Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks
With this study, we address the optimal phase balancing problem in three-phase networks with asymmetric loads in reference to a mixed-integer quadratic convex (MIQC) model. The objective function considers the minimization of the sum of the square currents through the distribution lines multiplied b...
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MDPI AG
2021-08-01
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| Online Access: | https://www.mdpi.com/2073-431X/10/9/109 |
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| author | Oscar Danilo Montoya Luis Fernando Grisales-Noreña Edwin Rivas-Trujillo |
| author_facet | Oscar Danilo Montoya Luis Fernando Grisales-Noreña Edwin Rivas-Trujillo |
| author_sort | Oscar Danilo Montoya |
| collection | DOAJ |
| description | With this study, we address the optimal phase balancing problem in three-phase networks with asymmetric loads in reference to a mixed-integer quadratic convex (MIQC) model. The objective function considers the minimization of the sum of the square currents through the distribution lines multiplied by the average resistance value of the line. As constraints are considered for the active and reactive power redistribution in all the nodes considering a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>×</mo><mn>3</mn></mrow></semantics></math></inline-formula> binary decision variable having six possible combinations, the branch and nodal current relations are related to an extended upper-triangular matrix. The solution offered by the proposed MIQC model is evaluated using the triangular-based three-phase power flow method in order to determine the final steady state of the network with respect to the number of power loss upon the application of the phase balancing approach. The numerical results in three radial test feeders composed of 8, 15, and 25 nodes demonstrated the effectiveness of the proposed MIQC model as compared to metaheuristic optimizers such as the genetic algorithm, black hole optimizer, sine–cosine algorithm, and vortex search algorithm. All simulations were carried out in MATLAB 2020<i>a</i> using the CVX tool and the Gurobi solver. |
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| format | Article |
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| language | English |
| last_indexed | 2024-03-10T07:47:44Z |
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| spelling | doaj.art-c0e83e214cae4bea9215f7e165511bee2023-11-22T12:33:25ZengMDPI AGComputers2073-431X2021-08-0110910910.3390/computers10090109Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric NetworksOscar Danilo Montoya0Luis Fernando Grisales-Noreña1Edwin Rivas-Trujillo2Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 110231, ColombiaDepartamento de Mecatrónica y Electromecánica, Instituto Tecnológico Metropolitano, Medellín 050012, ColombiaFacultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 110231, ColombiaWith this study, we address the optimal phase balancing problem in three-phase networks with asymmetric loads in reference to a mixed-integer quadratic convex (MIQC) model. The objective function considers the minimization of the sum of the square currents through the distribution lines multiplied by the average resistance value of the line. As constraints are considered for the active and reactive power redistribution in all the nodes considering a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>×</mo><mn>3</mn></mrow></semantics></math></inline-formula> binary decision variable having six possible combinations, the branch and nodal current relations are related to an extended upper-triangular matrix. The solution offered by the proposed MIQC model is evaluated using the triangular-based three-phase power flow method in order to determine the final steady state of the network with respect to the number of power loss upon the application of the phase balancing approach. The numerical results in three radial test feeders composed of 8, 15, and 25 nodes demonstrated the effectiveness of the proposed MIQC model as compared to metaheuristic optimizers such as the genetic algorithm, black hole optimizer, sine–cosine algorithm, and vortex search algorithm. All simulations were carried out in MATLAB 2020<i>a</i> using the CVX tool and the Gurobi solver.https://www.mdpi.com/2073-431X/10/9/109approximated mixed-integer quadratic convex modelphase balancing problemasymmetric distribution networkstriangular-based power flow method |
| spellingShingle | Oscar Danilo Montoya Luis Fernando Grisales-Noreña Edwin Rivas-Trujillo Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks Computers approximated mixed-integer quadratic convex model phase balancing problem asymmetric distribution networks triangular-based power flow method |
| title | Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| title_full | Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| title_fullStr | Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| title_full_unstemmed | Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| title_short | Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks |
| title_sort | approximated mixed integer convex model for phase balancing in three phase electric networks |
| topic | approximated mixed-integer quadratic convex model phase balancing problem asymmetric distribution networks triangular-based power flow method |
| url | https://www.mdpi.com/2073-431X/10/9/109 |
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