We live near Dominicus. The power company is CEB (which is the sister to CEPM). The B is for Bayhibe. As AnnaC says, they have a plant on the road between Bayahibe and Dominicus. It is a private company. CEPM serves Bavaro/Punta Cana.
When the main power goes off, they fire up the huge diesel generators to generate electricity.
The power goes off where we live about once every two weeks. But, within 15 minutes, usually, it is back on. Very reliable. We posted the prices a while back. There is a base rate - I don't remember exactly, maybe equal to about $8 USD, then 25 cents a kwh. Worth the cost. We have two bedrooms with a/c and living room. Run it in late afternoon and all night, rarely pay more than 4500 pesos/month.
We do not have an electric clothes dryer, if you do, it will cost a bit more.
Generators/batteries are not necessary if you have service from CEB.