The tendencies and perspective directions of development of modern digital devices of relay protection and automation (RPA) are considered. One of the promising ways to develop protection and control systems is the development of fundamentally new algorithms for recognizing emergency modes. They work in accordance with the triggering rule, which is formed after processing the results of model experiments. These algorithms are able to simultaneously control a large number of features or mode parameters (current, voltage, resistance, phase, etc.). Thus, the algorithms are multidimensional. This approach in RPA becomes available since the computing power of modern processors is quite enough to process the required amount of statistical data on the parameters of possible normal and emergency operation modes of electrical network sections. The application of classical machine learning algorithms in RPA tasks is analyzed, in particular, methods of k-nearest neighbors, logistic regression, and support vectors. The use of specialized trainable triggering elements is studied both for building new protections and for improving the sophistication of traditional types of relay protection devices. The developed triggering elements of the multi-parameter RPA contribute to an increase in the sensitivity and recognition of accidents. The proposed methods for recognizing emergency modes are appropriate for implementation in intelligent electronic devices (IEDs) of digital substations.