基于风电场总功率条件分布的电力系统经济调度二次规划方法
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摘要
在含风电电力系统随机调度中,需要考虑由风电功率的预测误差导致的随机性成本,通常为风电功率随机变量的积分形式,并基于迭代算法求解。迭代算法在求解过程中由于步长选取等原因,难以保证较好的收敛性能。本文提出一种基于风电场总功率条件分布的经济调度二次规划方法,首先基于截断通用分布的混合形式对风电功率边缘分布建模,结合Copula理论,得到多风电场总功率条件分布,在避免使用高维分布的基础上考虑多风电场出力的相关性。以总功率条件分布为输入,建立同时优化机组出力和系统备用置信度的经济调度模型。将含风电功率积分形式的调度模型转化为二次规划形式,从而能够被现有的求解软件高效可靠求解。最后,在IEEE30-Bus标准系统中对本文方法进行了验证。
In the power system stochastic economic dispatch with wind power integration, the uncertainty cost caused by wind power forecast error needs to be considered. The uncertainty cost is usually formulated as an integral form of wind power random variable and solved based on an iterative algorithm, which is difficult to guarantee the convergence performance due to the step size selection. In this paper, a convex optimization for economic dispatch based on multiple wind farms sum power conditional distribution was proposed. Firstly, the wind power marginal distribution was modeled based on the mixture form of truncated versatile distribution. Copula theory was used to obtain the conditional distribution of multiple wind farms sum power, and the power correlation of multi wind farms was considered to avoid the use of high-dimensional distribution. Taking the sum power conditional distribution as input, an economic dispatch model was established to optimize the unit output and system reserve confidence. The economic dispatch model with wind power integration was transformed into a quadratic programming, which can be solved by off-the-shelf solver reliably and efficiently. Finally, the proposed methods were verified in IEEE 30-Bus system.
In the power system stochastic economic dispatch with wind power integration, the uncertainty cost caused by wind power forecast error needs to be considered. The uncertainty cost is usually formulated as an integral form of wind power random variable and solved based on an iterative algorithm, which is difficult to guarantee the convergence performance due to the step size selection. In this paper, a convex optimization for economic dispatch based on multiple wind farms sum power conditional distribution was proposed. Firstly, the wind power marginal distribution was modeled based on the mixture form of truncated versatile distribution. Copula theory was used to obtain the conditional distribution of multiple wind farms sum power, and the power correlation of multi wind farms was considered to avoid the use of high-dimensional distribution. Taking the sum power conditional distribution as input, an economic dispatch model was established to optimize the unit output and system reserve confidence. The economic dispatch model with wind power integration was transformed into a quadratic programming, which can be solved by off-the-shelf solver reliably and efficiently. Finally, the proposed methods were verified in IEEE 30-Bus system.
引文
[1]杨明,周安平,赵斌,等.电力系统运行调度中的高阶不确定性及其对策评述[J].电力系统自动化2018,42(12):179-189.Yang Ming,Zhou Anping,Zhao Bin,et al.Higherorder uncertainty and corresponding strategies of operation and dispatching for power system[J].Automation of Electric Power Systems,2018,42(12):179-189.
[2]Zhang Ning,Kang Chongqing,Xia Qing,et al.Aconvex model of risk-based unit commitment for day-ahead market clearing considering wind power uncertainty[J].IEEE Transactions on Power Systems,2014,30(3):1582-1592.
[3]Zhang Ning,Kang Chongqing,Xia Qing,et al.Modeling conditional forecast error for wind power in generation scheduling[J].IEEE Transactions on Power Systems,2014,29(3):1316-1324.
[4]Jiang Haiyan,Xu Jian,Sun Yuanzhang,et al.Dynamic reserve demand estimation model and cost-effectivity oriented reserve allocation strategy for multi-area system integrated with wind power[J].IET Generation,Transmission&Distribution,2018,12(7):1606-1620.
[5]南晓强,李群湛,赵元哲,等.计及风电预测可信度的经济调度及辅助决策方法[J].电力系统自动化,2013,37(19):61-67.Nan Xiaoqiang,Li Qunzhan,Zhao Yuanzhe,et al.An economic dispatch and decision making method based on credibility of wind power forecasting[J].Automation of Electric Power Systems,2013,37(19):61-67.
