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https://www.youtube.com/watch?v=ZXde6BfgMGc&list=PLeyXRzjKojuVuZ9N_M62t-JAoG8y92b_1

## Contexts in source publication

**Context 1**

... power is examined between the ZOH and FOH constructed systems the difference is clear. With the ZOH the converter voltages are corrupted with high speed transients when the machine is moving with a high velocity. The converter voltages for the FOH based system look like a filtered version of the ZOH converter voltages, as can be seen in Fig. 10. Over an average time period this would not be a problem however this would lead to poor power quality, unnecessary high harmonics on the grid, unavoidable instantaneous overvoltages which could lead to permanent damage to the LPMG, the machine side converter and the grid side converter. The simulated waveform shown in Fig. 11 displays ...

**Context 2**

... as can be seen in Fig. 10. Over an average time period this would not be a problem however this would lead to poor power quality, unnecessary high harmonics on the grid, unavoidable instantaneous overvoltages which could lead to permanent damage to the LPMG, the machine side converter and the grid side converter. The simulated waveform shown in Fig. 11 displays the in- stantaneous powers from the ZOH and FOH systems extracted from a Bretschneider Spectrum with a significant height H s = 3m and a significant wave period T s = 0.9rad.s −1 [27]. The combination of the voltage spikes in the ZOH converter voltage and the overshoots in the current transients produce high frequency ...

**Context 3**

... quality of the instantaneous power can be examined using a spectrum analyser (Fig. 12). With the spectrum anal- ysis it is shown that the power from the FOH system at frequencies higher than the Bretschneider spectrum bandwidth are superior when compared to the powers from the ZOH system. This reduction of noise at higher frequencies could reduce the design complexity of components connected to the grid. ...

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## Citations

... However, power losses that occur during the power transmission and power generation stages significantly affect the real power production of the WEC [1]. Therefore, focusing only on hydrodynamic performance and mechanical power may mislead design solutions [7], lead to ineffective control algorithms [8] and unrealistic expectations from a device [9]. ...

This article demonstrates the benefits of optimising the drivetrain to improve the level and quality of electrical power output from a wave energy converter. The study considers a spherical buoy connected to a permanent magnet synchronous generator through a mechanical drive. The wave energy converter is equipped with a model predictive control system that maximises electrical power from the generator. Three different scenarios are compared: (i) when the drivetrain is not optimised, (ii) when only the gear ratio is optimised, (iii) and when both gear ratio and flywheel inertia are optimised. The performance of all three configurations is compared in terms of their effect on the generator operating range, the natural frequency of the system, the amount of generated electrical power, and control forces. The results demonstrate that the drivetrain optimisation leads to a significant increase in the electrical power output while shifting the generator's operating range to areas with the highest efficiency. Moreover, drivetrain designs that utilise a flywheel reduce the power take-off loads and facilitate smoother power production.

... • coupling between the BEM solver NEMOH and the mild-slope wave propagation model MILDwave, Unlike existing wave-to-wire models such as [2,3], which focus on a specific Wave Energy Converter (WEC) technology, or those such as [4,5] that deal with a single objective of power maximization, the model proposed in this study has the dual goal of (i), accurately representing the wave field around the array and (ii), allowing a fast and accurate calculation of the power output of a given WEC array project. In this study, the W2W model introduced in the bullet points above is tested for a realistic scenario of a proposed commercial WEC array project. ...

In this study, a series of modules is integrated into a wave-to-wire (W2W) model that links a Boundary Element Method (BEM) solver to a Wave Energy Converter (WEC) motion solver which are in turn coupled to a wave propagation model. The hydrodynamics of the WECs are resolved in the wave structure interaction solver NEMOH, the Power Take-off (PTO) is simulated in the WEC simulation tool WEC-Sim, and the resulting perturbed wave field is coupled to the mild-slope propagation model MILDwave. The W2W model is run for verified for a realistic wave energy project consisting of a WEC farm composed of 10 5-WEC arrays of Oscillating Surging Wave Energy Converters (OSWECs). The investigated WEC farm is modelled for a real wave climate and a sloping bathymetry based on a proposed OSWEC array project off the coast of Bretagne, France. Each WEC array is arranged in a power-maximizing 2-row configuration that also minimizes the inter-array separation distance d x and d y and the arrays are located in a staggered energy maximizing configuration that also decreases the along-shore WEC farm extent. The WEC farm power output and the near and far-field effects are simulated for irregular waves with various significant wave heights wave peak periods and mean wave incidence directions β based on the modelled site wave climatology. The PTO system of each WEC in each farm is modelled as a closed-circuit hydraulic PTO system optimized for each set of incident wave conditions, mimicking the proposed site technology, namely the WaveRoller® OSWEC developed by AW Energy Ltd. The investigation in this study provides a proof of concept of the proposed W2W model in investigating potential commercial WEC projects.

