**Abstract**

Synchronous generators produce almost 95% of the world's electricity. Even a small improvement in their efficiency represents huge savings. Electromechanical oscillations of synchronous generators are harmful—they cause losses and can even lead to instability. An additional control system, called a power system stabilizer (PSS), is used to damp the oscillations of synchronous generators. The commercial realizations of the power system stabilizers are based on the use of the linear control theory. The effectiveness of these power system stabilizers is small, because of the nonlinear and time-varying characteristics of the synchronous generators. The application of robust and adaptive control represents an adequate theoretical basis for ensuring optimal damping of the electromechanical oscillations in a wide operating range. This work reviews the applicability of the advanced control theories to develop power system stabilizers. The work is focused on selecting the appropriate robust and adaptive control theories for the power system stabilizer implementation. The applicability and advantages are presented of the sliding mode control and the direct adaptive control, along with an evaluation of their impact on the operation improvement.

**Keywords:** sliding mode control, direct adaptive control, synchronous generator, power system stabilizer, operation of synchronous generator
