The probabilistic minimum dominating set problem

Boria, Nicolas; Murat, Cécile; Paschos, Vangélis Th.

doi:10.1016/j.dam.2016.10.016

Cited by 4 publications

(1 citation statement)

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“…As studied in the literature for the SCP, the coverage relationship is not always deterministic, and thus the probabilistic set covering problem was proposed (see [6]). As a special case of the SCP, the MDS problem may suffer from uncertainty, which leads to the study of probabilistic MDS (PMDS) problem [7,8].…”

Section: Introductionmentioning

confidence: 99%

The probabilistic and reliable connected power dominating set problems

Sun

Fan

2018

Optim Lett

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As a variation of minimum dominating set problem, the power dominating set problem is proposed to achieve the complete observation of a power system by placing the smallest number of PMUs. Under different contingencies consisting line outages or PMU losses, the reliability of observation for each bus should be guaranteed to ensure the security and robustness of the power system. Thus, the probabilistic power dominating set (PPDS) problem is proposed in this paper. Given a pre-specified reliability level for each bus in the power system to be observed and known distribution of random events, an integer programming formulation, with consideration of zero-injection property, is presented for the PPDS problem. Additionally, the reliable connected power dominating set problem is studied to meet two requirements, including the connectivity of the PMU subgraph and the reliability of the connectivity of this subgraph. Numerical experiments based on several IEEE test cases are performed to find the best deployment of PMUs satisfying different requirements.

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Section: Introductionmentioning

confidence: 99%