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Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 609464, 5 pages

http://dx.doi.org/10.1155/2013/609464

## Buoy-Rope-Drum Wave Power System

Research Center of Mechanics and Mechatronic Equipment, Shandong University, Weihai 264209, China

Received 28 June 2013; Revised 1 November 2013; Accepted 1 November 2013

Academic Editor: Fabrizio Marignetti

Copyright © 2013 Linsen Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A buoy-rope-drum wave power system is a new type of floating oscillating buoy wave power device, which absorbs energy from waves by buoy-rope-drum device. Based on the linear deep water wave theory and pure resistive load, with cylinder buoy as an example, the research sets up the theoretical model of direct-drive buoy-rope-drum wave power efficiency and analyzes the influence of the mass and load of the system on its generating efficiency. It points out the two main categories of the efficient buoy-rope-drum wave power system: light thin type and resonance type, and optimal designs of their major parameters are carried out on the basis of the above theoretical model of generating efficiency.

#### 1. Introduction

As one of renewable clean energies, ocean wave energy is receiving more and more emphasis due to the double crisis of fossil energy and environment pollution [1–3]. Thousands of patents on wave power have been approved, while only a small proportion has been applied to commercial use on a large scale, the ultimate reasons for which are the great risk and high cost of wave power due to the complex and variable sea conditions [4, 5]. Therefore, the study of how to develop new type of wave power technology to enhance reliability and reduce the generating cost has become the focus of the wave power research [6–8].

A new type of floating wave power device is discussed in this paper based on the buoy-rope-drum system, which is simple in structure and costs less in laying and maintaining compared with the old oscillating buoy wave power device. The paper first introduces the working principles of buoy-rope-drum technology and studies the theoretical model and influential factors of the generating efficiency of direct-drive buoy-rope-drum wave power device on the basis of linear deep water theory and pure resistive load.

#### 2. Buoy-Rope-Drum Wave Power System

##### 2.1. Operating Principle of Buoy-Rope-Drum Wave Power

As shown in Figure 1, buoy-rope-drum wave power system consists of gravity anchor, rope, rope guider, generator, heating pipe, buoyant, and monitoring room. One respect of rope is tied to the gravity anchor on the bottom of the sea; the other respect is wound around the drum of the generator casing through the rope guide. When waves push the buoyant hull to rise, the rope will drag the drum to rotate, which will then drive the rotor (magnetic steel casing) of permanent magnet alternator to rotate around the stator winding so as to generate alternating current, which will supply power for the resistive load in the heating pipe after being monitored. When the buoyant hull falls with waves, the drum will collect the rope automatically under the action of the motor’s built-in coiling spring. Because an overrunning clutch is installed between the drum and magnetic steel casing, the magnetic steel casing does not rotate when the drum rotates backward, and the buoyant hull does not generate power during falling.

##### 2.2. Generating Features of Buoy-Rope-Drum Wave Power

(1)The device absorbs wave energy with the buoy-rope-drum device, which is simple in structure. The main component of the system is on the surface of the water, which hardly needs diving maintenance. Thus, the buoy-rope-drum wave power system costs less in manufacturing, laying, and maintenance compared to the current floating oscillating buoy wave power device.(2)This device, which is water resistant, is equipped with low-speed permanent magnetic generator with no speed-up gearing, generator’s casing adopted as drum, and built-in rope collecting coiling spring. The compact structure, light mass, and small moment of inertia all contribute to the small inertia load and strong ability of collecting wave energy.

#### 3. The Theoretical Model of System’s Generating Efficiency

##### 3.1. Dynamic Analysis

Figure 2 shows the buoy in the rising process with still water level as reference level. stands for the distance from reference level to static water level of the buoy, with upward direction as the positive direction, stands for the vertical distance from reference level to surface level, with upward direction as the positive direction, and stands for the static draft of the buoy.

With the whole device as the study object, because the buoy is floating on the sea, the whole time and the added mass of entrained water are so small that the added inertia force can be ignored, only the viscous force which formed at the bottom of the buoy when wave and buoy move at different speed. In vertical direction, based on Newton’s second law, we have where is the buoyancy of the device in , is the viscous force in , is the gravity of the device in , is the tension of the rope in , is the mass of the device in kg, and is the acceleration of the buoy in .

With the roll wheel as the study object, because the moment of the coil spring is so small that it can be ignored, based on the axial rotation dynamics equation, we have
where is the radius of the roll wheel in , is the moment of inertia of the device in kg m^{2}, is the angular acceleration in rad/s^{2}, and is the resistance torque formed by load in Nm.

