# Control Strategies Applied to Wave Energy Converters: State of the Art

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## Abstract

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## 1. Introduction

- Bathymetry and distance to shore: Near-shore facilities can have a direct affection on nearby coastal areas, maritime routes, fishing areas or visual impacts. Narrow and step near-shore continental shelfs can also have a negative impact for economic reasons, mainly installation (including grid connectivity) and maintenance.
- Electricity infrastructure: On the contrary, if we move large distances from the shore to minimize the previously cited negative impacts over coastal areas, it can significantly increase the relevant cost of cabling and substations, especially for areas with large depths.
- Potential environmental impacts: Underwater noise, sediment dispersal, increased turbidity, electromagnetic field effects (EMF), wave radiation and diffraction alteration can lead to significant changes to coastal morphology; fixed structures can also generate artificial reef effect. It is concluded that environmental impacts for MRE are hardly clear and not sufficiently quantified, hence, more research is necessary about this topic.
- Economics: The great diversity of MRE technologies and the early development status result in a wide range of levelized cost of energy (LCOE) [3], in the particular case of wave energy ranging from 108 €/MWh to 530 €/MWh. This level of economic uncertainty creates a less favorable environment for investments.
- Legal and regulatory framework: There is a lot of uncertainty in this regard for MRE, and it is not adequately addressed by the relevant national/international entities. Many key parameters affecting directly any MRE installation are interrelated with several other aspects such as the environmental impact assessment, rights and ownership, international law, management of ocean space, etc.

## 2. Wave Energy Technology

#### 2.1. Wave Energy Converters

#### 2.1.1. Location

- Onshore: Located in coast proximity, commonly affected by swallow waters (h/λ < 1/25), where h is the water depth and λ is the wavelength. These converters are usually integrated in a breakwater, dam, fixed to a cliff or rest on the seabed. The distinctive characteristics for these converters are easy maintenance and installation. The drawbacks are that coastline waves have less energy than deep-water waves along with a potential coastline reshape.
- Nearshore: They are installed close to the shore, commonly affected by swallow or intermediate waters (1/25 < h/λ < 1/2). Their deployment and maintenance expenses are limited since they do not need mooring systems as they are usually fixed or rest on the seabed.
- Offshore: They are placed in deep waters (h/λ > 1/2), far from the shore. They are able to harvest energy from the most energetic places, but installation and maintenance can be much more expensive because of the required mooring systems (high depth), long underwater cabling, underwater substations and offshore maintenance.

#### 2.1.2. Dimensions of the Prime Mover and Orientation with Respect to the Wave

- Attenuators: The length of the device is of the same order of magnitude (or larger) than the wavelength; these devices are oriented in such a way that they are parallel to the incident wave.
- Terminators: Similar in dimensions to attenuators but placed perpendicular to the incident wave.
- Point Absorbers: Axisymmetric devices capable of harvesting waves from any direction, known as antenna effect, their dimensions are usually an order of magnitude lower than the wavelength.

#### 2.1.3. Working Principle

#### 2.2. Power Take-Off Systems

- Efficiency: The larger the number of intermediate steps, the greater are the mechanical and transformation losses that we obtain as a result of the PCC. This causes a reduction in the annual energy production (AEP), which in turn affects the levelized cost of the electricity (LCOE), increasing it.
- Reliability: The offshore equipment undergoes an accelerated degradation in comparison with the same equipment implemented within a ground installation due to the high salinity of the maritime environment where it is implemented. This fact makes it desirable to minimize the amount of equipment to monitor and maintain while the equipment is in operation.

#### 2.2.1. Air Turbines

#### 2.2.2. Hydraulic Systems

#### 2.2.3. Hydro Turbines

#### 2.2.4. Direct Mechanical Drive Systems

#### 2.2.5. Direct Electrical Drive Systems

## 3. Control Strategies

#### 3.1. Numerical Modeling

_{ex}(t) and control force f

_{pto}(t), respectively. ${Z}_{i}\left(\omega \right)$ is the intrinsic impedance in the frequency domain of the system as

_{PTO}as in (5) is referred to as optimal, reactive or complex conjugate control which is the solution to the so-called impedance-matching problem. Technically, reactive control refers only to the fact that the PTO reactance must cancel the inherent reactance. However, the PTO resistance and the hydrodynamic resistance must also be equal. Thus, complex-conjugate control is a more accurate description since it refers to the fact that the optimum PTO impedance equals the complex conjugate of the intrinsic impedance.

