Developing and Investigating a 1D Model for a System of Tidal Lagoons

Abstract

The Bristol Channel has one of the largest tidal ranges in the world, with a mean tide of nearly 10.5 m at Avonmouth, and speculations on how to harness this energy date back well over a century. One method is tidal range by the use of tidal lagoons, which operates on principles akin to hydropower. The lagoon is essentially an enclosed reservoir near the coast, which can maintain the inside water level while the outside rises and falls with the tide. When a sufficient head difference between the inside and outside water level is achieved, the turbine gates open and the flow drive the turbines.

This thesis explores a novel modelling approach consisting of a 1D channel based on the inertial form of the Saint-Venant Equations, coupled with 0D tidal lagoons. The model was built in Modelica. The 1D channel subsystem was modelled first, and validated by comparison with tidal constituents at multiple measuring stations in the domain. The channel model’s accuracy was deemed sufficient, with root-mean-square deviations ranging from 0.29 to 0.67 m. With the model validated, the nature of the tidal resonance in the channel was investigated, where the natural period was determined to be located between 7-8 hours. It was shown that the natural period is heavily dependent on the tidal wave propagation velocity, which is in accordance with the quarter-wavelength resonance theory.

The 0D tidal lagoon subsystem was coupled with the 1D channel and validated by considering the proposed Swansea lagoon design by Tidal Lagoon Power and comparing the results with the current literature. The lagoon was found to be operating as expected in dual generation, and the annual energy generation was 425 GWh. The energy production is slightly conservative compared to literature, but within reason. The lagoons' impact on the channel hydrodynamics were also investigated, and it was found to have a significant effect, particularly in the narrow section of the estuary. The influence of the lagoon-channel coupling on energy generation was also explored: As the hydrodynamic impact increases, the energy generation from the system as a whole decreases.

A 2D model was also utilised to explore the higher-order and near-field effects that would potentially be lost in a 1D model, like localised dips in water elevation, reduced circulation zones, jets and more. The 2D results indicate that consideration of the localised effects is crucial when designing tidal lagoons.

The tidal lagoons were also implemented, and the Swansea lagoon had an annual energy generation of 408 GWh, closely matching the 1D model. Three larger tidal lagoons were also implemented, however not successfully scaled to match the 1D model due to time constraints. Operational tidal lagoons were also shown to have a tremendous influence on the water elevation in the channel.

In conclusion, the 1D modelling approach is potentially as a powerful tool to supplement more detailed 2D models, and it can potentially replace the 0D models ordinarily used for optimisation and sensitivity analyses in the preliminary investigations.