The explosions occurred in the town of Amorebieta in Vizcaya province, Spanish National Radio said.
It said there were no casualties.
The Basque press agency Vasco Press quoted police as saying that the blasts were preceded by an anonymous call to the Gara newspaper from someone purporting to be a member of the armed Basque separatist group ETA.
The caller said four devices had been placed near the power plant.
Cadena Ser radio said no one was injured in the blasts, and that they had caused only "minor" damage.
Workers at the plant were evacuated before the explosions, the news agency Efe said.
It quoted witnesses as saying the explosions were small.