A simple method, based on Machine Learning Radial Basis Functions, RBF, is developed for estimating voltage stability margins in power systems. A reduced set of magnitude and angles of bus voltage phasors is used as input. Observability optimization technique for locating Phasor Measurement Units, PMUs, is applied. A RBF is designed and used for fast calculation of voltage stability margins for online applications with PMUs. The method allows estimating active local and global power margins in normal operation and under contingencies. Optimized placement of PMUs leads to a minimum number of these devices to estimate the margins, but is shown that it is not a matter of PMUs quantity but of PMUs location for decreasing training time or having success in estimation convergence. Compared with previous work, the most significant enhancement is that our RBF learns from PMU data. To test the proposed method, validations in the IEEE 14-bus system and in a real electrical network are done.