Numerical polynomial homotopy continuation method to locate all the power flow solutions
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Numerical polynomial.pdf
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231.12 KB
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Author(s)
Nguyen, Hung Dinh
Mehta, Dhagash
Turitsyn, Konstantin
Date Issued
September 2016
Journal
IET Generation, Transmission & Distribution
Publisher
Institution of Engineering and Technology
Citation
Nguyen, Hung Dinh; Mehta, Dhagash and Turitsyn, Konstantin. “Numerical Polynomial Homotopy Continuation Method to Locate All the Power Flow Solutions.” IET Generation, Transmission & Distribution 10, no. 12 (September 2016): 2972–2980 © 2016 The Institution of Engineering and Technology
Version
Original manuscript
Abstract
The manuscript addresses the problem of finding all solutions of power flow equations or other similar non-linear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly the direct methods for transient stability analysis and voltage stability assessment. Here, the authors introduce a novel form of homotopy continuation method called the numerical polynomial homotopy continuation method that is mathematically guaranteed to find all the solutions without ever encountering a bifurcation. Since finding real solutions is much more challenging, first the authors embed the real form of power flow equation in complex space, and then track the generally unphysical solutions with complex values of real and imaginary parts of the voltages. The solutions converge to physical real form in the end of the homotopy. The so-called gamma-trick mathematically rigorously ensures that all the paths are well-behaved along the paths, so unlike other continuation approaches, no special handling of bifurcations is necessary. The method is embarrassingly parallelisable. The authors demonstrate the technique performance by solving several test cases up to the 14 buses. Finally, they discuss possible strategies for scaling the method to large size systems, and propose several applications for security assessments.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1049/iet-gtd.2015.1546
