In this paper we propose an optimal dispatch scheme for a cascaded hybrid hydro-solar power system, i.e., a hydroelectric system coupled with solar generation, that maximises the head levels of each dam, and minimises the spillage effects. As a result more water is stored in the dams to meet a given amount of energy providing more flexibility to the system in dry months. This dispatch scheme is based on the development of a simplified hydroelectric power system model which has low computational burden and may be implemented for the short-term operation of a cascaded hydro-solar hybrid power system. To this end, the nonconvex relationships that describe the system physical constraints, e.g., hydroelectric power output, are transformed into affine relationships; thus reducing the computational complexity. The transformations are based on the construction of convex envelopes around bilinear functions, piecewise affine functions, and exploitation of optimisation properties. We validate the proposed framework and quantify the benefits of coupling hydroelectric and solar resources in terms of live water volume in dams and amount of solar a system may withstand with the Tana river cascade located in Kenya through an analysis of incorporating actual system data.