Admittance stability model and equivalent circuit analysis of three-phase AC systems in different coordinate systems

In recent years, with a large number of distributed energy sources connected to the grid, the distribution network has shown a clear trend towards the use of power electronics. As a power conversion interface, the stability of the converter's interaction with the grid has received considerable attention. Adequate admittance (impedance) modeling of the three-phase grid-connected converter is a prerequisite for analyzing the stability and resonance characteristics of the grid-connected system. Understanding the internal mechanisms and proposing effective solutions are crucial to enable power systems to effectively cope with the impact of power electronics. Therefore, by studying the admittance equivalence relationship and equivalent circuit of three-phase AC systems in various coordinate systems, this paper focuses on solving the non-uniqueness problem of impedance admittance modeling of three-phase converter system. It is proposed that the input admittance of the three-phase asymmetrical system in the dq and fb rotating coordinate systems is a 2-order matrix and equivalent. The input admittance of the three-phase unbalanced system in the alpha beta and "12" static coordinate systems is a 4-order matrix and equivalent. From both theoretical analysis and simulation verification, it is shown that the number of eigenvalues of the three-phase asymmetrical system in the stationary coordinate system is twice that in the rotating coordinate system, and the overall damping of the system is improved. The control strategy based on the stationary coordinate system will make the system more stable. The second contribution of this paper is to establish the equivalent circuit of the three-phase symmetric converter system by the node admittance matrix and extend it to the multi-machine system to explain the system instability mechanism by the circuit resonance mechanism. Finally, the frequency coupling phenomenon is studied for the three-phase asymmetrical converter system, and it is explained that it cannot establish an equivalent circuit similar to the three-phase symmetrical converter system. The equivalent circuit model of the three-phase symmetrical converter system is proposed. The admittance model equivalence in the synchronous rotating coordinate system is explained by admittance eigenvalue, and stability margin of asymmetric system in rotating coordinate system is lower than that in stationary coordinate system by total damping of system. image