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Experimental study on the performance of a floating array-point-raft wave energy converter under random wave conditions
Renewable Energy 139 (2019) 538e550
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Experimental study on the performance of a floating array-point-raft wave energy converter under random wave conditions Shaohui Yang a, b, c, *, Hongzhou He a, b, Hu Chen a, b, Yongqing Wang a, b, Hui Li a, b, Songgen Zheng b a b c
College of Mechanical and Energy Engineering, Jimei University, Xiamen 361021, China Key Laboratory of Energy Cleaning Utilization and Development of Fujian Province, Xiamen, 361021, China Key Laboratory of Ocean Renewable Energy Equipment of Fujian Province, Xiamen, 361021, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 September 2017 Received in revised form 22 October 2018 Accepted 16 February 2019 Available online 18 February 2019
An array-point-raft wave energy converter (ARR WEC) integrating multiple-point absorption and raft type wave energy capturing technologies is proposed and experimentally investigated in this study. A 10 kW pilot device was developed, and a three-month real sea test was carried out in the Taiwan Strait, China. The experimental results confirmed the feasibility and effectiveness of the new system. The overall performance, heaving performance, power output and wave energy conversion efficiency of the pilot APR WEC running under random waves are reported and analyzed in detail. The heaving motions of the oscillating buoys and the instantaneous and average power output of the permanent magnet generator (PMG) are affected significantly by the number of oscillating buoys used to collect wave energy. More oscillating buoys used increase the production of electricity and improve the power quality, but lead to the reduction of energy conversion efficiency in long wave periods. The increase of electrical resistance of PMG results in an increased wave conversion efficiency. The experimental results obtained are valuable in the optimal design and operation of the ARR WEC system proposed. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Wave energy conversion Oscillating buoy Random waves Experimental study
1. Introduction Ocean wave energy has many advantages such as abundant reserves, wide distribution and high energy density, which bares tremendous potential as a source of renewable energy. The related technologies for capturing and converting wave energy have continually been developed and improved during the last decades. Two basic categories of wave energy converters (WECs) have been proposed, namely terminators and attenuators [1]. Attenuators are devices where seawater physically pushes and induces motion in the WECs structure and energy is converted by dampening this motion [2] and according to the horizontal dimension of the WECs, the attenuators are subdivided into point absorption WECs and raft WECs. The development of WECs from concept to commercial stage has been found to be difficult, slow and expensive. Although substantial progress has been achieved in the theoretical and numerical modelling of WECs, the final prototype tests under real sea
* Corresponding author. College of Mechanical and Energy Engineering, Jimei University, Xiamen City, Fujian Province, 361021, China. E-mail addresses: [email protected], [email protected] (S. Yang). https://doi.org/10.1016/j.renene.2019.02.093 0960-1481/© 2019 Elsevier Ltd. All rights reserved.
conditions are still essential. According to the recent literature [3e12], many sea trials of point absorption and raft type WECs have been performed. The simplest point absorption WEC is a single oscillating buoy reacting against a fixed frame of reference (the sea bottom or a bottom-fixed structure). An early attempt was the device G-1T containing mainly a rectangular buoy (1.8 m in length and 1.2 m in width at water line level) whose vertical motion was guided by a steel structure fixed to a breakwater, for which the sea test performed in Tokyo Bay was reported [3]. Another example was the Norwegian-Buoy containing mainly a spherical floater which could perform heaving oscillations relative to a strut connected to an anchor on the sea bed through a universal joint, for which a smallsize prototype with a buoy diameter of 1 m was tested in Trondheim Fjord [4]. Besides, a converter named L-10 in which one oscillating buoy drove a linear electrical generator was developed at Oregon State University, USA, and a 10 kW prototype with a buoy outer radius of 3.5 m was deployed and tested off Newport, Oregon [5]. The concept of a single buoy reacting against the seabed may raise difficulties due to the distance between the free surface and the bottom and to the tidal oscillations in sea level [6]. Double-buoy
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point absorption WECs are classified as a third-generation wave energy device where the wave energy capturing process is not influenced by tidal range because of its floating structure [7]. A good example for the double-buoy heaving system is the IPS invented by Sven, for which a half-scale prototype was tested in sea trials in the Pacific Ocean off the coast of Oregon [6]. The Wavebob developed in Ireland consisted of two co-axial axisymmetric buoys, whose relative axial motions were converted into electric energy through a high pressure oil system; a 1/4th scale model was tested in the sheltered waters of Galway Bay [8]. The Ocean Power Technologies company in USA developed a double-buoy WEC named PowerBuoy, where a disc-shaped floater reacted against a submerged cylindrical body, terminated at its bottom end by a large horizontal damper plate whose function was to increase the inertia through the added mass of the surrounding water; a 40 kW pro~ a in northern Spain [9]. totype was deployed off the coast of Santon Compared with the point absorption WECs, a very limited number of raft type WECs have been reported in the literature [6,10and11]. The Pelamis raft type WEC [10,11] designed and manufactured by the Ocean Power Delivery Company in Scotland had a snake-like articulated structure and included five floating cylindrical sections (150 m long, 3.5 m diameter, 750 kW rated power) which allowed not only pitching motion but also yawing motion. It was placed on the sea surface with a depth of 50 me60 m where the piston was driven by the angular displacement of adjacent cylindrical sections to convert wave energy into hydraulic energy [10,11]. The McCabe raft WEC (40 m in length and 4 m in width) was studied jointly by the University College Cork and the Queen's University Belflast in Ireland and was tested in sea trials [6], which was composed of three rectangular steel pontoons hinged together; the intermediate pontoon was smaller, and a damping plate was installed under it to increase the added mass, making the motion range of the intermediate pontoon relatively smaller so as to increase the relative angular displacement of the pontoons at the front and back ends. The point absorption or raft type wave energy capturing
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technologies have been proved to be feasible in above-mentioned sea trials. However none of them has been commercialized yet because of their deficiencies [13]. On the one hand point absorption WECs usually have smaller geometric dimensions versus the wave length, making their wave energy capturing efficiency not affected by the direction of the incident wave, but on the other hand they usually have relatively high natural frequencies compared with the wave frequency, so that perform very poorly under the typical waves of the wide oceans [6]. Moreover, they are easily damaged under the extreme wave conditions when the vibration amplitude is beyond pre-set normal range [14]. The main merit of raft type WECs is that there exists only angular displacement among the adjacent rafts which would not be excessively large even under huge waves, resulting in higher reliability and safety. However, raft WECs must be laid out along the wave direction and have a relatively high cost compared with the WECs laid perpendicular to the wave direction [10,15]. In order to make use of the advantages and at the same time make up for the deficiencies of the point absorption and raft type WECs, the two wave energy conversion technologies have been recently integrated by some researchers [16e20]. For instance, the WEPTOS WEC, which was studied substantially by the researchers from Aalborg University [16,17], is composed of two floating symmetrical frames that support a multitude of identical rotors (i.e. oscillating buoys). The relative motions between the rotors and symmetrical frames are dampened by ratchet mechanisms to convert wave energy to mechanical energy. Seven different physical models related to WEPTOS were tested in the wave flume or under the real sea conditions [17]. The other typical example is the WaveStar WEC [18e20] where multiple oscillating bodies are connected to the fixed central platform through actuating arms. A sea trial test carried out at Hanstholm proved its feasibility. Inspired by the previous work on attenuator WECs mentioned above, we proposed an array-point-raft (APR) WEC, as shown in Fig. 1, where multiple oscillating buoys float symmetrically on the sea surface to capture wave energy just like a multi-point
Fig. 1. The prototype of APR WEC deployed at Taiwan Strait, developed by the Jimei University, China.
