A novel Q-limit guided continuation power flow method for voltage stability analysis

This paper presents a novel bifurcation point computation method based on the continuation power flow method. The new method considers the reactive power limits of generators as a part of the algorithmic procedure. The algorithmic continuation steps are guided by the prediction of Q-limit breaking points. Lagrange polynomial interpolation formula is used in this paper in order to find the Q-limit breaking point indices that determine when a generatorpsilas regulating reactive power output has reached its limits. The algorithmic continuation steps will then be guided by skipping to the closest Q-limit breaking point, consequently reducing the number of continuation steps and saving computational time. The proposed method has been successfully applied to the IEEE 9, 30 and 118 bus test systems.

[1]  M. Enns,et al.  Fast Linear Contingency Analysis , 1982, IEEE Transactions on Power Apparatus and Systems.

[2]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[3]  T. Carlsen,et al.  Voltage stability condition in a power transmission system calculated by sensitivity methods , 1990 .

[4]  Fernando L. Alvarado,et al.  Contingency ranking for voltage collapse via sensitivities from a single nose curve , 1999 .

[5]  I. Dobson,et al.  Sensitivity of Transfer Capability Margins with a Fast Formula , 2002, IEEE Power Engineering Review.

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

[7]  Ying Chen,et al.  A Jacobian-free Newton-GMRES(m) method with adaptive preconditioner and its application for power flow calculations , 2006, IEEE Transactions on Power Systems.

[8]  O. Alsac,et al.  Security analysis and optimization , 1987, Proceedings of the IEEE.

[9]  J. W. Walker,et al.  Direct solutions of sparse network equations by optimally ordered triangular factorization , 1967 .

[10]  G. C. Ejebe,et al.  Methods for contingency screening and ranking for voltage stability analysis of power systems , 1995 .

[11]  D. Hill,et al.  Fast calculation of a voltage stability index , 1992 .

[12]  William F. Tinney,et al.  Power Flow Solution by Newton's Method , 1967 .

[13]  M. Saunders,et al.  Solution of Sparse Indefinite Systems of Linear Equations , 1975 .

[14]  A.C.Z. de Souza,et al.  Tracing PV and QV curves with the help of a CRIC continuation method , 2006, IEEE Transactions on Power Systems.

[15]  I. Duff,et al.  The effect of ordering on preconditioned conjugate gradients , 1989 .

[16]  Hiroyuki Mori,et al.  A preconditioned fast decoupled power flow method for contingency screening , 1995 .

[17]  Rüdiger Seydel.  On a class of bifurcation test functions , 1997 .

[18]  G. Taylor,et al.  A novel Q-Limit guided Continuation Power Flow method , 2009, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[19]  Hsiao-Dong Chiang,et al.  CPFLOW: a practical tool for tracing power system steady-state stationary behavior due to load and generation variations , 1995 .

[20]  Ke Chen,et al.  A performance-index guided continuation method for fast computation of saddle-node bifurcation in power systems , 2003 .

[21]  Hsiao-Dong Chiang,et al.  Toward a practical performance index for predicting voltage collapse in electric power systems , 1995 .

[22]  A. O. Ekwue,et al.  Voltage stability analysis on the NGC system , 1998 .

[23]  R. Bacher,et al.  Application of non-stationary iterative methods to an exact Newton-Raphson solution process for power flow equations , 1996 .

[24]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[25]  I. C. Decker,et al.  Conjugate gradient methods for power system dynamic simulation on parallel computers , 1996 .

[26]  R. Seydel.  Practical Bifurcation and Stability Analysis , 1994 .

[27]  R. Seydel.  ON DETECTING STATIONARY BIFURCATIONS , 1991 .

[28]  W. F. Tinney,et al.  Sparse Vector Methods , 1985, IEEE Transactions on Power Apparatus and Systems.

[29]  Robert A. W. van Amerongan.  A general-purpose version of the fast decoupled load flow , 1989 .

[30]  Alexander J. Flueck,et al.  Investigating the installed real power transfer capability of a large scale power system under a proposed multiarea interchange schedule using CPFLOW , 1996 .

[31]  H. Dag,et al.  Block-bordered diagonalization and parallel iterative solvers , 1994 .

