The stability problem of weak grid connected converter interfaced generation (CIG) cannot be ignored. For multiple weak grid connected CIGs with different parameters, the system oscillation characteristics and equivalence methods still need to be further studied. This paper first discusses the oscillation characteristics when CIGs are perfectly coupled, perfectly decoupled and their general conditions respectively. Based on the Monte Caro simulation, the number of critical eigenvalues, the participation of each CIG to critical eigenvalues and the correlative parameters to participation are analyzed. Then the single-CIG and multi-CIG equivalence methods are proposed for stations containing nonidentical CIGs. The CIG parameters of a single-CIG equivalent model are identified based on the consistency of the output admittance characteristics. According to the different participations of CIGs with critical eigenvalues, the station is equivalent to a multi-CIG model. Results of large simulation samples show that the two equivalent models can both preserve the critical eigenvalues very well, and can be used for stability analysis. Furthermore, the multi-CIG equivalent model can also very well reflect the participation of CIGs in detailed models, and can be used for damping control study.

In practical operations, low-frequency oscillation (LFO) occurs and leads to converter blocking when multiple electrical rail vehicles at the platform are powered by the traction network. This paper proposes a small-signal model in state-space form for multiple vehicle-grid systems based on a dynamic phasor. This model uses the phasor amplitude and phase as variables to accurately describe the dynamics of the converter phase-domain control. An eigenvalue based-method is introduced to investigate the LFO with advantages of acquiring all oscillatory modes and analyzing participation factors. Two low-frequency dominant modes are identified by eigenvalues. Mode shape reveals that one of the modes involves the oscillations between the grid-connected converters and the traction network, and the other one involves the oscillations among these converters. Then the sensitivities of these two low-frequency modes to different system parameters are analyzed. Participation factors of system state variables, when the number of connected vehicle increases, are compared. Finally, the theoretical analysis is verified by nonlinear time-domain simulations and the modal analysis based on the estimation of signal parameters via the rotational invariance techniques (ESPRIT) method.