化专业，2004：45-46
[50]基于机会约束规划的含风电场电力系统优化调度研究：[广西大学硕士学位论文].南宁：广西大学电力系统及其自动化专业，2011：53-66
[51]吉庆丰.蒙特卡罗方法及其在水力学中的应用.南京：东南大学出版社，2004
[52]刘宝碇，赵金艳，王纲.不确定规划及应用.北京：清华大学出版社，2003
[53]宋连庆，何金武，闫广新等.并网风电场穿透功率极限确定方法探讨，可再生能源，2009，27(3)：35-38
[54] Kim Cherl-Jin ; Lee Kwan-Yong ; Kim Young-Tae ; Shin Heung-Kyo. Design andPerformance Analysis of Single phase Self excited Induction Generators.Electrical Machines and Systems, 2005. ICEMS 2005. 85-98
[55]廖萍，李兴源.风电场穿透功率极限计算方法综述.电网技术，2008，32（10）；5-12.
[56] Bertsimas D. Pachamanova D. Sim M. Robust linear optimization under generalnorms[J]. Operations Research Letters, 2004,32(2): 510-516
[57]张伯明，陈寿孙，严正.高等电力网络分析.清华大学出版社，2007，326－328
[58]电力工业部电力规划设计总院.电力系统设计手册.中国电力出版社，1998，188-189
[2]袁铁江，晁勤，李义岩，袁建党等.基于风电极限穿透功率的经济调度优化模型的研究.电力系统保护与控制，2011-01-11,39（1）.17-22
[3]赵海翔，关洪亮，范高峰等.基于静态安全和稳定约束的地区电网接入风电容量算法.中国电力，2007，40（3）78-83
[4]邓元昌，余志，流沙.基于尾流实验的风电场装机容量估算方法.中山大学报（自然版），2010，49(6).53-47
[5]袁玉琪.中国风力发电项目电价和激励机制研究[D].华北电力大学，2007
[6]安艳丽.风力发电运行价值分析与研究：[河北农业大学硕士学位论文].郑州：河北农业大学农业电气化与自动化专业，2011：23-26
[7]钱科军，袁越，石晓丹，ZHOU Chengke，分布式发电环境效益.鞠平.中国电机工程学报.2008-10-15,28（29）；11-15
[8]张希良.可再生能源促进法论证报告.2005
[9]任博强，彭鸣鸿，蒋传文等.记及风电成本的电力系统短期经济调度建模：电力系统保护与控制.2010，38（14）68-72
[10] B.Singh and L.B.Shilpkar.Steady state analysis of Single phase Self excitedInduction Generator. IEE Proc-Gener. Transm. Vol. 146, No. 5, September 1999, ,4821- 4829
[11] Mr.M.Senthilkumar. Optimal Capacitor for Maximum Output Power Tracking ofSelf Excited Induction Generator Using Fuzzy Logic Approach. (IJCSE)International Journal on Computer Science and Engineering. Vol. 02, No. 05,2010
[12] M.Senthil kumar, Dr.N.Kumaresan and Dr.M.Subbiah .Performance evaluation ofself excited induction generator using Fuzzy Logic. Power Electronics (IICPE),2010 India International Conference.
[13] M.H.Haque. Self-Excited Single-phase and Three-phase Induction Generators inRemote Areas. 5th International Conference on Electrical and ComputerEngineering. ICECE 2008
[14]张硕，李庚银，周明.考虑输电线路故障的风电场容量可信度计算.中国电机工程学报，2010,30（6）；19-25
[15]雷亚洲，王伟胜，印永华，等.一种静态安全约束下的确定电力系统风电准入功率极限的优化方法.中国电机工程学报，2001，21(6)：25-28
[16] Qianghua Fang, Le Ma, Xiangwu Yan, The Calculation of wind power penetrationlimit Based on DC power flow algorithm, Power and Energy EngineeringConference(APPEEC), 2010 Asia-Pacific
[17]郑国强，鲍海，陈树勇.基于近似线性规划的风电装机容量优化的改进算法.中国电机工程学报，2004，24(10)：68-71
[18]吴俊玲，周双喜，孙建锋，等.并网风力发电场的最大注入功率分析.电网技术，2004，28(2)：28232
[19]申洪，梁军，戴慧珠.基于电力系统暂态稳定分析的风电装机容量计算.电网技术，2002，26(8)：8-11
[20]雷亚洲，王伟胜，印永华，等.基于机会约束规划的风电风电装机容量计算.中国电机工程学报，2002，22(5)：32-35
[21] Xiaoqing Han, Yong Yan. Wind Power Penetration Limit Calculation Based onPower System Reliability, Sustainable Power Generation and Supply, 2009,SUPERGEN’09. International Conference on Page(s):1-4
[22]吴俊，李国杰，孙元章.基于随机规划的并网风电场最大注入功率计算.电网技术，2007，31(14)：15219
[23]乔嘉赓，徐飞，鲁宗相，等．基于相关机会规划的风电装机容量优化分析.电力系统自动化，2008，32(10)：84-87，103
[24] Schlueter. R.A, Park. G.L. A Modified Unit Commitment and Generation Controlfor Utilities with Large Wind Generation Penetrations. IEEE Transactions onPower Apparatus and Systems, Vol, PAS-104,No.7,July 1985
[25] Christensen J F , et al . Methods and models for evaluating the impact ofdecentralized generation. CIGRE Session, 1998
[26]王伟胜，冯双磊，张义斌.风电场最大装机容量和电网短路容量的关系，2005，9 (2)31-34.
