# A Novel Multiport Hybrid Wave Energy System for Grid-Connected and Off-Grid Applications

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## Abstract

**:**

## 1. Introduction

## 2. System Configuration and Operation Principle

#### 2.1. Conventional Hybrid Wave Energy System

#### 2.2. Multiport Hybrid Wave Energy System

#### 2.3. Modulation Principle of Nine-Switch Converter

## 3. Modeling and Control Strategy

#### 3.1. dq Model of a PMLG

#### 3.2. Power Grid Model

#### 3.3. Energy Storage Model

#### 3.3.1. Supercapacitor Model

#### 3.3.2. Battery Model

#### 3.4. Control Strategy

_{q}is provided by Equation (11), where $\beta $ is the hydrodynamic damping coefficient of the float [7]. The d-axis current is set to zero to reduce changes in the reactive power, and the independent control of the dq-axis current is realized through feedforward decoupling.

## 4. Simulation Analysis

## 5. Experimental Verification

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**HESS model. (

**a**) First-order RC circuit model of a supercapacitor; (

**b**) simple equivalent model of a battery.

**Figure 10.**Simulation of PMLG side: (

**a**) back-EMF; (

**b**) three-phase current; (

**c**) active power; (

**d**) reactive power.

**Figure 11.**Simulation of grid-connected multiport HWES: (

**a**) three-phase voltage; (

**b**) three-phase current; (

**c**) dc bus voltage; (

**d**) modulation.

**Figure 12.**Simulation of an off-grid multiport HWES: (

**a**) power of load and average power of the PMLG; (

**b**) power of the HESS; (

**c**) SOC of the HESS; (

**d**) modulation.

**Figure 14.**Off-grid HWES experimental results: (

**a**) velocity of translator; (

**b**) back-EMF; (

**c**) power of the load and PMLG; (

**d**) power of the HESS; (

**e**) dc bus voltage; (

**f**) modulation.

State | SA1 | SA2 | SA3 | V_{A} | V_{U} |
---|---|---|---|---|---|

1 | ON | OFF | OFF | U_{dc} | U_{dc} |

2 | ON | OFF | ON | U_{dc} | 0 |

3 | OFF | ON | ON | 0 | 0 |

PMLG Side |
---|

PM linkage: ${\psi}_{f}=5\text{}\mathrm{Wb}$, Pole pitch: $\lambda =0.2\text{}\mathrm{m}$, Stator resistance: ${R}_{S}=1\text{}\mathsf{\Omega}$, Stator inductance: $L=0.08\text{}\mathrm{H}$, Diffraction force: peak = 600 N, frequency = 5 Hz (during 0–5 s); peak = 1000 N, frequency = 3 Hz (during 5–10 s). |

Grid side |

Amplitude of phase-to-ground voltage: ${V}_{\mathrm{amp}}=220\text{}\mathrm{V}$, Frequency of voltage: $f=50\text{}\mathrm{Hz}$, Grid filter: ${R}_{f}=0.1\text{}\mathsf{\Omega}$, ${L}_{f}=10\text{}\mathrm{mH}$. |

HESS and load side |

Battery voltage: 250 V, Battery capacitance: 100 Ah, Supercapacitor voltage: 200 V, Supercapacitor capacitance: 80 F, Filter inductance: 5 mH, Load power: 1000 W. |

Nine-switch converter |

DC bus voltage: ${U}_{dc}=1000\text{}\mathrm{V}$, DC-link capacitance: 1 mF, Power device: IGBT/Diode. |

Parameter | Value | Parameter | Value |
---|---|---|---|

dc bus voltage | 100 V | Battery rated voltage | 25 V |

Stator resistance | 3.8 Ω | Battery capacitance | 65 Ah |

Permanent magnetic linkage | 0.265 Wb | Supercapacitor rated voltage | 25 V |

Polar distance | 0.016 m | Supercapacitor capacitance | 80 F |

d-axis/q-axis inductance | 0.02 H | Load power | 32 W |

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## Share and Cite

**MDPI and ACS Style**

Yu, W.; Ma, R.; Xu, D.; Huang, L.; Wang, S.
A Novel Multiport Hybrid Wave Energy System for Grid-Connected and Off-Grid Applications. *Sustainability* **2023**, *15*, 2175.
https://doi.org/10.3390/su15032175

**AMA Style**

Yu W, Ma R, Xu D, Huang L, Wang S.
A Novel Multiport Hybrid Wave Energy System for Grid-Connected and Off-Grid Applications. *Sustainability*. 2023; 15(3):2175.
https://doi.org/10.3390/su15032175

**Chicago/Turabian Style**

Yu, Wei, Ruiyang Ma, Darui Xu, Lei Huang, and Shixiang Wang.
2023. "A Novel Multiport Hybrid Wave Energy System for Grid-Connected and Off-Grid Applications" *Sustainability* 15, no. 3: 2175.
https://doi.org/10.3390/su15032175