Compensation was owed to customers who were left without power when severe "once in a generation" winds swept across the UK in November last year.
However, the customers received far more than was intended due to an error in the cheque.
One Twitter user shared a photo of the eye-watering number he received in the post.
He wrote: "Thank you for our compensation payment, Northern Powergrid, for the several days we were without power following Storm Arwen."
"Before I bank the cheque, however, are you 100 per cent certain you can afford this? £trillionpounds".
The picture shows the customer had received a cheque for 2,324,252,080,110 British pounds ($A4.4 trillion).
The tweet has accrued over 24,000 likes in just three hours, as others joined in to poke fun at the error.
"Bank it! Then share it equally between us all," one Twitter user wrote.
"I think you own Northern Powergrid now," another joked.
The supplier confirmed 74 of their customers had been given compensation cheques with an incorrect payment amount and thanked those who were "honest" about the error.
They added the 74 customers were located within the Halifax and Newcastle postcodes of the UK, reassuring them that a correct payment will be on its way soon.
A spokeswoman for Northern Powergrid said: "As soon as we identified the clerical error, which was caused by the electricity meter reference number being incorrectly quoted as the payment sum, we ensured all 74 customers' cheques were stopped so they could not be cashed.''
"We have been investigating how this error happened and carrying out checks of previous payments."
"We thank those customers who were honest and contacted us and we have been making contact directly over the weekend with all 74 customers affected to make them aware, apologise for the error and reassure them that a correct payment will be issued to them on Monday."