Energy function and unstable solutions by the means of an augmented Jacobian

This paper investigates the energy function technique for load margin calculation when an algebraic set of equations is considered, so only the system potential energy is calculated. The unstable solutions, demanded by energy-based methods, are qualitatively analyzed and an approach for finding such solutions is proposed. The whole iterative process is obtained with the help of the Newton’s method, enabling a fast, reliable and accurate sub-optimal solution. The accuracy and speed up of the method are assessed by comparing it with the continuation method. This assessment is carried out with the help of some sample power systems, since they contain several important operating restrictions. These systems are analyzed with their limits considered, in order to make the results more realistic.