Calculating optimal system parameters to maximize the distance to saddle-node bifurcations

Abstract
This paper presents a new methodology to calculate parameters of a nonlinear system, so that its distance to a saddle-node bifurcation is maximized with respect to the particular parameters that drive the system to bifurcation. The technique is thoroughly justified, specifying the conditions when it can be applied and the numeric mechanisms to obtain the desired solutions. A comparison is also carried out between the proposed method and a known methodology to determine closest saddle-node bifurcations in a particular power system model, showing that the new technique is a generalization of the previous method. Finally, applications to power systems are discussed, particularly regarding the design of some FACTS devices, and a simple generator-line-load example is studied to illustrate the use of the proposed technique to determine the optimal shunt and/or series compensation to maximize distances to voltage collapse. The effect of the optimal compensation on the stability of the sample system is also analyzed.