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This paper addresses the computation of the margin to the maximum loading limit. In the maximum loading point, the minimum singular value of the load flow Jacobian matrix becomes zero. A new generalized singular value analysis is proposed to compute this critical singular value far away of the singular point. In addition, a second order approximation of the load flow equations is formulated and used to determine the margin to the loading limit in physical terms of MW and MVAr. The proposed algorithm is computationally efficient. It is formulated so that it could consider different models for the power system components. It takes into account operating and equipment limits, such as the reactive power generator limits. The algorithm is tested in two systems: a 6-machines test system, which is a CIGRE benchmark for voltage instability studies; and the IEEE-118 buses system.