Analysis of Electromechanical Swings of a Turbogenerator Based on a Fractional-Order Circuit Model

This paper addresses the issue of rotor swings in a high-power synchronous generator during stable operation with a stiff power grid. The analysis of electromechanical swings was conducted using a circuit model incorporating fractional-order derivatives. Assuming that variations in the load angle under small disturbances from a stable equilibrium are minor, a linearized differential equation describing the electrodynamic state of the synchronous machine was derived. Based on this linearized equation of motion and the identified parameters of the equivalent circuit, calculations were performed for a 200 MW turbogenerator. The results indicate that the electromechanical swings are characterized by a constant pulsation and a low damping factor. Calculations were also carried out using a lumped-parameter equivalent circuit model. Based on the obtained results, it can be stated that the fractional-order model provides a more accurate fit of the frequency characteristics compared with the classical model with the same number of rotor equivalent circuits. The relative approximation errors for the fractional-order model are, for the d-axis (one rotor equivalent circuit), relative magnitude error δm = 1.53% and relative phase error δφ = 6.32%, and for the q-axis (two rotor equivalent circuits), δm = 3.2% and δφ = 8.3%. To achieve comparable approximation accuracy for the classical model, the rotor electrical circuit must be replaced with two equivalent circuits in the d-axis and four equivalent circuits in the q-axis, yielding relative errors of δm = 2.85% and δφ = 6.51% for the d-axis, and δm = 1.86% and δφ = 5.49% for the q-axis.