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In recent years, important efforts to improve monitoring, protection and control of power systems have been explored. In this connection, several novel approaches for assessing vulnerability in real time have been developed. However, most of the work is commonly focused on tackling stability phenomena, while the possible overloads are often treated as negligible in real-time power system security. But sometimes, high electric post-contingency currents might provoke overloads which could increase the system vulnerability problem. This paper presents a novel method for assessing the possibility of fast post-contingency overloads using Statistical Distribution Factors (SDFs) that allow computing an Overload Index (OVI) in real time. First, Monte Carlo-based contingency analysis is performed to iteratively calculate ac Distribution Factors (ac-DFs). After, SDFs are defined by the mean and standard deviation of ac-DFs. These SDFs are then used together with principal component analysis (PCA) and support vector machine classifier (SVM-C) in order to structure a table-based real-time post-contingency overload estimation algorithm, which allow computing OVIs depending on the actual operating state and the type of contingency. The proposal is tested on the IEEE New England 39-bus test system. Results show the feasibility of the methodology in alerting about fast possible overloads.