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absorption WEC, and the relative motions between the buoys and central platform are dampened by pinion power take-off (PTO) systems to convert wave energy to mechanical energy as done in raft type WECs. The central platform of the APR WEC also uses the V-shaped floating structure like the WEPTOS, because the experimental results [16] proved that the V-shaped (or A-shaped) structure could significantly decrease the mooring forces. But different from the WEPTOS, the floating central platform of the APR WEC is more like a barge, and the shape of the oscillating buoys and the design of the PTO system are also different. The use of the floating structure makes the APR WEC have a lower cost and lower requirements for installation environment than the Wavestar WEC whose central platform needs to be fixed at the bottom of the sea. A 10 kW prototype of APR WEC was designed and manufactured using a grant from the State Ocean Administration of China. The prototype was deployed between Xiaodeng Island and Xiaojinmen Island of Taiwan Strait, South China Sea. The straight-line distance between the prototype and the coast is 300 m. The seawater depth of the installation site is approximately 20 m. The wave energy resource of the experimental site is not rich, indicating that simply amplifying the size of each buoy cannot directly result in a larger energy output. An array composed of multiple small buoys may be an alternative solution to increase wave energy capturing capacity [21]. In this study, the test for analyzing the dynamic performances of the APR WEC in actual sea conditions was conducted from June to August, 2016. All of the design concepts, as illustrated in detail below, were realized and verified during the sea trial. The rest of the present paper is organized as follows. In section 2, the design, structure and operating principle of APR WEC are introduced. The experiment procedure and test instruments are described in Section 3. Then the performance characteristics of APR WEC are analyzed in detail based on sea trial data in Sections 4. Finally, the conclusions of the study are summarized in Section 5.
2. Conceptual design 2.1. The components of APR WEC As shown in Fig. 2, APR WEC is mainly composed of a floating central platform, ten oscillating buoys, ten two-way transmission gears, a mooring system, two PMGs and submarine cables. Tied to the mooring float by a wire rope, the floating central platform appears like a wedge-shaped barge. The anchor chains, anchor blocks and mooring float constitute the mooring system. Due to the design of the interior of the mooring float [22], the central platform can rotate freely around the mooring float and align automatically towards the incident waves, thus eliminating the influence of incident wave directions on the system. As shown in Fig. 2(c), the ten oscillating buoys are divided into two linear arrays (buoys I-V as the first array, and buoys VI-X as the second array) and arranged evenly on both sides of the central platform. Because of the difference such as the hydrodynamic coefficient, mass property, geometric shape and so on between the oscillating buoys and the central platform, the oscillation amplitude of the central platform is much smaller than that of the oscillating buoys, leading to relative motions between them. The relative motions are then transformed into mechanical energy of the horizontal rotation shaft by the two-way transmission gears (see Section 2.3 for details), and eventually into electric energy for output. The dimensions of the prototype are shown in Fig. 2(b) and (c). The central platform has a length of 18 m, maximum width of 8 m, height of 2.4 m, designed draught of 1.3 m, and displacement of 96t. The diameter of the mooring float is 3 m, and the height is 2.5 m. The length of each anchor chain is 50 m, and the weight of each anchor block is 8000 kg.
2.2. Oscillating buoy As shown in Fig. 3(a), every oscillating buoy used in the experiment is cylindrical and connected to the central platform by an actuating arm. The diameter of the buoy is 1.2 m, and the length is 1.7 m. Ballast can be filled into the buoys through a rounded hatch cover to adjust the draft of each buoy. The weight of each buoy (including the actuating arm and other necessary accessories) is 250 kg. 2.3. Two-way transmission gearset Many WECs adopt hydraulic systems as the PTOs to convert wave energy into electric energy, where hydraulic oil leakage is a common problem which is unavoidable in marine environments [13]. Mechanical gear transmission is an alternative method to convert wave energy efficiently. A two-way transmission gearset was designed and used in APR WEC, which mainly includes an actuating shaft, three kinds of pinions and a driven shaft, as shown in Fig. 4. The actuating shaft is fixed to the actuating arm of each oscillating buoy. When the oscillating buoy ascends or descends under the wave excitation force, the actuating shaft will be driven to rotate forwards or backwards. An overrunning clutch is installed in the interior of the reversing pinion which converts the reciprocating motion of the actuating pinion into unidirectional rotary motion of the driven pinion, and the result is that the driven shaft rotates continuously in one direction. 2.4. Array driven mode The array driven mode of APR WEC is shown in Fig. 5. Five oscillating buoys are arranged in a linear array and actuate simultaneously a horizontal shaft to rotate unidirectionally. The horizontal shaft is composed of multiple driven shafts of two-way transmission gearsets. With a transmission ratio of 1:25, the overdrive gearbox enhances the rotational velocity of the horizontal shaft to the rated velocity of PMG. Two PMGs are installed on both sides of the prototype, respectively. The nominal power and single phase nominal output voltage of each PMG are 5 kW and 220 V. Four different electrical resistances (5U, 10U, 20U and 30U) are connected to each PMG through 450 m-long subsea power cables. A flywheel with a moment of inertia of 100 kgm2 works as an energy accumulator to attenuate the effect of wave energy fluctuations. 3. Experimental set-up The emphasis of this investigation is to analyze the dynamic performance of APR WEC in different random wave climates. Some gauges and sensors were selected to monitor the operating data of the prototype during the sea trial. A pressure-type directional wave recorder (Model: MIDAS DWR) was fixed on the seabed, right under the mooring float, to collect the data of wave height and period every thirty minutes, of which the accuracy is ±0.04%. A three-month on-site wave data measurement was carried out, with the statistical occurrence frequencies of half-hourly averaged wave periods and heights shown in Table 1 where Hs denotes the significant wave height and Te denotes the energy wave period. According to Table 1, the most frequently occurring wave conditions were within the energy wave period of 3.0e4.5s and the significant wave height of 0.3e1.2 m. Fig. 6 shows the power spectral density (PSD) plot of the measured wave elevation which is obtained by processing the raw wave height spectrum through a third order polynomial filter.
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Fig. 2. Schematic diagram and geometric parameters of the APR WEC.
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Fig. 3. Oscillating buoy used in the experiment.
Fig. 4. Two-way transmission gearset used in the experiment.
Six displacement sensors (Model: SCAH2000) were installed on the still water line of the oscillating Buoys I-V and the central platform to detect their displacements. The measuring accuracy of these displacement sensors is ±0.1%. Two voltage gauges (Model: GTVB-500) with a measuring accuracy of ±0.25% and two current gauges (Model: TKC-BSD40) with an accuracy of ±0.5% were used to measure the output voltages and currents of PMGs. The shortest sampling frequency of all of the displacement sensors, voltage gauges and current gauges is 20 Hz. The instantaneous output power of PMG can be calculated by multiplying the output voltage and the current together. During the experiment, all data was acquired and processed by a
wireless remote monitoring system especially developed for this prototype as shown in Fig. 7, which helped achieve unattended operation of all the devices and improving the efficiency of the experiments. 4. Results and discussion 4.1. Overall operating performance In the first month of the experiment, all the ten oscillating buoys were put in the seawater to collect wave energy, and the electrical resistance of PMG was set at 30U. The data from the series of sea
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Fig. 5. The array driven mode of APR WEC.
