Interval arithmetic in current injection power flow analysis

Abstract This paper incorporates interval arithmetic into current injection method to solve power flow problem under both load and line data uncertainty. In this new methodology, the resulting interval nonlinear system of equations is solved using Krawczyk method. The proposed methodology is implemented in the Matlab environment using the Intlab toolbox. Results are compared with those obtainable by Monte Carlo simulations. IEEE test systems and a South – southeastern Brazilian network are used.

[1]  G.P. Dimuro,et al.  Towards interval analysis of the load uncertainty in power electric systems , 2004, 2004 International Conference on Probabilistic Methods Applied to Power Systems.

[2]  M. Ramaswamy,et al.  On-line estimation of bus voltages based on fuzzy logic , 2004 .

[3]  Ulrich W. Kulisch,et al.  Advanced Arithmetic for the Digital Computer, Design of Arithmetic Units , 2002, RealComp.

[4]  Fernando L. Alvarado,et al.  Interval arithmetic in power flow analysis , 1991 .

[5]  N. Martins,et al.  An augmented Newton–Raphson power flow formulation based on current injections , 2001 .

[6]  R. B. Kearfott,et al.  Applications of interval computations , 1996 .

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

[8]  Siegfried M. Rump,et al.  INTLAB - INTerval LABoratory , 1998, SCAN.

[9]  Ali Reza Seifi,et al.  Fuzzy load flow in balanced and unbalanced radial distribution systems incorporating composite load model , 2010 .

[10]  Sakti Prasad Ghoshal,et al.  Development of a new algorithm for power flow analysis , 2011 .

[11]  G.K. Stefopoulos,et al.  Probabilistic power flow with nonconforming electric loads , 2004, 2004 International Conference on Probabilistic Methods Applied to Power Systems.

[12]  Kevin Tomsovic,et al.  Boundary load flow solutions , 2004 .

[13]  Alfredo Vaccaro,et al.  An Affine Arithmetic-Based Methodology for Reliable Power Flow Analysis in the Presence of Data Uncertainty , 2010, IEEE Transactions on Power Systems.

[14]  Z. Hu,et al.  A probabilistic load flow method considering branch outages , 2006, IEEE Transactions on Power Systems.

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

[16]  V. N. Pande,et al.  Fuzzy power flow solutions with reactive limits and multiple uncertainties , 2005 .

[17]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[18]  R. Palma-Behnke,et al.  Fuzzy Arithmetic for the DC Load Flow , 2010, IEEE Transactions on Power Systems.

[19]  N. Martins,et al.  Developments in the Newton Raphson power flow formulation based on current injections , 1999 .

[20]  T. Kulworawanichpong.  Simplified Newton–Raphson power-flow solution method , 2010 .

[21]  Vander Menengoy da Costa,et al.  A second order power flow based on current injection equations , 2005 .

[22]  Vander Menengoy da Costa,et al.  Developments in the analysis of unbalanced three-phase power flow solutions , 2007 .

[23]  N. Martins,et al.  Three-phase power flow calculations using the current injection method , 2000 .

[24]  Nelson Martins,et al.  Improved representation of control adjustments into the Newton–Raphson power flow , 2003 .

[25]  Shouxiang Wang,et al.  Reliability-oriented distribution network reconfiguration considering uncertainties of data by interval analysis , 2012 .