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EDF is to offer "goodwill payments" to customers left without power during Dartford's blackout.
The energy supplier says it will offer the compensation to "those worst affected" by the power-cut, which left homes and businesses across the town in darkness for almost 72 hours.
Police have launched an investigation into the incident, which they think was started by thieves tampering with cables at Dartford Creek.
An EDF spokesman said: "Whilst this incident was caused by malicious action and was not due to a failure of our network, it is our intention to offer a goodwill payment to those customers who have been worst affected. We are working on the details of this and discussing it with our Regulator."
The spokesman said the company would be writing to customers with details in the next seven days.
Power supplies were eventually restored to Dartford on Thursday, almost three days after the start of the blackout on Monday at 12.45pm. But some have still been suffering short power interruptions while engineers switched customers back from generators to the main network and returned the system to normal operation.