A simpler and exact mathematical model for the computation of the minimal power losses tree

This paper presents a new model to compute the tree of minimum active power losses in distribution systems. The main idea consists of using a non-conventional group of variables instead of the classical bus complex voltages, in addition to algebraically formulating the topological and electrical constraints before the actual radial configuration is determined. The new variables allow to set out a simpler mathematical optimization problem where, additionally, the product of continuous and binary variable does not appear, so one of the main problems related to the mathematical reconfiguration problem is avoided. The final minimization problem is made up of linear and quadratic equality and inequality constraints, also being linear the objective function. The new proposed model has been tested on different systems used specifically in the literature. In all the cases the reached solution matches the better known and even in same cases it has been improved.