Table 1 Statistical frequency of on-site wave resource during the experiment. Hs (m)
Te (s) <2.5
2.5e3.0
3.0e3.5
3.5e4.0
4.0e4.5
4.5e5.0
5.0e5.5
<0.3 0.3e0.6 0.6e0.9 0.9e1.2 1.2e1.5 1.5e1.8 1.8e2.1 2.1e3.0 Total
12 28 14 5
37 86 66 42 28
52 323 606 104 62 1 1
1 14 58 26 12 1
259
1149
26 232 302 108 89 27 5 2 791
2 26 142 56 65 8 2
59
82 426 772 282 110 5 8 5 1690
301
112
5.5e6.0 4 12 3
19
Total 212 1140 1972 626 365 42 16 7 4380
Fig. 6. PSD plot of measured wave elevation. Fig. 7. The wireless remote monitoring system.
trials are shown in Fig. 8. As illustrated in Fig. 8 (a), the maximum significant wave height was 1.75 m, occurred on 27th June, 2016. On the same day, the electrical energy generated by the two PMGs was the maximum, reaching 75.31 kWh (Fig. 8 (b)). On 3rd June, the electrical energy generated was the minimum, just 1.22 kWh. It can be calculated that the average electrical energy generated per day was 28.09 kWh and the accumulative electrical energy was 842.7 kWh during the 30 days. As shown in Fig. 8(c) which displays
the half-hour mean output power of the prototype on 27th June, the maximum half-hour mean output power was 9.03 kW, corresponding to a 1.75 m significant wave height and 5.45s energy wave period. The relationship between the half-hour mean power output and significant wave height is shown in Fig. 8 (d) which contains 2325 data points. It can be seen that the half-hour mean output
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Fig. 8. The overall performance of APR-WEC in June 2016.
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power almost equals to zero when the significant wave height is less than 0.45 m, i.e., both of the PMGs cannot generate electricity when the wave height is too small. The output power increases with the significant wave height when it is greater than 0.45 m. It also can be found that the variation of the output power is more significant within the wave height range of 0.6me1.3 m than that in other zones.
4.2. Heaving performance For studying the effect of the number of oscillating buoys on the heaving response and output power in a random wave climate, comparison tests in three cases were performed by changing the number of oscillating buoys on each side of the prototype in the next two months. The heave motions of Buoys I-V and the central platform were recorded and stored by the wireless remote monitoring system. Fig. 9 illustrates the time histories of these heave motions when Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U (R is the electrical resistance of each PMG). In Case 1, all the ten oscillating buoys were put in the seawater to collect wave energy. The transient displacement data of Buoys IV are shown in Fig. 9 (a). It can be found that the oscillation amplitudes and phases of the five buoys have distinct differences. The
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vibration of Buoy-III is the most strenuous, even greater than BuoyI. The oscillation amplitudes of Buoy-II, Buoy-IV and Buoy-V are relatively small. In Case 2, six oscillating buoys (Buoys I, III, V, VI, VIII and X) were used. As illustrated in Fig. 9 (b), the heave motion of Buoy-I is slightly greater than Buoy-III. In Case 3, just two oscillating buoys (Buoys III and VIII) were put in the seawater, the heaving motion of Buoy-III is shown in Fig. 9 (c). Fig. 10 illustrates the heave motion of the central platform in the three cases mentioned above. It is clear that the number of the buoys used in the experiments has no obvious effect on the heave motion of the central platform. Because no sensors were used to detect the heave motions of Buoys VI-X, the detailed transient displacement data of them were not obtained in the three cases. But during the course of the experiment, we observed that the buoys' heave motions on both sides of the central platform were very similar. Fig. 11 shows the PSD plots of the APR WEC heaving displacements in the three cases when Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U. As shown in Fig. 11(a), the peaks of the PSD plots of the Buoys I, II, IV and V correspond to the same circular frequency, 1.28 rad/s, which is very close to the theoretical resonant frequency of each buoy, 1.32 rad/s. The PSD plot of Buoy III is different in shape from the other buoys. There are small fluctuations at the crest. In Fig. 11(b), the PSD values of Buoys I, III and V in Case 2 decrease gradually
Fig. 9. Heave motions of oscillating buoys in the three cases studied (Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U).
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Fig. 10. Heave motions of central platform in the three cases (Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U).
Fig. 11. The PSD plots of the APR WEC heaving displacements in the different cases (Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U).
along the direction of the incident wave propagation within the circular frequency range of 0.9 rad/s-1.8 rad/s. There are still slight fluctuations at the crest of the curve for Buoy III. As shown in Fig. 11(c), the PSD plot of the Buoy III in Case 3 is very similar to the PSD plots of the other buoys in Case 1 and Case 2, but the fluctuations at the crest of the curve vanish and the circular frequency corresponding to the peak is still 1.28 rad/s. For the central platform, the PSD plots in the three cases are almost the same as shown in Fig. 11(d). Both the peak and the circular frequency (0.79 rad/s) corresponding to the peak are obviously lower than the buoys.
4.3. Power output Given that the power output of the PMG2 is very analogous to the PMG1, we mainly analyze the power output characteristics of the PMG1 in the following sections. Fig. 12 shows the instantaneous power output of the PMG1 in the three cases when Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U. It can be found that the number of oscillating buoys can affect the amount and stability of instantaneous power output. Comparing the three curves in Fig. 12, one can see that the instantaneous power output of PMG1 in Case 1 is obviously larger
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Fig. 12. Instantaneous power output curves. Fig. 13. Average power output curves.
than that in Case 2 and Case 3. The result demonstrates that the instantaneous output electrical energy is higher when more oscillating buoys are used to collect wave energy. According to Fig. 12, the mean instantaneous power output of PMG1 reaches 2.36 kW in Case 1, while in the same wave climate, the value is 1.95 kW in Case 2 and 1.37 kW in Case 3. The standard deviation is a common quantitative index which is used frequently to evaluate the fluctuation of the power output in wind power generation [23,24]. We utilize the average deviation from the mean power output [24,25] to describe the fluctuation of the instantaneous power output, which can be calculated by:
AVD ¼
N PðtÞi P 1 X N i¼1 P
(1)
where t is the interval between two sampling times, PðtÞi is the power output at the ith sampling time, P is the average power output between the 1st and the Nth sampling times, and N denotes the number of the samplings. Table 2 shows the calculated AVD of the instantaneous power output in the three cases when Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U. The largest AVD always appears in Case 3 no matter if t is set at Te/8, Te/4, Te/2 or Te, and the smallest AVD appears in Case 1, indicating that the fluctuation of the instantaneous power output diminishes when more oscillating buoys are used. Fig. 13 presents the average power output curves in entire range of the wave periods when R is set at 30U. The average power output in Fig. 13 refers to the mean value of all half-hour power outputs at a particular wave period. It can be found that the average power output of the PMG1 increases monotonically with the increase of the wave period in the three cases. Whatever the wave period is, the average power output in Case 1 is always the highest and that in Case 3 the lowest. As demonstrated by the higher instantaneous and average power output in Figs. 12 and 13, the greater number of oscillating buoys used leads to higher power output.
