As Arizona voters go the polls, they have more control over their state’s power plants and climate policies than they might realize.

This year three of the five seats are up for grabs on the Arizona Corporation Commission, which regulates electric utilities. The commission has authority over how electricity is generated, among other things, and what customers pay.

In recent years, it has taken steps toward rolling back a clean-energy mandate passed by a previous Republican-led board. It has also made it harder to build community solar in a state renowned for its sunniness, its critics say, and easier to build new fossil-fuel-burning power plants.

These boards exist in states nationwide, and while most are appointed, similarly contentious races playing out in states like Louisiana and Montana, where they’re debating the future of coal power, which is particularly dirty, and what role natural gas, another fossil fuel, should have.

“It’s a fourth branch of government that nobody knows about who’s in your pocket every day,” said Robert Burns, a Republican who served on Arizona’s commission for eight years.

Starting two decades ago, the Republican-controlled commission had encouraged a transition to renewable energy based on simple economics: Renewables were getting cheaper than fossil fuels. It initially required utilities it regulates to become 15-percent renewable by 2025 and later, during Mr. Burns’s tenure, he sought to eliminate greenhouse-gas emissions from power plants by 2050.