... MPC maximises the average power over a prediction horizon by minimising an economic cost function [10]. It has been shown in [11], that simply maximising the mechanical average power was insufficient when extracting electrical power; therefore including the PTO losses within the optimisation was shown to be imperative. ...

... where λ f d = p 2 λ f d , λ f d is the flux linkage, p is the number of poles and τ is the pole pitch. This realistic PTO has associated losses, which must ne taken into account when maximising the electrical power extracted from the wave, [11], [18]. In this work a cascade control scheme is used, where an economic MPC sends piecewise linear set points to a faster inner control loop that controls the current of the LPMG to produce the desired PTO force. ...

... This continuous average electrical power equation can be transformed into a discrete form using the trapezoidal rule. This discrete average electrical power approximation J(k) (11) can be maximised using quadratic programming (QP) over the prediction horizon N , to produce the optimal PTO forces over the horizon u q (k + i). ...

In this paper, an economic Model Predictive Control (MPC) is used to investigate the effects that arise from the model mismatch between the control and the system. It is shown that the average electrical power is affected by the modelling discrepancies, but that the performance is still acceptable. A move-blocking technique is incorporated into the structure of the control horizon of the MPC, where the move-blocking decreases the computational burden whilst maintaining system performance, hence drastically reducing the optimisation solving time. The MPC with the move-blocking incorporated is then tested on the most significant mismatch, where it is shown that the control horizon of the MPC can be drastically reduced while maintaining system performance.

... When the PTO is included in the system, (Polinder et al., 2004), a cascade control scheme can be easily implemented, where the slower outer loop sends piecewise linear reference points to the faster inner PTO force control loop, (Montoya Andrade et al., 2014;Cretel et al., 2011). In (O'Sullivan and Lightbody, 2015), it is shown that it is essential to include the PTO power losses within the cost function, as the average power can dramatically reduce when the WEC operates away from its natural frequency. ...

... In previous work (O'Sullivan and Lightbody, 2016a), viscosity effects were not considered. Here, it is initially assumed that the MPC prediction model is linear as in (O'Sullivan and Lightbody, 2015) with no viscous modelling included. However, the non-linear simulation model includes viscosity as described in equations (8) and (9). ...

In this paper, the non-linear effects of viscosity on the performance of a Wave Energy Converter (WEC) system are analysed. A standard linear Model Predictive Control (MPC) is used to show the negative effects that the unaccounted non-linear viscosity force in the hydrodynamic system has on the power absorption. A non-linear MPC (NLMPC) is then implemented, where the non-linear viscosity effects are included in the optimisation. A linear drag coefficient estimate of the non-linear viscosity is then included in the linear MPC; creating a Linear Viscous Model Predictive Control. When constraints are incorporated, it is shown that a single choice of the linear viscous drag coefficient for use within the linear MPC can provide comparable results to the non-linear MPC approach, over a wide range of sea states.

... Many have analysed MPC with the objective of maximising the average mechanical power over a prediction horizon [13e15]. Much of this research uses ideal PTO systems; unfortunately, the inclusion of a non-ideal PTO can significantly decrease the average electrical power extracted if the cost function is based on the mechanical power [16]. Including an imperfect PTO efficiency as a soft constraint [17e19] in the cost improves the outcome, as the average electrical power is maximised. ...

... A direct drive linear permanent magnet generator (LPMG) was implemented in Refs. [16,21] with a first order hold (FOH) MPC [22], due to its maximum shear PTO force capability [23], which is needed during the point absorbers high oscillations. ...

... For the system to be controlled via MPC, the system has to be presented in the discrete domain. For the discretisation, a First Order Hold (FOH) was chosen as it produces better power quality [16] and is well suited to the cascade control structure adapted here. The discrete state space model is, ...

This paper highlights the need to optimise the performance of the complete wave to wire system, instead of designing the individual subsystems. In this work a point absorber wave energy converter operating in heave mode separately, coupled to a Linear Permanent Magnet Generator (LPMG); where the results are obtained in simulation. The PTO force is controlled by a machine side back-to-back voltage source converter (VSC), which is connected to a constant DC-link voltage. Model Predictive Control (MPC) is then used to maximise the absorbed electrical power with the resistive losses of the PTO included; this is compared with classical control methods. The optimal force produced from the MPC incorporates legitimate physical and electrical constraints of the WEC and LPMG -the importance of including such constraints within the optimisation is shown. Field weakening and a uni-directional power flow constraint are then incorporated to help prevent poor grid power quality when fluctuations in the DC-link occur. It is assumed that the constrained optimal control approach produces the highest possible electrical power available. This means that it is now possible to clearly see the effect of physical design choices on the performance on a level playing field.

