# Designing and Testing Composite Energy Storage Systems for Regulating the Outputs of Linear Wave Energy Converters

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## Abstract

**:**

## 1. Introduction

## 2. Proposed System

## 3. Controls of Linear Wave Energy Converters (LWECs)

_{coil}could be exploited as boost inductor, for the purpose of achieving lower power loss and avoiding an additional component. The free boost inductor or the generator coil is connected in front of the H-bridge. IGBTs and fast recovery diodes could be adopted for the H-bridges, but the switching frequency is supposed to be carefully controlled below the generator coil’s self-resonance frequency.

_{on}, the IGBT switches are on and the inductor current increases from an initial value to a peak value ${i}_{p}$, replacing the energy given up in the last cycle, energy being drawn from the input. When the IGBT switches are off, the diode conducts for the rest of the cycle t

_{off}, and ${i}_{L}$ falls to a lower value than ${i}_{p}$. This lower value is the initial value of the next cycle, but never becomes zero unless V

_{in}reaches zero. The inductor’s energy is transferred to the output during t

_{off}.

## 4. A Composite Energy Storage System

#### 4.1. Energy Storage Components

#### 4.2. Interface Circuits

_{1}, and extracts excessive power from the DC link. When S

_{1}is on, current goes through S

_{1}, the inductor L and the electrical energy storage device are charged by the electrical power from the DC link. When S

_{1}is off, the inductor L turns to discharge mode, current goes through D

_{2}, the electrical energy storage device is maintaining charge mode. In the boost mode, the terminal voltage of energy storage device is stepped up and release energy to DC link. When S

_{2}is on, the energy storage device charges up inductor L. When S

_{2}is off, the energy storage device and inductor L works in conjunction and both discharge energies to the DC link and maintain the DC link voltage.

#### 4.3. Control of Super Capacitors and Batteries

_{fd}is taken from the DC link. An error signal is obtained by subtracting u

_{fd}from a designed value of DC link voltage u

_{ref}, and then fed to a proportional/integral stages (PI). A current reference i

_{ref}is used to compare with i

_{L}the instant inductor currents of interface circuits shown in Figure 7, and then an error signal is generated and adjusted for generating pulse width modulation (PWM) signals to control the inductor currents.

#### 4.4. Capacity of Energy Storage Component

_{bat}the required capacity of batteries in A·h, where V

_{max}is the maximum terminal voltage and V

_{min}is the related minimum terminal voltage:

_{cap}the required capacitance of super capacitors:

## 5. Hardware Implementation

## 6. Results and Discussion

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

${P}_{Li}$ | Power output of Li-ion battery |

${P}_{sc}$ | Power output of super-capacitor |

${P}_{W}$ | Power output of LWEC |

${P}_{E}$ | Total power output of energy storage |

${P}_{G}$ | Steady power output |

${P}_{L}$ | Load |

$M$ | Mass of moving parts of LWEC |

${F}_{e}$ | Wave excitation force |

$U$ | Device translational velocity |

${K}_{e}$ | Mechanical spring stiffness |

${R}_{e}$ | Mechanical resistance |

${K}_{g}$ | Generator spring stiffness |

${R}_{g}$ | Generator resistance |

${u}_{i}$ | Input voltage of DC-DC converter |

$L$ | Inductance of DC-DC converter |

${i}_{L}$ | Inductance current of DC-DC converter |

${i}_{ref}$ | Current reference of DC-DC converter |

${u}_{fd}$ | Feedback voltage of DC-DC converter |

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**Figure 1.**Electromotive force (EMF) waveform of a tubular linear wave energy converter (LWEC) (1 phase).

**Figure 3.**System model and loading of LWEC. (

**a**) Resistive loading; (

**b**) Capacitive-resistive loading.

**Figure 4.**Current paths of AC/DC boost H-bridge (1 phase): (

**a**) Z2 and Z4 switched on; (

**b**) Z2 and Z4 switched off; (

**c**) Z1 and Z3 switched on; and (

**d**) Z1 and Z3 switched off.

**Figure 5.**Waveforms of boost converter in continuous mode: (

**a**) Voltage and inductor current waveforms; (

**b**) Inductor current; (

**c**) Switch current; and (

**d**) Diode current.

**Figure 7.**Current paths of the interface circuit of super capacitors and batteries. (

**a**) Buck mode, S

_{1}is on; (

**b**) Buck mode, D

_{2}is on; (

**c**) Boost mode, S

_{2}is on; and (

**d**) Boost mode, D

_{1}is on.

**Figure 16.**Experimental results of DC link voltage and the emulated electrical outputs for LWEC driven with different wave amplitudes.

Parameters | Values |
---|---|

DC supply | 500 V/10 A |

DC bus filtering capacitor | 2200 μF |

IGBT used for H-bridge | IRG4BC20U |

Recovery diode used for H-bridge | HFA08TB60 |

Low-pass LC filter | 1.4 mH/20 μF |

Generator coil’s resistance/inductance | 20 Ω/0.4 H |

Li-batteries voltage/capacity | 51.2 V/6 A·h |

Super capacitors | 52 F/15 V (3 in series) |

Buck/boost filtering inductor | 5 mH |

Load | 33.3 Ω |

Topologies | Average DC Link Voltage (V) | Average Output Power (W) | DC Link Voltage Ripples (V) |
---|---|---|---|

Rectifier diodes(without battery-super capacitor system) | 192 | 88 | 120 |

Boost AC/DC converter(without battery-super capacitor system) | 315 | 236 | 133 |

Boost AC/DC converter(with battery-super capacitor system) | 315 | 236 | 7 |

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**MDPI and ACS Style**

Nie, Z.; Xiao, X.; Hiralal, P.; Huang, X.; McMahon, R.; Zhang, M.; Yuan, W.
Designing and Testing Composite Energy Storage Systems for Regulating the Outputs of Linear Wave Energy Converters. *Energies* **2017**, *10*, 114.
https://doi.org/10.3390/en10010114

**AMA Style**

Nie Z, Xiao X, Hiralal P, Huang X, McMahon R, Zhang M, Yuan W.
Designing and Testing Composite Energy Storage Systems for Regulating the Outputs of Linear Wave Energy Converters. *Energies*. 2017; 10(1):114.
https://doi.org/10.3390/en10010114

**Chicago/Turabian Style**

Nie, Zanxiang, Xi Xiao, Pritesh Hiralal, Xuanrui Huang, Richard McMahon, Min Zhang, and Weijia Yuan.
2017. "Designing and Testing Composite Energy Storage Systems for Regulating the Outputs of Linear Wave Energy Converters" *Energies* 10, no. 1: 114.
https://doi.org/10.3390/en10010114