Table 2 The average deviation of the instantaneous power output in the three cases. AVD
Te/8
Te/4
Te/2
Te
Case 1 Case 2 Case 3
0.798 0.854 0.998
0.864 0.974 1.086
0.616 0.644 0.938
0.612 0.636 0.934
4.4. Energy conversion efficiency The energy conversion efficiency of APR WEC is one of the important performance indexes, defined in this paper as:
h¼
Pmean Pwave
(2)
where Pmean is the average value of half-hour output electrical power of PMG1, and Pwave is the average wave power of in deep water which was given by Wanan [26]:
Pwave ¼
rg2 2 H Te L 64p s
(3)
where r is the seawater density, g is the gravity acceleration, and L is the valid width along the direction of the incident wave and can be calculated as:
L ¼ nl sin
b 2
(4)
where l is the length of each oscillating buoy, and b is the included angle of the wedge-shaped central platform. For the present prototype, l is 1.7 m (see Fig. 3(a)) and b equals to 300 (see Fig. 2(c)). The energy conversion efficiency of APR WEC working in the three cases is shown in Fig. 14. A common observation is that the energy conversion efficiency gets higher when more oscillating buoys are used in short wave periods (i.e. high wave frequencies), and on the contrary, the efficiency gets lower when more buoys are used in long wave periods (i.e. low wave frequencies). Furthermore, it is interesting to notice that there always exists a wave period which leads to an equal energy conversion efficiency of APR WEC in all the three cases regardless of the electrical resistance. As shown in Fig. 14(a) when R ¼ 30U, the energy conversion efficiencies are equal at Te ¼ 3.15s in the three cases. When Te is less than 3.15s, the efficiency in Case 1 is higher than that of the other two cases, while when Te is larger than 3.15s, the efficiency in Case 1 becomes the lowest. It also can be found that the variation of the energy efficiency is the most gradual in Case 1 and the steepest in Case 3. In other words, the range of the response wave period gets wider when more oscillating buoys are used. The peak value of the energy conversion efficiency appears at about Te ¼ 5s in all of the
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Fig. 14. The energy conversion efficiency for different number of oscillating buoys.
three cases. In Fig. 14(b) where R ¼ 20U, the point independent of energy wave period is at Te ¼ 3.31s. The curve pattern in Fig. 14(b) is similar to that in Fig. 14(a). In Fig. 14(c) and (d), there are no obvious peak values. The energy efficiency increases gradually with the wave period in the three cases. When Te is less than 3s, there is no electrical power output and the energy efficiency equals to zero in Case 3 because the wave excitation force is too small to overcome the mechanical resistance of APR WEC in short wave periods. In Fig. 14 (c) and (d), the points independent of n are at Te ¼ 3.52s and Te ¼ 3.61s, respectively. Comparing Fig. 14 (a) through (d), it can be found that the corresponding Te decreases as the electrical resistance of PMG increases. The effects of the electrical resistance of PMG1 are shown in Fig. 15. The energy conversion efficiency increases with the resistance when the number of oscillating buoys is fixed. This is because increasing the resistance makes the electrical damping coefficient be closer to the optimum damping coefficient. The nature frequency of the WEC is close to the incident wave frequency. As a result, the efficiency under R ¼ 30U is the largest. In Cases 1, 2 and 3, the maximum efficiencies are 9.53%, 14.57% and 26.65%, respectively. 5. Conclusions A floating array-point-raft wave energy converter was developed, and a three-month experiment was carried out in real sea conditions in Taiwan Strait, China. The experimental results verified the feasibility of the new system. The overall performance, heaving
performance, output power and wave energy conversion efficiency of the pilot device under random waves were reported and analyzed in detail in this paper. The experiments proved that wave energy can be converted effectively to electrical energy by utilizing the relative motion between the floating central platform and multiple oscillating buoys. During the experimental process, the maximum half-hour mean output power reached 9.03 kW, corresponding to a significant wave height of 1.75 m and energy wave period of 5.45s. When the significant wave height was in the range of 0.6me1.3 m, its effect on the output power was more obvious. Three experimental cases were carried out by changing the number of oscillating buoys. It is found that the heaving performances of the buoys are very different from each other. When all the ten buoys were used under the significant wave height of 1.5 m and wave period of 5s, the third buoy along the direction of incident wave vibrated the most. However, similar phenomenon did not appear when just six buoys (three on each side of the central platform) were used. It also can be observed that the oscillation amplitude of the central platform is much smaller than that of the buoys. The results of the power output of PMG indicate that the output power increases and the variation range of output power decreases in the case that more oscillating buoys are used, which means that more buoys are beneficial to increasing the production of electricity and improving the power quality. Moreover, the energy conversion efficiency is affected by not only the number of oscillating buoys but also the electrical resistance of PMG. The increase of the resistance results in increased conversion efficiency.
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Fig. 15. The comparison of the energy conversion efficiency under different electrical resistance.
It is also worth noting that the wave energy conversion efficiency decreases in long wave periods when more buoys are used. The power output increases very slowly when the significant wave height exceeds 1.3 m. The present APR WEC cannot work normally when the significant wave height is greater than 2 m, so the operational capacity in extreme wave conditions needs to be enhanced too. For making up for these inadequate aspects, we plan to further optimize the APR WEC to reduce the mutual interference between each oscillating buoy and the central platform and improve the wave energy conversion efficiency and the system reliability. Acknowledgements The authors would like to acknowledge the support of the National Natural Science Foundation of China (Grant No. 51779104), the Natural Science Foundation of Fujian Province, China (Grant Nos. 2016J01247 and 2016J01245), the New Century Talent Support Program of Fujian Province, China (Grant No. JA13170) and the Foreign Cooperation Program of Fujian Province, China (Grant No. 2016I010003). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.renene.2019.02.093. References [1] H. Yue, W. Rafael, B. Cecilia, Review on electrical control strategies for wave energy converting system, Renew. Sustain. Energy Rev. 31 (2014) 329e342. [2] A. Atena, P. Roozbeh, R. Soheil, Parametric study of two-body floating-point wave absorber, J. Mar. Sci. Appl. 15 (2016) 41e49. [3] T. Hirohisa, Sea trial of a heaving buoy wave power absorber, in: Proceeding of 2nd International Symposium on Wave Energy Utilization, Trondheim,
Norway, 1982. [4] K. Budal, J. Falnes, L.C. Iversen, et al., The Norwegian wave power buoy project, in: Proceeding of 2nd International Symposium on Wave Energy Utilization, Trondheim, Norway, 1982. [5] R. Waters, M. Stalberg, O. Danielsson, et al., Experimental results from sea trials of an offshore wave energy system, Appl. Phys. Lett. 90 (2007) 102e111. nio, O. Falca ~o, Wave energy utilization: a review of the technologies, [6] F. Anto Renew. Sustain. Energy Rev. 14 (2010) 899e918. [7] J. Falnes, Wave-energy conversion through relative motion between two single-mode oscillating bodies, J. Offshore Mech. Arctic Eng. 121 (1999) 32e38. [8] J. Weber, F. Mouwen, A. Parrish, et al., Wavebob research and development network and tools in the context of systems engineering, in: Proceedings of 8th European Wave Tidal Energy Conference, 2009, pp. 416e420. Norway. [9] J. Prudell, M. Stoddard, E. Amon, et al., A permanent-magnet tubular linear generator for ocean wave energy conversion, IEEE Trans. Ind. Appl. 46 (2010) 2392e2400. [10] R. Chris, Measurements of the slow drift dynamics of a model Pelamis wave energy converter, Renew. Energy 31 (2006) 257e269. [11] G.J. Dalton, R. Alcorn, T. Lewis, Case study feasibility analysis of the Pelamis wave energy convertor in Ireland, Portugal and North America, Renew. Energy 35 (2010) 443e455. [12] L. Wang, J. Isberg, E. Tedeschi, Review of control strategies for wave energy conversion systems and their validation: the wave-to-wire approach, Renew. Sustain. Energy Rev. 81 (2018) 366e379. [13] L. Iraide, A. Jon, C. Salvador, Review of wave energy technologies and the necessary power-equipment, Renew. Sustain. Energy Rev. 27 (2013) 413e434. [14] Y. Lin, J.B. Bao, H. Liu, et al., Review of hydraulic transmission technologies for wave power generation, Renew. Sustain. Energy Rev. 50 (2015) 194e203. [15] S. Zheng, Y. Zhang, Numerical study on the dynamics of a two-raft energy conversion device, J. Fluid Struct. 58 (2015) 271e290. [16] A. Pecher, J.P. Kofoed, T. Larsen, et al., Experimental study of the WEPTOS wave energy converter, in: the 31st International Conference on Ocean, Offshore, and Arctic Engineering (OMAE2012) , Rio de Janeiro, Brazil, 2012. [17] A. Pecher, J.P. Kofoed, T. Larsen, et al., The extensive R&D behind the WEPTOS WEC, in: Proceedings of the 1st International Conference on Renewable Energies Offshore, Lisbon, Portugal, 2014. ~rio, M. Kamarlouei, et al., Power take-off concept for wave [18] J.F. Gaspar, M. Calva energy converters based on oil-hydraulic transformer units, Renew. Energy 86 (2016) 1232e1246. [19] J.F. Gaspar, M. Kamarlouei, A. Sinha, et al., Speed control of oil-hydraulic power take-off system for oscillating body type wave energy converters, Renew.