[32]  H. Sasaki,et al.  A predictor/corrector scheme for obtaining Q-limit points for power flow studies , 2005, IEEE Transactions on Power Systems.

[33]  Fernando L. Alvarado,et al.  Sensitivity of the loading margin to voltage collapse with respect to arbitrary parameters , 1997 .

[34]  Claudio A. Canizares,et al.  Voltage Stability Indices , 2003 .

[35]  I. Dobson,et al.  Voltage Collapse Margin Sensitivity Methods applied to the Power System of Southwest England , 1998 .

[36]  F.D. Galiana,et al.  The Continuation Method in Power System Optimization: Applications to Economy-Security Functions , 1985, IEEE Transactions on Power Apparatus and Systems.

[37]  Ian A. Hiskens,et al.  Direct calculation of reactive power limit points , 1996 .

[38]  Hsiao-Dong Chiang,et al.  Enhanced look-ahead load margin estimation for voltage security assessment , 2004 .

[39]  H. Chiang,et al.  A more efficient formulation for computation of the maximum loading points in electric power systems , 1995 .

[40]  Hadi Saadat,et al.  Power System Analysis , 1998 .

[41]  Timothy A. Davis,et al.  A column approximate minimum degree ordering algorithm , 2000, TOMS.

[42]  Eduardo N. Asada,et al.  Critical evaluation of direct and iterative methods for solving Ax=b systems in power flow calculations and contingency analysis , 1999 .

[43]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[44]  I. Dobson,et al.  Voltage collapse in power systems , 1992, IEEE Circuits and Devices Magazine.

[45]  M. A. Pai,et al.  A new preconditioning technique for the GMRES algorithm in power flow and P-V curve calculations , 2003 .

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

[47]  A.C.Z. de Souza,et al.  Comparison of performance indices for detection of proximity to voltage collapse , 1996 .

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

[49]  W. Arnoldi.  The principle of minimized iterations in the solution of the matrix eigenvalue problem , 1951 .

[50]  Alexander J. Flueck,et al.  A new continuation power flow tool for investigating the nonlinear effects of transmission branch parameter variations , 2000 .

[51]  O. Alsac,et al.  Fast Decoupled Load Flow , 1974 .

[52]  J. Shewchuk.  An Introduction to the Conjugate Gradient Method Without the Agonizing Pain , 1994 .

[53]  A. Jennings.  Influence of the Eigenvalue Spectrum on the Convergence Rate of the Conjugate Gradient Method , 1977 .

[54]  Haohang Su,et al.  A compressed BiCGStab algorithm for power and ground network analysis , 2007, 2007 7th International Conference on ASIC.

[55]  Vladimir Brandwajn,et al.  Partial Matrix Refactorization , 1986, IEEE Transactions on Power Systems.

[56]  F. Galiana,et al.  An investigation of the solution to the optimal power flow problem incorporating continuation methods , 1990 .

[57]  H. Mori,et al.  Hybrid continuation power flow with linear-nonlinear predictor , 2004, 2004 International Conference on Power System Technology, 2004. PowerCon 2004..

[58]  S. McFee,et al.  On the application of a pre-conditioned conjugate gradient algorithm to power network analysis , 1993 .

[59]  W. F. Tinney,et al.  Sparsity-Oriented Compensation Methods for Modified Network Solutions , 1983, IEEE Transactions on Power Apparatus and Systems.

[60]  Venkataramana Ajjarapu,et al.  Optimal continuation power flow , 1995 .

[61]  Adam Semlyen.  Fundamental concepts of a Krylov subspace power flow methodology , 1996 .

[62]  R. Seydel.  Numerical computation of branch points in nonlinear equations , 1979 .

[63]  Malcolm Irving,et al.  Voltage security and reactive power management , 2004 .

[64]  Gene H. Golub,et al.  Matrix computations , 1983 .

[65]  A. Semlyen,et al.  A New Preconditioned Conjugate Gradient Power Flow , 2002, IEEE Power Engineering Review.

[66]  C. Kelley.  Iterative Methods for Linear and Nonlinear Equations , 1987 .

[67]  A. Kurita,et al.  The power system failure on July 23, 1987 in Tokyo , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[68]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .