Backers say the financial lifeline for the plants is needed to prevent them closing within the next two years.
The Ohio House plans to vote on the measure Tuesday after lawmakers in the Senate approved the plan last week. Republican Gov. Mike DeWine has said he intends to sign it into law.
Critics say the state's residents and businesses shouldn't be forced to pay a fee that will benefit the nuclear plants' owners.
Opponents led by the natural gas industry have vowed to ask voters to overturn the legislation in a statewide referendum next year.
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