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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 non-smooth. In this paper we intend to deeper investigate under which conditions the power system loadability boundary will have no visible corner at an intersection of a saddle-node bifurcation part and a switching loadability limit part of the boundary. We propose that such points are called Tangential Intersection Points.