# Maximum Power Control Algorithm for Power Take-Off System Based on Hydraulic System for Floating Wave Energy Converters

## Abstract

**:**

## 1. Introduction

^{2}[10]. In other words, even if the necessary support structure is ignored, the weight becomes excessive, making it impossible to implement a linear generator [11]. Direct drive linear generators have been proposed many times because of their advantages due to their ability to directly convert linear input motion into electrical energy. In this way, the energy conversion chain is greatly simplified using a limited number of components [9]. Instead, we used another system that was more prevalent in real-world applications. Other systems first store sea wave energy, pressurize the fluid through a piston pump, and then convert this energy into electricity using an alternator driven by a hydraulic turbine or volumetric expander [12]. In other words, linear generators are currently the subject of ongoing research [13,14], as direct drive solutions have sufficient advantages.

## 2. PTO System Configuration and Modeling

#### 2.1. FWEC Power Conversion Chain

#### 2.2. Hydraulic System Modeling

#### 2.3. Permanent Magnet Synchronous Generator (PMSG) Modeling

_{e}of PMSG, can be expressed as follows

_{e}using Equations (11) and (12) as follows:

_{e}can be calculated as follows, using the relationship between the instantaneous power generation and the angular velocity of the turbine:

#### 2.4. Power Converter Configuration and Modeling

## 3. Load Control Algorithm for Maximum Power Control of FWEC

#### 3.1. Speed Control Algorithm-Based P&O Algorithm

#### 3.2. Optimal Torque Control Algorithm

## 4. Results

#### 4.1. Simulation Results Obtained under Regular Wave Conditions

#### 4.2. Simulation Results Obtained under Irregular Wave Conditions

_{s}= 0.75 m and T

_{p}= 4.75 s. The pitch RAO for each period of the floating body and damping ratio of the floating body motion according to the PTO force in the irregular wave input conditions were calculated using CFD and are shown in Figure 16.

_{s}= 0.75 m, T

_{p}= 4.75 s). Figure 16b shows the damping ratio of the pitch motion of the floating body according to the load. According to the irregular wave input conditions, the pitch angle of the floating body can be calculated as the product of the wave spectrum and pitch PAO of the floating body. The damping of the pitch angle of the floating body due to the increase in F

_{pto}as the pressure of the hydraulic system increases can be calculated using the damping ratio shown in Figure 16b. In the simulation for the maximum power control algorithm under irregular wave conditions, the speed control algorithm based on the P&O algorithm and the optimal torque control algorithm were applied. The power generation performance and characteristics of the PTO system according to each algorithm were analyzed under irregular input conditions, and a suitable load control algorithm for a PTO system applying a hydraulic system was developed. Because actual sea wave energy is an irregular input condition, the performance of the proposed maximum power control algorithm for a hydraulic-based PTO system can be verified by analyzing the control algorithm under irregular wave input conditions.

_{s}= 0.75 m, T

_{p}= 4.75 s). Unlike the regular wave conditions, because the input energy changes rapidly, a large difference occurs in the load control value and the pressure change according to the initial reference rpm; accordingly, a large difference occurs in the PTO force. As shown in Figure 17c,d, because the pitch angle of the floating body decreases with increasing PTO force, the velocity of the floating body and the flow rate generated in the circuit also decrease. As the PTO force increases and the floating body motion decreases, there is a PTO force that can yield the maximum power, similar to the regular wave simulation. That is, because the actual input wave cannot be predicted, the speed control algorithm based on the P&O algorithm can control the maximum output power by appropriately adjusting the initial reference rpm and the rpm change rate according to the input wave energy.

_{s}= 0.75 m, T

_{p}= 4.75 s). If the initial reference rpm is high, the pressure cannot increase because a significant flow rate is used to drive the hydraulic motor. Therefore, owing to the low pressure, the PTO force required to absorb a large amount of input power cannot be achieved. However, when the initial reference rpm is low, the pressure in the circuit increases, and accordingly, the necessary PTO force can be obtained, which can further increase the absorbed power. As the pressure in the circuit increases, the electrical load can be increased, as shown in Figure 18c,d, and, accordingly, the output power can be increased.

