Newsday reports that LIPA has begun returning $129 million of the money through incremental rate cuts spread over three years.
Beginning in April, customers will see an average $2.85 reduction in their monthly bill for the rest of the year, and $1.50 a month for 2012 and 2013.
LIPA approved a measure to change the way it calculates the charges at a meeting in January.
LIPA's interim chief executive, Michael Hervey, says the company became aware of the "lost" power last summer.
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