Impact of the exciter voltage limit to small signal stability region of a three-bus power system

We investigate the influence of non-differential components to the power system small signal stability region in this paper. A method named unified expression function (UEF) is introduced to describe the piecewise, continuous and non-differential function in the small signal stability study. It converts non-differential points of the original function to poles of the UEF’s derivative function. Then the derivative at those poles can be approximated by UEF’s left-hand or right-hand derivative limits according to the requirement. Based on this method, impact of the exciter voltage limit to power system small signal stability region is then deeply discussed using a simple three-bus power system. We find that the exciter voltage limit can change elements of the system Jacobian matrix so as to cause jump of the system critical eigenvalue. As a result, two new Hopf bifurcation boundaries and a new instability hole emerge in the small signal stability region. When the exciter voltage limit varies, the new instability hole and the new Hopf bifurcation boundaries will change significantly. It makes the topological characteristics of the small signal stability region much more complicated. Since there are many non-differential components in power systems, they should be correctly considered in power system stability studies.