In the year 2015-2018, there are many sub- and super-synchronous interaction (S$<^>2$SI) events, happened in China. However, traditional transient stability models, electro-magnetic transient (EMT) models and hybrid TS and EMT simulation methods fail to capture the desired wide frequency band interactions between large-scale AC grids and wind farms. To accurately and efficiently capture wide frequency band interactions between AC grids and wind farms, a simulation method which can extend the time-step to 500 $\mu$s and further adopt the multi-rate structure is highly required. For this objective, we propose a multi-rate co-simulation method, in which the target system is partitioned into electro-magnetic transient (EMT) and shifted frequency phasor (SFP) subsystems, represented by our proposed transformation based SFP models and the traditional EMT models, respectively. The simulation efficiency of simulating large-scale AC grids is significantly improved by adopting a much larger time-step. Further, the multi-rate multi-domain transmission-line model (MD-TLM) and the multi-rate frequency dependent MD-TLM are respectively proposed to reflect wide-band interactions between AC grids and wind farms. Eventually, the multi-rate co-simulation is implemented based on the efficient SFP models, network partitioning, and so-called the multi-rate (FD)-MD-TLM. The performance (efficiency and accuracy) of the proposed method has been fully validated on a practical system integrating large AC grids and wind farms.