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The manuscript addresses the problem of finding all solutions of power flow equations or other similar nonlinear system of algebraic equations.
D. N. Bernstein, “The number of roots of a system of equations,” Funkts. Anal. Pril. , vol. 9, pp. 1–4, 1975
1975
Earlier work this paper cites.
A. G. Kushnirenko, “Newton polytopes and the bezout theorem,” Funkts. Anal. Pril. , vol. 10, no. 3, 1976
1976
Earlier work this paper cites.
A. G. Khovanski, “Newton polyhedra and the genus of complete intersections,” Funkts. Anal. Pril. , vol. 12, no. 1, pp. 51–61, 1978
1978
Earlier work this paper cites.
N. Kakimoto, Y. Ohnogi, H. Matsuda, and H. Shibuya, “Transient Stability Analysis of Large-Scale Power System by Lyapunov’s Direct Method,” Power Apparatus and Systems, IEEE Transactions on , no. 1, pp. 160–167, 1984
1984
Earlier work this paper cites.
P. Varaiya, F. F. Wu, and R. L. Chen, “Direct methods for transient stability analysis of power systems: Recent results,” in Proceedings of the IEEE . IEEE, 1985, pp. 1703–1715
1985
Earlier work this paper cites.
A. Morgan and A. Sommese, “A homotopy for solving general polynomial systems that respects m-homogeneous structures,” Applied Mathematics and Computation , vol. 24, no. 2, pp. 101 – 113, 1987
1987
Earlier work this paper cites.
F. M. A. Salam, L. Ni, S. Guo, and X. Sun, “Parallel processing for the load flow of power systems: the approach and applications,” in Decision and Control, 1989., Proceedings of the 28th IEEE Conference on , Dec 1989, pp. 2173–2178 vol.3
1989
Earlier work this paper cites.
S. A. J. Morgan, A P and L. T. Watson, “Finding all isolated solutions to polynomial systems using hompack,” ACM Trans. Math. Softw. , vol. 15, no. 2, pp. 93–122, 1989
1989
Earlier work this paper cites.
H.-D. Chiang and J. S. Thorp, “The closest unstable equilibrium point method for power system dynamic security assessment,” Circuits and Systems, IEEE Transactions on , vol. 36, no. 9, pp. 1187–1200, 1989
1989
Earlier work this paper cites.
G. D. Prasad, A. Jana, and S. Tripathy, “Modifications to newton-raphson load flow for ill-conditioned power systems,” International Journal of Electrical Power & Energy Systems , vol. 12, no. 3, pp. 192 – 196, 1990
1990
Earlier work this paper cites.
T. Overbye and C. De Marco, “Voltage security enhancement using energy based sensitivities,” Power Systems, IEEE Transactions on , vol. 6, no. 3, pp. 1196–1202, Aug 1991
1991
Earlier work this paper cites.
T. Overbye and C. Demarco, “Improved techniques for power system voltage stability assessment using energy methods,” Power Systems, IEEE Transactions on , vol. 6, no. 4, pp. 1446–1452, Nov 1991
1991
Earlier work this paper cites.
H.-D. Chiang and L. Fekih-Ahmed, “On the direct method for transient stability analysis of power system structure preserving models,” in Circuits and Systems, 1992. ISCAS ’92. Proceedings., 1992 IEEE International Symposium on . IEEE, 1992, pp. 2545–2548
1992
Earlier work this paper cites.
V. Ajjarapu and C. Christy, “The continuation power flow: a tool for steady state voltage stability analysis,” Power Systems, IEEE Transactions on , vol. 7, no. 1, pp. 416–423, 1992
1992
Earlier work this paper cites.
W. Ma and J. Thorp, “An efficient algorithm to locate all the load flow solutions,” Power Systems, IEEE Transactions on , vol. 8, no. 3, pp. 1077–1083, Aug 1993
1993
Earlier work this paper cites.
W. Ma and J. Thorp, “An efficient algorithm to locate all the load flow solutions,” Power Systems, IEEE Transactions on , vol. 8, no. 3, pp. 1077–1083, 1993
1993
Earlier work this paper cites.
P. Kundur, Power System Stability and Control , New York, 1994
1994
Earlier work this paper cites.
J. M. Rojas, “A convex geometric approach to counting the roots of a polynomial system,” Theor. Comput. Sci. , vol. 133, no. 1, pp. 105–140, 1994
1994
Earlier work this paper cites.
A. Zobian and M. Ilic, “A steady state voltage monitoring and control algorithm using localized least square minimization of load voltage deviations,” Power Systems, IEEE Transactions on , vol. 11, no. 2, pp. 929–938, 1996
1996
Cited alongside, same era.
T. Y. Li and X. Wang, “The bkk root count in c n c^{n} ,” Math. Comp , vol. 65, pp. 1477–1484, 1996
1996
Cited alongside, same era.
J. M. Rojas and X. Wang, “Counting affine roots of polynomial systems via pointed newton polytopes,” J. Complex. , vol. 12, no. 2, pp. 116–133, 1996
1996
Cited alongside, same era.
C.-W. Liu and J. S. Thorp, “A novel method to compute the closest unstable equilibrium point for transient stability region estimate in power systems,” Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on , vol. 44, no. 7, pp. 630–635, 1997
1997
Cited alongside, same era.
H.-D. Chiang, Direct Methods for Stability Analysis of Electric Power Systems , ser. Theoretical Foundation, BCU Methodologies, and Applications. Hoboken, NJ, USA: John Wiley & Sons, Mar. 2011
2011
Later among the works it cites.
D. Mehta, “Numerical Polynomial Homotopy Continuation Method and String Vacua,” Adv.High Energy Phys. , vol. 2011, p. 263937, 2011
2011
Later among the works it cites.
