基于稀疏多项式混沌展开的可用输电能力不确定性量化分析
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摘要
作为未来电力系统的重要特征,高比例可再生能源并网显著增强了电力系统运行的不确定性。在此背景下,量化不确定性因素对可用输电能力(available transfer capability,ATC)的影响,对于保障电力市场交易顺利开展和互联电网安全稳定运行具有重要意义。为此,提出一种基于稀疏多项式混沌展开(sparse polynomial chaos expansion,sPCE)的概率ATC计算和全局灵敏度分析(global sensitivity analysis,GSA)方法。该方法仅需要较少次数的确定性ATC计算便能够获得ATC概率特征和输入随机变量的全局灵敏度指标。通过IEEE118节点系统下多个测试场景的算例分析,验证了所提方法的有效性。
As the important feature of future power systems, high proportion of renewable energy integration increases the operational uncertainty of the power system. The fast and accurate evaluation of available transfer capability(ATC) is of great significance to ensure electricity market transaction and stability of interconnected grids. Quantifying the impact of uncertainty factors can help the following planning and operating of the system. Therefore, a sparse polynomial chaos expansion(sPCE) based probabilistic ATC assessment and global sensitivity analysis(GSA) method was proposed. In the method, sPCE was built after few times of deterministic ATC evaluations and employed instead of the original model to perform the probabilistic ATC and calculate the sensitivity indices. The case studies on IEEE 118 bus system with several scenarios demonstrated the effectiveness of the proposed method.
As the important feature of future power systems, high proportion of renewable energy integration increases the operational uncertainty of the power system. The fast and accurate evaluation of available transfer capability(ATC) is of great significance to ensure electricity market transaction and stability of interconnected grids. Quantifying the impact of uncertainty factors can help the following planning and operating of the system. Therefore, a sparse polynomial chaos expansion(sPCE) based probabilistic ATC assessment and global sensitivity analysis(GSA) method was proposed. In the method, sPCE was built after few times of deterministic ATC evaluations and employed instead of the original model to perform the probabilistic ATC and calculate the sensitivity indices. The case studies on IEEE 118 bus system with several scenarios demonstrated the effectiveness of the proposed method.
引文
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[13]Wu Hao,Zhou Yongzhi,Dong Shufeng,et al.Probabilistic load flow based on generalized polynomial chaos[J].IEEE Transactions on Power Systems,2017,32(1):820-821.
[14]Sheng Hao,Wang Xiaozhe.Applying polynomial chaos expansion to assess probabilistic available delivery capability for distribution networks with renewables[J].IEEE Transactions on Power Systems,2018,33(6):6726-6735.
[15]Sobol I M.Sensitivity estimates for nonlinear mathematical models[J].Mathematical Modelling and Computational Experiment,1993,1(4):407-414.
[16]Sobol I M.Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J].Mathematics and computers in simulation,2001,55(1-3):271-280.
[17]Xiu Dongbin.Numerical methods for stochastic computations:a spectral method approach[M].New Jersey:Princeton University Press,2010:68-88.
[18]Tropp J A.Greed is good:algorithmic results for sparse approximation[J].IEEE Transactions on Information Theory,2004,50(10):2231-2242.
[19]Ni Fei,Nijhuis M,Nguyen P H,et al.Variance-based global sensitivity analysis for power systems[J].IEEETransactions on Power Systems,2018,33(2):1670-1682.
[20]Index of data Illinois Institute of Technology[EB/OL].Chicago,IL:Illinois Institute of Technology.http://motor.ece.iit.edu/data/.
[2]康重庆,姚良忠.高比例可再生能源电力系统的关键科学问题与理论研究框架[J].电力系统自动化,2017,41(9):2-11.Kang Chongqing,Yao Liangzhong.Key scientific issues and theoretical research framework for power systems with high proportion of renewable energy[J].Automation of Electric Power Systems,2017,41(9):2-11(in Chinese).
[3]Du Pengwei,Li Weifeng,Ke Xinda,et al.Probabilisticbased available transfer capability assessment considering existing and future wind generation resources[J].IEEETransactions on Sustainable Energy,2015,6(4):1263-1271.
