Modelling and optimal control of tidal barrages: A moment-based approach

Tidal barrages generate electrical energy using the tidal height variations throughout the day, and stand out from other renewable energy schemes because of their inherent storage capabilities and the relatively slow variation of the tides, allowing flexibility in their operation. The resulting optimal control problem of operating tidal barrages has unique features that call for a range of possible operating modes (generating, sluicing and pumping). This paper presents a comprehensive model for tidal barrage power plants, using the La Rance power plant as case study. The operation of the hydraulic turbines is modelled using a generic hill chart, which accounts for all possible operating points (not only those with maximum efficiency, as commonly seen in the literature). An artificial neural network was designed and trained to obtain a compact function approximation for the hill chart. The optimal control problem is solved using moment-based control, a mathematical tool from the family of weighted residual methods, broadly applied in wave energy control. Moment-based control is implemented by parameterising the external and control inputs with a harmonic expansion, and the nature of the frequency range required for an efficient parameterisation is explored.