# Design and analysis of bidirectional driven float-type wave power generation system

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## Abstract

The dynamic model for a bidirectional driven float-type wave power generation system design is presented in this paper. The gravity, buoyancy and drag force acting on the wave energy converter (WEC) are all analyzed. The analytical expression of the torque applied on the rotor is given based on a linear model of the switched reluctance generator (SRG). The SRG usually rotates with low velocity in the WEC system. In this situation, current chopping control (CCC) is adopted with fixed turn-on angle and turn-off angle control mode to have a quick response for SRG. Further, in order to make the float keep in phase with the wave so as to improve the power generation efficiency, the reference current is dynamically adjusted according to the wave motion at all working stages. Then maximum power point tracking (MPPT) of system is achieved. A simulation model is developed in MATLAB for the bidirectional driven float-type wave power generation system with real wave statistical characteristics taken into account. Simulation results show that the WEC can output desired torque periodically with high efficiency and good adaptability. Therefore, the feasibility of applying a SRG in a WEC is also verified.

### Keywords

Wave energy converter Force analysis Current chopping control Dynamical reference current setting Maximum power point tracking## 1 Introduction

As energy shortage and environment pollution are growing more serious, most governments in the world are aware of the strategic significance of renewable energy exploitation and utilization [1, 2, 3]. It has been proved that wave energy is a promising renewable energy resource [4]. Thus, more and more attention has been paid to wave energy generation with considerable progress achieved.

Ocean wave energy has huge potential, and it is more stable and predictable than wind and solar power [5]. Ocean energy is stored in the ocean in various forms, such as tides, temperature gradient, waves and ocean currents, etc. From the 1970s, many wave energy converters (WECs) have been invented [6]. With wave energy converters, the wave energy can be extracted into different forms of energy to be stored or used [7]. However, only a small amount of WEC equipment went through rigorous testing on the open sea [8]. Among these converters, Duck, French Flexible Bag, Clam, Archimedes Wave Swing (AWS), and Oscillating Water Column (OWC) technologies are more popular than other wave energy conversion technologies. At the same time, different control strategies have been implemented for the corresponding WECs [5, 8, 9, 10, 11, 12, 13, 14]. At present, the OWC system is possibly considered to be the most reliable type of WEC because of its good structural strength [15]. However, it still has not been widely utilized for wave energy conversion due to its low efficiency and other economic reasons. In 2003, Hadano proposed a float-type wave power generation system for off-shore use with many advantages, such as high efficiency, easy maintenance, and good mobility and adaptability [4]. The structure of this WEC is smart, in which the float moving in the vertical direction is used to capture the wave energy. The captured energy is then transmitted to the generator with rotational motion. It is noted that the proposed float-type wave power generation system can extract energy only when the sea wave is rising, or when it is falling, which gives low efficiency. Therefore, it deserves more attention and further development [16].

Generator selection is crucial to the overall operation of the WEC system. The permanent magnet synchronous motor (PMSM) has been applied in wave power generation with satisfactory performance [17, 18, 19]. Nevertheless, the PMSM rotor is made of permanent magnetic material, which is relatively expensive and easily damaged. Since the speed of the wave energy converter is variable, a back-to-back full converter is essential in such systems, so that the control system structure becomes complicated. In contrast with PMSM, the structure of the switched reluctance generator (SRG) is rather simple, with no windings and permanent magnets on the rotor. Further, the SRG can generate DC power directly with strong fault tolerance [20]. Therefore, the SRG is suitable to work in the harsh sea environment.

The SRG can be controlled through various parameters, such as the turn-on angle, the turn-off angle, the maximum allowable current, as well as the supply voltage. Consequently, several methods including angle position control (APC), current chopping control (CCC), chopped voltage control, as well as intelligent algorithms can be used to control the SRG [21, 22, 23]. Nowadays, the SRG has been applied to wind power generation to reduce the system cost [24]. Different control methods of SRGs for variable-speed wind energy applications have been investigated in [25, 26, 27]. These application examples have suggested the possibility of using SRG in wave power generation systems. Of course, specific features of a wave energy converter should be fully considered in attempting this integration.

In this paper, a bidirectional driven float-type wave power generation system with a SRG is proposed. Two ratchet wheels are equipped, and the driving pulley 6 can rotate the SRG rotor in one direction. With this design, the modified WEC can always convert wave energy to mechanical energy, whether the float rises or falls. Then the captured energy is transformed into electrical energy. From the mechanical perspective this improves the generating efficiency. Also, the float can be controlled to keep pace with the wave when a suitable current reference value is set according to the wave conditions. This achieves maximum power point tracking and the generating efficiency is further improved. A simulation model is developed to verify the electrical energy generation ability of this WEC design and to demonstrate the feasibility of applying SRG in a wave power generation system.

