A Novel Adaptive Preconditioner Based CPF-GMRES Algorithm

Abstract:

This paper presents a novel CPF-GMRES algorithm based on an adaptive preconditioner to overcome the computational bottleneck in the analysis of large-scale power system voltage stability with CPF. Considering the combination details of CPF and GMRES, an adaptive preconditioning structure is proposed to reduce the formation times of preconditioner. Initialize the preconditioning matrix in the predictor of CPF, and modify it with Broyden method in the corrector. Large number add-in strategy and a replenished one are applied to deal with the influence of PVPQ bus-type switching. Numerical results with IEEE 118-bus test system and a real power grid verify the effectiveness of the proposed algorithm, and indicate that a remarkable speed advantage is obtained compared with the conventional CPF-GMRES with the preconditioner of ILU factorization.

• Periodical: Advanced Materials Research (Volumes 1070-1072)
• Pages: 731-738
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1070-1072.731
• Online since: December 2014
• Authors: Hao Zheng*, Jin Quan Zhao, Kun Men, Jian Hua Yin, Chao Hong
• Keywords: Adaptive Preconditioner, Continuation Power Flow, GMRES Method, PVPQ Bus-Type Switching

References

[1] K. Iba, H. Suzuki, M. Egawa and T. Watanabe, Calculation of Critical Loading Condition with Nose Curve Using Homotopy Continuation Method, IEEE Trans. On Power Systems, Vol. 6, NO. 2, 1991, p.584~593.

DOI: 10.1109/59.76701

[2] V. Ajjarupu and C. Christy, The Continuation Power Flow: a Tool for Steady State Voltage Stability Analysis, IEEE Trans. On Power Systems, Vol. 7, NO. 1, 1992, pp.416-423.

DOI: 10.1109/59.141737

[3] H. D. Chiang, A. J. Flueck, K. S. Shah and N. Balu, CPFLOW: a Practical Tool for Tracing Power System Steady-state Stationary Behavior due to Load and Generation Variations, IEEE Trans. On Power Systems, Vol. 10, NO. 2, 1995, pp.623-634.

DOI: 10.1109/59.387897

[4] A. J. Flueck and J. R. Dondeti, A New Continuation Power Flow Tool for Investigating the Nonlinear Effects of Transmission Branch Parameter Variations, IEEE Trans. On Power Systems, Vol. 15, NO. 1, 2000, p.223~227.

DOI: 10.1109/59.852125

[5] J.Q. Zhao, H. D. Chiang and H. Li, A New Contingency Parameterization CPF Model and Sensitivity Method for Voltage Stability Control, IEEE Power Engineering Society General Meeting, San Francisco, U.S.A., 12-16 June 2005, pp.1681-1687.

DOI: 10.1109/pes.2005.1489420

[6] X.P. Zhang, P. Ju and E.J. Handschin, Continuation Three-Phase Power Flow: A Tool for Voltage Stability Analysis of Unbalanced Three-Phase Power Systems, IEEE Trans. On Power Systems, Vol. 20, NO. 3, 2005, p.1320 – 1329.

DOI: 10.1109/tpwrs.2005.851950

[7] A. Dukpa, B. Venkatesh and M. El-Hawary, Application of Continuation Power Flow Method in Radial Distribution Systems, Electric Power Systems Research, Vol. 79, NO. 11, 2009, pp.1503-1510.

DOI: 10.1016/j.epsr.2009.05.003

[8] A.B. Neto and D.A. Alves, Improved Geometric Parameterisation Techniques for Continuation Power Flow, IET generation, transmission & distribution, Vol. 4, NO. 12, 2010, pp.1349-1359.

DOI: 10.1049/iet-gtd.2010.0048

[9] P. Xu, X. Wang and V. Ajjarapu, Continuation Power Flow With Adaptive Stepsize Control via Vonvergence Monitor, IET generation, transmission & distribution, Vol. 6, NO. 7, 2012, pp.673-679.

DOI: 10.1049/iet-gtd.2011.0573

[10] Y. Saad and M. H. Schultz, GMRES: a Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM Journal on scientific and statistical computing, Vol. 7, NO. 3 1986, pp.856-869.

DOI: 10.1137/0907058

[11] A. J. Flueck and H. D. Chiang, Solving the Nonlinear Power Flow Equations With a Newton Process and GMRES, IEEE International Symposium on Circuits and Systems, 15 May 1996, pp.657-660.

DOI: 10.1109/iscas.1996.540033

[12] A. Semlyen, Fundamental Concepts of a Krylov Subspace Power Flow Methodology, IEEE Trans. On Power Systems, Vol. 11, NO. 3, 1996, pp.1528-1537.

DOI: 10.1109/59.535694

[13] A. J. Flueck and H. D. Chiang, Solving the Nonlinear Power Flow Equations With an Inexact Newton Method Using GMRES, IEEE Trans. On Power Systems, Vol. 13, No. 2, 1998, pp.267-273.

DOI: 10.1109/59.667330

[14] Y. Zhang and H. D. Chiang, Fast Newton-FGMRES Solver for Large-scale Power Flow Study, IEEE Trans. On Power Systems, Vol. 25, NO. 2, 2010, pp.769-776.

DOI: 10.1109/tpwrs.2009.2036018

[15] Y. Chen, C. Shen and J. Wang, Distributed Transient Stability Simulation of Power Systems Based on a Jacobian-free Newton-Gmres Method, IEEE Trans. On Power Systems, Vol. 24, NO. 1, 2009, pp.146-156.

DOI: 10.1109/tpwrs.2008.2009393

[16] W. Xu and W. Li, Efficient Preconditioners for Newton-GMRES Method With Application to Power Flow Study, IEEE Trans. On Power Systems, Vol. 28, NO. 4, 2013, pp.4173-4180.

DOI: 10.1109/tpwrs.2013.2267782

[17] H. Mori and K. Seki, Continuation Newton-GMRES Power Flow With Linear and Nonlinear Predictors,. Large Engineering Systems conference on Power Engineering, Montreal, Quebec, Canada, 2007, pp.171-175.

DOI: 10.1109/lescpe.2007.4437373

[18] J. Jasni, N. Azis, H. Hizam, et al. An Efficient Generalized Minimized Residual Simulation Technique for Continuation Power Flow Studies, Asian Journal of Applied Sciences, Vol. 1, NO. 2, 2008, pp.136-146.

DOI: 10.3923/ajaps.2008.136.146

[19] J. Jasni, H. Hizam, M. Z. A. Kadir, et al. Determination of Proximity to Static Voltage Collapse Using CPF-GMRES, IEEE 2nd International Power and Energy Conference, Johor Bahru, Malaysia 1-3 December, 2008, pp.520-525.

DOI: 10.1109/pecon.2008.4762521

[20] M. Eidiani, H. Zeynal, A. K. Zadeh, et al, Voltage Stability Assessment: an Approach With Expanded Newton Raphson-Sydel, 5th International Power Engineering and Optimization Conference, Shah Alam, Selangor, Malaysia, 6-7 June 2011, pp.31-35.

DOI: 10.1109/peoco.2011.5970424

[21] J. Q. Zhao, H. D. Chiang and B. M. Zhang, Study on PV-PQ Bus Type Switching Logic in Power Flow Computation, Proceedings of the CSEE, Vol 25, NO. 1, 2005, pp.54-59. (In Chinese).