ESB Networks said that crews were working to restore power to 4,500 customers, mainly in the Dublin area.
A spokesman said that 2,200 households and businesses were without power in Julianstown near Drogheda in Co Louth.
A further 1,100 customers are affected in Pelletstown in north Dublin.
The spokesman said each fault was being risk assessed.
He said some of the faults involve underground cables.