基于vine-Copula的发电商运营损益动态风险VaR评估方法
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摘要
电力市场环境下,负荷和电价的波动、可再生电源的随机出力、网络拓扑结构的变化、系统运行方式的调整等大量不确定因素为发电商的运营收益增加了不同程度的风险。为了帮助发电商准确评估自身风险并以此制定合适的报价策略及机组发电计划,提出了基于vine-Copula理论的发电商损益风险价值(VaR)评估模型。首先,基于交流潮流,建立了电网日前动态经济调度最优潮流模型,用以计算节点边际电价;随后,引入pair-Copula理论构建了多个发电商损益函数的高维vine-Copula相依结构;最后,通过VaR的定义求出不同置信度下发电商运营组合风险的VaR值。基于IEEE 39节点系统的算例验证了所提模型和方法的有效性。
In the power market environment, the fluctuation of load and electricity price, the random output of renewable power supply, the change of network topology, the adjustment of the system operation mode and a large number of uncertainties add risks for the operating income of generation companies(GenCos). In order to help GenCos accurately evaluate their own risks and formulate appropriate bidding strategies and generating unit plans, a vine-Copula theory based value at risk(VaR) evaluation model is presented for the profit and loss of GenCos. Firstly, based on the AC power flow, the optimal power flow model for day-ahead dynamic economic dispatch of power grid is established to calculate the locational marginal price. Then, the pair-Copula theory is introduced to construct the high dimensional vine-Copula dependent structure of the profit and loss functions of GenCos. Finally, the VaRs of operating combined risk of GenCos under different confidence levels are calculated based on the definition of VaR. The example of IEEE 39-bus system is taken to verify the effectiveness of the proposed model and method.
In the power market environment, the fluctuation of load and electricity price, the random output of renewable power supply, the change of network topology, the adjustment of the system operation mode and a large number of uncertainties add risks for the operating income of generation companies(GenCos). In order to help GenCos accurately evaluate their own risks and formulate appropriate bidding strategies and generating unit plans, a vine-Copula theory based value at risk(VaR) evaluation model is presented for the profit and loss of GenCos. Firstly, based on the AC power flow, the optimal power flow model for day-ahead dynamic economic dispatch of power grid is established to calculate the locational marginal price. Then, the pair-Copula theory is introduced to construct the high dimensional vine-Copula dependent structure of the profit and loss functions of GenCos. Finally, the VaRs of operating combined risk of GenCos under different confidence levels are calculated based on the definition of VaR. The example of IEEE 39-bus system is taken to verify the effectiveness of the proposed model and method.
引文
[1] 马莉,文福拴,倪以信,等.考虑风险约束的发电公司报价策略研究[J].电力系统自动化,2003,27(23):6-11.MA Li, WEN Fushuan, NI Yixin, et al. Risk-constrained optimal bidding strategies for generation companies in electricity market environment[J]. Automation of Electric Power Systems, 2003, 27(23): 6-11.
[2] RODRIGUEZ C P, ANDERS G J. Bidding strategy design for different types of electric power market participants[J]. IEEE Transactions on Power Systems, 2004, 19(2): 964-971.
[3] HUANG Hao, LI Fangxing. Bidding strategy for wind generation considering conventional generation and transmission constraints[J]. Journal of Modern Power Systems and Clean Energy, 2015, 3(1): 51-62.
[4] 祝锦舟,张焰,杨增辉,等.一种含风电场的发电系统可靠性解析计算方法[J].中国电机工程学报,2017,16(16):4671-4679.ZHU Jinzhou, ZHANG Yan, YANG Zenghui, et al. An analytical method for reliability evaluation of generation system with wind farm[J]. Proceedings of the CSEE, 2017, 16(16): 4671-4679.
[5] LISNIANSKI A, ELMAKIAS D, LAREDO D, et al. A multi-state Markov model for a short-term reliability analysis of a power generating unit[J]. Reliability Engineering & System Safety, 2012, 98(1): 1-6.
