Energy Benefit in Tidal Power Schemes' by Helen Suckling Abstract Predictions of energy output from a barrage in the Severn Estuary can be made by using a mathematical model describing the operation of the barrage linked to one of tidal flow. Estimates of the likely energy production from such a barrage have been made using a flat surface model of the estuary which incorporates real machinery operating characteristics. The flow through the barrage can be controlled optimally in order to obtain the greatest amount of energy from the tides. The energy predictions made by using the flat surface model are examined using a hydrodynamic model of flow in the estuary. A simple one-dimensional hydrodynamic model of the tidal flow in the Severn Estuary is presented. The area of the estuary under consideration is that which lies between approximately Berkeley in Gloucestershire and 11 fracombe on the North Devon coast. The only open boundary is assumed to be the seaward boundary. No account is taken of flow into the estuary from rivers. Finite amplitude shallow water wave equations, together with a representation of bottom friction, are used to describe the tidal behaviour in the estuary. The crosssectional topography of the estuary is assumed to be a rectangle. The boundary conditions are that there is no flow through the landward boundary and the water level at the seaward boundary is a known function of time. The equations are solved numerically as a system of ordinary differential equations. A simple Runge-Kutta method is used. The mqdel is used to obtain predictions of the level and time of high and low tide at certain points along the estuary. The results are compared with those obtained by using another, but more complex, onedimensional model. In the region of computation, the accuracy of the results of the two models are comparable. The effect of varying both the coefficient of friction and the form of the friction term is examined. The effect of linearizing the governing equations is also studied. A model of a tidal power barrage, sited between Weston-super-Mare and Cardiff, is then incorporated into the hydrodynamic model. The operation 'of the barrage is determined by using an open loop control, obtained by using a flat surface model of the estuary. The extent to which hydrodynamic effects may modify the energy predictions made by the flat surface are examined. variation of the time at which generation is allowed to start is found to affect the amount of energy predicted by the hydrodynamic model. The costate equations, which are necessary for the solution of the optimal control problem are derived, but the solution of these equations is not presented