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Energy 97 (2016) 769e783. [20] M.M.K. Rico, E. Hansen, E. Vidal, Discrete displacement hydraulic power takeoff system for the wavestar wave energy converter, Energies 6 (2013) 36e48. [21] L. Zhen, Q. Na, S. Hongda, Experimental study on hydrodynamic performance of a wave energy converter within multi-heaving-buoys, Int. J. Energy Res. 37 (2017) 156e172. [22] Hongzhou He, Songgen Zheng, Shaohui Yang, et al., A kind of mooring system for a floating wave power generation platform, China: 201410419394 4 (2014) 08 (In chinese). [23] M. Jannati, S.H. Hosseinian, B. Vahidi, et al., A significant reduction in the costs of battery energy storage systems by use of smart parking lots in the power
fluctuation smoothing process of the wind farm, Renew. Energy 87 (2016) 1e14. [24] T. Ikegami, C.T. Urabe, T. Saitou, et al., Numerical definitions of wind power output fluctuations for power system operations, Renew. Energy 115 (2018) 6e15. [25] B. Ni, C. Sourkounis, Energy yield and power fluctuation of different control methods for wind energy converters, IEEE Trans. Ind. Appl. 47 (2011) 1480e1486. [26] S. Wanan, L. Anthony, Assessment of wave energy extraction from seas: numerical validation, J. Energy Resour. Technol. 134 (2012) 178e186.
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Experimental study on the performance of a floating array-point-raft wave energy converter under random wave conditions Shaohui Yang a, b, c, *, Hongzhou He a, b, Hu Chen a, b, Yongqing Wang a, b, Hui Li a, b, Songgen Zheng b a b c
College of Mechanical and Energy Engineering, Jimei University, Xiamen 361021, China Key Laboratory of Energy Cleaning Utilization and Development of Fujian Province, Xiamen, 361021, China Key Laboratory of Ocean Renewable Energy Equipment of Fujian Province, Xiamen, 361021, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 September 2017 Received in revised form 22 October 2018 Accepted 16 February 2019 Available online 18 February 2019
An array-point-raft wave energy converter (ARR WEC) integrating multiple-point absorption and raft type wave energy capturing technologies is proposed and experimentally investigated in this study. A 10 kW pilot device was developed, and a three-month real sea test was carried out in the Taiwan Strait, China. The experimental results confirmed the feasibility and effectiveness of the new system. The overall performance, heaving performance, power output and wave energy conversion efficiency of the pilot APR WEC running under random waves are reported and analyzed in detail. The heaving motions of the oscillating buoys and the instantaneous and average power output of the permanent magnet generator (PMG) are affected significantly by the number of oscillating buoys used to collect wave energy. More oscillating buoys used increase the production of electricity and improve the power quality, but lead to the reduction of energy conversion efficiency in long wave periods. The increase of electrical resistance of PMG results in an increased wave conversion efficiency. The experimental results obtained are valuable in the optimal design and operation of the ARR WEC system proposed. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Wave energy conversion Oscillating buoy Random waves Experimental study
1. Introduction Ocean wave energy has many advantages such as abundant reserves, wide distribution and high energy density, which bares tremendous potential as a source of renewable energy. The related technologies for capturing and converting wave energy have continually been developed and improved during the last decades. Two basic categories of wave energy converters (WECs) have been proposed, namely terminators and attenuators [1]. Attenuators are devices where seawater physically pushes and induces motion in the WECs structure and energy is converted by dampening this motion [2] and according to the horizontal dimension of the WECs, the attenuators are subdivided into point absorption WECs and raft WECs. The development of WECs from concept to commercial stage has been found to be difficult, slow and expensive. Although substantial progress has been achieved in the theoretical and numerical modelling of WECs, the final prototype tests under real sea
* Corresponding author. College of Mechanical and Energy Engineering, Jimei University, Xiamen City, Fujian Province, 361021, China. E-mail addresses: [email protected], [email protected] (S. Yang). https://doi.org/10.1016/j.renene.2019.02.093 0960-1481/© 2019 Elsevier Ltd. All rights reserved.
conditions are still essential. According to the recent literature [3e12], many sea trials of point absorption and raft type WECs have been performed. The simplest point absorption WEC is a single oscillating buoy reacting against a fixed frame of reference (the sea bottom or a bottom-fixed structure). An early attempt was the device G-1T containing mainly a rectangular buoy (1.8 m in length and 1.2 m in width at water line level) whose vertical motion was guided by a steel structure fixed to a breakwater, for which the sea test performed in Tokyo Bay was reported [3]. Another example was the Norwegian-Buoy containing mainly a spherical floater which could perform heaving oscillations relative to a strut connected to an anchor on the sea bed through a universal joint, for which a smallsize prototype with a buoy diameter of 1 m was tested in Trondheim Fjord [4]. Besides, a converter named L-10 in which one oscillating buoy drove a linear electrical generator was developed at Oregon State University, USA, and a 10 kW prototype with a buoy outer radius of 3.5 m was deployed and tested off Newport, Oregon [5]. The concept of a single buoy reacting against the seabed may raise difficulties due to the distance between the free surface and the bottom and to the tidal oscillations in sea level [6]. Double-buoy
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point absorption WECs are classified as a third-generation wave energy device where the wave energy capturing process is not influenced by tidal range because of its floating structure [7]. A good example for the double-buoy heaving system is the IPS invented by Sven, for which a half-scale prototype was tested in sea trials in the Pacific Ocean off the coast of Oregon [6]. The Wavebob developed in Ireland consisted of two co-axial axisymmetric buoys, whose relative axial motions were converted into electric energy through a high pressure oil system; a 1/4th scale model was tested in the sheltered waters of Galway Bay [8]. The Ocean Power Technologies company in USA developed a double-buoy WEC named PowerBuoy, where a disc-shaped floater reacted against a submerged cylindrical body, terminated at its bottom end by a large horizontal damper plate whose function was to increase the inertia through the added mass of the surrounding water; a 40 kW pro~ a in northern Spain [9]. totype was deployed off the coast of Santon Compared with the point absorption WECs, a very limited number of raft type WECs have been reported in the literature [6,10and11]. The Pelamis raft type WEC [10,11] designed and manufactured by the Ocean Power Delivery Company in Scotland had a snake-like articulated structure and included five floating cylindrical sections (150 m long, 3.5 m diameter, 750 kW rated power) which allowed not only pitching motion but also yawing motion. It was placed on the sea surface with a depth of 50 me60 m where the piston was driven by the angular displacement of adjacent cylindrical sections to convert wave energy into hydraulic energy [10,11]. The McCabe raft WEC (40 m in length and 4 m in width) was studied jointly by the University College Cork and the Queen's University Belflast in Ireland and was tested in sea trials [6], which was composed of three rectangular steel pontoons hinged together; the intermediate pontoon was smaller, and a damping plate was installed under it to increase the added mass, making the motion range of the intermediate pontoon relatively smaller so as to increase the relative angular displacement of the pontoons at the front and back ends. The point absorption or raft type wave energy capturing
539
technologies have been proved to be feasible in above-mentioned sea trials. However none of them has been commercialized yet because of their deficiencies [13]. On the one hand point absorption WECs usually have smaller geometric dimensions versus the wave length, making their wave energy capturing efficiency not affected by the direction of the incident wave, but on the other hand they usually have relatively high natural frequencies compared with the wave frequency, so that perform very poorly under the typical waves of the wide oceans [6]. Moreover, they are easily damaged under the extreme wave conditions when the vibration amplitude is beyond pre-set normal range [14]. The main merit of raft type WECs is that there exists only angular displacement among the adjacent rafts which would not be excessively large even under huge waves, resulting in higher reliability and safety. However, raft WECs must be laid out along the wave direction and have a relatively high cost compared with the WECs laid perpendicular to the wave direction [10,15]. In order to make use of the advantages and at the same time make up for the deficiencies of the point absorption and raft type WECs, the two wave energy conversion technologies have been recently integrated by some researchers [16e20]. For instance, the WEPTOS WEC, which was studied substantially by the researchers from Aalborg University [16,17], is composed of two floating symmetrical frames that support a multitude of identical rotors (i.e. oscillating buoys). The relative motions between the rotors and symmetrical frames are dampened by ratchet mechanisms to convert wave energy to mechanical energy. Seven different physical models related to WEPTOS were tested in the wave flume or under the real sea conditions [17]. The other typical example is the WaveStar WEC [18e20] where multiple oscillating bodies are connected to the fixed central platform through actuating arms. A sea trial test carried out at Hanstholm proved its feasibility. Inspired by the previous work on attenuator WECs mentioned above, we proposed an array-point-raft (APR) WEC, as shown in Fig. 1, where multiple oscillating buoys float symmetrically on the sea surface to capture wave energy just like a multi-point
Fig. 1. The prototype of APR WEC deployed at Taiwan Strait, developed by the Jimei University, China.