[6] ROY B, RAJESH K, YI Gao, et al. Adequacy assessment considerations in wind integrated power systems[J]. IEEE Transactions on Power Systems, 2012, 27(4): 2297-2305.
[7] 刘文霞,秦浩,王凌飞,等.考虑失负荷风险的配电网光/储与计划孤岛协同规划[J].电力系统自动化,2017,41(19):30-36.DOI:10.7500/AEPS20161215007.LIU Wenxia, QIN Hao, WANG Lingfei, et al. Coordinated planning of photovoltaic/battery energy storage and planned island in distribution networks considering risk of lost load[J]. Automation of Electric Power Systems, 2017, 41(19): 30-36.DOI: 10.7500/AEPS20161215007.
[8] 丁明,钱宇骋,张晶晶,等.基于风险评估的电力系统连锁故障协调控制模型[J].电力系统自动化,2016,40(7):1-8.DING Ming, QIAN Yucheng, ZHANG Jingjing, et al. Coordinated control model of power system cascading failures based on risk assessment[J]. Automation of Electric Power Systems, 2016, 40(7): 1-8.
[9] 蒋程,刘文霞,张建华,等.含风电接入的发输电系统风险评估[J].电工技术学报,2014,29(2):260-270.JIANG Cheng, LIU Wenxia, ZHANG Jianhua, et al. Risk assessment of generation and transmission systems considering wind power penetration[J]. Transactions of China Electrotechnical Society, 2014, 29(2): 260-270.
[10] 康重庆,白利超,夏清,等.电力市场中发电商的风险决策[J].中国电机工程学报,2004,24(8):4-9.KANG Chongqing, BAI Lichao, XIA Qing, et al. Risk decision-making of generators in electricity market[J]. Proceedings of the CSEE, 2004, 24(8): 4-9.
[11] 张少华,王晛,康小宁,等.计入发电商风险偏好的电力市场古诺均衡分析[J].电网技术,2011,9(9):176-180.ZHANG Shaohua, WANG Xian, KANG Xiaoning, et al. Integration of Genco’s risk preference in Cournot equilibrium analysis of electricity markets[J]. Power System Technology, 2011, 9(9): 176-180.
[12] 刘敏,吴复立.电力市场环境下发电商电能分配策略研究[J].中国电机工程学报,2008,28(25):111-117.LIU Min, WU Fuli. Trading strategy of generation company in electricity market[J]. Proceedings of the CSEE, 2008, 28(25): 111-117.
[13] 周辉,侯云鹤,吴耀武,等.现货市场中考虑系统运行约束的发电投资风险估计[J].中国电机工程学报,2008,28(13):99-105.ZHOU Hui, HOU Yunhe, WU Yaowu, et al. Risk assessment of generation investment in spot market considering operation constraints[J]. Proceedings of the CSEE, 2008, 28(13): 99-105.
[14] 卫志农,陈妤,黄文进,等.考虑条件风险价值的虚拟电厂多电源容量优化配置模型[J].电力系统自动化,2018,42(4):39-46.DOI:10.7500/AEPS20170621008.WEI Zhinong, CHEN Yu, HUANG Wenjin, et al. Optimal allocation model for multi-energy capacity of virtual power plant considering conditional value-at-risk[J]. Automation of Electric Power Systems, 2018, 42(4): 39-46. DOI:10.7500/AEPS20170621008.
[15] 张兴平,陈玲,武润莲.加权CVaR下的发电商多时段投标组合模型[J].中国电机工程学报,2008,28(16):79-83.ZHANG Xingping, CHEN Ling, WU Runlian. Analysis of multi-period combined bidding of power suppliers based on weighted CVaR[J]. Proceedings of the CSEE, 2008, 28(16): 79-83.
[16] 吕梦璇,娄素华,刘建琴,等.含高比例风电的虚拟电厂多类型备用协调优化[J].中国电机工程学报,2018,38(10):2874-2882.Lü Mengxuan, LOU Suhua, LIU Jianqin, et al. Coordinated optimization of multi-type reserve in virtual power plant accommodated high shares of wind power[J]. Proceedings of the CSEE, 2018, 38(10): 2874-2882.
