Robust Control via LMIs Applied to Small-Signal Stability in Power Systems

This article proposes the application of a linear quadratic regulator feedback controller designed via linear matrix inequalities using the $\mathfrak{D}$-stability concept to add damping to low-frequency electromechanical oscillations and ensure the stability of the single machine infinite bus electric power system, which was modeled using the current sensitivity model considering polytopic uncertainties. The objective is to insert a stabilizing signal into the system through the automatic voltage regulator of the synchronous generator. In the simulations, parametric variations in the system load are considered, as well as exogenous disturbances in the form of an increase in the mechanical input power on the generator’s shaft. In addition, the performance of the proposed controller is compared with optimal control approaches already known in the literature. Therefore, according to the obtained results, it is possible to verify that the proposed control approach is efficient for stabilizing the system since it has better performance indices than the optimal control approach, as well as the response in the frequency domain shows that the proposed controller is robust, thus accrediting the control strategy as a powerful tool in the study of small-signal stability in electrical power systems.