# An Iterative Refining Approach to Design the Control of Wave Energy Converters with Numerical Modeling and Scaled HIL Testing

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. The Proposed Procedure

## 3. HIL Test Bench

^{2}by adding a flywheel.

#### 3.1. Wave Energy Converter Emulator

#### 3.2. Electric Generator

_{r}), the mechanical torque (T

_{m}) and electrical power (P

_{e}), while its outputs are a torque or speed set-point, depending on the implemented control.

#### 3.3. Programming the PLC

_{e}

^{*}) that is applied to the generator to get the required turbine speed. This reference torque is sent to the back-to-back converter where the current control loops follow this set-point as well as control the voltage on the DC link and the injected grid power.

## 4. Simulink Models and Adaptations for HIL Testing Framework

#### 4.1. Wave-to-Wire Model

_{p}, the significant wave height H

_{s}, and the turbine head loss. Please note that to have an accurate W2W model, it is reasonable that the OWC block has a fully coupled approach, where the primary PTO pneumatic output power is influenced by the following elements in the whole conversion system.

_{r}of the generator is an input of the air turbine model, and the load torque T

_{e}due to the electric load of the generator (B2B converter and electric grid) is an input of the drive train model. When the pneumatic power of the air flow generated by the OWC is higher than the turbine load, the turbine rotates applying a torque T

_{m}to the generator (drive train), which produces a sinusoidal electricity at a frequency f

_{gen}proportional to the rotational speed ω

_{r}, with a generated power P

_{gen}. The B2B converter is the interface with the electrical grid. It converts the AC input at f

_{gen}to an AC output synchronized with the voltage at 50 Hz of the grid. P

_{el}is the power at the output of the whole WEC.

_{r}is also the input of the controller, who generates a control signal T

_{e}

^{*}, giving information to the B2B converter on the load torque (or electrical torque) T

_{e}needed to have the desired rotational speed.

#### 4.2. Air Turbines Modeling

_{x}air speed at the turbine inlet; ω

_{r}rotational speed; $K=\rho bln/2$ characteristic constant; $\phi ={V}_{x}/r{\omega}_{r}$ flow coefficient; Δp pressure drop across the turbine; Q flow rate; T

_{m}mechanical torque; T

_{e}electrical torque; J moment of inertia; P

_{rot}mechanical power at the shaft; P

_{pneu}pneumatic power at the inlet; C

_{a}input coefficient; C

_{t}torque coefficient; η efficiency, the equations for the turbine are given by [37]:

_{t}and C

_{a}are evaluated by mean of LUTs.

#### 4.3. Drive Train Modeling

_{friction}is the resistive frictional torque.

#### 4.4. Control Laws

_{opt}function shown in Figure 10; (ii) a torque control where the current rotor speed is compared to a reference value to maintain constant the speed. Typically, the former is an instantaneous control that can be effectively applied to systems with low inertia. The latter is a sea-state control that needs an offline calculation of the optimum reference speed for each sea state and is more suitable for high inertia systems. In our system, the inertia has an intermediate value, and then we cannot say in advance what is better [38]. Thus, we chose to test both to find the optimum (the one that gives the highest power at the output given the same input). Issues related to peak-to-average power ratio and the need for overrating the power converters are not considered in this work but are well discussed in Refs. [20,39].

#### 4.5. Scaling, Compensations, and Adaptations

_{n,turbine}to the one of the test bench T

_{n,testbench}. Consequently, it can be calculated by the relation:

_{n}in Figure 11) or the torque reference, with the electric signal that represents them at the dSPACE and the PLC interfaces. V

_{FS}in Figure 11 is the full-scale range of the rotational speed signal.

#### 4.6. Simulink Models of the Electric PTO

_{e}

^{*}is not strictly necessary, because this signal is really generated by the PLC. We put this block only to easily export the signal data in MATLAB.

_{sp}is the constant set-point of the rotor speed, ω

_{r}(t) is the actual rotor speed, K

_{p}and K

_{i}are the proportional and the integral coefficients, respectively.

## 5. Experimental Results

_{s}= 1.6 m. As shown, the match between measurements and simulations is very good.

_{adjust}= 1 in the model of Figure 13), the rotational speed is always higher than the optimum one (e.g., as shown in Figure 16 with H

_{s}= 1 m). The rotor speed cannot vary rapidly as the optimum one due to the inertia (in this case, at the real scale, it is 0.1 kg⋅m

^{2}).

_{adjust}> 1.

_{adjust}, the mean power measured during the tests can be taken as reference.

_{pneu}> be the mean pneumatic power at the turbine inlet, <P

_{mech}> the mean power at the shaft of the turbine and <P

_{el}> the mean power at the output of the electric generator, then these powers change with K

_{adjust}. For each sea state, an optimum value of K

_{adjust}can be found to obtain the maximum efficiency of the whole converter. For example, considering the conditions of Figure 16, the <P

_{el}> can be increased from 3.2 kW to 4 kW changing K

_{adjust}from 1 to 2.8 as shown in Figure 17. This value results the one that gives the highest mean generator power when H

_{s}= 1 m, then optimizing the applied control law only for a specific sea-state.

_{adjust}can be changed to maximize the <P

_{el}>. At each wave height, the optimum K

_{adjust}is different. Then, the control law is dependent on the incident wave.