## 2 Structure of bidirectional driven float-type wave power generation system

In the mechanical part, the float moves up and down driven by waves, pulling pulley 2 and pulley 3 to rotate in opposite directions. During the wave falling period, only pulley 2, ratchet wheel 1 and driving pulley 4 work to drive the driving pulley 6. If the rotating speed of pulley 2 is equal to that of driving pulley 4 and the wave keeps falling, the connection between pulley 2 and driving pulley 4 is maintained by ratchet wheel 1. Similarly, during the wave rising period, only pulley 3, ratchet wheel 2 and driving pulley 5 work to drive the driving pulley 6. When pulley 3 keeps pace with driving pulley 5 through ratchet wheel 2 and the driving force is continually on pulley 3, the SRG rotating speed will increase. Through this process, the wave energy is captured and converted into mechanical energy. One thing to be noted is that two ratchet wheels ensure the rotor of SRG rotates in single direction during the whole process. The torque applied on the rotor is always negative, whether wave rises or falls. The work efficiency is greatly improved, compared with that of a single-direction driven float-type wave power system, which works only when the wave is rising, or only when it is falling.

In this work, two power converters and one capacitance are used for the connection between the SRG and the grid. The constant capacitance voltage is important, as self-excitation mode is used for the SRG. On the grid side, a voltage and current double closed-loop pulse-width modulation (PWM) inverter is used to improve the power factor. The float state and the rotor position determine the working efficiency of the WEC, which is greatly affected by the electromagnetic torque and the wave driving force. The power converter on generator side controls the current flowing in the SRG windings by the CCC method, which determines the electromagnetic torque. At the same time, the reference current is adjusted dynamically to achieve the maximum power point tracking of system. It is noted that the turn-on angle and the turn-off angle are fixed for the control of SRG.

## 3 Analysis of switched reluctance generator

One 6/4 SRG is applied in the bidirectional driven float-type wave power generation system and a linear model of the SRG is used to analyze the SRG average output torque.

*I*

_{p}and the electromagnetic torque

*T*

_{e}are shown in Fig. 2.

Figure 2 shows that the SRG would output negative electromagnetic torque, only when the SRG rotor angle *θ* satisfies *θ* _{4}<*θ*<*θ* _{5}, where *θ* _{4}, *θ* _{5} indicate the beginning and the end of negative inductance slope region respectively. In other regions, electromagnetic torque is positive or zero.

*L**(

*θ*) can usually be represented as

*K*of inductance can be given as

*β*

_{s}is the stator pole arc.

*I*

_{max}is the maximum current allowed to flow in one phase of the SRG;

*ε*is the step function. The total electromagnetic torque

*T*

_{e}and the average value

*T*

_{av}can be derived as

## 4 Analysis of bidirectional driven float-type wave power generation system

The float moves with vertical motion under the excitation force from waves and the force *F* _{f} transmitted through the supporting cable. Then the oscillatory rotation of the input shafts occurs. Two ratchet wheels and driving pulleys are used to convert these oscillatory rotations to the unidirectional rotation output shaft, which is then geared up to drive the SRG.

It is evident that the state of wave motion as well as the WEC physical structure have great impact on the output torque of the WEC. In the following, the float motion and the SRG running state are analyzed to get an analytical expression for the output torque.

### 4.1 Force analysis of the WEC

The float’s motion is affected mainly by the buoyancy force *F* _{buoy}, the viscous drag force *F* _{D} and gravity *G* _{f}.

*V*of the immersed part of float and the density

*ρ*of sea water. It can be written as

*g*is the acceleration of gravity.

*C*

_{d}is the viscosity drag coefficient;

*v*is the relative velocity between the vertical velocity of sea water and that of the float; and

*A*is the float’s cross-sectional area perpendicular to the water plane.

The viscosity coefficient *C* _{d} is generally determined by experimental data, and a simple method is to put the float into the sea water and allow it to move freely while measuring its amplitude attenuation. Experimental results show that the *C* _{d} value of typical floats is 0.015~0.020.

When the sea level rises or falls, the volume of the submerged float changes, causing *F* _{buoy} and *F* _{ D } to change too. Then the forces are not in balance and the float will be pulled to move on the vertical dimension.

*H*can be expressed as

*H*

_{float}is the height of the float;

*h*

_{initial}is that of the submerged part; and

*x*

_{f}and

*x*

_{w}are the displacements of the float and the water level respectively, which are measured upward from the stationary state as shown in Fig. 3.

*F*

_{f}is the tensile force in the cable supporting the float;

*m*

_{float}is the mass of float.

*F*

_{M}in the cable supporting the counterweight. The forces on the counterweight are shown in Fig. 4.

*m*

_{M}is the mass of the counterweight; and

*x*

_{M}is the displacement of the counterweight.

The second equation in (15) indicates that the resultant force exerted on the float must be in the same positive direction as the float motion.

*R*is the radius of the driving pulley 6;

*k*is the ratio of the gear box;

*J*is the moment of inertia;

*ω*

_{pulley}is the angular velocity of the driving pulley 6; and

*F*is the force produced by driving pulley 4 or driving pulley 5.

When the inequalities described by (15) cannot be satisfied, the connection will disappear. Further, the friction of the pulleys and ratchets is assumed to be insignificant compared to other forces, and the cable is assumed to have a non-slip connection to the driving pulleys.

