Small-Signal Impedance Modeling of Synchronous Generators Based on a Sixth-Order Electromechanical Coupling Model

Under the high penetration of renewable energy in modern power systems, wide-band impedance modeling of synchronous generators plays a critical role in grid stability analysis. Traditional third- and fourth-order models, which neglect flux dynamics and electromechanical coupling effects, struggle to accurately characterize impedance characteristics across wide frequency ranges. This paper proposes a sixth-order electromechanical coupling impedance model based on small-signal analysis. The model establishes a differential-algebraic framework incorporating stator flux dynamics, three rotor damping windings, and excitation/governor control systems. By designing a cross-coupling compensation matrix in the dq-axis rotating coordinate system, it achieves full-frequency-band (0.1-1000 Hz) impedance characterization. A frequency-sweep test platform was implemented in MATLAB/Simulink. Theoretical calculations and simulations within the $1-10000 \mathrm{~Hz}$ range demonstrate that the sixth-order model significantly improves high-frequency accuracy ($\gt10 \mathrm{~Hz}$) compared to traditional third-order models. Furthermore, matrix transformation techniques simplify high-dimensional computations, avoiding numerical complexity. The proposed model provides a precise frequency-domain tool for suppressing wide-band oscillations and evaluating stability in renewable-energy-integrated power grids.