Non-linear mathematical programming applied to electric power systems stability

Non-linear optimization has been increasing its application in the fields of power system planning and operation in the last decades. The availability of non-linear optimization solvers allows formulating the optimization problem as a standard problem, reducing the effort of power system engineers and increasing the confidence in the results. One of the topics of recent development is the non-linear optimization applied to power system stability. The objective of this chapter is to review applications of non-linear optimization in power system stability, considering different categories of stability. In the text, the simplifications assumed in order to obtain a formulation that retains the main characteristics of each power system stability problem are explicitly included. Two topics are mainly considered: the well developed problem of long term voltage stability and the recent advances in transient stability.