The second power cut in two days left more than 3,000 properties in Pontefract without power this morning (Wednesday).
A Northern Powergrid spokeswoman said 3,000 customers in the town had no power earlier because of a fault on the network.
She added: “We apologise for the inconvenience to our customers and we are working hard to get supplies fully restored as soon as we can.
“We are also working to find the exact cause of the fault and repair it.”
Nine properties are still without power.