The second chapter presents WAM (Wide area monitoring) systems and their mode of operation. The role of the WAM system is monitoring based on synchronized phasor measurements in the transmission network. The PMU (Phasor measurement unit) unit is one of the most important elements of a WAM system. It is a device for synchronized measured phasors. The devices are installed in several places in the system, where they measure voltage, current and frequency change phasors. The advantage of these systems over SCADA (Supervisory control and data acquisition) systems is the higher data sampling rate. Higher speeds help monitor the system during faster disturbances. WAM systems have made great strides, however applications that exploit the measured data are still in the phase of intensive research. The basics of stability in the power system are presented in the third chapter. The stability of the rotor angle, voltage stability, frequency stability and the influence of renewable sources on the system are described. The paper pays special attention to the problem of endangering the stability of the rotor angle of the power system due to the increased integration of renewable energy sources that do not use synchronous generators. Problems arise due to the uncertainty of the production and use of asynchronous generators and converters. The application of the WAM system in the detection of rotor angle oscillations, and then protection against loss of synchronism, is the topic of the fourth chapter. The traditional protection against synchronism loss is presented first, followed by possible improvements based on synchronized measurements. Modern protection is adaptable, ie it changes its parameters according to the current conditions in the network. There are a number of applications that try to use PMU measurements to estimate angle stability. Several algorithms are presented that have the task of predicting future events based on past events. Each presented method has certain advantages and disadvantages when implemented in the system. The most complex method of prediction is the use of a neural network. The neural network is capable of learning and changing its actions based on input and output parameters.