On synchronization of third-order power systems governed by second-order networked Kuramoto oscillators incorporating first-order magnitude dynamics

This study explores the sufficient conditions for achieving synchronization in the third-order one-axis generator models in modern power systems, characterized by the second-order networked Kuramoto oscillators integrating the first-order amplitude dynamics. First, we provide detailed descriptions of dynamic models for this particular class of third-order power systems, which are governed by second-order networked Kuramoto oscillators incorporating first-order voltage magnitude dynamics. Then, we show that if the phase difference of oscillators is less than pi/2 and the initial amplitudes are positive, then the amplitudes are bounded and possess a positive lower bound. Furthermore, under specific conditions on the coupling strength, inertia, and oscillator parameters, we prove that the third-order model exhibits a frequency synchronization and the derivatives of amplitudes converge to zero. Numerical simulations are performed to support our main results.