An active heave compensation system comprises a motor generator to interact with a load so as to drive the load in a first part of a heave motion cycle and to regenerate at least part of energy with which the load has been driven in a second part of the heave motion cycle, and an electrical storage element for storing the regenerated energy. The active heave compensation system further comprises a power supply electrically connected to the motor generator and the electrical storage element for providing electrical power to at least the motor generator, and a control unit configured to control the power supply substantially in synchronism with the heave motion.