0600099 20250317084450.820241101235959.9 85153256678 000973226900001 10.1007/s11081-023-09801-3 30 s. P cav_un_epca*02971911389-4420244 (2024)2973-3002Springer Electric power distribution network Optimal power flow Convex relaxation Pareto-front cav_un_auth*0475404 Desveaux V. FR K cav_un_auth*0475405 Handa Marouan UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR JP Ústav teorie informace a automatizace AV ČR, v. v. i. https://library.utia.cas.cz/separaty/2024/MTR/handa-0600099.pdf https://link.springer.com/article/10.1007/s11081-023-09801-3 GA22-15524S GA ČR CZ cav_un_auth*0447354 In this work, we are interested in an optimal power flow problem with fixed voltage magnitudes in distribution networks. This optimization problem is known to be non-convex and thus difficult to solve. A well-known solution methodology consists in reformulating the objective function and the constraints of the original problem in terms of positive semi-definite matrix traces, to which we add a rank constraint. To convexify the problem, we remove this rank constraint. Our main focus is to provide a strong mathematical proof of the exactness of this convex relaxation technique. To this end, we explore the geometry of the feasible set of the problem via its Pareto-front. We prove that the feasible set of the original problem and the feasible set of its convexification share the same Pareto-front. From a numerical point of view, this exactness result allows to reduce the initial problem to a semi-definite program, which can be solved by more efficient algorithms. WOS BB 10000 10100 10102 2025 RVO:67985556 https://hdl.handle.net/11104/0357459 S C OPERATIONSRESEARCH&MANAGEMENTSCIENCE|MATHEMATICS.INTERDISCIPLINARYAPPLICATIONS|ENGINEERING.MULTIDISCIPLINARY 2.1 0.2 5.3 0.00201 0.582 1645 50 0.573 42.71 2.58 714 Q2 1.600 61 Q2 48.9 0.51 Q2 56.7 2024 85153256678 SCOPUS PUBMED 000973226900001 WOS cav_un_epca*0297191 Optimization and Engineering Roč. 24 č. 4 2024 2973 3002 1389-4420 1573-2924 Springer