Investigation of Non-zero Duality Gap Solutions to a Semidefinite Relaxation of the Optimal Power Flow Problem. Molzahn, D. K., Lesieutre, B. C., & DeMarco, C. L. In 47th Hawaii International Conference on System Sciences, pages 2325-2334, January, 2014.
Paper
Link doi abstract bibtex Recently, a semi definite programming relaxation of the power flow equations has been applied to the optimal power flow problem. When this relaxation is "tight" (i.e., the solution has zero duality gap), a globally optimal solution is obtained. Existing literature investigates sufficient conditions whose satisfaction guarantees zero duality gap solutions. However, there is limited study of non-zero duality gap solutions. By illustrating the feasible spaces for optimal power flow problems and their semi definite relaxations, this paper investigates examples of non-zero duality gap solutions. Results for large system models suggest that non-convexities associated with small subsections of the network are responsible for non-zero duality gap solutions.
@inproceedings{molzahn_lesieutre_demarco-hicss2014,
author={D. K. Molzahn and B. C. Lesieutre and C. L. DeMarco},
booktitle={47th Hawaii International Conference on System Sciences},
title={{Investigation of Non-zero Duality Gap Solutions to a Semidefinite Relaxation of the Optimal Power Flow Problem}},
year={2014},
pages={2325-2334},
month={January},
doi={10.1109/HICSS.2014.293},
keywords={Optimal Power Flow},
abstract={Recently, a semi definite programming relaxation of the power flow equations has been applied to the optimal power flow problem. When this relaxation is "tight" (i.e., the solution has zero duality gap), a globally optimal solution is obtained. Existing literature investigates sufficient conditions whose satisfaction guarantees zero duality gap solutions. However, there is limited study of non-zero duality gap solutions. By illustrating the feasible spaces for optimal power flow problems and their semi definite relaxations, this paper investigates examples of non-zero duality gap solutions. Results for large system models suggest that non-convexities associated with small subsections of the network are responsible for non-zero duality gap solutions.},
url_Paper={molzahn_lesieutre_demarco-hicss2014.pdf},
url_Link={http://ieeexplore.ieee.org/document/6758891/},
}
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