M. Maniatis and D. Mehta, “Minimizing Higgs Potentials via Numerical Polynomial Homotopy Continuation,” Eur.Phys.J.Plus , vol. 127, p. 91, 2012
2012
Later among the works it cites.
D. Mehta, Y. H. He, and J. D. Hauenstein, “Numerical Algebraic Geometry: A New Perspective on String and Gauge Theories,” JHEP , vol. 1207, p. 018, 2012
2012
Later among the works it cites.
D. Mehta, J. D. Hauenstein, and M. Kastner, “Energy landscape analysis of the two-dimensional nearest-neighbor p h i 4 phi^{4} model,” Phys.Rev. , vol. E85, p. 061103, 2012
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T. Van Cutsem and C. Vournas, Voltage stability of electric power systems . Springer, 1998, vol. 441
1998
Cited alongside, same era.
J. Verschelde, “Algorithm 795: Phcpack: a general-purpose solver for polynomial systems by homotopy continuation,” ACM Trans. Math. Softw. , vol. 25, no. 2, pp. 251–276, 1999
1999
Cited alongside, same era.
T. Li, “Solving polynomial systems by the homotopy continuation method,” Handbook of numerical analysis , vol. XI, pp. 209–304, 2003
2003
Cited alongside, same era.
J. Lee, “A novel homotopy-based algorithm for the closest unstable equilibrium point method in nonlinear stability analysis,” in Circuits and Systems, 2003. ISCAS ’03. Proceedings of the 2003 International Symposium on . IEEE, 2003, pp. –III–11
2003
Cited alongside, same era.
J. Lee, “Dynamic gradient approaches to compute the closest unstable equilibrium point for stability region estimate and their computational limitations,” Automatic Control, IEEE Transactions on , vol. 48, no. 2, pp. 321–324, 2003
2003
Cited alongside, same era.
T. Gunji, S. Kim, M. Kojima, A. Takeda, K. Fujisawa, and T. Mizutani, “Phom – a polyhedral homotopy continuation method for polynomial systems,” Computing , vol. 73, no. 1, pp. 57–77, 2004
2004
Cited alongside, same era.
J. Lee and H.-D. Chiang, “A singular fixed-point homotopy method to locate the closest unstable equilibrium point for transient stability region estimate,” Circuits and Systems II: Express Briefs, IEEE Transactions on , vol. 51, no. 4, pp. 185–189, 2004
2004
Cited alongside, same era.
C.-W. Liu, C.-S. Chang, J.-A. Jiang, and G.-H. Yeh, “Toward a cpflow-based algorithm to compute all the type-1 load-flow solutions in electric power systems,” Circuits and Systems I: Regular Papers, IEEE Transactions on , vol. 52, no. 3, pp. 625–630, 2005
2005
Cited alongside, same era.
2012
Later among the works it cites.
D. K. Molzahn, B. C. Lesieutre, and H. Chen, “Counterexample to a continuation-based algorithm for finding all power flow solutions,” Power Systems, IEEE Transactions on , vol. 28, no. 1, pp. 564–565, 2013
2013
Later among the works it cites.
C. Hughes, D. Mehta, and J.-I. Skullerud, “Enumerating Gribov copies on the lattice,” Annals Phys. , vol. 331, pp. 188–215, 2013
2013
Later among the works it cites.
J. Hauenstein, Y. H. He, and D. Mehta, “Numerical elimination and moduli space of vacua,” JHEP , vol. 1309, p. 083, 2013
2013
Later among the works it cites.
D. Martinez-Pedrera, D. Mehta, M. Rummel, and A. Westphal, “Finding all flux vacua in an explicit example,” JHEP , vol. 1306, p. 110, 2013
2013
Later among the works it cites.
Y. H. He, D. Mehta, M. Niemerg, M. Rummel, and A. Valeanu, “Exploring the Potential Energy Landscape Over a Large Parameter-Space,” JHEP , vol. 1307, p. 050, 2013
2013
Later among the works it cites.
D. Mehta, D. A. Stariolo, and M. Kastner, “Energy landscape of the finite-size spherical three-spin glass model,” Phys.Rev. , vol. E87, no. 5, p. 052143, 2013
2013
Later among the works it cites.
B. Greene, D. Kagan, A. Masoumi, D. Mehta, E. J. Weinberg, and X. Xiao, “Tumbling through a landscape: Evidence of instabilities in high-dimensional moduli spaces,” Phys.Rev. , vol. D88, no. 2, p. 026005, 2013
2013
Later among the works it cites.
N. Yorino, E. Popov, Y. Zoka, Y. Sasaki, and H. Sugihara, “An Application of Critical Trajectory Method to BCU Problem for Transient Stability Studies,” Power Systems, IEEE Transactions on , vol. 28, no. 4, pp. 4237–4244, 2013
2013
Later among the works it cites.
P. E. Hristov, N. Yorino, Y. Zoka, Y. Sasaki, and H. Sugihara, “Robust method for detection of CUEP for power system transient stability screening,” Innovative Smart Grid Technologies Europe (ISGT EUROPE), 2013 4th IEEE/PES , pp. 1–5, 2013
2013
Later among the works it cites.
Hung Nguyen Dinh, Yong Tae Yoon, Minh Y Nguyen, “A new approach for corrective and preventive control to unsolvable case in power networks having ders,” JEET , vol. 8, no. 3, pp. 411–420, May 2013
2013
Later among the works it cites.
2014
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Nguyen, Hung D and Turitsyn, Konstantin S, “Appearance of multiple stable load flow solutions under power flow reversal conditions,” in Power and Energy Society General Meeting . IEEE, 2014
2014
Closest in time.