... Authentic PTOs are non-ideal systems that can come in the form of a pneumatic, hydraulic [3] or electrical [22] system. In previous work [23], a realistic electrical linear permanent magnet generator (LPMG) [24] was chosen due to its high output force capabilities and its suitability for array absorbers. The optimisation shown in [23] included the resistive losses and the physical constraints of the LPMG. ...

... In previous work [23], a realistic electrical linear permanent magnet generator (LPMG) [24] was chosen due to its high output force capabilities and its suitability for array absorbers. The optimisation shown in [23] included the resistive losses and the physical constraints of the LPMG. However, the non-linear electrical current and voltage constraints were not included in the optimisation, which would lead to feasibility issue and which are important for the protection of the power electronics. ...

... For the system to be controlled via MPC, the system has to be represented in the discrete domain, based on a first order hold, instead of a conventional zero order hold. The FOH was chosen as it produces better power quality [23]. The discrete state space model is as follows, ...

This paper investigates the use of field weakening to improve the electrical power capture of a wave-to-wire wave energy conversion system. The system consists of a Linear Permanent Magnet Generator (LPMG) as the power take off, which produces a physical Power Take Off (PTO) force that is controlled by a machine side Voltage Source Converter (VSC). The electrical power is then maximised using Model Predictive Control (MPC), in accordance with the systems constraints. Field weakening is then included in the systems optimisation, where this paper shows how field weakening can increase the PTO force range, hence, increasing feasibility and decreasing the chances of permanent damage during wave energy periods of low DC-link voltage.

... The rated losses (in percent) are therefore to be multiplied by approximately a factor 4-5 to find out the real losses in percentage of the extracted power. This requires a generator with very high efficiency, and is regarded as unfeasible since the appropriate technology does not exist [11]. The generator that is proposed here in principle meets both these requirements, and if the rated losses are 2-3% reactive control is feasible, provided that the power electronic system and the electric storage system is efficient. ...

A force-dense and very efficient direct drive transverse flux generator aimed for wave power applications is being developed at the Royal Institute of Technology in Sweden. The machine is specialized for low speeds, and the design of a linear version is presented in this paper. The basic electromagnetic design is given as well as an overview of the mechanical design. The benefits of such machines at low speeds are described in detail. The challenges that the machine type have are also presented, and suggestions are made on how they can be handled. Geometrical and calculated performance data is given for a prototype machine that is to be constructed during 2017. The possibility of using the machine type for control methods such as reactive control is also discussed. The machine is predicted to have an efficiency of 97-98% at speeds as low as 0.7 m/s, and a shear stress of 100-120 kN/m², corresponding to 200-240 kN/m² if only half the active area is counted as active which is custom for such machines.

... A number of W2W models have been presented in the literature for different types of WECs: overtopping converters [6], oscillating water columns (OWCs) [7], or wave-activated converters with different PTO strategies, e.g., hydraulic [8][9][10][11][12][13], mechanical [1,14], magnetic [13], or linear generators [15,16]. ...

... The other studies utilise constant torque and/or efficiency values to emulate the generator. However, in the case of W2W models based on direct conversion using linear generators, dynamics of the electric generators are generally included, as shown in [15,16], although [16] simplifies the analysis by assuming no field weakening. ...

... The other studies utilise constant torque and/or efficiency values to emulate the generator. However, in the case of W2W models based on direct conversion using linear generators, dynamics of the electric generators are generally included, as shown in [15,16], although [16] simplifies the analysis by assuming no field weakening. ...

Control of wave energy converters (WECs) has been very often limited to hydrodynamic control to absorb the maximum energy possible from ocean waves. This generally ignores or significantly simplifies the performance of real power take-off (PTO) systems. However, including all the required dynamics and constraints in the control problem may considerably vary the control strategy and the power output. Therefore, this paper considers the incorporation into the model of all the conversion stages from ocean waves to the electricity network, referred to as wave-to-wire (W2W) models, and identifies the necessary components and their dynamics and constraints, including grid constraints. In addition, the paper identifies different control inputs for the different components of the PTO system and how these inputs are articulated to the dynamics of the system. Examples of pneumatic, hydraulic, mechanical or magnetic transmission systems driving a rotary electrical generator, and linear electric generators are provided.