More than 2,000 properties in the Costessey area were left without electricity tonight.
UK Power Networks says engineers are still working to restore power to 355 of its customers following a problem on its high voltage network.
An underground cable fault at 8.25pm left 2,074 houses in the Dereham Road area without electricity.
The operator said the majority of customers had their electricity supplies restored to normal in stages by 9.20pm.
A spokeswoman said: 'We would like to reassure the remaining customers that we are working as quickly as is safely possible to restore their power.
'We realise how difficult it can be to be without power, particularly during the cold weather, and apologise for any inconvenience.'
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