Conic formulation of QPCCs applied to truly sparse QPs

Bomze, Immanuel M.; Peng, Bo

doi:10.1007/s10589-022-00440-5

Cited by 3 publications

(1 citation statement)

References 39 publications

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“…Here, Equation ( 15) corresponds to a non-convex constraint, as it represents the contour of a cone due to the equality imposition [41].…”

Section: Conic Programming Applicationmentioning

confidence: 99%

A Robust Conic Programming Approximation to Design an EMS in Monopolar DC Networks with a High Penetration of PV Plants

Montoya,

Serra,

Gil-González

2023

Energies

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This research addresses the problem regarding the efficient operation of photovoltaic (PV) plants in monopolar direct current (DC) distribution networks from a perspective of convex optimization. PV plant operation is formulated as a nonlinear programming (NLP) problem while considering two single-objective functions: the minimization of the expected daily energy losses and the reduction in the expected CO2 emissions at the terminals of conventional generation systems. The NLP model that represents the energy management system (EMS) design is transformed into a convex optimization problem via the second-order cone equivalent of the product between two positive variables. The main contribution of this research is that it considers the uncertain nature of solar generation and expected demand curves through robust convex optimization. Numerical results in the monopolar DC version of the IEEE 33-bus grid demonstrate the effectiveness and robustness of the proposed second-order cone programming model in defining an EMS for a monopolar DC distribution network. A comparative analysis with four different combinatorial optimizers is carried out, i.e., multiverse optimization (MVO), the salp swarm algorithm (SSA), the particle swarm optimizer (PSO), and the crow search algorithm (CSA). All this is achieved while including an iterative convex method (ICM). This analysis shows that the proposed robust model can find the global optimum for two single-objective functions. The daily energy losses are reduced by 44.0082% with respect to the benchmark case, while the CO2 emissions (kg) are reduced by 27.3771%. As for the inclusion of uncertainties, during daily operation, the energy losses increase by 22.8157%, 0.2023%, and 23.7893% with respect to the benchmark case when considering demand uncertainty, PV generation uncertainty, and both. Similarly, CO2 emissions increase by 11.1854%, 0.9102%, and 12.1198% with regard to the benchmark case. All simulations were carried out using the Mosek solver in the Yalmip tool of the MATLAB software.

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“…Here, Equation ( 15) corresponds to a non-convex constraint, as it represents the contour of a cone due to the equality imposition [41].…”

Section: Conic Programming Applicationmentioning

confidence: 99%

A Robust Conic Programming Approximation to Design an EMS in Monopolar DC Networks with a High Penetration of PV Plants

Montoya,

Serra,

Gil-González

2023

Energies

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A Square Departure From Symmetry in Matrix Cones

Bomze,

Dür

2024

Vietnam J. Math.

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Conic optimization problems are usually understood to be problems over some cone of symmetric matrices like the semidefinite or the copositive matrix cone. In this note, we investigate the changes that have to be made when moving from symmetric to nonsymmetric matrices. We introduce the proper definitions and study the dual of a cone of nonsymmetric matrices. Next, we attempt to generalize the well known concept of cp-rank to nonsymmetric matrices. Finally, we derive some new results on symmetric and nonsymmetric copositive-plus matrices.

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