[17] CONEJO A, RAQUEL G, CARRION M. Optimal involvement in futures markets of a power producer[J]. IEEE Transactions on Power Systems, 2008, 23(2): 703-711.
[18] 张江林,夏榆杭,段登伟,等.基于WCVaR评估的虚拟发电厂能量市场收益-风险模型[J].电力系统自动化,2017,41(9):77-83.DOI:10.7500/AEPS20160716004.ZHANG Jianglin, XIA Yuhang, DUAN Dengwei, et al. Benefit-risk model of virtual power plant in energy market based on WCVaR assessment[J]. Automation of Electric Power Systems, 2017, 41(9): 77-83. DOI: 10.7500/AEPS20160716004.
[19] 蔡泓忻.新电改下发电企业多市场交易收益分析及营销策略研究[D].北京:华北电力大学,2017.CAI Hongxin. Research on multi-market transaction benefit and marketing strategy of power generation enterprise under the new reform of electric power system[D]. Beijing: North China Electric Power University, 2017.
[20] 陈亮亮.风力发电项目风险评价与控制研究[D].北京:华北电力大学,2016.CHEN Liangliang. The risk assessment and control research of the wind power projects[D]. Beijing: North China Electric Power University, 2016.
[21] CHOI J Y, RIM S H, PARK J H. Optimal real time pricing of real and reactive powers[J]. IEEE Transactions on Power Systems, 1998, 13(4): 1226-1231.
[22] 宋嗣博,郭红霞,杨苹,等.基于节点边际电价的电力市场分区策略研究[J].电力建设,2017,38(9):132-138.SONG Sibo, GUO Hongxia, YANG Ping, et al. Electricity market partitioning strategy based on locational marginal price[J]. Electric Power Construction, 2017, 38(9): 132-138.
[23] 刘琳,侯志俭,于佐东.输电阻塞情况下电能计价的LMP方法[J].华东电力,2004,32(8):26-29.LIU Lin, HOU Zhijian, YU Zuodong. LMP method for electricity pricing during power transmission congestion[J]. East China Electric Power, 2004, 32(8): 26-29.
[24] HOLTON G A. Value at risk:theory and practice[M]. London, UK: Academic Press, 2003.
[25] 何建华,何祖威,胡效雷.基于成本分析的火电厂日前市场竞价上网报价[J].重庆大学学报(自然科学版),2008,31(3):276-279.HE Jianhua, HE Zuwei, HU Xiaolei. Study of quotes on the web for electric power in market based on cost analysis[J]. Journal of Chongqing University(Natural Science Edition), 2008, 31(3): 276-279.
[26] 胡青.基于Copula的投资组合风险分析[J].中小企业管理与科技,2018,1(1):67-70.HU Qing. Portfolio risk analysis based on Copula[J]. Management & Technology of SME, 2018, 1(1): 67-70.
[27] 鲁思瑶,徐美萍.基于扭曲混合Copula和ARMA-GARCH-t模型的投资组合风险分析——以上证综指、中证综合债和上证基金为例[J].数理统计与管理,2017,36(6):1131-1140.LU Siyao, XU Meiping. Risk analysis for portfolio based on distorted mixture-Copula and ARMA-GARCH-t model—taking Shanghai Composite Index,CSI Universe Bond Index and SSE Fund Index for example[J]. Jouranl of Applied Statistics and Management, 2017, 36(6): 1131-1140.
[28] 贺学强,易丹辉.基于动态Copula方法的股票组合VaR估计[J].统计与决策,2010(17):11-14.HE Xueqiang, YI Danhui. VaR estimation of stock portfolio based on dynamic Copula method[J]. Statistics and Decision, 2010(17): 11-14.
[29] NELSEN R B. An introduction to Copulas[M]. Heidelberg, Germany: Springer-Verlag, 1999.
