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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Bibliographic Details
Published in:Computers (Basel) 2021, Vol.10 (9), p.109
Main Authors: Montoya, Oscar Danilo, Grisales-Noreña, Luis Fernando, Rivas-Trujillo, Edwin
Format: Article
Language:English
Subjects:
approximated mixed-integer quadratic convex model
asymmetric distribution networks
Balancing
Electrical networks
Feeders
Genetic algorithms
Heuristic methods
Load
Methods
Mixed integer
Nodes
Optimization
phase balancing problem
Power flow
Reactive power
Search algorithms
triangular-based power flow method
Trigonometric functions
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Summary: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 3×3 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 2020a using the CVX tool and the Gurobi solver.
ISSN:2073-431X
2073-431X
DOI:10.3390/computers10090109