Numerical polynomial homotopy continuation method to locate all the power flow solutions
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 stabi...
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| Format: | Article |
| Language: | en_US |
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Institution of Engineering and Technology
2017
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| Online Access: | http://hdl.handle.net/1721.1/109296 https://orcid.org/0000-0003-2610-5161 https://orcid.org/0000-0002-7997-8962 |
| _version_ | 1826208428507267072 |
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| author | Nguyen, Hung Dinh Mehta, Dhagash Turitsyn, Konstantin |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Nguyen, Hung Dinh Mehta, Dhagash Turitsyn, Konstantin |
| author_sort | Nguyen, Hung Dinh |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:05:18Z |
| format | Article |
| id | mit-1721.1/109296 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:05:18Z |
| publishDate | 2017 |
| publisher | Institution of Engineering and Technology |
| record_format | dspace |
| spelling | mit-1721.1/1092962022-09-28T18:21:01Z Numerical polynomial homotopy continuation method to locate all the power flow solutions Nguyen, Hung Dinh Mehta, Dhagash Turitsyn, Konstantin Massachusetts Institute of Technology. Department of Mechanical Engineering Nguyen, Hung Dinh Turitsyn, Konstantin 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. 2017-05-23T15:33:09Z 2017-05-23T15:33:09Z 2016-09 2016-04 Article http://purl.org/eprint/type/JournalArticle 1751-8687 1751-8695 http://hdl.handle.net/1721.1/109296 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 https://orcid.org/0000-0003-2610-5161 https://orcid.org/0000-0002-7997-8962 en_US http://dx.doi.org/10.1049/iet-gtd.2015.1546 IET Generation, Transmission & Distribution Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institution of Engineering and Technology arXiv |
| spellingShingle | Nguyen, Hung Dinh Mehta, Dhagash Turitsyn, Konstantin Numerical polynomial homotopy continuation method to locate all the power flow solutions |
| title | Numerical polynomial homotopy continuation method to locate all the power flow solutions |
| title_full | Numerical polynomial homotopy continuation method to locate all the power flow solutions |
| title_fullStr | Numerical polynomial homotopy continuation method to locate all the power flow solutions |
| title_full_unstemmed | Numerical polynomial homotopy continuation method to locate all the power flow solutions |
| title_short | Numerical polynomial homotopy continuation method to locate all the power flow solutions |
| title_sort | numerical polynomial homotopy continuation method to locate all the power flow solutions |
| url | http://hdl.handle.net/1721.1/109296 https://orcid.org/0000-0003-2610-5161 https://orcid.org/0000-0002-7997-8962 |
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