_{s}= 0.75 m, T

_{p}= 4.75 s, using 150 rpm initially corresponded to 0.602 kWh, which yielded the highest power generation. At ≤150 rpm initially, the pressure in the circuit increased further, and more power could be obtained. However, at ≤80 rpm, the power supply of the power converter did not operate; therefore, it was not considered as a control reference value.

_{s}= 0.75 m, T

_{p}= 4.75 s). Similar to the speed control algorithm based on the P&O algorithm, because the input energy changes rapidly, there are large differences in the load control value and pressure variability with the torque coefficient; accordingly, the PTO force also varies considerably. As shown in Figure 20c,d, because the movement of the floating body decreases according to the PTO force, the speed of the floating body and the flow rate generated in the circuit also decrease. These tendencies are the same as those observed using the speed control algorithm. The higher the torque coefficient, the more the load is applied at the same rpm; thus, the pressure increases further.

_{s}= 0.75 m, T

_{p}= 4.75 s). If the torque coefficient is low, the initial rpm is high, and accordingly, the flow rate for driving the hydraulic motor is high. That is, the pressure in the circuit is low, making the PTO force far from the optimal value for absorbing the input energy. However, as the torque coefficient increases, the pressure in the circuit increases, and accordingly, the PTO force that can further increase the absorbed power can be obtained. As the pressure in the circuit increases, the electrical load can be increased, as shown in Figure 21c,d, and accordingly, the amount of output power can be increased. However, as shown in Figure 21, when the torque coefficient increases to a certain value (k = 0.34), the output power generation decreases because the rpm decreases as the load increases. That is, as the torque coefficient increases and the pressure in the circuit increases, the movement of the floating body decreases. Therefore, the maximum power generation can only be obtained by selecting an appropriate torque coefficient according to the input energy and environmental characteristics.

_{s}= 0.75 m, T

_{p}= 4.75 s, the torque coefficient for obtaining the maximum power generation of the optimal torque control algorithm was 0.24, and 0.911 kWh of power could be generated.