According to (1) and (2), we have
where can be formulated as follows [9]:
where is the specific gravity of the sea water with the value being set as 10094 N/m^{3}, is the cross-sectional area of the buoy in m^{2}, is the draft in , is the wave number, and
where is the wave length in . can be formulated as follows [9]:
where is the linear coefficient of friction of the sea water in Ns/m, is the rising velocity of wave in m/s, is the rising velocity of the buoy in m/s, and

As the load is pure resistive, the generator can be simply modelled with a damping coefficient; then, where is the resistance coefficient of the electrical generator in Ns.

Substituting (4)~(9) into (3), we have Let where is wave height in and is the wave angular frequency in rad/s.

Then where can be calculated as follows: Substituting (12) into (10), then Let Equation (14) is simplified as follows: The solution of (16) is where and are the integration constants, determined by the initial conditions and is the lag angle of the buoy relative to wave in rad. The steady component of (17) is Then Let Then

##### 3.2. Generating Efficiency Derivation

With pure resistive load, the instantaneous power of load is where is the instantaneous power of load in , is the load current in , is the load resistance in , is the electromotive force of generator in , is the resistance of generator winding in , and is the electromotive force coefficient in Vs/m.

Substituting (21) into (22), then the instantaneous power of the load in the rising process is as follows The generation of the device in a wave period is Wave energy occupied by the buoy in a wave period is [9] where is the wave period in s and is the buoy diameter in m; then, the generating efficiency of buoy-rope-drum wave power system is

#### 4. The Influence Factors of System Generating Efficiency

##### 4.1. Some Parameters of System

According to many years’ observation data of the Yellow Sea, the rated sea conditions are shown in Table 1.

The major parameters of the buoy are shown in Table 2.

Based on the equivalence principle of dissipated energy within the wave period, the linear coefficient of friction of the sea water can be derived from the method based on nonlinear coefficient of friction of the sea water [9]:
where is the sea-water density with the value being set as 1030 kg/m^{3}; is the nonlinear coefficient of friction of the sea water, with the value being set as 1.2 [10]; is the wave amplitude, with the value being set as 0.5 m; is the buoy amplitude, with the value being set as 0.4 m; and is the wave angular frequency, with the value being set as 2 rad/s.

Substituting the above parameters into (27), we have

##### 4.2. The Influence of System Mass and Load on the Generating Efficiency [11]

With system mass and load as variables and on the basis of the values of the above parameters, the calculating formulas of correlation coefficient are as follows: According to (29)~(35), after setting the system correlation parameters, generating efficiency is the dual function of the system’s mass and load, whose image can be obtained by Matlab as shown in Figure 3.

According to the distribution feature of the high efficiency points, the buoy-rope-drum wave system can be divided into two categories.

*(**1) Light Thin Type of System.* Generating efficiency of the light thin system increases as the load resistance decreases. The power of the wave acting on the buoy mainly transforms to the tension of the rope because the small mass brings about the small inertial load of the system, then drives the generator, and outputs useful work through resistive load. Due to the light and thin buoy, the amplitudes of the buoy and the wave are approximately the same, making the average velocity of the buoy under the rated sea conditions nearly constant, which means that the average value of the output voltage is nearly constant. All the above conditions and the adaptation of the pure resistive load contribute to the outcome that the useful power increases as the load resistance decreases. This type of system is relatively stable, but the mass of the actual engineering prototype should be big enough to meet the demands of strength and stiffness. For example, when the diameter of the buoy is 2.4 m, the mass of the system should be at least 1 ton. As shown in Figure 3, when the value of load resistance is set as 14 Ω, the highest generating efficiency can reach approximately 21%.

*(**2**) Resonance Type of System.* As shown in Figure 3, when the system mass is 11 tons, its generating efficiency increases as the load resistance increases, because when the diameter of the buoy is 2.4 m and the system mass is 11 tons, the natural frequency of the system is 2 rad/s, which happens to be the frequency of the wave under the rated sea conditions, and then the system is in the resonance state. In the resonance state, the system can accumulate the power, so that the amplitude of the buoy will continue to increase, so will the generating efficiency, which will ultimately lead to the destruction of the system. Therefore, the resonance type of system has to be designed appropriately to adjust the damping and then adjust the amplitude of the buoy to control the system in stable resonance. For example, when the diameter of the buoy is 2.4 m, the mass of the system is 11 tons and the value of the system’s amplitude is set as 0.5 m; then, the load resistance is 38 Ω, when the generating efficiency of the system is 22%.

#### 5. Conclusion

Buoy-rope-drum wave power system is a new type of floating oscillating buoy wave power device, which absorbs energy from waves by buoy-rope-drum structure, simple in structure and cost efficient in laying and maintaining. By studying the generating efficiency of direct-drive buoy-rope-drum wave power system, this paper divides the high efficient buoy-rope-drum wave power system into two categories: the light thin type and the resonance type. The former is relatively stable while the latter needs to set reasonable load to make sure of the stability of the system. The conclusions above provide theoretical guidance for the research and development of the engineering prototype of the buoy-rope-drum wave power system for sea trials.

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