[6]王雅平,林舜江,杨智斌,等.微电网多目标随机动态优化调度算法[J].电工技术学报,2018,33(10):2196-2207.Wang Yaping,Lin Shunjiang,Yang Zhibin,et al.Multi-objective stochastic dynamic optimal dispatch algorithm of microgrid[J].Transactions of China Electrotechnical Society,2018,33(10):2196-2207.
[7]夏鹏,刘文颖,蔡万通,等.基于风电离散化概率序列的机会约束规划优化调度方法[J].电工技术学报,2018,33(21):5069-5079.Xia Peng,Liu Wenying,Cai Wantong,et al.Optimal scheduling method of chance constrained programming based on discrete wind power probability sequences[J].Transactions of China Electrotechnical Society,2018,33(21):5069-5079.
[8]孙欣,方陈,沈风,等.考虑风电出力不确定性的发用电机组组合方法[J].电工技术学报,2017,32(4):204-211.Sun Xin,Fang Chen,Shen Feng,et al.An integrated generation-consumption unit commitment model considering the uncertainty of wind power[J].Transactions of China Electrotechnical Society,2017,32(4):204-211.
[9]王红,张文,刘玉田.考虑分布式电源出力不确定性的主动配电网量测配置[J].电力系统自动化,2016,40(12):9-14,74.Wang Hong,Zhang Wen,Liu Yutian.Measurement placement in active distribution networks considering output uncertainty of distributed generators[J].Automation of Electric Power Systems,2016,40(12):9-14,74.
[10]张衡,程浩忠,曾平良,等.考虑经济性与安全性的发输电联合优化规划[J].电力系统自动化,201741(21):62-69.Zhang Heng,Cheng Haozhong,Zeng Pingliang,et al Generation and transmission expansion planning considering economy and safety[J].Automation of Electric Power Systems,2017,41(21):62-69.
[11]徐箭,洪敏,孙元章,等.基于经验Copula函数的多风电场出力动态场景生成方法及其在机组组合中的应用[J].电力自动化设备,2017,37(8):81-89.Xu Jian,Hong Min,Sun Yuanzhang,et al.Dynamic scenario generation based on empirical Copula function for outputs of multiple wind farms and its application in unit commitment[J].Electric Power Automation Equipment,2017,37(8):81-89.
[12]Hetzer John,Yu David C,Bhattarai K.An economic dispatch model incorporating wind power[J].IEEETransactions on Energy Conversion,2008,23(2):603-611.
[13]王豹,徐箭,孙元章,等.基于通用分布的含风电电力系统随机动态经济调度[J].电力系统自动化,2016,40(6):17-24.Wang Bao,Xu Jian,Sun Yuanzhang,et al.Stochastic dynamic economic dispatch of power systems considering wind power based on versatile probability distribution[J].Automation of Electric Power Systems,2016,40(6):17-24.
[14]Zhang Zhaosui,Sun Yuanzhang,Gao David Wenzhong,et al.A versatile probability distribution model for wind power forecast errors and its application in economic dispatch[J].IEEE Transactions on Power Systems,2013,28(3):3114-3125.
[15]Tang Chenghui,Xu Jian,Sun Yuanzhang,et al.Look-ahead economic dispatch with adjustable confidence interval based on a truncated versatile distribution model for wind power[J].IEEE Transactions on Power Systems,2018,33(2):1755-1767.
[16]黄大为,张伟,韩学山.基于自适应风电功率场景选取的有功调度模型[J].电力系统自动化,2013,37(19):68-73,92.Huang Dawei,Zhang Wei,Han Xueshan.Active power dispatch based on self-adaptive wind power scenario selection[J].Automation of Electric Power Systems,2013,37(19):68-73,92.
[17]Bouffard Fran?ois,Galiana Francisco D.Stochastic security for operations planning with significant wind power generation[C]//IEEE Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century,Pittsburgh Pa USA,2008:306-316.
[18]Morales Juan M,Conejo Antonio J,Perez-Ruiz Juan.Economic valuation of reserves in power systems with high penetration of wind power[J].IEEETransactions on Power Systems,2009,24(2):900-910.
