Science and Education Publishing World Journal Control Science and Engineering 2328-7330 2 1 2014 11 13 Studies of Contingencies in Power Systems through a Geometric Parameterization Technique, Part I: Mathematical Modeling 18 24 EN Bonini Neto A. Department of Biosystems Engineering, UNESP- São Paulo State University, Tupã, Brazil Alves D. A. WJCSE2014214 10.12691/wjcse-2-1-4 2014 10 25 2014 11 10 2014 11 13 An electrical power system is exposed to the occurrence of a large number of contingencies. However, only some of these are severe enough to cause significant damage (collapse voltage, for example) to the system. Thus, before the voltage stability analysis, is realized the selection and ordering of contingencies according to the impact this cause to the system, reducing the computational time of the analysis. This paper presents a geometric parameterization technique for the continuation power flow which allows the tracing complete of P-V curves and the calculation of the maximum loading point (MLP) of power systems without the ill-conditioning problems of Jacobian matrix (J). This occurs before and after a contingency, i.e., this technique provides all the P-V curve of the pre and post contingency with addition of a line in the λ-V andλ- plans. The results obtained with the methodology to the IEEE 14 and 30 bus systems show that the characteristics of the conventional method are improved and the convergence region around the singularity is enlarged. The goal is to present the method with simplicity and easy interpretation.