Spherical Tokamaks offer a number of potential advantages for a future fusion power plant. They have a high ratio of thermal to magnetic field pressure (beta) and strong flows, either of which could result in reduced turbulence. Fewer Toroidal Field (TF) coils and a different geometry offers the potential for new methods of remote maintenance and lower magnet costs. The UK Atomic Energy Authority has long had an interest in spherical tokamaks having hosted START, MAST and now MAST-U. Systems codes can be employed to scope out parameter space quickly by using a set of simplified models to rapidly determine feasible tokamak designs. Spherical tokamaks have a number of differences compared with their conventional aspect ratio counterparts, and we present the spherical tokamak specific models implemented in the systems code PROCESS. There is an alternative relation between the plasma current and the ratio of the toroidal magnetic field to the safety factor, to account for an increased ratio of I_p/aB that can be accommodated at low aspect ratio. We also include the contribution of the diamagnetic current to the overall plasma current, which is higher than in a conventional aspect ratio device due to the higher beta. Various options are available to alter the build of the device; these include the ability to remove the central solenoid and avoid inboard breeding blankets, to join the TF coils to a single centerpost, to reposition the shaping poloidal field coils within the TF coil, and to increase the divertor space. We apply low and high temperature superconducting magnets to spherical tokamaks within PROCESS and explore the balance-of-plant to illustrate the requirements for net electricity production. Using these models, we present a benchmarking of PROCESS against published spherical tokamak designs, and then highlight interesting areas of parameter space that a future spherical tokamak for energy production could be positioned to operate in.