Optimal Load Redistribution in Distribution Systems Using a Mixed-Integer Convex Model Based on Electrical Momentum
This paper addresses the problem concerning the efficient minimization of power losses in asymmetric distribution grids from the perspective of convex optimization. This research’s main objective is to propose an approximation optimization model to reduce the total power losses in a three-phase netw...
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MDPI AG
2023-04-01
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| author | Daniela Patricia Bohórquez-Álvarez Karen Dayanna Niño-Perdomo Oscar Danilo Montoya |
| author_facet | Daniela Patricia Bohórquez-Álvarez Karen Dayanna Niño-Perdomo Oscar Danilo Montoya |
| author_sort | Daniela Patricia Bohórquez-Álvarez |
| collection | DOAJ |
| description | This paper addresses the problem concerning the efficient minimization of power losses in asymmetric distribution grids from the perspective of convex optimization. This research’s main objective is to propose an approximation optimization model to reduce the total power losses in a three-phase network using the concept of electrical momentum. To obtain a mixed-integer convex formulation, the voltage variables at each node are relaxed by assuming them to be equal to those at the substation bus. With this assumption, the power balance constraints are reduced to flow restrictions, allowing us to formulate a set of linear rules. The objective function is formulated as a strictly convex objective function by applying the concept of average electrical momentum, by representing the current flows in distribution lines as the active and reactive power variables. To solve the relaxed MIQC model, the GAMS software (Version 28.1.2) and its CPLEX, SBB, and XPRESS solvers are used. In order to validate the effectiveness of load redistribution in power loss minimization, the initial and final grid configurations are tested with the triangular-based power flow method for asymmetric distribution networks. Numerical results show that the proposed mixed-integer model allows for reductions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>24.34</mn><mo>%</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>18.64</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4.14</mn><mo>%</mo></mrow></semantics></math></inline-formula> for the 8-, 15-, and 25-node test feeders, respectively, in comparison with the benchmark case. The sine–cosine algorithm and the black hole optimization method are also used for comparison, demonstrating the efficiency of the MIQC approach in minimizing the expected grid power losses for three-phase unbalanced networks. |
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| language | English |
| last_indexed | 2024-03-11T04:55:10Z |
| publishDate | 2023-04-01 |
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| spelling | doaj.art-767074b6de104c57a2b7bacdbaca93a32023-11-17T19:44:31ZengMDPI AGInformation2078-24892023-04-0114422910.3390/info14040229Optimal Load Redistribution in Distribution Systems Using a Mixed-Integer Convex Model Based on Electrical MomentumDaniela Patricia Bohórquez-Álvarez0Karen Dayanna Niño-Perdomo1Oscar Danilo Montoya2Grupo de Compatibilidad e Interferencia Electromagnética (GCEM), Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, 110231 Bogotá, ColombiaGrupo de Compatibilidad e Interferencia Electromagnética (GCEM), Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, 110231 Bogotá, ColombiaGrupo de Compatibilidad e Interferencia Electromagnética (GCEM), Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, 110231 Bogotá, ColombiaThis paper addresses the problem concerning the efficient minimization of power losses in asymmetric distribution grids from the perspective of convex optimization. This research’s main objective is to propose an approximation optimization model to reduce the total power losses in a three-phase network using the concept of electrical momentum. To obtain a mixed-integer convex formulation, the voltage variables at each node are relaxed by assuming them to be equal to those at the substation bus. With this assumption, the power balance constraints are reduced to flow restrictions, allowing us to formulate a set of linear rules. The objective function is formulated as a strictly convex objective function by applying the concept of average electrical momentum, by representing the current flows in distribution lines as the active and reactive power variables. To solve the relaxed MIQC model, the GAMS software (Version 28.1.2) and its CPLEX, SBB, and XPRESS solvers are used. In order to validate the effectiveness of load redistribution in power loss minimization, the initial and final grid configurations are tested with the triangular-based power flow method for asymmetric distribution networks. Numerical results show that the proposed mixed-integer model allows for reductions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>24.34</mn><mo>%</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>18.64</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4.14</mn><mo>%</mo></mrow></semantics></math></inline-formula> for the 8-, 15-, and 25-node test feeders, respectively, in comparison with the benchmark case. The sine–cosine algorithm and the black hole optimization method are also used for comparison, demonstrating the efficiency of the MIQC approach in minimizing the expected grid power losses for three-phase unbalanced networks.https://www.mdpi.com/2078-2489/14/4/229active power losseselectrical momentummixed-integer convex modelphase-balancingradial asymmetric distribution systems |
| spellingShingle | Daniela Patricia Bohórquez-Álvarez Karen Dayanna Niño-Perdomo Oscar Danilo Montoya Optimal Load Redistribution in Distribution Systems Using a Mixed-Integer Convex Model Based on Electrical Momentum Information active power losses electrical momentum mixed-integer convex model phase-balancing radial asymmetric distribution systems |
| title | Optimal Load Redistribution in Distribution Systems Using a Mixed-Integer Convex Model Based on Electrical Momentum |
| title_full | Optimal Load Redistribution in Distribution Systems Using a Mixed-Integer Convex Model Based on Electrical Momentum |
| title_fullStr | Optimal Load Redistribution in Distribution Systems Using a Mixed-Integer Convex Model Based on Electrical Momentum |
| title_full_unstemmed | Optimal Load Redistribution in Distribution Systems Using a Mixed-Integer Convex Model Based on Electrical Momentum |
| title_short | Optimal Load Redistribution in Distribution Systems Using a Mixed-Integer Convex Model Based on Electrical Momentum |
| title_sort | optimal load redistribution in distribution systems using a mixed integer convex model based on electrical momentum |
| topic | active power losses electrical momentum mixed-integer convex model phase-balancing radial asymmetric distribution systems |
| url | https://www.mdpi.com/2078-2489/14/4/229 |
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