[19]Papavasiliou Anthony,Oren Shmuel S,O'neill Richard P.Reserve requirements for wind power integration:a scenario-based stochastic programming framework[J].IEEE Transactions on Power Systems,2011,26(4):2197-2206.
[20]Zhou Boran,Geng Guangchao,Jiang Quanyuan Hierarchical unit commitment with uncertain wind power generation[J].IEEE Transactions on Power Systems,2015,31(1):94-104.
[21]赵冬梅,殷加玞.考虑源荷双侧不确定性的模糊随机机会约束优先目标规划调度模型[J].电工技术学报,2018,33(5):1076-1085.Zhao Dongmei,Yin Jiafu.Fuzzy random chance constrained preemptive goal programming scheduling model considering source-side and load-side uncertainty[J].Transactions of China Electrotechnical Society,2018,33(5):1076-1085.
[22]甘伟,艾小猛,方家琨,等.风-火-水-储-气联合优化调度策略[J].电工技术学报,2017,32(增刊1):11-20.Gan Wei,Ai Xiaomeng,Fang Jiakun,et al.Coordinated optimal operation of the wind,coal,hydro,gas units with energy storage[J].Transactions of China Electrotechnical Society,2017,32(S1):11-20.
[23]Yan Xihui,Quintana Victor H.An efficient predictorcorrector interior point algorithm for securityconstrained economic dispatch[J].IEEE Transactions on Power Systems,1997,12(2):803-810.
[24]Draxl Caroline,Clifton Andrew,Hodge Bri-Mathias The wind integration national dataset(wind)toolkit[J].Applied Energy,2015,151:355-366.
[2]Zhang Ning,Kang Chongqing,Xia Qing,et al.Aconvex model of risk-based unit commitment for day-ahead market clearing considering wind power uncertainty[J].IEEE Transactions on Power Systems,2014,30(3):1582-1592.
[3]Zhang Ning,Kang Chongqing,Xia Qing,et al.Modeling conditional forecast error for wind power in generation scheduling[J].IEEE Transactions on Power Systems,2014,29(3):1316-1324.
[4]Jiang Haiyan,Xu Jian,Sun Yuanzhang,et al.Dynamic reserve demand estimation model and cost-effectivity oriented reserve allocation strategy for multi-area system integrated with wind power[J].IET Generation,Transmission&Distribution,2018,12(7):1606-1620.
[5]南晓强,李群湛,赵元哲,等.计及风电预测可信度的经济调度及辅助决策方法[J].电力系统自动化,2013,37(19):61-67.Nan Xiaoqiang,Li Qunzhan,Zhao Yuanzhe,et al.An economic dispatch and decision making method based on credibility of wind power forecasting[J].Automation of Electric Power Systems,2013,37(19):61-67.
[6]王雅平,林舜江,杨智斌,等.微电网多目标随机动态优化调度算法[J].电工技术学报,2018,33(10):2196-2207.Wang Yaping,Lin Shunjiang,Yang Zhibin,et al.Multi-objective stochastic dynamic optimal dispatch algorithm of microgrid[J].Transactions of China Electrotechnical Society,2018,33(10):2196-2207.
[7]夏鹏,刘文颖,蔡万通,等.基于风电离散化概率序列的机会约束规划优化调度方法[J].电工技术学报,2018,33(21):5069-5079.Xia Peng,Liu Wenying,Cai Wantong,et al.Optimal scheduling method of chance constrained programming based on discrete wind power probability sequences[J].Transactions of China Electrotechnical Society,2018,33(21):5069-5079.
[8]孙欣,方陈,沈风,等.考虑风电出力不确定性的发用电机组组合方法[J].电工技术学报,2017,32(4):204-211.Sun Xin,Fang Chen,Shen Feng,et al.An integrated generation-consumption unit commitment model considering the uncertainty of wind power[J].Transactions of China Electrotechnical Society,2017,32(4):204-211.
[9]王红,张文,刘玉田.考虑分布式电源出力不确定性的主动配电网量测配置[J].电力系统自动化,2016,40(12):9-14,74.Wang Hong,Zhang Wen,Liu Yutian.Measurement placement in active distribution networks considering output uncertainty of distributed generators[J].Automation of Electric Power Systems,2016,40(12):9-14,74.
