A framework to study critical loadability solutions

This work proposes a framework to analyze critical loadability solutions of the power flow equations based on an optimization problem. Rectangular coordinates are used to model the steady state power network equations with Newtont´s method applied to solve the optimization problem. The extensions proposed here include: 1) a decomposition scheme to speed up the iterative process; 2) the treatment of the generated reactive power limits through an accurate unidimensional search technique, which exploits the quadratic form of the power flow equations expressed in rectangular coordinates; 3) the use of sensitivity relationships determined as a by-product of the iterative process to identify critical areas and 4) the determination of loading factor × voltage magnitude curves, departing from the critical loadability point. Numerical results obtained with power systems of different sizes show the main features of the proposed methodology.