Small-signal impedance modelling of synchronous generators with excitation control in hybrid power systems

The increasing share of inverter-based renewable generation has fundamentally altered the dynamic behaviour of electric power systems, while conventional synchronous generators continue to play a critical role in ensuring reliable operation. This paper develops an impedance-based small-signal model of a representative transmission network, focusing on synchronous machines and inverter-based resources in the positive-sequence domain. Analytical impedance expressions are derived for each component and validated through MATLAB/Simulink frequency scans. Using these models, stability is assessed via the Bode criterion to evaluate interactions among synchronous machines, converter-based generation, and the grid. The results reveal that undamped low-frequency resonances can arise, if the synchronous generators are tied to a meshed grid, where there is little to no load. However, once enough damping is acquired through enabling load in the system, stability is preserved even in changing PV operating conditions or if the excitation controllers are detuned.