An analytical approach for power system frequency stability evaluation

Recent years have seen high penetration of renewable energies, which have significantly reduced the inertia of bulk power systems. As a result, the frequency behaviour of power systems is becoming more complex. To resolve this technical challenge, there is a particularly strong interest in developing analytical solutions for frequency dynamics studies. This study first describes a second-order frequency dynamics model for power systems with renewable energies. A non-linear perturbation approach is suggested to drive the analytical solution of the model. It is shown that, under many circumstances, frequency dynamics can be effectively approximated using a linear model. Subsequently, the article describes a fourth-order linear frequency dynamics model that takes into account governor-turbines. A polynomial eigenvalue method is proposed to identify the dominant and non-dominant modes of the solution of the four-order model. It is demonstrated that the dominant mode has a decisive impact on frequency behaviour, while the non-dominant modes influence the relative frequency oscillations only. Finally, the study derives the analytical expressions of the standard frequency performance metrics and examines the impact of damping and inertia parameters. The introduced results are verified using two test systems, demonstrating the accuracy and effectiveness of the suggested method.