Modelling of hydrodynamic effects and optimization of energy benefit in tidal power schemes.
Energy Benefit in Tidal Power Schemes' by Helen Suckling
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
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