A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids
Phase balancing is a classical optimization problem in power distribution grids that involve phase swapping of the loads and generators to reduce power loss. The problem is a non-linear integer and, hence, it is usually solved using heuristic algorithms. This paper proposes a mathematical reformulat...
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MDPI AG
2021-02-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/5/1972 |
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| author | Alejandro Garces Walter Gil-González Oscar Danilo Montoya Harold R. Chamorro Lazaro Alvarado-Barrios |
| author_facet | Alejandro Garces Walter Gil-González Oscar Danilo Montoya Harold R. Chamorro Lazaro Alvarado-Barrios |
| author_sort | Alejandro Garces |
| collection | DOAJ |
| description | Phase balancing is a classical optimization problem in power distribution grids that involve phase swapping of the loads and generators to reduce power loss. The problem is a non-linear integer and, hence, it is usually solved using heuristic algorithms. This paper proposes a mathematical reformulation that transforms the phase-balancing problem in low-voltage distribution networks into a mixed-integer convex quadratic optimization model. To consider both conventional secondary feeders and microgrids, renewable energies and their subsequent stochastic nature are included in the model. The power flow equations are linearized, and the combinatorial part is represented using a Birkhoff polytope <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">B</mi><mn>3</mn></msub></semantics></math></inline-formula> that allows the selection of phase swapping in each node. The numerical experiments on the CIGRE low-voltage test system demonstrate the use of the proposed formulation. |
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| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T00:36:06Z |
| publishDate | 2021-02-01 |
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| spelling | doaj.art-03b9bd8962b043d89cd5b822c85fbe3a2023-12-11T18:08:45ZengMDPI AGApplied Sciences2076-34172021-02-01115197210.3390/app11051972A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential MicrogridsAlejandro Garces0Walter Gil-González1Oscar Danilo Montoya2Harold R. Chamorro3Lazaro Alvarado-Barrios4Programa de Ingeniería Eléctrica, Universidad Tecnológica de Pereira, Pereira 660003, ColombiaGrupo GIIEN, Facultad de Ingeniería, Campus Robledo, Institución Universitaria Pascual Bravo, Medellín 050036, ColombiaFacultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 11021, ColombiaDepartment of Electrical Engineering at KTH, Royal Institute of Technology, SE-100 44 Stockholm, SwedenDepartment of Engineering, Universidad Loyola Andalucía, 41704 Sevilla, SpainPhase balancing is a classical optimization problem in power distribution grids that involve phase swapping of the loads and generators to reduce power loss. The problem is a non-linear integer and, hence, it is usually solved using heuristic algorithms. This paper proposes a mathematical reformulation that transforms the phase-balancing problem in low-voltage distribution networks into a mixed-integer convex quadratic optimization model. To consider both conventional secondary feeders and microgrids, renewable energies and their subsequent stochastic nature are included in the model. The power flow equations are linearized, and the combinatorial part is represented using a Birkhoff polytope <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">B</mi><mn>3</mn></msub></semantics></math></inline-formula> that allows the selection of phase swapping in each node. The numerical experiments on the CIGRE low-voltage test system demonstrate the use of the proposed formulation.https://www.mdpi.com/2076-3417/11/5/1972phase-balancingconvex approximationsheuristic algorithmunbalanced power distribution gridsmicrogridscombinatorial optimization |
| spellingShingle | Alejandro Garces Walter Gil-González Oscar Danilo Montoya Harold R. Chamorro Lazaro Alvarado-Barrios A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids Applied Sciences phase-balancing convex approximations heuristic algorithm unbalanced power distribution grids microgrids combinatorial optimization |
| title | A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids |
| title_full | A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids |
| title_fullStr | A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids |
| title_full_unstemmed | A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids |
| title_short | A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids |
| title_sort | mixed integer quadratic formulation of the phase balancing problem in residential microgrids |
| topic | phase-balancing convex approximations heuristic algorithm unbalanced power distribution grids microgrids combinatorial optimization |
| url | https://www.mdpi.com/2076-3417/11/5/1972 |
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