An Efficient Homotopy Method for Solving the Post-Contingency Optimal Power Flow to Global Optimality
Optimal power flow (OPF) is a fundamental problem in power systems analysis for determining the steady-state operating point of a power network that minimizes the generation cost. In anticipation of component failures, such as transmission line or generator outages, it is also important to find opti...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9966487/ |
| _version_ | 1811185534782930944 |
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| author | Sangwoo Park Elizabeth Glista Javad Lavaei Somayeh Sojoudi |
| author_facet | Sangwoo Park Elizabeth Glista Javad Lavaei Somayeh Sojoudi |
| author_sort | Sangwoo Park |
| collection | DOAJ |
| description | Optimal power flow (OPF) is a fundamental problem in power systems analysis for determining the steady-state operating point of a power network that minimizes the generation cost. In anticipation of component failures, such as transmission line or generator outages, it is also important to find optimal corrective actions for the power flow distribution over the network. The problem of finding these post-contingency solutions to the OPF problem is challenging due to the nonconvexity of the power flow equations and the large number of contingency cases in practice. In this paper, we introduce a homotopy method to solve for the post-contingency actions, which involves a series of intermediate optimization problems that gradually transform the original OPF problem into each contingency-OPF problem. We show that given a global solution to the original OPF problem, a global solution to the contingency problem can be obtained using this homotopy method, under some conditions. With simulations on Polish and other European networks, we demonstrate that the effectiveness of the proposed homotopy method is dependent on the choice of the homotopy path and that homotopy yields an improved solution in many cases. For at least 5% of the test cases, bad local minima were identified, and the homotopy method yielded a solution that was significantly better than state-of-the-art interior point methods in terms of reducing the violation cost during a catastrophic contingency scenario. |
| first_indexed | 2024-04-11T13:31:04Z |
| format | Article |
| id | doaj.art-68d650706897410881dac2f30eeebca1 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-11T13:31:04Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-68d650706897410881dac2f30eeebca12022-12-22T04:21:49ZengIEEEIEEE Access2169-35362022-01-011012496012497810.1109/ACCESS.2022.32241629966487An Efficient Homotopy Method for Solving the Post-Contingency Optimal Power Flow to Global OptimalitySangwoo Park0https://orcid.org/0000-0002-0355-7272Elizabeth Glista1https://orcid.org/0000-0003-2870-3659Javad Lavaei2https://orcid.org/0000-0003-4294-1338Somayeh Sojoudi3https://orcid.org/0000-0001-7177-7712Department of Industrial Engineering and Operations Research, University of California Berkeley, Berkeley, CA, USADepartment of Mechanical Engineering, University of California Berkeley, Berkeley, CA, USADepartment of Industrial Engineering and Operations Research, University of California Berkeley, Berkeley, CA, USADepartment of Electrical Engineering and Computer Sciences, University of California Berkeley, Berkeley, CA, USAOptimal power flow (OPF) is a fundamental problem in power systems analysis for determining the steady-state operating point of a power network that minimizes the generation cost. In anticipation of component failures, such as transmission line or generator outages, it is also important to find optimal corrective actions for the power flow distribution over the network. The problem of finding these post-contingency solutions to the OPF problem is challenging due to the nonconvexity of the power flow equations and the large number of contingency cases in practice. In this paper, we introduce a homotopy method to solve for the post-contingency actions, which involves a series of intermediate optimization problems that gradually transform the original OPF problem into each contingency-OPF problem. We show that given a global solution to the original OPF problem, a global solution to the contingency problem can be obtained using this homotopy method, under some conditions. With simulations on Polish and other European networks, we demonstrate that the effectiveness of the proposed homotopy method is dependent on the choice of the homotopy path and that homotopy yields an improved solution in many cases. For at least 5% of the test cases, bad local minima were identified, and the homotopy method yielded a solution that was significantly better than state-of-the-art interior point methods in terms of reducing the violation cost during a catastrophic contingency scenario.https://ieeexplore.ieee.org/document/9966487/Power systemsoptimal power flownonconvex optimizationcontingency analysis |
| spellingShingle | Sangwoo Park Elizabeth Glista Javad Lavaei Somayeh Sojoudi An Efficient Homotopy Method for Solving the Post-Contingency Optimal Power Flow to Global Optimality IEEE Access Power systems optimal power flow nonconvex optimization contingency analysis |
| title | An Efficient Homotopy Method for Solving the Post-Contingency Optimal Power Flow to Global Optimality |
| title_full | An Efficient Homotopy Method for Solving the Post-Contingency Optimal Power Flow to Global Optimality |
| title_fullStr | An Efficient Homotopy Method for Solving the Post-Contingency Optimal Power Flow to Global Optimality |
| title_full_unstemmed | An Efficient Homotopy Method for Solving the Post-Contingency Optimal Power Flow to Global Optimality |
| title_short | An Efficient Homotopy Method for Solving the Post-Contingency Optimal Power Flow to Global Optimality |
| title_sort | efficient homotopy method for solving the post contingency optimal power flow to global optimality |
| topic | Power systems optimal power flow nonconvex optimization contingency analysis |
| url | https://ieeexplore.ieee.org/document/9966487/ |
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