The Met Office issued a two-day weather warning for Tuesday and Wednesday in which it said possible outages could hit Leeds, Sheffield, Hull and other areas of Yorkshire.
Currently, there are two power cuts in Hull, affecting more than 100 homes in total, and two in York, affecting 40 more homes.
There are 50 homes in Harrogate, along the LS22 border, without power while another outage has hit LS25.
Further cuts have been reported in Halifax, Selby, Doncaster, Rotherham and Barnsley.
Northern Powergrid says its teams are 'working hard to restore power as quickly as possible' to those affected and lists that the cables which serve power have been affected.
The forecast for Leeds lists heavy rain for the rest of Tuesday, with more wet weather on the way.
The full forecast:
Cloudy tonight with outbreaks of rain continuing. Strong winds across Humber easing through the evening, with light winds for many parts overnight. Near gales developing along exposed windward coasts and hills towards the end of the night. Minimum temperature 12 °C.
Cloudy and windy at first with patchy rain during the morning. Becoming drier and brighter by the afternoon with sunny spells, lighter winds and a scattering of showers. Maximum temperature 18 °C.
How to stay safe in a storm
Before the storm
Secure loose objects such as ladders, garden furniture or anything else that could be blown into windows and other glazing and break them
Close and securely fasten doors and windows, particularly those on the windward side of the house, and especially large doors such as those on garages
Park vehicles in a garage, if available; otherwise keep them clear of buildings, trees, walls and fences
Close and secure loft trapdoors with bolts, particularly if roof pitch is less than 30°
If the house is fitted with storm shutters over the windows then ensure that these are closed and fastened
If chimney stacks are tall and in poor condition, move beds away from areas directly below them
During the storm
Stay indoors as much as possible
If you do go out, try not to walk or shelter close to buildings and trees
Keep away from the sheltered side of boundary walls and fences - if these structures fail, they will collapse on this side
Do not go outside to repair damage while the storm is in progress
If possible, enter and leave your house through doors in the sheltered side, closing them behind you
Open internal doors only as needed, and close them behind you
Take care when driving on exposed routes such as bridges, or high open roads, delay your journey or find alternative routes if possible
Slow down and be aware of side winds, particular care should be taken if you are towing or are a high sided vehicle
Do not drive unless your journey is really necessary
After the storm
Be careful not to touch any electrical/telephone cables that have been blown down or are still hanging
Do not walk too close to walls, buildings and trees as they could have been weakened
Make sure that any vulnerable neighbours or relatives are safe and help them make arrangements for any repairs