Structural models of system stabilizers of power grids that are used to improve damping of power system oscillations by controlling the excitation of synchronous power plants turbogenerators are considered in the article. Mathematical and structural models of such a system stabilizer for various orders of its transfer function according to the IEEE recommendations are proposed for implementation in computer design systems, in particular, for the computer analysis system of the DAKAR power grids.

An analysis of the existing system stabilizers that recommended by the IEEE Association for Power Systems was perform. Each of which has an application that is appropriate to the existing excitation system of the turbine generator. The structures of the existing system stabilizers are reviewed. To build their model on the basis of IEEE recommendations, it is suggested to use a canonical form of observation for the transformation of the system stabilizer structural scheme. This transformation provides the possibility to create mathematical models of such systems for the excitation circuit of a synchronous generator, both in the form of a structural model and in the form of a system of differential equations corresponding to such a structure. MATLAB with Control System Toolbox library was used to analyze the frequency and step response characteristics of the system stabilizer models, which made it possible to analyze the frequency and time characteristics of the recommended IEEE system stabilizers and their models derived from the canonical observation form.

According to the recommendations of the IEEE, the denominator of the system stabilizer transfer function is from the first to the fifth order, which, accordingly, expands the range of used mathematical models. For their analysis, generalized mathematical and structural models were created on the basis of the developed transfer function of the system stabilizer, which became the basis for the development of the corresponding first- to fifth-order models. For each such model, the corresponding model order in the article shows both a structural diagram and a mathematical model in the form of a Cauchy differential system. The results of computer simulation confirmed the adequacy of the developed models and their easy using.

*IEEE**Recommended**Practice**for Excitation System Models for Power System Stability Studies. IEEE Power Engineering Society, IEEE Std 421.5™ 2005 (Revision of IEEE Std 421.5-1992). Approved 25 October 2005 IEEE-SA Standards Board.**Prabha**Kundur.**Power**System**Stability and Control. Power System Engineering Series. – McGraw-Hill, Inc. 1994. 1176 pp. ISBN 0-07-035958-X.**G.**Rogers.**Power**System**Oscillations.**Springer**Science**& Business Media, 2012.**Eslami**M.,**Shareef**H., Mohamed A.. Application of artificial intelligent techniques in PSS design: a survey of the state-of-the-art methods, Przeglad Elektrotechniczny (Electr. Rev.) 87 (4) (2011).**Stativa**A.,**Gavrilas**M.,**Stahie V. Optimal tuning and placement of power system stabilizer using particle swarm optimization algorithm, in: International Conference and Exposition on Electrical and Power Engineering (EPE) 2012, IEEE, 2012, pp. 242–247.**Safari**A.**A PSO procedure for a coordinated tuning of power system stabilizers for multiple operating conditions, J. Appl. Res. Technol. 11 (5) (2013) 665–673.**Padiyar**K. R. Power System Dynamics, BS Publications, 2008.**State**Space**Models**(by**Professor**Zoran Gajic, Rutgers University Electrical and Computer Engineering Department) – https://www.ece.rutgers.edu/~gajic/psfiles/canonicalforms.pdf – 2018.**Zhang F. (2011) Matrix Polynomials and Canonical Forms. In: Matrix Theory. Universitext. Springer, New York, NY. [Print ISBN 978-1-4614-1098-0]**Gajic**Z.**Solutions**Manual**for**Linear**Dynamic**Systems**and Signals. – 311 pages, Prentice Hall, Upper Saddle River, May 2003, [ISBN 0130191205].**MATLAB.**– © 1994-2020 The MathWorks, Inc. – https://www.mathworks.com/**Ode113**: Solve nonstiff differential equations – variable order method. – https://www.math- works.com/help/matlab/ref/ode113.html?s_tid=srchtitle**Control**System Toolbox: Design and analyze control systems. – https://www.math- works.com/help/control/index.html*