Whether it's by buying and using a trillion tokens strategically or by inserting synchronized malicious jobs it should be possible to find some resonant frequencies in the line frequency control system. By loading and unloading multi-megawatts of draw you could get the local supply throttling up and down enough desynchronize from the larger grid. If you could get real time measurements of the line frequency you could use that to tune your malicious load and do the whole 'pushing a kid at the peak of their swing' thing.
To mitigate you would have to put dummy loads or some kind of minute-scale power storage onsite or nearby to compute loads.