An electrically-variable transmission has three modes of operation. The power in each of the modes of operation is split by differential gearing into a mechanical path and an electrical path between the input shaft of the transmission and the output shaft of the transmission. This is accomplished with three planetary gearsets and four torque-transmitting mechanisms that are judiciously engaged to provide the three modes of operation, which are an input-split mode and two compound-split modes. The transmission can be part of a system with electrical storage devices, which will supplement the engine power during some periods of operation.