A non-linear mathematical model for the digital twin of an underwater kite energy generator

We propose a detailed nonlinear mathematical model for a kite-like underwater energy generator describing its motion with six degrees of freedom (DoF), i.e. its translational and rotational coordinates and velocities in the presence of ocean currents. This work is the result of the long-term deployment of such a generator, the GEMSTAR prototype, which is operated in the laboratory facilities of RENEW-MEL. Marine renewables have attracted the attention of both the scientific community and industry due to their enormous production potential. Although several technologies are already available for commercial use, energy production from tidal currents still struggles with high operating costs, mainly due to component failures in the marine environment and the difficulty of maintenance underwater or at sea. To reduce these costs, it is necessary to carry out preventive maintenance and provide the equipment with fault detection and isolation functions. In view of the special characteristics of the GEMSTAR, it is also necessary to control its position to prevent the cable from twisting and to maximize its energy production by ensuring that the device is aligned with the current flow. For such tasks, the use of a digital twin is of great benefit. A digital twin is the digital counterpart to a physical device. It emulates a physical system with the help of an adaptable mathematical real-time model. In this work, the mathematical modeling of the device is performed by considering a few hypotheses: The mooring cable is assumed to be non-extensible and with a negligible weight. Furthermore, the hydrodynamic forces are modeled by considering the kite as a series of discrete bodies that do not interfere with each other's motion in the water. The dynamics of the kite with its six degrees of freedom are described by the description of the forces and moments acting on it, using a Newtonian approach for each of its components - the two turbines, the two tanks and the rudders. The model was developed in the MATLAB/Simulink environment and all its parameters can be easily modified to describe similar kite-like generators. The parameters for the model are obtained either from the design of the device or through numerical simulations that use Blade Moment Elementum Theory to model the behavior of the turbines. The validation of the model is based on real flow data from a future installation site, collected with an acoustic Doppler current profiler (ADCP) over one-year measurement campaigns. The performance of the model will be further evaluated with a physical prototype that will be tested at sea as part of the RENEW-MEL laboratory experiments. The study also demonstrates the model’s ability to operate in real time, a prerequisite for digital twin applications. Once the GEMSTAR prototype has been deployed at sea, its digital twin will be experimentally validated and used for maintenance and control of the device. This will allow fine-tuning of the model parameters and testing its ability to predict the operation and lifetime of GEMSTAR, with particular attention to the effects of biofouling phenomena.