ESB Networks is working to restore power to hundreds of homes in the Twin Towns.
A series of faults in Stranorlar and Ballybofey has led to more than 600 homes losing their electricity supply.
ESB staff say they hope to re-connect all the homes by teatime.
Around 20 homes are also without power in Fanad Head, with a further two dozen customers outside Donegal Town.
There are 10,000 faults nationwide following thunder and lightning storms earlier today.
More cuts are expected tomorrow with two storms set to hit Ireland, with Donegal taking the brunt of high winds.