Yes it is possible for a country to run on 100% renewable energy only. However, currently there are only three countries in the world that are running solely on renewable energy. Bonaire, Costa Rica and Iceland.
Bonaire: The switch from fossil-fueled to renewable energy meant more affordable electricity for this Caribbean island’s 14,500 residents. Bonaire houses 12 wind turbines that generate almost all of its power. The country is also developing a system that would use local algae to create biofuel.
Costa Rica: Costa Rica’s president announced that the country had been running on 100 percent renewable energy since the start of 2015 and is working on plans to become carbon neutral within the next six years. They’re investing in hydro-power and geothermal power (volcanoes) and are considering wind and solar options as well.
Iceland: The island currently generates all of its energy with renewables, which is largely attributed to hydro-power – approximately two-thirds. Like Costa Rica, Iceland also taps its volcanic roots for development of geothermal renewable energy. This could meet nearly all of Iceland’s heat and hot water requirement.