An electronic device may have a power system with a battery. The device may include power management circuitry that helps distribute power from the battery to components within the device. To prevent an excessive load from being applied to the battery and the battery from dropping below a cut-off voltage, power management circuitry may control power consumption by components in the device. Power consumption models in the power management circuitry may be used to ensure that maximum allowable power consumption levels are not exceeded. To help accurately and quickly manage power consumption decisions, each component may have characteristic power consumption values that characterize the power consumption profile of the component. These characteristic power consumption values may be provided to the power management circuitry with a request for power consumption and the power management circuitry may determine maximum allowable power consumption for the component based on the characteristic power consumption values.