[4]Rodrigues A B,da Silva M G.Probabilistic assessment of available transfer capability based on Monte Carlo method with sequential simulation[J].IEEE Transactions on Power Systems,2007,22(1):484-492.
[5]罗钢,石东源,蔡德福,等.计及相关性的含风电场电力系统概率可用输电能力快速计算[J].中国电机工程学报,2014,34(7):1024-1032.Luo Gang,Shi Dongyuan,Cai Defu,et al.Fast calculation of probabilistic available transfer capability considering correlation in wind power integrated systems[J].Proceedings of the CSEE,2014,34(7):1024-1032(in Chinese).
[6]王成山,王兴刚,孙玮.含大型风电场的电力系统概率最大输电能力快速计算[J].中国电机工程学报,2008,28(10):56-62.Wang Chengshan,Wang Xinggang,Sun Wei.Fast calculation and analysis of probabilistic total transfer capability in power system including large-scale wind farms[J].Proceedings of the CSEE,2008,28(10):56-62(in Chinese).
[7]李欣然,贺仁睦,章健,等.负荷特性对电力系统静态电压稳定性的影响及静态电压稳定性广义实用判据[J].中国电机工程学报,1999,19(4):26-30.Li Xinran,He Renmu,Zhang Jian,et al.Effect of load characteristics on power system stead-state voltage stability and the practical criterion of voltage stability[J].Proceedings of the CSEE,1999,19(4):26-30(in Chinese).
[8]Hiskens I A,Alseddiqui J.Sensitivity,approximation,and uncertainty in power system dynamic simulation[J].IEEE Transactions on Power Systems,2006,21(4):1808-1820.
[9]闫常友,周孝信,康建东,等.潮流转移灵敏度以及安全评估指标研究[J].中国电机工程学报,2010,30(19):7-13.Yan Changyou,Zhou Xiaoxin,Kang Jiandong,et al.Flow transferring sensitivity and security index analysis[J].Proceedings of the CSEE,2010,30(19):7-13(in Chinese).
[10]Preece R,Milanovi?J V.Assessing the applicability of uncertainty importance measures for power system studies[J].IEEE Transactions on Power Systems,2016,31(3):2076-2084.
[11]Xiu Dongbin,Karniadakis G E.Modeling uncertainty in flow simulations via generalized polynomial chaos[J].Journal of Computational Physics,2003,187(1):137-167.
[12]鲍海波,韦化.考虑风电的电压稳定概率评估的随机响应面法[J].中国电机工程学报,2012,32(13):77-85.Bao Haibo,Wei Hua.A stochastic response surface method for probabilistic evaluation of the voltage stability considering wind power[J].Proceedings of the CSEE,2012,32(13):77-85(in Chinese).
[13]Wu Hao,Zhou Yongzhi,Dong Shufeng,et al.Probabilistic load flow based on generalized polynomial chaos[J].IEEE Transactions on Power Systems,2017,32(1):820-821.
[14]Sheng Hao,Wang Xiaozhe.Applying polynomial chaos expansion to assess probabilistic available delivery capability for distribution networks with renewables[J].IEEE Transactions on Power Systems,2018,33(6):6726-6735.
[15]Sobol I M.Sensitivity estimates for nonlinear mathematical models[J].Mathematical Modelling and Computational Experiment,1993,1(4):407-414.
[16]Sobol I M.Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J].Mathematics and computers in simulation,2001,55(1-3):271-280.
[17]Xiu Dongbin.Numerical methods for stochastic computations:a spectral method approach[M].New Jersey:Princeton University Press,2010:68-88.
[18]Tropp J A.Greed is good:algorithmic results for sparse approximation[J].IEEE Transactions on Information Theory,2004,50(10):2231-2242.
[19]Ni Fei,Nijhuis M,Nguyen P H,et al.Variance-based global sensitivity analysis for power systems[J].IEEETransactions on Power Systems,2018,33(2):1670-1682.
[20]Index of data Illinois Institute of Technology[EB/OL].Chicago,IL:Illinois Institute of Technology.http://motor.ece.iit.edu/data/.