The National Grid has reported 460 homes were without power in south, west and mid Wales early on Monday afternoon.
The largest incident was in Fairwater, Cardiff where 123 properties were without supply.
There were about 100 properties in Barry that were cut off and a further 90 without power in Swansea.
There have also been power cuts in St Clears, Aberdare and Merthyr Tydfil.
In north Wales, SP Energy Networks said a power cut was affecting the Llanaelhaearn area of Gwynedd.
There have also been power cuts in Rhyl, Denbigh, Llanberis and Morfa Nefyn.
The fire services have said several trees had been brought down, with incidents passed on to the councils.
The M48 Severn Bridge was closed and the Cleddau crossing is closed for high-sided vehicles.