- The result is frequency dependent, implying a great optimization difficulty for irregular seas containing a mixture of frequencies.
- Future knowledge of the excitation force may be required. While this knowledge is straightforward for regular waves, it is more complex for irregular seas.
- Since force and velocity can have opposite signs, the PTO may need to supply power for some parts of the sinusoidal cycle.
- The optimal control takes no constrains into consideration; it is more than likely a real system will have velocity and displacement constrains.

#### 3.2. Damping Control

_{pto}> 0 is the PTO damping coefficient. This methodology does not require a prediction of the excitation force, thus making it a simple strategy to implement. In fact, it is the one we can usually find in the demonstrators or pre-commercial devices currently deployed around the world. Conventionally, it only requires knowing the instantaneous value of the PTO velocity, for which measurement instruments are usually available in the market.

_{pto}that maximizes the instantaneous power absorbed, can be easily calculated for regular waves. However, in practice, where the incident wave is irregular (defined by the wave spectrum), B

_{pto}is more difficult to calculate because of the changes in the spectral components of the incident wave which are not constant over time, so a real time feedback control for a time-varying damping value is required.

_{pto}. This particular strategy is still very common in recent WEC prototypes by technology developers (given the simplicity of implementation).

#### 3.2.1. Constant Damping Control

#### 3.2.2. Time-Varying Damping Control

#### 3.3. Reactive Control

_{pto}and K

_{pto}), taking into account constrains such as PTO power rating or displacement limits, adjusting the resistance of the PTO to avoid non-linear approaches [33]. Therefore, we will need to consider the generic approach to a PTO characterization as explained in Section 3.1.

#### 3.4. Latching/Unlatching

#### 3.5. Model Predictive Control

#### 3.6. Others

## 4. Conclusions and Further Research

_{pto}and K

_{pto}). In this article, we have classified different wave energy technologies based on different criteria commonly used in the literature. Optimal control strategy (complex conjugate control) based on solving the impedance matching problem is impractical for implementation, given the need for future knowledge of the excitation force in irregular waves and the absence of constrains in force and speed for the PTO. Hence, suboptimal control techniques are required, such as damping, reactive (misleading definition which should be revised to suboptimal reactive), latching, MPC and other novelty control ideas.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Oscillating water column working mode of operation [22].

**Figure 3.**Floating structure with multiples bodies mode of operation. Reprinted from [22].

**Figure 5.**Overtopping mode of operation [22].

**Figure 6.**Oscillating wave surge mode of operation [22].

**Figure 7.**Hierarchical control structure. Manipulated variable depends on the PTO: Bypass valves, swashplate angle, excitation current or conduction angle. Optimal force/velocity calculated as setpoint for the feedforward control.

**Figure 9.**Linear damping–WEC simulation for regular waves. In the upper graphic PTO force (blue) is compared with PTO velocity (red). The lower graphic represents ideal power output (blue) and power output considering electrical losses (red); negative values for power means the WEC is delivering energy to the grid.

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**MDPI and ACS Style**

Maria-Arenas, A.; Garrido, A.J.; Rusu, E.; Garrido, I.
Control Strategies Applied to Wave Energy Converters: State of the Art. *Energies* **2019**, *12*, 3115.
https://doi.org/10.3390/en12163115

**AMA Style**

Maria-Arenas A, Garrido AJ, Rusu E, Garrido I.
Control Strategies Applied to Wave Energy Converters: State of the Art. *Energies*. 2019; 12(16):3115.
https://doi.org/10.3390/en12163115

**Chicago/Turabian Style**

Maria-Arenas, Aleix, Aitor J. Garrido, Eugen Rusu, and Izaskun Garrido.
2019. "Control Strategies Applied to Wave Energy Converters: State of the Art" *Energies* 12, no. 16: 3115.
https://doi.org/10.3390/en12163115