School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, China

Impedance analysis method is widely used for stability research of interconnected systems with power electronic converters due to its simplicity and effectiveness. However, when using traditional methods for the frequency-domain impedance modelling, nonlinear transformations (Park transform and its inverse transform) are required for the coordinate system transformation, which can lead to convolutional operations and corresponding frequency shifts of different periodic components, and the process is relatively cumbersome. This paper proposes an equivalent impedance modeling method of direct-drive permanent magnet synchronous generator (D-PMSG) based on time-domain differential operators of complex vectors to solve the above problems. This method directly linearizes small signals within the neighborhood of the stable operation trajectory of the time-domain periodic system, and the exponential rotation factor is used to flexibly reflect the time-varying characteristics of the system after disturbance. By combining time-domain differential operators to effectively characterize the dynamic characteristics of the control links in interconnected systems, the repeated transformation of the coordinate system during frequency-domain impedance modeling is avoided, and the complexity of analytical modeling is greatly reduced. In addition, the proposed method can more clearly explain the physical meaning of the frequency coupling phenomenon generated by the grid-connected inverter of the D-PMSG when the interconnected system is disturbed. At the same time, it can explain the impact of the initial phase of the fundamental voltage on the phase frequency characteristics of the coupling component. Finally, the effectiveness of the proposed algorithm is verified through simulation.