×
Deng, Jiao-Jiao; Chiang, Hsiao-Dong; Zhao, Tian-Qi

Newton method and trajectory-based method for solving power flow problems: nonlinear studies. (English) Zbl 1317.65118

Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 6, Article ID 1530018, 24 p. (2015).
Summary: This paper analyzes the convergence properties and convergence region of a class of trajectory-based power flow methods. The convergence region of the trajectory-based method is a connected set and possesses the near-by property. The convergence region of Newton method and trajectory-based method in solving power flow problems are numerically investigated. Since the convergence region of trajectory-based method corresponds to the stability region of the nonlinear dynamic system, the stability regions of two dynamic systems are computed. The numerical results indicate that the stability region of the dynamic system possesses better geometry features than the convergence region of Newton method. These properties make the trajectory-based power flow method robust, especially on heavy loading conditions.

MSC:

65H10 Numerical computation of solutions to systems of equations
34D05 Asymptotic properties of solutions to ordinary differential equations
94C99 Circuits, networks

Keywords:

power flow; dynamic system; trajectory; Newton method; stability region; convergence region
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1002/rnc.1605 · Zbl 1218.37036 · doi:10.1002/rnc.1605
[2] DOI: 10.1109/TPWRS.2003.810905 · doi:10.1109/TPWRS.2003.810905
[3] DOI: 10.1007/BF00941054 · Zbl 0651.90067 · doi:10.1007/BF00941054
[4] DOI: 10.1109/9.357 · Zbl 0639.93043 · doi:10.1109/9.357
[5] DOI: 10.1142/S0218127404011879 · Zbl 1072.37035 · doi:10.1142/S0218127404011879
[6] Deng J. J., J. Appl. Math. 11 pp 633– (2013)
[7] DOI: 10.1142/S0218127411029653 · Zbl 1248.28010 · doi:10.1142/S0218127411029653
[8] DOI: 10.2307/2687062 · Zbl 0995.65505 · doi:10.2307/2687062
[9] DOI: 10.1002/cpa.3160320302 · Zbl 0408.65032 · doi:10.1002/cpa.3160320302
[10] DOI: 10.1137/S0036142996304796 · Zbl 0911.65080 · doi:10.1137/S0036142996304796
[11] DOI: 10.1109/TAC.2004.829603 · Zbl 1365.90272 · doi:10.1109/TAC.2004.829603
[12] DOI: 10.1109/TPWRS.2008.2004820 · doi:10.1109/TPWRS.2008.2004820
[13] DOI: 10.1007/BF03025411 · Zbl 1052.30502 · doi:10.1007/BF03025411
[14] DOI: 10.1016/S1007-5704(03)00006-6 · Zbl 1073.47056 · doi:10.1016/S1007-5704(03)00006-6
[15] DOI: 10.1142/S0218127404011399 · Zbl 1129.37332 · doi:10.1142/S0218127404011399
[16] DOI: 10.1109/TPAS.1974.293985 · doi:10.1109/TPAS.1974.293985
[17] DOI: 10.1016/j.amc.2009.06.041 · Zbl 1175.65055 · doi:10.1016/j.amc.2009.06.041
[18] DOI: 10.1109/67.560872 · doi:10.1109/67.560872
[19] DOI: 10.1109/TPAS.1967.291823 · doi:10.1109/TPAS.1967.291823
[20] DOI: 10.1109/MPER.1982.5519878 · doi:10.1109/MPER.1982.5519878
[21] DOI: 10.1109/59.852123 · doi:10.1109/59.852123
[22] DOI: 10.1109/AIEEPAS.1956.4499318 · doi:10.1109/AIEEPAS.1956.4499318
[23] DOI: 10.1109/T-PAS.1977.32334 · doi:10.1109/T-PAS.1977.32334
[24] DOI: 10.1016/j.epsr.2011.09.002 · doi:10.1016/j.epsr.2011.09.002
[25] Zhang L. H., Pacific J. Optim. 4 pp 259– (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.