Abstract
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.
Highlights
Three-phase electric networks are the most common topology at medium- and lowvoltage distribution levels to supply electricity to residential, industrial, and commercial users in urban and rural areas [1,2]
An approximated mixed-integer quadratic convex (MIQC) model combined with the triangular-based power flow method for asymmetric distribution networks was proposed in this study in order to solve the optimal phase balancing problem in medium-voltage distribution grids
The numerical results for three test feeders composed of 8, 15, and 25 nodes demonstrate that the proposed MIQC model reaches the optimal solution in the 8- and 25-bus systems with reductions in the power losses of 24.34% and 4.16%, respectively, relative to the benchmark cases
Summary
Three-phase electric networks are the most common topology at medium- and lowvoltage distribution levels to supply electricity to residential, industrial, and commercial users in urban and rural areas [1,2]. In order to validate the feasibility and optimality of the solution, a triangular-based three-phase power flow method has been implemented to determine the initial and final power losses in the network. The numerical results of the present study demonstrate the effectiveness and robustness of the proposed MIQC model as compared to metaheuristic optimizers such as the genetic algorithms, SCA, BHO, and VSA in three individual radial test feeders composed of 8, 15, and 25 nodes.
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