A downhole on-demand power source system can include at least one first energy storage device located within a wellbore disposed in a subterranean formation in a first inactive state. The system can also include at least one first trigger that initiates the at least one first energy storage device from the first inactive state to a first active state. The at least one first energy storage device, once initiated, can provide a first power to an electrical load disposed in the wellbore proximate to the at least one first energy storage device. The at least one first energy storage device, when in the first inactive state, is incapable of providing the first power.