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absorption WEC, and the relative motions between the buoys and central platform are dampened by pinion power take-off (PTO) systems to convert wave energy to mechanical energy as done in raft type WECs. The central platform of the APR WEC also uses the V-shaped floating structure like the WEPTOS, because the experimental results [16] proved that the V-shaped (or A-shaped) structure could significantly decrease the mooring forces. But different from the WEPTOS, the floating central platform of the APR WEC is more like a barge, and the shape of the oscillating buoys and the design of the PTO system are also different. The use of the floating structure makes the APR WEC have a lower cost and lower requirements for installation environment than the Wavestar WEC whose central platform needs to be fixed at the bottom of the sea. A 10 kW prototype of APR WEC was designed and manufactured using a grant from the State Ocean Administration of China. The prototype was deployed between Xiaodeng Island and Xiaojinmen Island of Taiwan Strait, South China Sea. The straight-line distance between the prototype and the coast is 300 m. The seawater depth of the installation site is approximately 20 m. The wave energy resource of the experimental site is not rich, indicating that simply amplifying the size of each buoy cannot directly result in a larger energy output. An array composed of multiple small buoys may be an alternative solution to increase wave energy capturing capacity [21]. In this study, the test for analyzing the dynamic performances of the APR WEC in actual sea conditions was conducted from June to August, 2016. All of the design concepts, as illustrated in detail below, were realized and verified during the sea trial. The rest of the present paper is organized as follows. In section 2, the design, structure and operating principle of APR WEC are introduced. The experiment procedure and test instruments are described in Section 3. Then the performance characteristics of APR WEC are analyzed in detail based on sea trial data in Sections 4. Finally, the conclusions of the study are summarized in Section 5.
2. Conceptual design 2.1. The components of APR WEC As shown in Fig. 2, APR WEC is mainly composed of a floating central platform, ten oscillating buoys, ten two-way transmission gears, a mooring system, two PMGs and submarine cables. Tied to the mooring float by a wire rope, the floating central platform appears like a wedge-shaped barge. The anchor chains, anchor blocks and mooring float constitute the mooring system. Due to the design of the interior of the mooring float [22], the central platform can rotate freely around the mooring float and align automatically towards the incident waves, thus eliminating the influence of incident wave directions on the system. As shown in Fig. 2(c), the ten oscillating buoys are divided into two linear arrays (buoys I-V as the first array, and buoys VI-X as the second array) and arranged evenly on both sides of the central platform. Because of the difference such as the hydrodynamic coefficient, mass property, geometric shape and so on between the oscillating buoys and the central platform, the oscillation amplitude of the central platform is much smaller than that of the oscillating buoys, leading to relative motions between them. The relative motions are then transformed into mechanical energy of the horizontal rotation shaft by the two-way transmission gears (see Section 2.3 for details), and eventually into electric energy for output. The dimensions of the prototype are shown in Fig. 2(b) and (c). The central platform has a length of 18 m, maximum width of 8 m, height of 2.4 m, designed draught of 1.3 m, and displacement of 96t. The diameter of the mooring float is 3 m, and the height is 2.5 m. The length of each anchor chain is 50 m, and the weight of each anchor block is 8000 kg.
2.2. Oscillating buoy As shown in Fig. 3(a), every oscillating buoy used in the experiment is cylindrical and connected to the central platform by an actuating arm. The diameter of the buoy is 1.2 m, and the length is 1.7 m. Ballast can be filled into the buoys through a rounded hatch cover to adjust the draft of each buoy. The weight of each buoy (including the actuating arm and other necessary accessories) is 250 kg. 2.3. Two-way transmission gearset Many WECs adopt hydraulic systems as the PTOs to convert wave energy into electric energy, where hydraulic oil leakage is a common problem which is unavoidable in marine environments [13]. Mechanical gear transmission is an alternative method to convert wave energy efficiently. A two-way transmission gearset was designed and used in APR WEC, which mainly includes an actuating shaft, three kinds of pinions and a driven shaft, as shown in Fig. 4. The actuating shaft is fixed to the actuating arm of each oscillating buoy. When the oscillating buoy ascends or descends under the wave excitation force, the actuating shaft will be driven to rotate forwards or backwards. An overrunning clutch is installed in the interior of the reversing pinion which converts the reciprocating motion of the actuating pinion into unidirectional rotary motion of the driven pinion, and the result is that the driven shaft rotates continuously in one direction. 2.4. Array driven mode The array driven mode of APR WEC is shown in Fig. 5. Five oscillating buoys are arranged in a linear array and actuate simultaneously a horizontal shaft to rotate unidirectionally. The horizontal shaft is composed of multiple driven shafts of two-way transmission gearsets. With a transmission ratio of 1:25, the overdrive gearbox enhances the rotational velocity of the horizontal shaft to the rated velocity of PMG. Two PMGs are installed on both sides of the prototype, respectively. The nominal power and single phase nominal output voltage of each PMG are 5 kW and 220 V. Four different electrical resistances (5U, 10U, 20U and 30U) are connected to each PMG through 450 m-long subsea power cables. A flywheel with a moment of inertia of 100 kgm2 works as an energy accumulator to attenuate the effect of wave energy fluctuations. 3. Experimental set-up The emphasis of this investigation is to analyze the dynamic performance of APR WEC in different random wave climates. Some gauges and sensors were selected to monitor the operating data of the prototype during the sea trial. A pressure-type directional wave recorder (Model: MIDAS DWR) was fixed on the seabed, right under the mooring float, to collect the data of wave height and period every thirty minutes, of which the accuracy is ±0.04%. A three-month on-site wave data measurement was carried out, with the statistical occurrence frequencies of half-hourly averaged wave periods and heights shown in Table 1 where Hs denotes the significant wave height and Te denotes the energy wave period. According to Table 1, the most frequently occurring wave conditions were within the energy wave period of 3.0e4.5s and the significant wave height of 0.3e1.2 m. Fig. 6 shows the power spectral density (PSD) plot of the measured wave elevation which is obtained by processing the raw wave height spectrum through a third order polynomial filter.