### 4.2 Solutions for WEC dynamics

*F*

_{f},

*F*and

*F*

_{M}, the equation of motion of the float can be derived as

Since the float motion shows a high degree symmetry when the wave rises and falls, the system is discussed here only under the condition of \(\text{sgn} (\dot{x}_{\text{f}} ){ = }1\).

*t*=

*t*

_{on}, and the system satisfies

*A*

_{on}is a constant depending on intrinsic properties of the WEC, determined by its structure and its working environment. It can be expressed as

*T*applied to the rotor is given as

*T*applied on rotor doesn’t exist. The equations of motion of the float and the SRG are derived respectively as

*V*

_{off}and the displacement is

*H*

_{off}, when WEC has just finished driving the SRG. In the complex frequency domain, (34) can be expressed as

*A*

_{off}is another constant determined by the structure of the WEC and its working environment. It can be written as

Usually, the float experiences vertical motion driven by the sea water, but its trajectory is not in exact conformity with that of the wave. The float trajectory contains two sinusoidal components which are caused by its self-oscillation and the wave excitation respectively. In detail, the period of self-oscillation is determined by the mechanical part of the WEC structure, shown in Fig. 1, and the seawater density. If the WEC is designed rationally, this period will be relatively small, so that the float can track the sea water well. Otherwise, the self-oscillation would be the dominant factor of float motion, and the float would lose the ability to keep pace with the wave. This would decrease the efficiency of the WEC. It is obvious that when the float is completely submerged in the seawater or hanging in the air, the WEC would also be inefficient.

Note that the torque *T* will act on the driving pulley 6, only when the absolute value of the belt pulleys’ line speed is equal to that of the tooth driving pulleys, and the belt pulleys’ line speed is rising. However, the SRG can directly output electrical energy, whether the wave rises or falls. It is essential for the mechanical energy to be converted into electrical energy in time so as to capture the wave energy as soon as possible. If the time point is delayed, the captured energy will be wasted. Thus, a proper control strategy is needed.

## 5 Control strategy for bidirectional driven float-type wave power generation

Exciting of the phase current is a necessary starting step for the SRG. The excitation process produces an output current in proportion to the voltage of an auxiliary excitation battery. The output current is restrained by the maximum allowed current value. In order to fully utilize the SRG windings, it is important to maintain the winding current in the negative inductance slope region at all times. Further, in the proposed system, the SRG rotates with low velocity, so the electromotive force will be relatively small. In addition, the windings are used as part of the rapid charging circuit. In this situation, CCC is the best control method for the SRG. Current flowing in the conducting phase is restrained by the reference current, which determines the generator torque. Since the ability to capture wave energy is closely related to the electromagnetic torque, it is important to set an appropriate reference current to realize the system’s maximum power point tracking ability.

As mentioned above, the float trajectory differs from that of the wave, owing to its self-oscillation. When driving pulleys rotate the SRG, the WEC completes the energy absorption process, and transfers the captured mechanical energy into SRG. In the next phase, the absolute value of the float velocity decreases and the transferred energy should be released. So, on the one hand, electrical energy would be generated. On the other hand, the WEC can recapture the wave energy, once the SRG rotor is pulled to rotate with increasing velocity. If the float velocity is equal to zero at this time point, the largest amount of electrical energy can be converted and transmitted to the power grid or loads.

Note that when there is an irregular wave, the reference current can be obtained by multiplying *ξ* by a correction coefficient according to the predicted wave characteristics so as to achieve more energy transfer.

## 6 Model and control strategy verification

Model parameters

Parameters | Value | |
---|---|---|

Wave | Period | 2.5 s |

Amplitude | 0.35 m | |

Float | Radius | 1 m |

Mass | 1680 kg | |

Height | 0.7 m | |

Counterweight | Mass | 150 kg |

Driving pulley | Radius | 0.18 m |

Gearbox | Gear ratio | 10.15 |

Seawater | Density | 1028 kg/m |

*T*applied on the rotor is shown in Figs. 11 and 12 shows the corresponding power curve. It can be seen from Fig. 11 that negative torque can always be generated and various reference current settings can be used to generate different torques. It is noted that, in this process, electrical energy would be generated whether the sea wave rises or falls.

Moreover, we have also found that the wave energy converter can output the desired torque periodically with the efficiency of conversion from mechanical to electrical energy up to 55% and good adaptability to wave conditions. Thus the feasibility of applying a SRG to WEC is verified.

## 7 Conclusion

A novel bidirectional driven-float WEC is proposed including a SRG. Ratchet wheels are used to make the SRG run whether the float rises or falls. Dynamic reference current setting is used to achieve the control target of maximum power point tracking come true. The dynamic model for the bidirectional driven float-type wave power generation system has been demonstrated in a wave-generation system for the mechanical part and MATLAB for the electrical energy conversion. This has proved that the proposed system has high efficiency and good prospect of application in real wave conditions.

## Notes

### Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 51577124), the Key Technologies Research and Develop Program of Tianjin (No. 15ZCZDGX00980) and Tianjin Research Program of Application Foundation and Advanced Technology (No. 15JCZDJC32100).

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