The distribution network operator said the goodwill payment will mean that households will receive an additional amount depending on how long they were without power.
It said seven days without power will mean that customers will receive an additional £154 on top of their £770 statutory payment.
Last week, Ofgem stated it had agreed with companies to compensate and give more money to customers most impacted by the Storm Arwen.
SSEN Managing Director Chris Burchell said: “This 20% enhancement will be paid automatically and combined with lifting the payment cap, for those last to be reconnected, will result in an additional payment of £560.”
Jim Savege, Chief Executive of Aberdeenshire Council, commented: “What our communities have been through in the past week or more has been unprecedented. It is a testament to the power and resilience of the communities that they have supported each other throughout this and my huge thanks to everyone who stepped up.”