Just last summer, Northern Indiana Public Service Co. planned to retire two of its five remaining coal-fired power plants by 2023. Now, it plans to do away with all of them over the next decade, and buy more solar and wind power instead.

The Midwestern company’s decision is part of a shift among some American utilities toward less costly energy sources. The companies are accelerating the closure of coal plants, as wind and solar power become more economical alternatives, aided by federal subsidies, and natural gas continues...