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