Energy storage devices are an essential part of hybrid and electric vehicles. The most commonly used ones are batteries, ultra capacitors and high speed flywheels. Among these, the flywheel is the only device that keeps the energy stored in the same form as the moving vehicle, i.e. mechanical energy. In order to connect the flywheel with the vehicle drive line, a suitable means is needed which would allow the flywheel to vary its speed continuously, in other words a continuously variable transmission (CVT) is needed. To improve the efficiency and speed ratio range of the variators, a power spilt CVT (PSCVT) can be employed. This paper discusses the kinematics of PSCVT used to connect the flywheel to the driveline. A methodology describing the characteristic equations of speed ratio, power flow and efficiency of the PSCVT for various types including power recirculating and multi regime in both directions of power flow has been presented. An example of a PSCVT for a flywheel energy storage system (FESS) is computed using the derived equations and the results compared.