基于改进稀疏概率分配法的计及参数不确定性的电力系统时域仿真
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摘要
快速准确的电力系统不确定性时域仿真方法是电力系统不确定性动态及暂态分析的重要工具,其计算精度及速度亟待提升。该文提出了基于改进稀疏概率分配法的电力系统时域不确定性仿真新方法。首先提出了基于Kronrod方法的改进稀疏概率分配法,即利用Kronrod方法对高斯点进行拓展得到嵌套型高斯点,使样本集合满足嵌套特性,大幅度减少了样本数量,并且能适用于不确定参数服从任意分布的情形;进而将该方法应用于计及参数不确定性的电力系统时域仿真,得到了计及参数不确定性的电力系统时域仿真新方法。该文提出的方法可以综合考虑时域仿真中各种不确定参数的影响,快速获得不确定参数的概率密度函数、期望及方差。算例证明了该方法的有效性。
A fast and accurate time-domain simulation method of power system with uncertain parameters is an important tool for power system dynamic and transient analysis,whose accuracy and speed require improving. A new time-domain simulation method based on improved sparse probabilistic collocation method was proposed in this paper.First, an improved sparse probabilistic collocation method based on the Kronrod extension method was proposed, which extends the Gaussian quadrature points to nested ones, greatly reducing the sampling size and can adapt to any distribution of the uncertain parameters. Next, the new time-domain simulation method of power system with uncertain parameters based on the improved method was presented. The method proposed can evaluate the influence of various uncertain parameters on the simulation results and fast obtain the probabilistic density function, expectation and variance of the uncertain parameters. Several cases validate the effectiveness of the proposed method.
A fast and accurate time-domain simulation method of power system with uncertain parameters is an important tool for power system dynamic and transient analysis,whose accuracy and speed require improving. A new time-domain simulation method based on improved sparse probabilistic collocation method was proposed in this paper.First, an improved sparse probabilistic collocation method based on the Kronrod extension method was proposed, which extends the Gaussian quadrature points to nested ones, greatly reducing the sampling size and can adapt to any distribution of the uncertain parameters. Next, the new time-domain simulation method of power system with uncertain parameters based on the improved method was presented. The method proposed can evaluate the influence of various uncertain parameters on the simulation results and fast obtain the probabilistic density function, expectation and variance of the uncertain parameters. Several cases validate the effectiveness of the proposed method.
引文
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[18]Gautschi W.On generating orthogonal polynomials[J].Siam Journal on Scientific&Statistical Computing,2012,3(3):289-317.
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[21]Ganapathysubramanian B,Zabaras N.Sparse grid collocation schemes for stochastic natural convection problems[J].J.Comput.Phys,2007,225(1):652-685.
[2]张巍峰,车延博,刘阳升.电力系统可靠性评估中的改进拉丁超立方抽样方法[J].电力系统自动化,2015,39(4):52-57.Zhang Weifeng,Che Yanbo,Liu Yangsheng.Improved Latin hypercube sampling method for reliability evaluation of power systems[J].Automation of Electric Power Systems,2015,39(4):52-57(in Chinese).
[3]Hou G,Vittal V.Determination of transient stability constrained interface real power flow limit using trajectory sensitivity approach[J].IEEE Transactions on Power Systems,2013,28(3):2156-2163.
[4]Dong Han,Jin Ma,Ren-Mu He.Multi-parameter uncertainty analysis in power system dynamic simulation:a new solution based on the stochastic response surface method and trajectory sensitivity method[J].Electric Machines&Power Systems,2012,40(5):17.
[5]Zhao J,Xue Y,Xu Y,et al.Trajectory sensitivity analysis on the equivalent one-machine-infinite-bus of multi-machine systems for preventive transient stability control[J].IET Generation,Transmission&Distribution,2015,9(3):276-286.
[6]王守相,郑志杰,王成山.计及不确定性的电力系统时域仿真的区间算法[J].中国电机工程学报,2007,27(7):40-44.Wang Shouxiang,Zheng Zhijie,Wang Chengshan.Power system time domain simulation under uncertainty based on interval method[J].Proceedings of the CSEE,2007,27(7):40-44(in Chinese).
[7]Jiang C,Zhao W,Liu J,et al.A new numerical simulation for stochastic transient stability analysis of power systems integrated wind power[C]//International Conference on Power System Technology.Chengdu,China:IEEE,2014,2788-2793.
[8]Dong Z Y,Zhao J H,Hill D J.Numerical simulation for stochastic transient stability assessment[J].IEEETransactions on Power Systems,2012,27(4):1741-1749.
[9]Hockenberry J R,Lesieutre B C.Evaluation of uncertainty in dynamic simulations of power system models:the probabilistic collocation method[J].IEEE Transactions on Power Systems,2004,19(3):1483-1491.
[10]伍双喜,吴文传,张伯明,等.电力系统仿真不确定度评估中拟合多项式阶次的确定[J].电网技术,2012,36(10):125-130.Wu Shuangxi,Wu Wenchuan,Zhang Boming,et al.Order selection for polynomial fitting in uncertainty evaluation of power system simulation by probability collocation method[J].Power System Technology,2012,36(10):125-130(in Chinese).
[11]伍双喜,张伯明,吴文传.电力系统仿真不确定性评估中主导参数的选择[J].电网技术,2013,37(4):999-1004.Wu Shuangxi,Zhang Boming,Wu Wenchuan.Selection of key parameters in uncertainty evaluation for power system simulation[J].Power System Technology,2013,37(4):999-1004(in Chinese).
[12]Xiu D.Numerical methods for stochastic computations.Aspectral method approach[M].Princeton:Princeton University Press,2010:78-83.
[13]Lin G,Elizondo M,Lu S,et al.Uncertainty quantification in dynamic simulations of large-scale power system models using the high-order probabilistic collocation method on sparse grids[J].International Journal for Uncertainty Quantification,2014,4(3):185-204.
[14]Xu L,Fan Y,Zhu H,et al.Nested sparse-grid stochastic collocation method and its application to gate delay modeling under process variations[J].Journal of Computer-Aided Design and Computer Graphics,2010,22(1):165-172.
[15]Genz A,Keister B D.Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight[J].Journal of Computational&Applied Mathematics,1997,71(2):299-309.
[16]Patterson T N L.The optimum addition of points to quadrature formulae[J].Mathematics of Computation,1968,22(104):847-856,s21-s31.
[17]陈建华,吴文传,张伯明,等.电力系统动态仿真中模型参数不确定性的定量分析[J].电网技术,2010,34(11):18-23.Chen Jianhua,Wu Wenchuan,Zhang Boming,et al.Quantitative evaluation of parameter uncertainty in power system dynamic simulation[J].Power System Technology,2010,34(11):18-23(in Chinese).
[18]Gautschi W.On generating orthogonal polynomials[J].Siam Journal on Scientific&Statistical Computing,2012,3(3):289-317.
[19]Novak E,Ritter K.High dimensional integration of smooth functions over cubes[J].Numerische Mathematik,1996,75(1):79-97.
[20]Bungartz H J,Griebel M.Sparse grids[J].Acta Numerica,2004,13(13):147-269.
[21]Ganapathysubramanian B,Zabaras N.Sparse grid collocation schemes for stochastic natural convection problems[J].J.Comput.Phys,2007,225(1):652-685.