[30] BEDFORD T, COOKE R M. Probability density decomposition for conditionally dependent random variables modeled by vines[J]. Annals of Mathematics and Artificial Intelligence, 2001, 32(1): 245-268.
[31] 马锋,魏宇,黄登仕.基于vine Copula方法的股市组合动态VaR测度及预测模型研究[J].系统工程理论与实践,2015,35(1):26-36.MA Feng, WEI Yu, HUANG Dengshi. Measurement of dynamic stocks portfolio VaR and its forecasting model based on vine Copula[J]. Systems Engineering—Theory & Practice, 2015, 35(1): 26-36.
[32] AKAIKE H. A new look at the statistical model identification[J]. IEEE Transactions on Automatic Control, 1974, 19(6): 716-723.
[33] 谢恺,宋依群,唐佳晖.发电商最优备用报价策略研究[J].电力系统保护与控制,2011,39(18):8-13.XIE Kai, SONG Yiqun, TANG Jiahui. Study on Genco’ optimal bidding strategies in reserve market[J]. Power System Protection and Control, 2011, 39(18): 8-13.
[34] 柏满迎,孙禄杰.三种Copula-VaR计算方法与传统VaR方法的比较[J].数量经济技术经济研究,2007,24(2):154-160.BAI Manying, SUN Lujie. The comparison between three Copula-VaR approaches and traditional VaR methods[J]. The Journal of Quantitative & Technical Economics, 2007, 24(2): 154-160.continuedonpage52)continued from page 45)
[2] RODRIGUEZ C P, ANDERS G J. Bidding strategy design for different types of electric power market participants[J]. IEEE Transactions on Power Systems, 2004, 19(2): 964-971.
[3] HUANG Hao, LI Fangxing. Bidding strategy for wind generation considering conventional generation and transmission constraints[J]. Journal of Modern Power Systems and Clean Energy, 2015, 3(1): 51-62.
[4] 祝锦舟,张焰,杨增辉,等.一种含风电场的发电系统可靠性解析计算方法[J].中国电机工程学报,2017,16(16):4671-4679.ZHU Jinzhou, ZHANG Yan, YANG Zenghui, et al. An analytical method for reliability evaluation of generation system with wind farm[J]. Proceedings of the CSEE, 2017, 16(16): 4671-4679.
[5] LISNIANSKI A, ELMAKIAS D, LAREDO D, et al. A multi-state Markov model for a short-term reliability analysis of a power generating unit[J]. Reliability Engineering & System Safety, 2012, 98(1): 1-6.
[6] ROY B, RAJESH K, YI Gao, et al. Adequacy assessment considerations in wind integrated power systems[J]. IEEE Transactions on Power Systems, 2012, 27(4): 2297-2305.
[7] 刘文霞,秦浩,王凌飞,等.考虑失负荷风险的配电网光/储与计划孤岛协同规划[J].电力系统自动化,2017,41(19):30-36.DOI:10.7500/AEPS20161215007.LIU Wenxia, QIN Hao, WANG Lingfei, et al. Coordinated planning of photovoltaic/battery energy storage and planned island in distribution networks considering risk of lost load[J]. Automation of Electric Power Systems, 2017, 41(19): 30-36.DOI: 10.7500/AEPS20161215007.
[8] 丁明,钱宇骋,张晶晶,等.基于风险评估的电力系统连锁故障协调控制模型[J].电力系统自动化,2016,40(7):1-8.DING Ming, QIAN Yucheng, ZHANG Jingjing, et al. Coordinated control model of power system cascading failures based on risk assessment[J]. Automation of Electric Power Systems, 2016, 40(7): 1-8.
[9] 蒋程,刘文霞,张建华,等.含风电接入的发输电系统风险评估[J].电工技术学报,2014,29(2):260-270.JIANG Cheng, LIU Wenxia, ZHANG Jianhua, et al. Risk assessment of generation and transmission systems considering wind power penetration[J]. Transactions of China Electrotechnical Society, 2014, 29(2): 260-270.
