Quadratic functions for efficient load balancing in the terminals of a substation of a three-phase asymmetric network with power loss reduction capabilities

This research addresses the problem of optimal load balancing in terminals of the three-phase substation by proposing three quadratic objective functions. These objective functions are formulated considering active, reactive, and apparent power consumptions aggregated at the terminals of the substation. The proposed formulation belongs to the mixed-integer quadratic models’ family, which can be solved globally with specialized mixed-integer convex tools. To evaluate the effect of load redistribution in the substation terminals, the 15- and 35-bus grids are tested using each of the proposed quadratic functions. In addition, Broyden's unbalanced power flow method is used to determine the extent of power loss reduction and enhancement of voltage profile. Numerical results confirm the effectiveness of the proposed mixed-integer quadratic model in enhancing electrical performance in three-phase asymmetric networks through load balancing at the substation terminals. After solving each quadratic function for the 15-bus grid, power losses were reduced between 12.9624% and 17.2550%, and these reductions were between 5.0771% and 7.7389% in the 35-bus grid.