In this paper, a comprehensive scheme is proposed for online monitoring of voltage stability using the Weighted Least Square Support Vector Machine (WLS-SVM) that the effect of overcurrent protection for transmission lines is factored in. The operation of protection systems, due to their nonlinear effect on the system graph, changes the linear and nonlinear equations of the system which cannot be solved by conventional methods. To prevent the maloperation of the overcurrent protection system, coordination between Directional Overcurrent Relays (DOCRs) has been done by linear programming to reach the globally optimum values for DOCR settings. As a result, WLS-SVM is used by implementing collected data from Phasor Measurement Units (PMUs). In addition to solving linear equations instead of quadratic equations, WLS-SVM solves the problems of noise sensitivity and lack of sparseness of the solutions. Also, Principal Component Analysis (PCA) has been used for the dimensionality reduction of the input vector applied to WLS-SVM in this work to make it suitable for real-time applications. Moreover, the measurement errors between measurements obtained from PMUs and the reference values have been taken into account. Then, real-time power system stability monitoring is performed by predicting a voltage stability assessment index using WLS-SVM to evaluate the voltage stability status in a real-time manner. Results of the proposed method regarding efficiency demonstrate high accuracy and better performance in comparison with other approaches. The simulation of the presented approach is carried out on the IEEE 39-bus and IEEE 118-bus systems.