[10] 康重庆,白利超,夏清,等.电力市场中发电商的风险决策[J].中国电机工程学报,2004,24(8):4-9.KANG Chongqing, BAI Lichao, XIA Qing, et al. Risk decision-making of generators in electricity market[J]. Proceedings of the CSEE, 2004, 24(8): 4-9.
[11] 张少华,王晛,康小宁,等.计入发电商风险偏好的电力市场古诺均衡分析[J].电网技术,2011,9(9):176-180.ZHANG Shaohua, WANG Xian, KANG Xiaoning, et al. Integration of Genco’s risk preference in Cournot equilibrium analysis of electricity markets[J]. Power System Technology, 2011, 9(9): 176-180.
[12] 刘敏,吴复立.电力市场环境下发电商电能分配策略研究[J].中国电机工程学报,2008,28(25):111-117.LIU Min, WU Fuli. Trading strategy of generation company in electricity market[J]. Proceedings of the CSEE, 2008, 28(25): 111-117.
[13] 周辉,侯云鹤,吴耀武,等.现货市场中考虑系统运行约束的发电投资风险估计[J].中国电机工程学报,2008,28(13):99-105.ZHOU Hui, HOU Yunhe, WU Yaowu, et al. Risk assessment of generation investment in spot market considering operation constraints[J]. Proceedings of the CSEE, 2008, 28(13): 99-105.
[14] 卫志农,陈妤,黄文进,等.考虑条件风险价值的虚拟电厂多电源容量优化配置模型[J].电力系统自动化,2018,42(4):39-46.DOI:10.7500/AEPS20170621008.WEI Zhinong, CHEN Yu, HUANG Wenjin, et al. Optimal allocation model for multi-energy capacity of virtual power plant considering conditional value-at-risk[J]. Automation of Electric Power Systems, 2018, 42(4): 39-46. DOI:10.7500/AEPS20170621008.
[15] 张兴平,陈玲,武润莲.加权CVaR下的发电商多时段投标组合模型[J].中国电机工程学报,2008,28(16):79-83.ZHANG Xingping, CHEN Ling, WU Runlian. Analysis of multi-period combined bidding of power suppliers based on weighted CVaR[J]. Proceedings of the CSEE, 2008, 28(16): 79-83.
[16] 吕梦璇,娄素华,刘建琴,等.含高比例风电的虚拟电厂多类型备用协调优化[J].中国电机工程学报,2018,38(10):2874-2882.Lü Mengxuan, LOU Suhua, LIU Jianqin, et al. Coordinated optimization of multi-type reserve in virtual power plant accommodated high shares of wind power[J]. Proceedings of the CSEE, 2018, 38(10): 2874-2882.
[17] CONEJO A, RAQUEL G, CARRION M. Optimal involvement in futures markets of a power producer[J]. IEEE Transactions on Power Systems, 2008, 23(2): 703-711.
[18] 张江林,夏榆杭,段登伟,等.基于WCVaR评估的虚拟发电厂能量市场收益-风险模型[J].电力系统自动化,2017,41(9):77-83.DOI:10.7500/AEPS20160716004.ZHANG Jianglin, XIA Yuhang, DUAN Dengwei, et al. Benefit-risk model of virtual power plant in energy market based on WCVaR assessment[J]. Automation of Electric Power Systems, 2017, 41(9): 77-83. DOI: 10.7500/AEPS20160716004.
[19] 蔡泓忻.新电改下发电企业多市场交易收益分析及营销策略研究[D].北京:华北电力大学,2017.CAI Hongxin. Research on multi-market transaction benefit and marketing strategy of power generation enterprise under the new reform of electric power system[D]. Beijing: North China Electric Power University, 2017.
[20] 陈亮亮.风力发电项目风险评价与控制研究[D].北京:华北电力大学,2016.CHEN Liangliang. The risk assessment and control research of the wind power projects[D]. Beijing: North China Electric Power University, 2016.
