A mathematical model, algorithm and program have been developed to study any types of complex asymmetric steady-state modes and transient processes of a multi-machine power system with a renewable energy source in phase coordinates, the results of which can be used in the operational control of power system operating modes with any type of emergency automation. The developed methodology and software package can also be used in industry to check the possibility of long-term operation in the considered asymmetrical mode from the point of view of the operating conditions of the system generators and electrical receivers, to determine the need to use baluns, to select their parameters and installation locations, to ensure the efficiency of asymmetrical modes , as well as for conducting various tests and analyzing accidents that have occurred.