Smaller scale electricity generation is increasingly cost-effective, supports smaller companies and delivers local jobs and growth, according to the study by think tank IPPR said.
If cities support local renewables, it would mean low-carbon subsidies are paid to their communities rather than to the multi-national companies.
Cities could cut bills for poorer households by getting into the energy market, targeting lower-income groups - who tend to be on more expensive rates - and controlling tariffs they pay.
The subsidies received for low-carbon power generation could be reinvested in energy efficiency measures such as insulation to help tackle fuel poverty.
City-run energy suppliers could be very popular, given the high level of trust for local authorities, shaking up the power market and restoring trust that has been damaged by the Big Six major energy suppliers, the report said.
There are a range of innovative steps cities could take to boost their local economy through energy generation.
In Aberdeen, the local authority is planning to use hydrogen produced from water using excess power from nearby offshore wind farms, to run the world's largest hydrogen bus fleet.
IPPR director Nick Pearce said: ""Local generation technologies like solar and medium-scale wind are radically transforming how energy systems operate, bringing to an end the dominance of centralised generation and distribution."