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One of the most important features of a reliable power system is its capability to supply the demand continuously. This continuous supply has been maintained by the transient stability of the system against large disturbances. The study of this type of stability is examined through different indicators. One of the common indicators to evaluate the transient stability of the power system is the well-known Critical Clearing Time (CCT) index. Conventional methods for calculating CCT have presented good accuracy, however, their computational cost is very high which makes them not suitable for real-time applications and real large-scale networks. Considering their ability to feature extraction of big data, deep neural networks can be utilized as reliable tools to cover these deficiencies. In this regard, to cover the shortcomings of the conventional methods, this paper proposes a method based on deep Convolutional Neural Networks (CNN) to estimate the CCT index in real-time power system applications. Moreover, to analyze a realistic case, nonlinear limiters of the excitation systems which have a considerable effect on transient stability index are considered in this study. Thanks to the using of several deep layers and the comprehensive established database, the accuracy of proposed method is appropriately high. Numerical studies on IEEE standard networks as well as a real case in Iran Power Grid (IPG) represents the advantages of the proposed method. • A deep-learning-based convolutional neural network is designed to estimate CCT index of power system. • Nonlinear limiters of the excitation system are taken into account. • A real case study in Iran grid is considered for simulation. • As a result, the transient stability of system is accurately determined in on-line manner. [ABSTRACT FROM AUTHOR]