A heave compensation system comprises a motor-generator to interact with a load and a control unit being arranged to control operation of the motor-generator. The control unit is arranged to: operate the motor-generator to drive the load in a first part of a wave motion cycle, and operate the motor-generator to regenerate in a second part of the wave motion cycle at least a part of the energy with which the load has been driven in the first part of the wave motion cycle. The heave compensation system comprises an electrical storage element to buffer at least part of the regenerated energy for powering the motor-generator in a following cycle of the wave motion.