[21] CHOI J Y, RIM S H, PARK J H. Optimal real time pricing of real and reactive powers[J]. IEEE Transactions on Power Systems, 1998, 13(4): 1226-1231.
[22] 宋嗣博,郭红霞,杨苹,等.基于节点边际电价的电力市场分区策略研究[J].电力建设,2017,38(9):132-138.SONG Sibo, GUO Hongxia, YANG Ping, et al. Electricity market partitioning strategy based on locational marginal price[J]. Electric Power Construction, 2017, 38(9): 132-138.
[23] 刘琳,侯志俭,于佐东.输电阻塞情况下电能计价的LMP方法[J].华东电力,2004,32(8):26-29.LIU Lin, HOU Zhijian, YU Zuodong. LMP method for electricity pricing during power transmission congestion[J]. East China Electric Power, 2004, 32(8): 26-29.
[24] HOLTON G A. Value at risk:theory and practice[M]. London, UK: Academic Press, 2003.
[25] 何建华,何祖威,胡效雷.基于成本分析的火电厂日前市场竞价上网报价[J].重庆大学学报(自然科学版),2008,31(3):276-279.HE Jianhua, HE Zuwei, HU Xiaolei. Study of quotes on the web for electric power in market based on cost analysis[J]. Journal of Chongqing University(Natural Science Edition), 2008, 31(3): 276-279.
[26] 胡青.基于Copula的投资组合风险分析[J].中小企业管理与科技,2018,1(1):67-70.HU Qing. Portfolio risk analysis based on Copula[J]. Management & Technology of SME, 2018, 1(1): 67-70.
[27] 鲁思瑶,徐美萍.基于扭曲混合Copula和ARMA-GARCH-t模型的投资组合风险分析——以上证综指、中证综合债和上证基金为例[J].数理统计与管理,2017,36(6):1131-1140.LU Siyao, XU Meiping. Risk analysis for portfolio based on distorted mixture-Copula and ARMA-GARCH-t model—taking Shanghai Composite Index,CSI Universe Bond Index and SSE Fund Index for example[J]. Jouranl of Applied Statistics and Management, 2017, 36(6): 1131-1140.
[28] 贺学强,易丹辉.基于动态Copula方法的股票组合VaR估计[J].统计与决策,2010(17):11-14.HE Xueqiang, YI Danhui. VaR estimation of stock portfolio based on dynamic Copula method[J]. Statistics and Decision, 2010(17): 11-14.
[29] NELSEN R B. An introduction to Copulas[M]. Heidelberg, Germany: Springer-Verlag, 1999.
[30] BEDFORD T, COOKE R M. Probability density decomposition for conditionally dependent random variables modeled by vines[J]. Annals of Mathematics and Artificial Intelligence, 2001, 32(1): 245-268.
[31] 马锋,魏宇,黄登仕.基于vine Copula方法的股市组合动态VaR测度及预测模型研究[J].系统工程理论与实践,2015,35(1):26-36.MA Feng, WEI Yu, HUANG Dengshi. Measurement of dynamic stocks portfolio VaR and its forecasting model based on vine Copula[J]. Systems Engineering—Theory & Practice, 2015, 35(1): 26-36.
[32] AKAIKE H. A new look at the statistical model identification[J]. IEEE Transactions on Automatic Control, 1974, 19(6): 716-723.
[33] 谢恺,宋依群,唐佳晖.发电商最优备用报价策略研究[J].电力系统保护与控制,2011,39(18):8-13.XIE Kai, SONG Yiqun, TANG Jiahui. Study on Genco’ optimal bidding strategies in reserve market[J]. Power System Protection and Control, 2011, 39(18): 8-13.
[34] 柏满迎,孙禄杰.三种Copula-VaR计算方法与传统VaR方法的比较[J].数量经济技术经济研究,2007,24(2):154-160.BAI Manying, SUN Lujie. The comparison between three Copula-VaR approaches and traditional VaR methods[J]. The Journal of Quantitative & Technical Economics, 2007, 24(2): 154-160.continuedonpage52)continued from page 45)