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The solution space of any set of power flow equations may contain different number of real-valued solutions.
Computation of critical boundaries on equilibrium manifolds
Werner C Rheinboldt · 1982
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Geometric Critical Point Analysis of Lossless Power System Models
J. Baillieul and C.I. Byrne · 1982
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Folds in solutions of two parameter systems and their calculation. part i
A Jepson and A Spence · 1985
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Computing all solutions to polynomial systems using homotopy continuation
Alexander Morgan and Andrew Sommese · 1987
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Numerical solution of a class of deficient polynomial systems
Tien-Yien Li, Tim Sauer, and James A Yorke · 1987
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Parallel processing for the load flow of power systems: the approach and applications
FMA Salam, L Ni, S Guo, and X Sun · 1989
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The cheater’s homotopy: an efficient procedure for solving systems of polynomial equations
TY Li, Tim Sauer, and JA Yorke · 1989
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Coefficient-parameter polynomial continuation
Alexander P Morgan and Andrew J Sommese · 1989
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Determining the solutions of the load flow of power systems: Theoretical results and computer implementation
S.X. Guo and F.M.A. Salam · 1990
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The continuation power flow: a tool for steady state voltage stability analysis
V. Ajjarapu and C. Christy · 1992
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An efficient algorithm to locate all the load flow solutions
Weimin Ma and James S Thorp · 1993
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Power system stability and control
Prabha Kundur, Neal J Balu, and Mark G Lauby · 1994
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Voltage stability of electric power systems
Thierry Van Cutsem and Costas Vournas · 1998
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Exploring the power flow solution space boundary
Ian Hiskens, Robert J Davy, et al · 2001
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Solving polynomial systems by the homotopy continuation method
Tien Yien Li · 2003
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Small-disturbance voltage stability of distribution systems with induction generators
Walmir Freitas, Luiz CP Da Silva, and Andre Morelato · 2005
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Toward a cpflow-based algorithm to compute all the type-1 load-flow solutions in electric power systems
Chih-Wen Liu, Chen-Sung Chang, Joe-Air Jiang, and Guey-Haw Yeh · 2005
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Impact of wind generation uncertainty on power system small disturbance voltage stability: A pcm-based approach
Ce Zheng and Mladen Kezunovic · 2012
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Bringing wind energy to market
Eilyan Y Bitar, Ram Rajagopal, Pramod P Khargonekar, Kameshwar Poolla, and Pravin Varaiya · 2012
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Paramotopy: Parameter homotopies in parallel, 2012
DANIEL J Bates, DANIEL A Brake, and MATTHEW E Niemerg · 2012
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Numerically solving polynomial systems with Bertini
Daniel J Bates, Jonathan D Hauenstein, Andrew J Sommese, and Charles W Wampler · 2013
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Wind power plant voltage stability evaluation
E Muljadi and YC Zhang · 2014
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Numerical Polynomial Homotopy Continuation Method to Locate All The Power Flow Solutions
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The Numerical solution of systems of polynomials arising in engineering and science
Andrew John Sommese and Charles Weldon Wampler · 2005
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Voltage stability analysis of wind farm integration into transmission network
Yongning Chi, Yanhua Liu, Weisheng Wang, and Huizhu Dai · 2006
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Maximizing power-system loadability in the presence of multiple binding complementarity constraints
Michael E Karystianos, Nicholas G Maratos, and Costas D Vournas · 2007
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20% wind energy by 2030: Increasing wind energy’s contribution to U.S. electricity supply
National Renewable Energy Laboratory · 2008
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On the validity of local approximations of the power system loadability surface
Magnus Perninge and Lennart Söder · 2011
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D. Mehta, H. Nguyen, and K. Turitsyn · 2014
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Power flow as an algebraic system
Jakub Marecek, Timothy McCoy, and Martin Mevissen · 2014
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Equilibria analysis of power systems using a numerical homotopy method
Souvik Chandra, Dhagash Mehta, and Aranya Chakrabortty · 2015
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Toward topologically based upper bounds on the number of power flow solutions
Daniel K Molzahn, Dhagash Mehta, and Matthew Niemerg · 2015
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Recent advances in computational methods for the power flow equations
Dhagash Mehta, Daniel K Molzahn, and Konstantin Turitsyn · 2015
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