Lithium-ion batteries have become essential for powering electric cars and storing energy generated by solar panels and wind turbines. But their drawbacks are also by now familiar: They use scarce minerals, are vulnerable to fires and explosions, and are pricey. A plentiful, safe and more affordable alternative would be worth a lot. On Wednesday, an energy company headed by the California billionaire Patrick Soon-Shiong announced that it had developed a rechargeable battery operating on zinc and air that can store power at far less than the cost of lithium-ion batteries. Tests of the zinc energy-storage systems have helped power villages in Africa and Asia as well as cellphone towers in the United States for the last six years, without any backup from utilities or the electric grid, Dr. Soon-Shiong said. “It could change and create completely new economies using purely the power of the sun, wind and air,” Dr. Soon-Shiong, a surgeon and a biotechnology entrepreneur, said in an interview in Los Angeles before the announcement.