A display may have an array of pixels illuminated using a backlight unit. The backlight unit may include multiple strings of light-emitting diodes (LEDs) and a boost converter for providing an output voltage to the multiple LED strings. The boost converter may have a single-phase single-switch, single-phase multi-switch, and/or multi-phase multi-switch configuration, where the switches are turned off when the peak current is reached. When transitioning from a single phase to a dual phase operation, the second (slave) phase current may be slowly ramped up. When transition from the dual phase to the single phase operation, the output voltage may be elevated while slowing ramping down the slave phase current. The boost converter may include a current detection circuit for adjusting the peak current of each phase to balance the average current levels. The boost converter may also include an in-rush current controller configured to sense a short fault.