ScottishPower electricity customers are being hit by a £40 annual increase in the rate they pay for the basic service.
The average standing service charge for electricity is increasing from £70 to £110 per year.
It is part of the average 10% price rise for electricity customers which the energy giant announced last month.
The new rate will come into effect from August 1 along with an average 19% price increase for gas customers.
The changes will not affect around 700,000 people who are on fixed or capped rates.
Previously, the average annual bill for an electricity-only customer paying by direct debit, including standing charge and consumption, was £443.80.
From August 1, this will increase by almost £50 to £491.84.
Of this, £40 represents the increase to the standing charge, which covers fixed costs and is similar to a telephone line rental charge.
A ScottishPower spokesman said: "The standing charge includes all of the costs on the bill that do not vary by household consumption and we have not materially changed many of these since 2006.
"Our standing charge for electricity has now been brought in line with some others in the market. These fixed costs apply to all users of electricity and we are required to ensure that our prices are cost-reflective.
"To keep overall prices as low as possible we have kept consumption charges to a minimum."
Age Scotland said the price increase was bad news for elderly people.
A spokesman said: "We're very concerned about the increase and it definitely will affect older people. There is a growing problem of fuel poverty for older people where they are spending a significant amount of money on trying to heat their home.
"This is a big blow for older people on very low incomes and it is something that we don't find justifiable at all."