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Article

Second-Order Cone Approximation for Voltage Stability Analysis in Direct-Current Networks

1
Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 11021, Colombia
2
Laboratorio Inteligente de Energía, Universidad Tecnológica de Bolívar, Cartagena 131001, Colombia
3
Grupo GIIEN, Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Campus Robledo, Medellín 050036, Colombia
4
Facultad de Ingeniería, Universidad Tecnológica de Pereira, Pereira 660003, Colombia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(10), 1587; https://doi.org/10.3390/sym12101587
Received: 16 August 2020 / Revised: 9 September 2020 / Accepted: 22 September 2020 / Published: 24 September 2020
(This article belongs to the Special Issue Symmetry in Renewable Energy and Power Systems)
In this study, the voltage stability margin for direct current (DC) networks in the presence of constant power loads is analyzed using a proposed convex mathematical reformulation. This convex model is developed by employing a second-order cone programming (SOCP) optimization that transforms the non-linear non-convex original formulation by reformulating the power balance constraint. The main advantage of the SOCP model is that the optimal global solution of a problem can be obtained by transforming hyperbolic constraints into norm constraints. Two test systems are considered to validate the proposed SOCP model. Both systems have been reported in specialized literature with 6 and 69 nodes. Three comparative methods are considered: (a) the Newton-Raphson approximation based on the determinants of the Jacobian matrices, (b) semidefinite programming models, and (c) the exact non-linear formulation. All the numerical simulations are conducted using the MATLAB and GAMS software. The effectiveness of the proposed SOCP model in addressing the voltage stability problem in DC grids is verified by comparing the objective function values and processing time. View Full-Text
Keywords: convex reformulation; direct current networks; non-linear optimization; numerical example; second-order cone programming; voltage stability margin convex reformulation; direct current networks; non-linear optimization; numerical example; second-order cone programming; voltage stability margin
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MDPI and ACS Style

Montoya, O.D.; Gil-González, W.; Molina-Cabrera, A. Second-Order Cone Approximation for Voltage Stability Analysis in Direct-Current Networks. Symmetry 2020, 12, 1587. https://doi.org/10.3390/sym12101587

AMA Style

Montoya OD, Gil-González W, Molina-Cabrera A. Second-Order Cone Approximation for Voltage Stability Analysis in Direct-Current Networks. Symmetry. 2020; 12(10):1587. https://doi.org/10.3390/sym12101587

Chicago/Turabian Style

Montoya, Oscar D., Walter Gil-González, and Alexander Molina-Cabrera. 2020. "Second-Order Cone Approximation for Voltage Stability Analysis in Direct-Current Networks" Symmetry 12, no. 10: 1587. https://doi.org/10.3390/sym12101587

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