Shell Energy Retail has been forced to pay £390,000 after overcharging around 12,000 accounts on its default tariffs.
Industry regulator Ofgem called on the company, which rebranded from First Utility in March 2019, to refund and compensate the customers affected, and pay an additional £200,000 to the watchdog's consumer redress fund.
Ofgem found that the utilities firm overcharged on its default tariffs after the price cap was introduced in January 2019, in order to help the UK's 11 million customers on poor-value default tariffs.
The regulator's price cap monitoring found that, between January and March 2019, Shell Energy Retail overcharged around 12,000 electricity and gas customer accounts by £100,736 collectively.
To rectify its failings, Shell Energy Retail has agreed to refund customers by re-crediting their accounts, and pay additional compensation.
Around 6,200 Shell Energy Retail customer accounts were on tariffs that were not compliant with the price cap, meaning they were paying above the regulated level for their gas or electricity.
Shell has said it will refund these customers, as well as paying them an additional £10 each.
The remaining 5,600 customer accounts experienced a delay in their energy price being reduced under the price cap after requesting to change to a cheaper way of paying for energy, which meant they were paying above the cap level for longer than necessary.
Shell will refund the customers and compensate them with an additional £5 each.
Shell Energy Retail also agreed to pay an additional £200,000 into Ofgem's voluntary redress fund to help support vulnerable customers.
The temporary default tariff cap was introduced to protect all customers on standard variable and default energy tariffs from paying poor-value rates.
The cap is currently £1,254 per year until September 30 2019 for households on dual fuel, single-rate based on typical consumption.
Ofgem said it will not take further "formal enforcement action", such as a fine, against the utility company because of the actions it has taken to reimburse customers.