## 5. Comparison of Real Sea Test and Simulation

#### 5.1. Comparison of P&O Algorithm-Based Speed Control Algorithm

#### 5.2. Comparison of Torque Control Algorithm

## 6. Conclusions

## Funding

## Conflicts of Interest

## Abbreviations

${\omega}_{pitch}$ | Pitch angular velocity of floating body |

${\theta}_{pitch}$ | Pitch angle of the floating body |

${Q}_{pump}$ | Rotary vane pump flow |

${D}_{pump}$ | Rotary vane pump displacement |

${F}_{PTO}$ | FTO force on floating body |

${F}_{opt}$ | Force of the FTO to obtain the maximum power generation |

${P}_{H}$ | High pressure in hydraulic piping |

${P}_{L}$ | Low pressure in hydraulic piping |

${Q}_{check}$ | Flow of check valve |

${Q}_{accu}$ | Accumulator flow |

${Q}_{motor}$ | Hydraulic motor flow |

${V}_{accu}$ | Accumulator volume |

${P}_{H\_pre}$ | Initial high pressure of hydraulic pipe |

${V}_{accu\_pre}$ | Accumulator initial volume |

$\gamma $ | Accumulator specific weight |

${D}_{motor}$ | Hydraulic motor displacement |

${T}_{m}$ | Mechanical torque |

${T}_{e}$ | Electrical torque |

${\omega}_{motor}$ | Hydraulic motor angular speed |

${L}_{dq}$ | D-Q axis inductance of generator |

${\omega}_{e}$ | Electrical angular frequency |

${i}_{dq}$ | D-Q axis generator current |

${V}_{dq}$ | D-Q axis generator voltage |

${\Psi}_{pm}$ | Generator flux linkage |

${R}_{s}$ | Generator armature resistance |

${P}_{e}$ | Electrical power |

${N}_{p}$ | Number of generator poles |

$D$ | DC/DC Converter duty ratio |

${T}_{sp}$ | DC/DC Converter controlled sampling |

${\omega}_{wave}$ | Period of input wave energy |

${\omega}_{reson}$ | Resonance period of input wave energy |

${B}_{pto}$ | Power take-off damping factor |

${P}_{abs}$ | Input absorption power |

${P}_{m}$ | Mechanical power |

${k}_{opt}$ | Torque damping factor |

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**Figure 1.**Basic hydraulic transmission system model: (

**a**) direct hydraulic motor system and (

**b**) rectifying valve accumulator motor.

**Figure 7.**(

**a**) Optimal PTO damping coefficient for each period. (

**b**) Output power generation performance according to the optimal PTO damping coefficient for each period and resonance period PTO damping coefficient.

**Figure 8.**(

**a**) CFD analysis plot for input conditions [37]. (

**b**) Simulation block diagram for comparison of load control algorithm performance.

**Figure 10.**(

**a**) Floating body motion, (

**b**) PTO force, (

**c**) floating body speed, and (

**d**) generated flow rate according to the initial reference rpm of the speed control algorithm under regular wave conditions (legend indicates initial rpm).

**Figure 11.**(

**a**) Pressure in the circuit, (

**b**) hydraulic motor rpm, (

**c**) mechanical and electrical torques, and (

**d**) load current according to the initial reference rpm of the speed control algorithm under regular wave conditions (legend indicates initial rpm).

**Figure 12.**Comparison of power generation results according to the initial reference rpm of the speed control algorithm under regular wave conditions (legend indicates initial rpm).

**Figure 13.**(

**a**) Float pitch angle, (

**b**) F

_{pto}, (

**c**) float velocity, and (

**d**) generated flow rate according to the torque coefficient of the optimal torque control algorithm under regular wave conditions (legends indicate torque coefficients).

**Figure 14.**(

**a**) Circuit pressure, (

**b**) hydraulic motor rpm, (

**c**) mechanical and electrical torques, and (

**d**) load current according to the torque coefficient of the optimal torque control algorithm under regular wave conditions (legends indicate torque coefficients).

**Figure 15.**Power generation comparison according to torque coefficient of optimal torque control algorithm under regular wave conditions (legends indicate torque coefficients).

**Figure 16.**(

**a**) Wave spectrum and pitch RAO and (

**b**) floating body pitch motion damping ratio according to the PTO force under irregular wave input conditions (H

_{s}= 0.75 m, T

_{p}= 4.75 s).

**Figure 17.**(

**a**) Float pitch angle, (

**b**) Fpto, (

**c**) float velocity, and (

**d**) generated flow rate according to the initial rpm of the speed control algorithm under irregular wave conditions (H

_{s}= 0.75 m, T

_{p}= 4.75 s) (legend indicates initial rpm).

**Figure 18.**(

**a**) Pressure in the circuit, (

**b**) hydraulic motor rpm, (

**c**) mechanical and electrical torque, and (

**d**) load current according to the initial rpm of the speed control algorithm under irregular wave conditions (H

_{s}= 0.75 m, T

_{p}= 4.75 s) (legend indicates initial rpm).

**Figure 19.**Comparison of the amount of power generated according to the initial rpm of the speed control algorithm under irregular wave conditions (H

_{s}= 0.75 m, T

_{p}= 4.75 s) (legend indicates initial rpm).

**Figure 20.**(

**a**) Floating body pitch angle, (

**b**) PTO force, (

**c**) floating body velocity, and (

**d**) occurrence flow rate according to torque coefficient of optimal torque control algorithm flux under irregular wave conditions (H

_{s}= 0.75 m, T

_{p}= 4.75 s) (legends indicate torque coefficients).