S. Yang et al. / Renewable Energy 139 (2019) 538e550
Fig. 2. Schematic diagram and geometric parameters of the APR WEC.
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Fig. 3. Oscillating buoy used in the experiment.
Fig. 4. Two-way transmission gearset used in the experiment.
Six displacement sensors (Model: SCAH2000) were installed on the still water line of the oscillating Buoys I-V and the central platform to detect their displacements. The measuring accuracy of these displacement sensors is ±0.1%. Two voltage gauges (Model: GTVB-500) with a measuring accuracy of ±0.25% and two current gauges (Model: TKC-BSD40) with an accuracy of ±0.5% were used to measure the output voltages and currents of PMGs. The shortest sampling frequency of all of the displacement sensors, voltage gauges and current gauges is 20 Hz. The instantaneous output power of PMG can be calculated by multiplying the output voltage and the current together. During the experiment, all data was acquired and processed by a
wireless remote monitoring system especially developed for this prototype as shown in Fig. 7, which helped achieve unattended operation of all the devices and improving the efficiency of the experiments. 4. Results and discussion 4.1. Overall operating performance In the first month of the experiment, all the ten oscillating buoys were put in the seawater to collect wave energy, and the electrical resistance of PMG was set at 30U. The data from the series of sea
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543
Fig. 5. The array driven mode of APR WEC.
Table 1 Statistical frequency of on-site wave resource during the experiment. Hs (m)
Te (s) <2.5
2.5e3.0
3.0e3.5
3.5e4.0
4.0e4.5
4.5e5.0
5.0e5.5
<0.3 0.3e0.6 0.6e0.9 0.9e1.2 1.2e1.5 1.5e1.8 1.8e2.1 2.1e3.0 Total
12 28 14 5
37 86 66 42 28
52 323 606 104 62 1 1
1 14 58 26 12 1
259
1149
26 232 302 108 89 27 5 2 791
2 26 142 56 65 8 2
59
82 426 772 282 110 5 8 5 1690
301
112
5.5e6.0 4 12 3
19
Total 212 1140 1972 626 365 42 16 7 4380
Fig. 6. PSD plot of measured wave elevation. Fig. 7. The wireless remote monitoring system.
trials are shown in Fig. 8. As illustrated in Fig. 8 (a), the maximum significant wave height was 1.75 m, occurred on 27th June, 2016. On the same day, the electrical energy generated by the two PMGs was the maximum, reaching 75.31 kWh (Fig. 8 (b)). On 3rd June, the electrical energy generated was the minimum, just 1.22 kWh. It can be calculated that the average electrical energy generated per day was 28.09 kWh and the accumulative electrical energy was 842.7 kWh during the 30 days. As shown in Fig. 8(c) which displays
the half-hour mean output power of the prototype on 27th June, the maximum half-hour mean output power was 9.03 kW, corresponding to a 1.75 m significant wave height and 5.45s energy wave period. The relationship between the half-hour mean power output and significant wave height is shown in Fig. 8 (d) which contains 2325 data points. It can be seen that the half-hour mean output
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Fig. 8. The overall performance of APR-WEC in June 2016.
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power almost equals to zero when the significant wave height is less than 0.45 m, i.e., both of the PMGs cannot generate electricity when the wave height is too small. The output power increases with the significant wave height when it is greater than 0.45 m. It also can be found that the variation of the output power is more significant within the wave height range of 0.6me1.3 m than that in other zones.
4.2. Heaving performance For studying the effect of the number of oscillating buoys on the heaving response and output power in a random wave climate, comparison tests in three cases were performed by changing the number of oscillating buoys on each side of the prototype in the next two months. The heave motions of Buoys I-V and the central platform were recorded and stored by the wireless remote monitoring system. Fig. 9 illustrates the time histories of these heave motions when Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U (R is the electrical resistance of each PMG). In Case 1, all the ten oscillating buoys were put in the seawater to collect wave energy. The transient displacement data of Buoys IV are shown in Fig. 9 (a). It can be found that the oscillation amplitudes and phases of the five buoys have distinct differences. The
545
vibration of Buoy-III is the most strenuous, even greater than BuoyI. The oscillation amplitudes of Buoy-II, Buoy-IV and Buoy-V are relatively small. In Case 2, six oscillating buoys (Buoys I, III, V, VI, VIII and X) were used. As illustrated in Fig. 9 (b), the heave motion of Buoy-I is slightly greater than Buoy-III. In Case 3, just two oscillating buoys (Buoys III and VIII) were put in the seawater, the heaving motion of Buoy-III is shown in Fig. 9 (c). Fig. 10 illustrates the heave motion of the central platform in the three cases mentioned above. It is clear that the number of the buoys used in the experiments has no obvious effect on the heave motion of the central platform. Because no sensors were used to detect the heave motions of Buoys VI-X, the detailed transient displacement data of them were not obtained in the three cases. But during the course of the experiment, we observed that the buoys' heave motions on both sides of the central platform were very similar. Fig. 11 shows the PSD plots of the APR WEC heaving displacements in the three cases when Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U. As shown in Fig. 11(a), the peaks of the PSD plots of the Buoys I, II, IV and V correspond to the same circular frequency, 1.28 rad/s, which is very close to the theoretical resonant frequency of each buoy, 1.32 rad/s. The PSD plot of Buoy III is different in shape from the other buoys. There are small fluctuations at the crest. In Fig. 11(b), the PSD values of Buoys I, III and V in Case 2 decrease gradually
Fig. 9. Heave motions of oscillating buoys in the three cases studied (Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U).
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Fig. 10. Heave motions of central platform in the three cases (Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U).
Fig. 11. The PSD plots of the APR WEC heaving displacements in the different cases (Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U).
along the direction of the incident wave propagation within the circular frequency range of 0.9 rad/s-1.8 rad/s. There are still slight fluctuations at the crest of the curve for Buoy III. As shown in Fig. 11(c), the PSD plot of the Buoy III in Case 3 is very similar to the PSD plots of the other buoys in Case 1 and Case 2, but the fluctuations at the crest of the curve vanish and the circular frequency corresponding to the peak is still 1.28 rad/s. For the central platform, the PSD plots in the three cases are almost the same as shown in Fig. 11(d). Both the peak and the circular frequency (0.79 rad/s) corresponding to the peak are obviously lower than the buoys.
