Some of the largest U.S. users of coal are thinking about getting into the solar-power business.

Executives at utilities American Electric Power Co. and Southern Co., seeing a potential threat to their business model on the horizon, are pondering how and when they might enter the market for installing solar panels at businesses and homes. Until now, that kind of "distributed" solar—as opposed to large-scale solar arrays—has mostly been the domain of newer companies like rooftop-solar-panel installer SolarCity Corp.

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