Crews have restored power to more than 12,000 customers overnight and were dispatched to the affected areas at first light to restore power to the rest of those affected.
They are asking people who come across fallen trees, wires or damaged electricity network, to never touch or approach them as they may be live and extremely dangerous.
They said people should report any damage to electricity infrastructure by calling 1850 372 999.
A clean-up operation is underway in parts of the west and northwest of the country in the aftermath of Storm Lorenzo.
ESB said while they have restored power to 12,000 homes, farms and businesses, they are still working to restore power to 3,600 customers.
A yellow wind warning for Dublin, Kildare, Laois, Longford, Wicklow, Offaly, Westmeath, Galway, Mayo, Roscommon and Clare has come to an end.