Optimal Demand Reconfiguration in Three-Phase Distribution Grids Using an MI-Convex Model

Abstract

The problem of the optimal load redistribution in electrical three-phase medium-voltage grids is addressed in this research from the point of view of mixed-integer convex optimization. The mathematical formulation of the load redistribution problem is developed in terminals of the distribution node by accumulating all active and reactive power loads per phase. These loads are used to propose an objective function in terms of minimization of the average unbalanced (asymmetry) grade of the network with respect to the ideal mean consumption per-phase. The objective function is defined as the l1-norm which is a convex function. As the constraints consider the binary nature of the decision variable, each node is conformed by a 3×3 matrix where each row and column have to sum 1, and two equations associated with the load redistribution at each phase for each of the network nodes. Numerical results demonstrate the efficiency of the proposed mixed-integer convex model to equilibrate the power consumption per phase in regards with the ideal value in three different test feeders, which are composed of 4, 15, and 37 buses, respectively.

Application of the Hurricane-Based Optimization Algorithm to the Phase-Balancing Problem in Three-Phase Asymmetric Networks

“…Since this study aims to obtain a single optimal connection for the system, it uses the constraints shown in Equations ( 5) and ( 6) [37].…”

An Improved Crow Search Algorithm Applied to the Phase Swapping Problem in Asymmetric Distribution Systems

“…Equations ( 2) and (3) define the apparent power balance constraints maintained at each phase and node of the ADS. Equations ( 4) and (5) ensure that loads take a unique connection form by using a matrix of connections (i.e., x n f g ) at each node [5]. Finally, the constraint presented in (6) defines the allowable limits of voltage regulation for all nodes of the system [15].…”

“…These systems generally operate in an asymmetric manner due to the following factors. (i) The configurations on the distribution lines are asymmetrical since the transposition criterion is not applicable due to the short length of the lines [4,5]. (ii) The nature of the loads may be 1ϕ, 2ϕ, or 3ϕ, which generates unbalances in voltages at the nodes and in the line currents [6].…”

Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks

“…Most of them are based on master-slave optimization strategies using metaheuristics and three-phase power flow methods. Some of the most recurrent optimization approaches are the Chu and Beasley genetic algorithms (CBGA) [3,5,6], particle swarm optimization [7], vortex search algorithm (VSA) [8], simulated annealing [9], black hole optimizer (BHO) [3], differential evolution algorithm [10], and sine-cosine algorithm (SCA) [11]. A characteristic of these methodologies is that the master stage is entrusted with the responsibility of determining the connection of the loads in all the nodes using an integer codification, which is then transferred to the slave stage where the asymmetric power flow problem is evaluated to determine the number of power losses, which would guide the exploration through the solution space.…”

“…It is worth mentioning that the proposed mixed-integer quadratic convex model was based on the convex formulation that was recently proposed in [11], which neglected the effect of the currents through the lines and the objective function associated with the total load consumption at the terminals of the substation, while our proposal includes a sensitive index in the objective function related to the minimization of the power losses under ideal voltage conditions considering the branch current calculations.…”