Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 762371, 24 pages
Research Article

A Parameterization Technique for the Continuation Power Flow Developed from the Analysis of Power Flow Curves

Electrical Engineering Department, São Paulo State University (UNESP), 15385-000 Ilha Solteira, SP, Brazil

Received 24 March 2012; Accepted 3 May 2012

Academic Editor: Cristian Toma

Copyright © 2012 Elisabete de Mello Magalhães et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents an efficient geometric parameterization technique for the continuation power flow. It was developed from the observation of the geometrical behavior of load flow solutions. The parameterization technique eliminates the singularity of load flow Jacobian matrix and therefore all the consequent problems of ill-conditioning. This is obtained by adding equations lines passing through the points in the plane determined by the loading factor and the total real power losses that is rewritten as a function of the real power generated by the slack bus. An automatic step size control is also provided, which is used when it is necessary. Thus, the resulting method enables the complete tracing of P-V curves and the computation of maximum loading point of any electric power systems. Intending to reduce the CPU time, the effectiveness caused by updating the Jacobian matrix is investigated only when the system undergoes a significant change. Moreover, the tangent and trivial predictors are compared with each other. The robustness and simplicity as well as the simple interpretation of the proposed technique are the highlights of this method. The results obtained for the IEEE 300-bus system and for real large systems show the effectiveness of the proposed method.