**1. Introduction**

Tidal-stream energy can contribute significantly to global renewable energy generation, and the UK has an estimated 10–15% of the global harvestable tidal resources [1]. Tidal stream turbine (TST) technology has developed to a stage where first large-scale commercial facilities are being deployed. For example, the MeyGen project, which has exported 17 GWh to the grid as of June 2019 [2], is proving to be a reliable and economically viable renewable energy source. However, the durability of such projects is a complicated subject because the loads on TSTs vary widely owing to the unsteady marine environment. Therefore, it is challenging to achieve 10–25 year fatigue lives for turbine. There are six main types of tidal energy convertors (TEC), namely, horizontal axis turbine, vertical axis turbine, oscillating hydrofoil, enclosed tips (venturi), archimedes screw, and tidal kite [3].

The design of tidal turbine station keeping systems varies based on the turbine architecture being considered and the method of attachment to the seabed being employed. At present, gravity-based structures, drilled monopiles, and drilled pin pile tripods are three widely used support structures for tidal turbines. To make tidal current generation commercially competitive with the traditional types of energy, the industry must focus on reducing the cost of generation of the tidal-stream energy. Two main cost factors that must be targeted are the installation and maintenance of the equipment. Therefore, flexible mooring-based systems are being used for the station keeping of floating tidal turbines, such as CoRMaT [4] and Minesto 'Tidal Kite'.

Modelling methods to investigate the dynamics of a tensioned mooring-based turbine have been discussed in this paper. The analysis and control of the marine mooring and cable system are presented in [5], where the method is used to solve the dynamics of the ship and offshore platform mooring system. Mooring systems from the offshore oil and gas and ship industry have been developed and applied to design some wave energy converters [6,7]. Research shows that the single point mooring system is suggested to be applied in large dimension wave energy converters owing to the ability to minimise environmental loads [8]. However these approaches are applied generally to mooring lines that are not fully tensioned and connected to a floating structure on the surface of water.

A submerged floating tidal current hydrokinetic turbine system named GEMSTAR was presented by [9]. GEMSTAR is a project developed at the the University of Naples and the first prototype has been tested in the towing tank. It reports that problems may arise in the design of the mooring system and structural optimization, as a consequence of the high loads due to turbine thrust and required buoyancy. However, the methods to calculate the thrust, torque, the buoyancy and other dynamic characteristics of the tensioned mooring turbine have not been investigated so far. The objective of this research is to build up a numerical model to simulate these characteristics of the tensioned mooring turbine.

In this paper, the system is assumed to be an inelastic mooring, and it is modelled based on an inverted pendulum system. A coupled pendulum with an external drive is expected to experience complicated dynamics. The existence of irregular vibrations and both periodic and chaotic trajectories of a mathematical double pendulum system is proven in [10]. The stabilisation of the inverted pendulum, which is a highly nonlinear system, has been studied extensively for control education and research purposes. However, the moored turbine system is a quasi-dynamic system owing to the external forces. The external forces such as loading on the turbine rotor blades and buoy are calculated using a wave coupled blade element momentum theory (BEMT). The code was developed at the University of Strathclyde to analyse the loading occurring on a turbine rotor-drive train when operating in energetic wave–current flow conditions [11].

#### **2. Methodology**

The focus of this study is to present a methodology to assess the behaviour of a neutrally buoyant turbine supported from a tensioned cable-based mooring system, where tension is introduced using a buoy working as a damper and fully submersed in water. The schematic of the system in operation is depicted in Figure 1.

**Figure 1.** Schematic of tensioned mooring turbine in operation.

In order to solve the dynamics of the tensioned mooring turbine in a wave–current coupled environment efficiently. The tensioned mooring system is modelled as a special type of triple pendulum, called an inverted flail. It consists of three pendulums: the first one is attached to a fixed point considered to be an anchor and to its end mass; the other two pendulums are joined. An original flail system without the external drive and gravity field is depicted in Figure 2. This system was analysed in [12].

**Figure 2.** Geometry of flail pendulum.

Unlike the original flail system, the tensioned mooring supported turbine is driven by external forces as the loads on the turbine and buoy. A wave–current coupled BEMT was utilised to calculate the loads on the turbine rotor blades. The code was developed at the University of Strathclyde to analyse the loading on a turbine rotor-drive train when operating in energetic wave–current flow conditions [13]. In addition, owing to the turbine being able to move and respond to the moving flow field generated by the waves, the resulting motions due to flow field interactions must be taken into consideration. By coupling the tensioned mooring system with the forces obtained from BEMT as the external drive forces in wave–current environments, it is efficient to calculate the dynamics of the turbine and mooring lines together at each time step in a long simulation window.
