A well service pump system supplies high pressure working fluid to a well. The pump system is a linear design which incorporates an electric motor, a variable frequency drive (VFD), a pump drive, closed loop variable flow rate hydraulic pumps, hydraulic ram cylinders, working fluid end cylinders, and a coupling to connect the hydraulic ram cylinders and the working fluid end cylinders. The electric motor powers the hydraulic system which, in turn, provides hydraulic fluid to operate the hydraulic ram cylinders. The VFD is connected to a single one of the hydraulic pumps at a time and applies power to the connected pump, via the pump drive, to drive the connected pump from a cold start to an operating speed. The VFD is connected sequentially, one pump at a time, to each of the hydraulic pumps and disconnected from each pump once the pump reaches the operating speed. Once the pump reaches operating speed, the pump is connected to receive power directly to the electric motor.