## 6. Conclusions

- The pneumatic power (as the electrical and mechanical ones) significantly depends on the turbine working conditions (a fully coupled modeling approach is important for this type of device).
- The MPPT control is more effective in following the optimum rotational speed than a torque control where the actual rotor speed is kept as much as possible equal to a set-point.
- The control law depends on the incident wave. Then, we can say that to improve the efficiency of the system, the OWC should be equipped with a system that measures the incident wave.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Flowchart of the procedure to set and optimize the control of a WEC at the early development stages.

**Figure 6.**Simulink model with rotor and wind speeds as inputs, and power and torque at the shaft as outputs.

**Figure 10.**Power characteristic of the Impulse turbine in Table 1. The air speed varies from 4 m/s to 12 m/s with a step of 1 m/s.

**Figure 11.**Scheme of the methodology for scaling, compensations, and adaptations that must be applied to the original model for the two-chambers OWC here considered.

**Figure 16.**Simulated (black traces) and measured (red traces) variables: (

**a**) pneumatic power; (

**b**) rotor speed; (

**c**) mechanical torque; (

**d**) electrical torque; (

**e**) mechanical power; (

**f**) electrical power. Sea state: H

_{s}= 1.6 m, T

_{s}= 5.1 s. Turbine: Impulse. Control law: MPPT.

**Figure 17.**Optimum and simulated rotor speeds with H

_{s}= 1 m, T

_{p}= 4.3 s using the model of Figure 13.

Turbine | |||
---|---|---|---|

Parameter | Wells | Dennis-Auld | Impulse |

r [m] | 0.25 | 0.25 | 0.25 |

l [m] | 0.16 | 0.16 | 0.15 |

b [m] | 0.055 | 0.1 | 0.1 |

n | 10 | 40 | 20 |

A [m^{2}] | 0.196 | 0.196 | 0.196 |

J [kg⋅m^{2}] | 0.2 | 0.5 | 0.1 |

Test ID | Description |
---|---|

#1 | MPPT control law (torque vs. rotational speed) |

#2 | Adjustment of the control law adopted for #1 tests to get the maximum output power at the grid |

#3 | Constant speed control with on-off law |

#4 | Constant speed control with PI |

**Table 3.**Sea states applied to each control law of the test plan in Table 2.

Sea state ID (Regular Waves) | ||||||
---|---|---|---|---|---|---|

#1 | #2 | #3 | #4 | #5 | #6 | |

H_{s} [m] | 0.6 | 0.8 | 1.0 | 1.2 | 1.4 | 1.6 |

T_{P} [s] | 3.1 | 3.6 | 4.0 | 4.4 | 4.7 | 5.1 |

**Table 4.**Powers and efficiencies obtained considering an Impulse turbine, with MPPT control; K

_{adjust}= 1.

Average Power [W] | Efficiency [%] | |||||
---|---|---|---|---|---|---|

H_{s} [m] | Pneumatic | Mechanical | Electrical | Turbine | Generator | Total |

0.6 | 1941 | 1364 | 999 | 70.3 | 73.2 | 51.5 |

0.8 | 3883 | 2655 | 2065 | 68.4 | 77.8 | 53.2 |

1 | 5894 | 4326 | 3256 | 73.4 | 75.3 | 55.2 |

1.2 | 7799 | 5258 | 4295 | 67.4 | 81.7 | 55.1 |

1.4 | 9658 | 6503 | 5385 | 67.3 | 82.8 | 55.8 |

1.6 | 11,820 | 7953 | 6663 | 67.3 | 83.8 | 56.4 |

**Table 5.**Powers and efficiencies obtained considering an Impulse turbine, with constant speed control (PI regulator).

Average Power [W] | Efficiency [%] | |||||
---|---|---|---|---|---|---|

H_{s} [m] | Pneumatic | Mechanical | Electrical | Turbine | Generator | Total |

0.6 | 1974 | 1526 | 824 | 77.3 | 54.0 | 41.7 |

0.8 | 3999 | 3075 | 1845 | 76.9 | 60.0 | 46.1 |

1 | 3975 | 2960 | 1774 | 74.5 | 59.9 | 44.6 |

1.2 | 8053 | 6135 | 3681 | 76.2 | 60.0 | 45.7 |

1.4 | 10,168 | 7777 | 4666 | 76.5 | 60.0 | 45.9 |

1.6 | 12,265 | 9229 | 5537 | 75.2 | 60.0 | 45.1 |

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## Share and Cite

**MDPI and ACS Style**

Delmonte, N.; Robles, E.; Cova, P.; Giuliani, F.; Faÿ, F.X.; Lopez, J.; Ruol, P.; Martinelli, L.
An Iterative Refining Approach to Design the Control of Wave Energy Converters with Numerical Modeling and Scaled HIL Testing. *Energies* **2020**, *13*, 2508.
https://doi.org/10.3390/en13102508

**AMA Style**

Delmonte N, Robles E, Cova P, Giuliani F, Faÿ FX, Lopez J, Ruol P, Martinelli L.
An Iterative Refining Approach to Design the Control of Wave Energy Converters with Numerical Modeling and Scaled HIL Testing. *Energies*. 2020; 13(10):2508.
https://doi.org/10.3390/en13102508

**Chicago/Turabian Style**

Delmonte, Nicola, Eider Robles, Paolo Cova, Francesco Giuliani, François Xavier Faÿ, Joseba Lopez, Piero Ruol, and Luca Martinelli.
2020. "An Iterative Refining Approach to Design the Control of Wave Energy Converters with Numerical Modeling and Scaled HIL Testing" *Energies* 13, no. 10: 2508.
https://doi.org/10.3390/en13102508