4.3. Power output Given that the power output of the PMG2 is very analogous to the PMG1, we mainly analyze the power output characteristics of the PMG1 in the following sections. Fig. 12 shows the instantaneous power output of the PMG1 in the three cases when Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U. It can be found that the number of oscillating buoys can affect the amount and stability of instantaneous power output. Comparing the three curves in Fig. 12, one can see that the instantaneous power output of PMG1 in Case 1 is obviously larger
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Fig. 12. Instantaneous power output curves. Fig. 13. Average power output curves.
than that in Case 2 and Case 3. The result demonstrates that the instantaneous output electrical energy is higher when more oscillating buoys are used to collect wave energy. According to Fig. 12, the mean instantaneous power output of PMG1 reaches 2.36 kW in Case 1, while in the same wave climate, the value is 1.95 kW in Case 2 and 1.37 kW in Case 3. The standard deviation is a common quantitative index which is used frequently to evaluate the fluctuation of the power output in wind power generation [23,24]. We utilize the average deviation from the mean power output [24,25] to describe the fluctuation of the instantaneous power output, which can be calculated by:
AVD ¼
N PðtÞi P 1 X N i¼1 P
(1)
where t is the interval between two sampling times, PðtÞi is the power output at the ith sampling time, P is the average power output between the 1st and the Nth sampling times, and N denotes the number of the samplings. Table 2 shows the calculated AVD of the instantaneous power output in the three cases when Hs ¼ 1.5 m, Te ¼ 5s and R ¼ 30U. The largest AVD always appears in Case 3 no matter if t is set at Te/8, Te/4, Te/2 or Te, and the smallest AVD appears in Case 1, indicating that the fluctuation of the instantaneous power output diminishes when more oscillating buoys are used. Fig. 13 presents the average power output curves in entire range of the wave periods when R is set at 30U. The average power output in Fig. 13 refers to the mean value of all half-hour power outputs at a particular wave period. It can be found that the average power output of the PMG1 increases monotonically with the increase of the wave period in the three cases. Whatever the wave period is, the average power output in Case 1 is always the highest and that in Case 3 the lowest. As demonstrated by the higher instantaneous and average power output in Figs. 12 and 13, the greater number of oscillating buoys used leads to higher power output.
Table 2 The average deviation of the instantaneous power output in the three cases. AVD
Te/8
Te/4
Te/2
Te
Case 1 Case 2 Case 3
0.798 0.854 0.998
0.864 0.974 1.086
0.616 0.644 0.938
0.612 0.636 0.934
4.4. Energy conversion efficiency The energy conversion efficiency of APR WEC is one of the important performance indexes, defined in this paper as:
h¼
Pmean Pwave
(2)
where Pmean is the average value of half-hour output electrical power of PMG1, and Pwave is the average wave power of in deep water which was given by Wanan [26]:
Pwave ¼
rg2 2 H Te L 64p s
(3)
where r is the seawater density, g is the gravity acceleration, and L is the valid width along the direction of the incident wave and can be calculated as:
L ¼ nl sin
b 2
(4)
where l is the length of each oscillating buoy, and b is the included angle of the wedge-shaped central platform. For the present prototype, l is 1.7 m (see Fig. 3(a)) and b equals to 300 (see Fig. 2(c)). The energy conversion efficiency of APR WEC working in the three cases is shown in Fig. 14. A common observation is that the energy conversion efficiency gets higher when more oscillating buoys are used in short wave periods (i.e. high wave frequencies), and on the contrary, the efficiency gets lower when more buoys are used in long wave periods (i.e. low wave frequencies). Furthermore, it is interesting to notice that there always exists a wave period which leads to an equal energy conversion efficiency of APR WEC in all the three cases regardless of the electrical resistance. As shown in Fig. 14(a) when R ¼ 30U, the energy conversion efficiencies are equal at Te ¼ 3.15s in the three cases. When Te is less than 3.15s, the efficiency in Case 1 is higher than that of the other two cases, while when Te is larger than 3.15s, the efficiency in Case 1 becomes the lowest. It also can be found that the variation of the energy efficiency is the most gradual in Case 1 and the steepest in Case 3. In other words, the range of the response wave period gets wider when more oscillating buoys are used. The peak value of the energy conversion efficiency appears at about Te ¼ 5s in all of the
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Fig. 14. The energy conversion efficiency for different number of oscillating buoys.
three cases. In Fig. 14(b) where R ¼ 20U, the point independent of energy wave period is at Te ¼ 3.31s. The curve pattern in Fig. 14(b) is similar to that in Fig. 14(a). In Fig. 14(c) and (d), there are no obvious peak values. The energy efficiency increases gradually with the wave period in the three cases. When Te is less than 3s, there is no electrical power output and the energy efficiency equals to zero in Case 3 because the wave excitation force is too small to overcome the mechanical resistance of APR WEC in short wave periods. In Fig. 14 (c) and (d), the points independent of n are at Te ¼ 3.52s and Te ¼ 3.61s, respectively. Comparing Fig. 14 (a) through (d), it can be found that the corresponding Te decreases as the electrical resistance of PMG increases. The effects of the electrical resistance of PMG1 are shown in Fig. 15. The energy conversion efficiency increases with the resistance when the number of oscillating buoys is fixed. This is because increasing the resistance makes the electrical damping coefficient be closer to the optimum damping coefficient. The nature frequency of the WEC is close to the incident wave frequency. As a result, the efficiency under R ¼ 30U is the largest. In Cases 1, 2 and 3, the maximum efficiencies are 9.53%, 14.57% and 26.65%, respectively. 5. Conclusions A floating array-point-raft wave energy converter was developed, and a three-month experiment was carried out in real sea conditions in Taiwan Strait, China. The experimental results verified the feasibility of the new system. The overall performance, heaving
performance, output power and wave energy conversion efficiency of the pilot device under random waves were reported and analyzed in detail in this paper. The experiments proved that wave energy can be converted effectively to electrical energy by utilizing the relative motion between the floating central platform and multiple oscillating buoys. During the experimental process, the maximum half-hour mean output power reached 9.03 kW, corresponding to a significant wave height of 1.75 m and energy wave period of 5.45s. When the significant wave height was in the range of 0.6me1.3 m, its effect on the output power was more obvious. Three experimental cases were carried out by changing the number of oscillating buoys. It is found that the heaving performances of the buoys are very different from each other. When all the ten buoys were used under the significant wave height of 1.5 m and wave period of 5s, the third buoy along the direction of incident wave vibrated the most. However, similar phenomenon did not appear when just six buoys (three on each side of the central platform) were used. It also can be observed that the oscillation amplitude of the central platform is much smaller than that of the buoys. The results of the power output of PMG indicate that the output power increases and the variation range of output power decreases in the case that more oscillating buoys are used, which means that more buoys are beneficial to increasing the production of electricity and improving the power quality. Moreover, the energy conversion efficiency is affected by not only the number of oscillating buoys but also the electrical resistance of PMG. The increase of the resistance results in increased conversion efficiency.
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Fig. 15. The comparison of the energy conversion efficiency under different electrical resistance.
It is also worth noting that the wave energy conversion efficiency decreases in long wave periods when more buoys are used. The power output increases very slowly when the significant wave height exceeds 1.3 m. The present APR WEC cannot work normally when the significant wave height is greater than 2 m, so the operational capacity in extreme wave conditions needs to be enhanced too. For making up for these inadequate aspects, we plan to further optimize the APR WEC to reduce the mutual interference between each oscillating buoy and the central platform and improve the wave energy conversion efficiency and the system reliability. Acknowledgements The authors would like to acknowledge the support of the National Natural Science Foundation of China (Grant No. 51779104), the Natural Science Foundation of Fujian Province, China (Grant Nos. 2016J01247 and 2016J01245), the New Century Talent Support Program of Fujian Province, China (Grant No. JA13170) and the Foreign Cooperation Program of Fujian Province, China (Grant No. 2016I010003). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.renene.2019.02.093. References [1] H. Yue, W. Rafael, B. Cecilia, Review on electrical control strategies for wave energy converting system, Renew. Sustain. Energy Rev. 31 (2014) 329e342. [2] A. Atena, P. Roozbeh, R. Soheil, Parametric study of two-body floating-point wave absorber, J. Mar. Sci. Appl. 15 (2016) 41e49. [3] T. Hirohisa, Sea trial of a heaving buoy wave power absorber, in: Proceeding of 2nd International Symposium on Wave Energy Utilization, Trondheim,
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