LQR Design Using LMIs and the Robust D-Stability Criterion for Low-Frequency Oscillation Damping in Power Systems

This article proposes the application of a linear quadratic regulator (LQR) optimized by linear matrix inequalities using the robust $\mathfrak{D}$-stability concept to ensure the stability of the single machine infinite bus system, which includes a generator and a load connected to an infinite bus. The power system is modeled using the current sensitivity model, which represents the nodal balance of currents at each bus of the power system. The objective is to damp the poles of interest existing in the power system with control techniques based on state feedback through the automatic voltage regulator of the synchronous generator. The obtained results allow to infer that the technique based on the robust $\mathfrak{D}$-stability concept is slightly more efficient than the LQR alone, what accredits it as a powerful tool for improving the small-signal stability of electric power systems.