Over the past decades, electric power systems (EPSs) have undergone an evolution from an ordinary bulk structure to intelligent flexible systems by way of advanced electronics and control technologies. Moreover, EPS has become a more complex, unstable and nonlinear structure with the integration of distributed energy resources in comparison with traditional power grids. Unlike classical approaches, physical methods, statistical approaches and computer calculation techniques are commonly used to solve EPS problems. Artificial intelligent (AI) techniques have especially been used recently in many fields. Deep neural networks have become increasingly attractive as an AI approach due to their robustness and flexibility in handling nonlinear complex relationships on large scale data sets. Major deep learning concepts addressing some problems in EPS have been reviewed in the present study by a comprehensive literature survey. The practices of deep learning and its combinations are well organized with up-to-date references in various fields such as load forecasting, wind and solar power forecasting, power quality disturbances detection and classifications, fault detection power system equipment, energy security, energy management and energy optimization. Furthermore, the difficulties encountered in implementation and the future trends of this method in EPS are discussed subject to the findings of current studies. It concludes that deep learning has a huge application potential on EPS, due to smart technologies integration that will increase considerably in the future.