Dimension reduction method for probabilistic power flow calculation

In this study, the probabilistic power flow (PPF) problem is modelled as a multiple integral with an implicit integrand. A detailed discussion is given about the dimension reduction (DR) method for solving PPF. To accommodate the dependency of the input random variables, Nataf transformation is introduced to map PPF problems in the independent standard normal space. Emphasis is put on the computational burden of DR method. Based on Taylor expansion, a deep sight is given in the residual error of univariate DR (UDR) method. Using the first four standardised central moments from UDR method, the generalised lambda distribution is employed to represent the probability distribution of the output variable. Finally, an IEEE-118 case is performed to check the proposed method.

[1]  Julio Usaola Probabilistic load flow with wind production uncertainty using cumulants and Cornish–Fisher expansion , 2009 .

[2]  A. Kiureghian,et al.  STRUCTURAL RELIABILITY UNDER INCOMPLETE PROBABILITY INFORMATION , 1986 .

[3]  Chun-Lien Su,et al.  Probabilistic load-flow computation using point estimate method , 2005 .

[4]  F. Milano,et al.  An open source power system analysis toolbox , 2005, 2006 IEEE Power Engineering Society General Meeting.

[5]  J. Usaola Probabilistic load flow in systems with wind generation , 2009 .

[6]  Yan-Gang Zhao,et al.  New Point Estimates for Probability Moments , 2000 .

[7]  Herschel Rabitz,et al.  Global uncertainty assessments by high dimensional model representations (HDMR) , 2002 .

[8]  M. Rosenblatt Remarks on a Multivariate Transformation , 1952 .

[9]  S. Rahman,et al.  A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics , 2004 .

[10]  C. Cañizares,et al.  Probabilistic Optimal Power Flow in Electricity Markets Based on a Two-Point Estimate Method , 2006, IEEE Transactions on Power Systems.

[11]  S. Rahman,et al.  A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics , 2004 .

[12]  J. Morales,et al.  Point Estimate Schemes to Solve the Probabilistic Power Flow , 2007, IEEE Transactions on Power Systems.

[13]  Julio Usaola,et al.  Probabilistic load flow with correlated wind power injections , 2010 .

[14]  Ronald N. Allan,et al.  Numerical techniques in probabilistic load flow problems , 1976 .

[15]  R.N. Allan,et al.  Evaluation Methods and Accuracy in Probabilistic Load Flow Solutions , 1981, IEEE Transactions on Power Apparatus and Systems.

[16]  Antonio J. Conejo,et al.  Probabilistic power flow with correlated wind sources , 2010 .