A dynamic programming algorithm for optimal design and operation of tidal range schemes

Abstract

Optimising the design and operation of tidal range schemes (TRS) to enhance TRS performance indicators such as energy output, turbine efficiency, and storage capacity has long been a critical challenge. Recent research has explored various computational algorithms to optimise TRS designs and operations. Xue et al. (2020, Energy, 200, pp. 117496) introduced a Genetic Algorithm (GA) to optimise the TRS operation, while Moreira et al. (2022, Ocean Engineering, 247, pp. 110657) implemented a reinforcement learning approach to make real-time decisions on tidal turbine operations. However, these methods do not guarantee finding the optimal solution, although approximate optimal solutions can be usually determined. In addition, these methods require substantial computational resource, preventing the optimisation of all relevant design parameters without imposing hard constraints. Consequently, these methods obtain only approximate optimal solutions with limited parameter search spaces. This becomes crucial as the tidal range schemes are being considered as energy storage facilities with many scenarios being available for operation. In addition, most previous optimisation work lumped the sluice gates and turbines usually spread along the TRS walls into one single sluice gate and one single turbine (Single-block hereafter). The variations of head differences at different sluice gates and turbines were neglected in the Single-block approach.

This research develops an efficient tabular dynamic programming (DP) algorithm to determine the optimal operation strategy for a TRS. DP algorithm has several advantages over the previous algorithms: (1) the solution is guaranteed to be globally optimal, subject to the discretisation error; (2) highly efficient, capable of optimising all parameters without hard constraints, and suitable for real-time operation; (3) enabling optimisation of multi-block TRS operation, in which different blocks of sluice gates and turbines are modelled separately; (4) straightforward parallelisation and deployment on hardware. The DP algorithm is integrated into a zero-dimensional modelling framework (Xue et al., 2020). Multi-block DP algorithm was also developed and tested. The optimised TRS operations were validated against TELEMAC2D hydro-dynamic model simulations. The operations of two proposed TRSs, namely the West Somerset and the North Wales tidal lagoons, were optimised with the DP algorithm. The details of the two schemes can be found in Guo et al. (2021, Renewable Energy, 179, pp. 2104–2123) and Vandercruyssen et al. (2022, Heliyon, 8, pp. 11381). Results show that our algorithm outperforms the GA method in terms of efficiency in obtaining the operations that maximise energy outputs. Our algorithm was also applied to evaluate the impact of number of turbines and sluice gates on the optimal TRS operations and energy outputs. Number of turbines ranging from 75 to 1750 were tested. Results confirm that the optimal energy generation of a TRS increases with the number of turbines for < 500. With more than 500 turbines, the energy outputs reach about 80% of the theoretical limit of the harvestable energy and stay constant. The DP algorithm has the potential for real-time TRS optimisation, which is important for unforeseeable wave environment such as storm surges, because of its flexibility and efficiency.