Modern electrical power systems are characterized by a high rate of transient processes, the use of digital monitoring and control systems, and the accumulation of a large amount of technological information. The active integration of renewable energy sources contributes to reducing the inertia of power systems and changing the nature of transient processes. As a result, the effectiveness of emergency control systems decreases. Traditional emergency control systems operate based on the numerical analysis of power system dynamic models. This allows for finding the optimal set of preventive commands (solutions) in the form of disconnections of generating units, consumers, transmission lines, and other primary grid equipment. Thus, the steady-state or transient stability of a power system is provided. After the active integration of renewable sources into power systems, traditional emergency control algorithms became ineffective due to the time delay in finding the optimal set of control actions. Currently, machine learning algorithms are being developed that provide high performance and adaptability. This paper contains a meta-analysis of modern emergency control algorithms for power systems based on machine learning and synchronized phasor measurement data. It describes algorithms for determining disturbances in the power system, selecting control actions to maintain transient and steady-state stability, stability in voltage level, and limiting frequency. This study examines 53 studies piled on the development of a methodology for analyzing the stability of power systems based on ML algorithms. The analysis of the research is carried out in terms of accuracy, computational latency, and data used in training and testing. The most frequently used textual mathematical models of power systems are determined, and the most suitable ML algorithms for use in the operational control circuit of power systems in real time are determined. This paper also provides an analysis of the advantages and disadvantages of existing algorithms, as well as identifies areas for further research.