In this paper, we present a methodology to solve the problem of optimization the expansion of long-term power transmission networks using a formulation that uses mathematical expressions that are alternatives to the Kirchhoff's second law and that are applied to the cycles critical of the system graph.The problem of planning transmission systems is part of the socalled NP-complete problems, which belong to a category of problems difficult to solve, for which no polynomial solution algorithms are known.The proposed methodology is applied to a test system from the specialized literature with very good results.