An electrically heated aerosol generating system for receiving an aerosol-forming substrate includes at least one heating element for heating the substrate to form the aerosol and a power supply for supplying power to the at least one heating element. The power supply includes a voltage source, two or more supercapacitors, and switches between the voltage source and the two or more supercapacitors. The switches are arranged so that, during a charging mode, the supercapacitors are connected so as to be charged by the voltage source and, during a heating mode, the supercapacitors are connected so as to discharge through the at least one heating element.