Following talks with the authority, SSE said it would identify customers who should have their meter replaced free of charge.
The council described the move as the first of a range of measures designed to help tackle fuel poverty. However, energy firms knocked back a plea for a freeze on tariffs.
Council leader Gordon Matheson Matheson said: "Having to find extra money to replace a meter is a very significant barrier to some of our most vulnerable citizens getting the best deals." SSE's managing director enterprise, Jim McPhillimy, said: "While we believe pre-payment meters still have an important role to play, we recognise that in some cases it is not suitable."