**Figure 21.**(

**a**) Pressure in the circuit, (

**b**) hydraulic motor rpm, (

**c**) mechanical and electrical torque, and (

**d**) electrical load current according to the torque coefficient of the optimal torque control algorithm under irregular wave conditions (H

_{s}= 0.75 m, T

_{p}= 4.75 s) (legends indicate torque coefficients).

**Figure 22.**The result of comparing the generation amounts according to the torque coefficient of the optimal torque control algorithm under irregular wave conditions (H

_{s}= 0.75 m, T

_{p}= 4.75 s) (legends indicate torque coefficients).

**Figure 23.**Comparison of output power generation performance according to torque coefficient of optimal torque control algorithm (legends indicate torque coefficients).

**Figure 24.**Input and output power generation and PTO system efficiency according to (

**a**) speed control algorithm and (

**b**) optimal torque control algorithm under the same irregular wave input conditions (H

_{s}= 0.75 m, T

_{p}= 4.75 s).

**Figure 25.**Performance of (

**a**) P&O algorithm-based speed control algorithm and (

**b**) optimal torque control algorithm according to input condition change.

**Figure 26.**Actual FWEC sea test photos: (

**a**) rotors, (

**b**) PTO system (including the hydraulic system, generator, and PCS), (

**c**) actual sea experiment, and (

**d**) measurement and control system.

**Figure 27.**Simulator input data results obtained using pitch angle data of a floating body in an actual sea test.

**Figure 28.**Comparison of PTO system characteristics according to real sea test results and P&O algorithm-based speed control algorithm of the simulator. (

**a**) rotation speed; (

**b**) mechanical pressure; (

**c**) flow rate; (

**d**) electrical load current.

**Figure 29.**Comparison of the amounts of power generated in the actual sea test and with the speed control algorithm based on the P&O algorithm of the simulator.

**Figure 30.**Comparison of the PTO system characteristics according to the actual sea test and optimal torque control simulation. (

**a**) rotation speed; (

**b**) mechanical pressure; (

**c**) flow rate; (

**d**) electrical load current.

**Table 1.**Input and output power of the PTO system and efficiency of the PTO system according to the initial reference rpm of the speed control algorithm based on the P&O algorithm.

Case (rpm) | Absorbed Power (kWh) | Output Power (kWh) | Efficiency (%) |
---|---|---|---|

300 | 5.45 | 5.09 | 92.99 |

350 | 5.33 | 5.22 | 97.94 |

400 | 5.45 | 5.35 | 98.12 |

500 | 4.11 | 3.75 | 91.22 |

**Table 2.**Input and output power according to the torque coefficient of the optimal torque control algorithm and the efficiency of the PTO system.

Case (k) | Absorbed Power [kWh] | Output Power (kWh) | Efficiency (%) |
---|---|---|---|

0.4 | 4.74 | 4.53 | 95.5 |

0.8 | 5.38 | 5.14 | 95.5 |

1.6 | 5.59 | 5.35 | 95.7 |

2.4 | 5.51 | 5.34 | 96.9 |

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## Share and Cite

**MDPI and ACS Style**

Roh, C.
Maximum Power Control Algorithm for Power Take-Off System Based on Hydraulic System for Floating Wave Energy Converters. *J. Mar. Sci. Eng.* **2022**, *10*, 603.
https://doi.org/10.3390/jmse10050603

**AMA Style**

Roh C.
Maximum Power Control Algorithm for Power Take-Off System Based on Hydraulic System for Floating Wave Energy Converters. *Journal of Marine Science and Engineering*. 2022; 10(5):603.
https://doi.org/10.3390/jmse10050603

**Chicago/Turabian Style**

Roh, Chan.
2022. "Maximum Power Control Algorithm for Power Take-Off System Based on Hydraulic System for Floating Wave Energy Converters" *Journal of Marine Science and Engineering* 10, no. 5: 603.
https://doi.org/10.3390/jmse10050603