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• The nonlinear spatio-temporal correlations of the collected measurements from the distribution systems are utilized to develop an unsupervised deep LSTM-AE network to learn the normal dynamics of the distribution systems. • A false data injection attack detection method is developed and implemented by utilizing the developed LSTM-AE neural network model. • Wide-ranging comprehensive experiments on different systems are developed to evaluate the proposed approach performance with quantitative and comparative analysis. • The utilization of LSTM-AE provides two main advantages over other detection techniques: (i) better detection statistics for larger distribution systems, (ii) the unnecessity of labeled attack samples. The utilization of distributed generation units (DG) in power distribution systems has increased the complexity of system monitoring and operation. Numerous information and communication technologies have been adopted recently to overcome the challenges and complexities associated with the integration of DG units in distribution systems. However, these technologies have created wide opportunities for energy theft and other types of cyber-physical threats. False data injection attacks (FDIA) illustrate a challenging threat for distribution systems for these are very tough to detect in reality. In this manuscript, we propose a spatio-temporal learning algorithm that is able to acquire the normal dynamics of distribution systems to overcome possible FDIA. First, we use a long short-term memory autoencoder (LSTM-AE) in acquiring the usual dynamics. After that, we employ the unsupervised trained model in detecting the numerous potentials of FDIAs in distribution systems by assessing the residual error of every measurement sample. This developed method is purely data-driven. This enables it to be robust to the distribution systems' nonlinearities and uncertainties which overcomes the weaknesses of the proposed detection algorithms in the literature. The efficacy of the developed detection method is assessed via different test case scenarios with numerous basic and stealth FDIAs. [ABSTRACT FROM AUTHOR]