In this work, the state estimation problem of electric power systems is represented through a mathematical programming approach. Initially, a non-linear mathematical model based on the classical method of weighted least squares is proposed to solve the state estimation problem for comparative purposes. Due to the inherent limitations that this classical model presents when dealing with errors in the set of measurements, a new mathematical model is proposed that can be used within an iterative procedure to reduce the impact of measurement errors on the estimated results. Several tests on a didactic 5-bus power system and IEEE benchmark power test systems showed the effectiveness of the proposed approach which achieved better results than the proposed classical state estimation model. The non-linear programming models proposed in this paper are implemented in the mathematical modeling language AMPL. Additionally, to validate the results of the proposed methodologies, the power system operation points are compared with the results obtained using the Matpower simulation package. The results allowed concluding that the proposed mathematical models can be successfully applied to perform state estimation studies in power systems.