Geometric Parameterization Technique for Continuation Power Flow Based on Quadratic Curve

Abstract

The electricity sector, especially in emerging countries, has experienced several transformations, mainly resulting from the increase of electricity demand. This encourages more investment in the generation sector and causes increasing concerns with the development and improvement of tools for static voltage stability analysis of electrical power systems. This paper presents a new geometric parameterization technique for continuation power flow (CPF) that works based on the addition of a parabola that passes through three points in the plane formed by the variables of total real power losses and loading factor. This technique eliminates the Jacobian matrix singularity at the maximum loading point, which allows obtaining the solution trajectory (P–V curve) without any need to change the parameter, which is a very common procedure in the currently available CPFs. Intending to define a simple and efficient step size control procedure, the total real power losses values are normalized by its base case value. The results obtained by applying the proposed technique to the IEEE-300 bus system and two real large systems of 638 and 787 buses show its effectiveness.