MATHEMATICAL MODELS FOR LOAD BALANCING IN POWER GRIDS USING SPECTRAL GRAPH THEORY

Electrical power is fundamental to virtually every aspect of modern life. With the increase in its consumption, it becomes a challenge to avoid failures in its distribution and transmission, such as blackouts, which have been observed in Brazil, causing damage to society. In order to contribute to the good operation of a power grid, our study aims to identify critical transmission lines, based on the electrical power in each of them, in order to ensure the reliability of the grid and prevent blackouts. We use a geometric approach based on the discrete Laplacian operator of the graph associated with the lattice. We have developed formulations of the load-balancing problem and a way to solve it based on the optimality conditions of the quadratic function of the problem, resulting in a faster and more efficient process, as observed in computational testing. These results are promising and make it possible to address variants of the load balancing problem in power grids.