To address the issue of frequency stability in microgrids with limited communication resources and bandwidth, this paper proposed an event-triggered control method based on a cloud-edge collaborative architecture. Firstly, to address the limited communication resources, event-triggered detector is set up at the edge to upload state variables and update control instructions only when the frequency deviation exceeds a pre-set threshold. Secondly, a fractional-order PI–PD controller is designed at the cloud control center, which achieves higher control degrees of freedom and stronger robustness than traditional integer-order PID control schemes. Additionally, to obtain better control parameters, an optimized design method based on an improved Big Bang-Big Crunch method (BB-BC3) is proposed for the fractional-order PI–PD controller. At last, a simulation example is given to prove the validity of the proposed method. Simulation results show that compared to the integer-order PI–PD controller, the fractional-order PI–PD controller based on the BB-BC3 algorithm proposed in this paper reduces the peak value of the response curve by 5%, and shortens the setting time by 0.14 s.