PV Curves for Steady-State Security Assessment with MATLAB

Most of the problem solutions oriented to the analysis of power systems require the implementation of sophisticated algorithms which need a considerable amount of calculations that must be carried out with a digital computer. Advances in software and hardware engineering have led to the development of specialized computing tools in the area of electrical power systems which allows its efficient analysis. Most of the computational programs, if not all of them, are developed under proprietary code, in other words, the users does not have access to the source code, which limits its usage scope. These programs are considered as black boxes that users only need to feed the required input data to obtain the results without knowing anything about the details of the inner program structure. In the academic or research areas this kind of programs does not fulfill all needs that are required hence it is common the usage of programming tools oriented to the scientific computing. These tools facilitate the development of solution algorithms for any engineering problem, by taking into account the mathematical formulations which define the solution of the proposed problem. Besides, it is also common that most of these programs are known as script or interpreted languages, such as MATLAB, Python and Perl. They all have the common feature of being high level programming languages that usually make use of available efficient libraries in a straightforward way. MATLAB is considered as a programming language that has become a good option for many researchers in different science and engineering areas because of it can allow the creation, manipulation and operation of sparse or full matrices; it also allows to the user the programming of any mathematical algorithm by means of an ordered sequence of commands (code) written into an ascii file known as script files. These files are portable, i.e. they can be executed in most of software versions in any processor under the operating systems Linux or windows. The main objective of this chapter consists in presenting an efficient alternative of developing a script program in the MATLAB environment; the program can generate characteristic curves power vs. voltage (PV curves) of each node in a power system. The curves are used to analyze and evaluate the stability voltage limits in steady state, and they are calculated by employing an algorithm known as continuous load flows, which are a variation of the Newton-Raphson formulation for load flows but it avoids any possibility of singularity during the solution process under a scenario of continuous load variation. To illustrate the application of this analysis tool, the 14-node IEEE test system is used to