[27] Wen-Tsuan Lai, Wei-Tzer Huang, Shiuan-Tai Chen, et al. Development of theShort-Circuit Capacities Curves for Distribution Systems Planning Using Matlab.Cybernetics and Intelligent Systems, 2006 IEEE Conference
[28]周双喜，王海超，陈寿孙.风力发电运行价值分析.电网技术，2006-7，30（14）；98-102
[29]刘振伟.风电并网影响及最大装机容量研究：[华中科技大学硕士学位论文] .武汉：华中科技大学电力系统及其自动化专业，2007，41-42
[30]万航羽.风电场模型研究及应用：[北京交通大学硕士学位论文].北京：北京交通大学电力系统及其自动化专业，2008：7-9
[31]魏学好，周浩.中国火力发电行业减排污染的环境价值标准估算[J].环境科学研究，2003,16(1)：53-57.
[32] IEC 61400-21：Wind Turbine Generator Systems.part 21：Measurement andAssessment of Power Quality Characteristics of Grid Connected WindTurbines[S].2001
[33] GRUBB M, JAMASB T, POLLITT M G. Delivering a low-carbon electricitysystem. Cambridge, UK：Cambridge, University Press,2008
[34]尹炼，刘文洲.风力发电[M].北京：中国电力出版社，2002.
[35]彭虎，郭玉峰，王松岩等.风电场分布特性的模式分析.电网技术，2010，34(9)：206-210
[36]徐玉琴，李学冬.基于改进免疫克隆算法的含分布式电源配电网规划方法.电网技术，2010，34(8)：96-101
[37] Artzner P, Delbaen F, Eber J, Heath D. Thinking Coherently. RISK, 1997, 10(11).68-71
[38]梁有为，胡志坚，陈友平.分布式发电及其在电力系统中的应用研究综述.电网技术，2003，12（2）；83-88
[39] Ion Boldea Syed A.Nasar. The Induction Machine Handbook.CRC Press,2002
[40]任博强，蒋传文，彭鸣鸿等.基于改进遗传算法的含风电场的电力系统短期经济调度及其风险管理.现代电力电，2010，27(1)；76-80
[41] Rockafellar R T, Uryasev S. Conditional Value-at-Risk for General LossDistributions. Journal of Banking and Finance. 2002, (26): 1443－1471
[42]胡军.电力资产分配的WCVaR的最优组合：[长沙理工大学硕士学位论文].长沙：长沙理工大学电力系统及其自动化专业，2009：25-29
[43]彭莎.CVaR理论在风电场穿透功率极限计算中的应用研究：[长沙理工大学硕士学位论文].长沙：长沙理工大学电力系统及其自动化专业，2011：23-26
[44]周任军，胡军，罗萧，胡敏，叶佳明.发电资产最优组合分配的WCVaR风险度量方法.长沙理工大学学报（自然版）.2009，6（3）38-42
[45] IPCC.Special report on carbon dioxide capture and storage . Cambridge：Cambridge [M] University Press,2005：2-4.
[46]甜春筝，李琼林，宋晓凯，风电场建模及其对接入电网稳定性的影响分析[J]．电力系统保护与控制，2009，1(10)：46-51．
[47]王壬，尚金成等.基于条件风险价值的购电组合优化及风险管理，电网技术，2006，30(20)：72-75
[48]张伯明，陈寿孙，严正.高等电力网络分析.清华大学出版社，2007，326－328
[49]风电场并网对系统影响分析及穿透功率极限优化算法：[华北电力大学硕士学位论文].北京：华北电力大学电力系统及其自动化专业，2004：45-46
[50]基于机会约束规划的含风电场电力系统优化调度研究：[广西大学硕士学位论文].南宁：广西大学电力系统及其自动化专业，2011：53-66
[51]吉庆丰.蒙特卡罗方法及其在水力学中的应用.南京：东南大学出版社，2004
[52]刘宝碇，赵金艳，王纲.不确定规划及应用.北京：清华大学出版社，2003
[53]宋连庆，何金武，闫广新等.并网风电场穿透功率极限确定方法探讨，可再生能源，2009，27(3)：35-38
[54] Kim Cherl-Jin ; Lee Kwan-Yong ; Kim Young-Tae ; Shin Heung-Kyo. Design andPerformance Analysis of Single phase Self excited Induction Generators.Electrical Machines and Systems, 2005. ICEMS 2005. 85-98
[55]廖萍，李兴源.风电场穿透功率极限计算方法综述.电网技术，2008，32（10）；5-12.
[56] Bertsimas D. Pachamanova D. Sim M. Robust linear optimization under generalnorms[J]. Operations Research Letters, 2004,32(2): 510-516
[57]张伯明，陈寿孙，严正.高等电力网络分析.清华大学出版社，2007，326－328
[58]电力工业部电力规划设计总院.电力系统设计手册.中国电力出版社，1998，188-189