An electrical submersible well pump assembly includes an electrical motor for driving a pump. A pressure compensating chamber contains a dielectric lubricant in fluid communication with an interior of the motor. A movable pressure compensating element has a first side in contact with the lubricant in the chamber. Movement of the element relative to the chamber causes a change in volume of the chamber. An electrical drive mechanism is connected with and moves the element. A controller senses a pressure difference between the lubricant pressure and the well fluid pressure and operates the drive mechanism in response. The element may be a piston, a bellows or telescoping tubes.