On the Validity of Local Approximations of the Power System Loadability Surface

Power system voltage security assessment is generally applied by considering the power system loadability surface. For a large power system, the loadability surface is a complicated hyper-surface in parameter space, and local approximations are a necessity for any analysis. Unfortunately, inequality constraints due to for example generator overexitation limiters and higher codimension bifurcations makes the loadability surface nonsmooth. This makes the use of local approximations limited and calls for a method for estimating the distance to a nonsmooth part of the surface. This paper suggests a method for calculating the distance from a point on the loadability surface to the closest point of nonsmoothness of the loadability surface. Although the method has its main application in estimating the validity of local approximations of the loadability surface, it can also be used, combined with other methods, when computing the distance from an operating point to the loadability surface.