Computation of Maximum Loading Points via the Factored Load Flow

This paper presents a fast and straightforward algorithm to obtain the maximum loading points of power systems by simply performing bisection searches between feasible and infeasible load flow cases. The proposed method exploits the ability and robustness of the factored load flow solution procedure to converge to complex solutions well beyond the maximum loadability points. Test cases on a diversity of benchmark cases show that the new method is computationally attractive when compared with existing continuation power flow methods.

[1]  Claudio A. Canizares,et al.  Point of collapse and continuation methods for large AC/DC systems , 1993 .

[2]  Andrew J. Korsak,et al.  On the Question of Uniqueness of Stable Load-Flow Solutions , 1972 .

[3]  Federico Milano,et al.  Equivalency of Continuation and Optimization Methods to Determine Saddle-Node and Limit-Induced Bifurcations in Power Systems , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  T. Cutsem.  A method to compute reactive power margins with respect to v , 1991, IEEE Power Engineering Review.

[5]  A. G. Expósito,et al.  Reliable load flow technique for radial distribution networks , 1999 .

[6]  A. Yokoyama,et al.  Multisolutions for Load Flow Problem of Power System and Their Physical Stability Test , 1980 .

[7]  Antonio J. Conejo,et al.  Electric Energy Systems : Analysis and Operation , 2008 .

[8]  G. Irisarri,et al.  Maximum loadability of power systems using interior point nonlinear optimization method , 1997 .

[9]  J. Baillieul,et al.  Geometric critical point analysis of lossless power system models , 1982 .

[10]  P. Kessel,et al.  Estimating the Voltage Stability of a Power System , 1986, IEEE Power Engineering Review.

[11]  N. Yorino,et al.  A method to approximate a closest loadability limit using multiple load flow solutions , 1997 .

[12]  I. Hiskens,et al.  Exploring the power flow solution space boundary , 2001, PICA 2001. Innovative Computing for Power - Electric Energy Meets the Market. 22nd IEEE Power Engineering Society. International Conference on Power Industry Computer Applications (Cat. No.01CH37195).

[13]  Thomas J. Overbye,et al.  Computation of a practical method to restore power flow solvability , 1995 .

[14]  Naoto Yorino,et al.  A simplified approach to estimate maximum loading conditions in the load flow problem , 1993 .

[15]  A. Arapostathis,et al.  Bifurcation analysis of the load flow equations , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[16]  Venkataramana Ajjarapu,et al.  The continuation power flow: a tool for steady state voltage stability analysis , 1991 .

[17]  T. Overbye.  A power flow measure for unsolvable cases , 1994 .

[18]  V. Vittal,et al.  Simplification, expansion and enhancement of direct interior point algorithm for power system maximum loadability , 1999 .

[19]  V. A. Venikov,et al.  Estimation of electrical power system steady-state stability in load flow calculations , 1975, IEEE Transactions on Power Apparatus and Systems.

[20]  Federico Milano,et al.  Power System Modelling and Scripting , 2010 .

[21]  Zechun Hu,et al.  Efficient Computation of Maximum Loading Point by Load Flow Method With Optimal Multiplier , 2008, IEEE Transactions on Power Systems.

[22]  S. Iwamoto,et al.  A Load Flow Calculation Method for III-Conditioned Power Systems , 1981 .

[23]  V. Ajjarapu,et al.  Continuation power flow with adaptive stepsize control via convergence monitor , 2012 .

[24]  R. E. Doherty,et al.  Fundamental considerations of power limits of transmission systems , 1925, Journal of the A.I.E.E..

[25]  R. C. Bergvall,et al.  Experimental Analysis of Stability and Power Limitations , 1924, Transactions of the American Institute of Electrical Engineers.

[26]  A. Gómez-Expósito,et al.  Factored solution of nonlinear equation systems , 2013, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[27]  G. C. Ejebe,et al.  Available transfer capability calculations , 1998 .

[28]  Chen-Sung Chang,et al.  Toward a CPFLOW-based algorithm to compute all the type-1 load-flow solutions in electric power systems , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Antonio Gómez Expósito,et al.  Factored solution of infeasible load flow cases , 2014, 2014 Power Systems Computation Conference.

[30]  B.K. Johnson.  Extraneous and false load flow solutions , 1977, IEEE Transactions on Power Apparatus and Systems.

[31]  Catalina Gomez-Quiles,et al.  Factorized Load Flow , 2013, IEEE Transactions on Power Systems.

[32]  K. Iba,et al.  Calculation of critical loading condition with nose curve using homotopy continuation method , 1991 .

[33]  L. V. Barboza,et al.  Unsolvable power flow - restoring solutions of the electric power network equations , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[34]  F. Galiana,et al.  Quantitative Analysis of Steady State Stability in Power Networks , 1981, IEEE Transactions on Power Apparatus and Systems.

[35]  A. Gomez-Exposito,et al.  Bilinear Power System State Estimation , 2012, IEEE Transactions on Power Systems.

[36]  Catalina Gomez-Quiles,et al.  Equality-constrained bilinear state estimation , 2013, IEEE Transactions on Power Systems.

[37]  Y. Tamura,et al.  A Load Flow Calculation Method for Ill-Conditioned Power Systems , 1981, IEEE Transactions on Power Apparatus and Systems.

[38]  Carlos J. Tavora,et al.  Equilibrium Analysis of Power Systems , 1972 .