[10]张衡,程浩忠,曾平良,等.考虑经济性与安全性的发输电联合优化规划[J].电力系统自动化,201741(21):62-69.Zhang Heng,Cheng Haozhong,Zeng Pingliang,et al Generation and transmission expansion planning considering economy and safety[J].Automation of Electric Power Systems,2017,41(21):62-69.
[11]徐箭,洪敏,孙元章,等.基于经验Copula函数的多风电场出力动态场景生成方法及其在机组组合中的应用[J].电力自动化设备,2017,37(8):81-89.Xu Jian,Hong Min,Sun Yuanzhang,et al.Dynamic scenario generation based on empirical Copula function for outputs of multiple wind farms and its application in unit commitment[J].Electric Power Automation Equipment,2017,37(8):81-89.
[12]Hetzer John,Yu David C,Bhattarai K.An economic dispatch model incorporating wind power[J].IEEETransactions on Energy Conversion,2008,23(2):603-611.
[13]王豹,徐箭,孙元章,等.基于通用分布的含风电电力系统随机动态经济调度[J].电力系统自动化,2016,40(6):17-24.Wang Bao,Xu Jian,Sun Yuanzhang,et al.Stochastic dynamic economic dispatch of power systems considering wind power based on versatile probability distribution[J].Automation of Electric Power Systems,2016,40(6):17-24.
[14]Zhang Zhaosui,Sun Yuanzhang,Gao David Wenzhong,et al.A versatile probability distribution model for wind power forecast errors and its application in economic dispatch[J].IEEE Transactions on Power Systems,2013,28(3):3114-3125.
[15]Tang Chenghui,Xu Jian,Sun Yuanzhang,et al.Look-ahead economic dispatch with adjustable confidence interval based on a truncated versatile distribution model for wind power[J].IEEE Transactions on Power Systems,2018,33(2):1755-1767.
[16]黄大为,张伟,韩学山.基于自适应风电功率场景选取的有功调度模型[J].电力系统自动化,2013,37(19):68-73,92.Huang Dawei,Zhang Wei,Han Xueshan.Active power dispatch based on self-adaptive wind power scenario selection[J].Automation of Electric Power Systems,2013,37(19):68-73,92.
[17]Bouffard Fran?ois,Galiana Francisco D.Stochastic security for operations planning with significant wind power generation[C]//IEEE Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century,Pittsburgh Pa USA,2008:306-316.
[18]Morales Juan M,Conejo Antonio J,Perez-Ruiz Juan.Economic valuation of reserves in power systems with high penetration of wind power[J].IEEETransactions on Power Systems,2009,24(2):900-910.
[19]Papavasiliou Anthony,Oren Shmuel S,O'neill Richard P.Reserve requirements for wind power integration:a scenario-based stochastic programming framework[J].IEEE Transactions on Power Systems,2011,26(4):2197-2206.
[20]Zhou Boran,Geng Guangchao,Jiang Quanyuan Hierarchical unit commitment with uncertain wind power generation[J].IEEE Transactions on Power Systems,2015,31(1):94-104.
[21]赵冬梅,殷加玞.考虑源荷双侧不确定性的模糊随机机会约束优先目标规划调度模型[J].电工技术学报,2018,33(5):1076-1085.Zhao Dongmei,Yin Jiafu.Fuzzy random chance constrained preemptive goal programming scheduling model considering source-side and load-side uncertainty[J].Transactions of China Electrotechnical Society,2018,33(5):1076-1085.
[22]甘伟,艾小猛,方家琨,等.风-火-水-储-气联合优化调度策略[J].电工技术学报,2017,32(增刊1):11-20.Gan Wei,Ai Xiaomeng,Fang Jiakun,et al.Coordinated optimal operation of the wind,coal,hydro,gas units with energy storage[J].Transactions of China Electrotechnical Society,2017,32(S1):11-20.
[23]Yan Xihui,Quintana Victor H.An efficient predictorcorrector interior point algorithm for securityconstrained economic dispatch[J].IEEE Transactions on Power Systems,1997,12(2):803-810.
[24]Draxl Caroline,Clifton Andrew,Hodge Bri-Mathias The wind integration national dataset(wind)toolkit[J].Applied Energy,2015,151:355-366.