Electrical Generator Design for Darrieus-Type Wave Energy Converter

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J. Ocean Eng. Technol. 2025;39(1):63-72

Publication date (electronic) : 2025 February 28

doi : https://doi.org/10.26748/KSOE.2024.091

Patrick Bach^1,2, Tsumoru Shintake³, Hideki Takebe⁴, Jun Fujita⁴, Toshio Shindou⁵, Kazuaki Uchibori⁶, Masayuki Shimizu⁷, Hiroyasu Ochiai⁸, Yoshiharu Yoshimura⁹, Isaku Kanno¹⁰

¹Engineer, Ichinomiya Denki Co., LTD, Hyogo, Japan

²PhD Student, Department of Mechanical Engineering, Kobe University, Kobe, Japan

³Professor, Okinawa Institute of Science and Technology (OIST), Onna-son Okinawa, Japan

⁴Researcher, Okinawa Institute of Science and Technology (OIST), Onna-son Okinawa, Japan

⁵Senior Engineer, Ichinomiya Denki Co., LTD, Hyogo, Japan

⁶Technical staff, Institute of Computational Fluid Dynamics (iCFD), Tokyo, Japan

⁷General Manager, Mitsubishi Heavy Industries Machinery Systems, Ltd., Kobe, Japan

⁸Senior Engineer, Mitsubishi Heavy Industries Machinery Systems, Ltd., Kobe, Japan

⁹Engineer, Mitsubishi Heavy Industries Machinery Systems, Ltd., Kobe, Japan

¹⁰Professor, Department of Mechanical Engineering, Kobe University, Kobe, Japan

Corresponding author Patrick Bach: +81-791-59-8200, pat-bach@ime-group.co.jp

This is a paper from the proceedings of 2024 Asian Offshore Wind, Wave, and Tidal Energy Conference held in Busan, S. Korea (Bach et al., 2024).

Received 2024 November 6; Revised 2024 November 28; Accepted 2024 December 9.

Abstract

1. Introduction

In recent years, climate-friendly energy production has attracted a great deal of attention among researchers exploring novel approaches for using renewable energy, with the share of renewable energy in global energy production constantly growing (Saavedra et al., 2021). Renewable energy sources contribute to CO₂ emission reduction and therefore considered environmentally friendly and less disruptive (Ang et al., 2022). They can be used in different areas depending on the energy generation method, including biomass, geothermal, hydroelectric, solar, wave, and wind (Owusu and Asumadu-Sarkodie, 2016). Wave energy converters (WECs) represent a broad research area that covers a range of electricity generation approaches. From the point of view of energy generation, they can be divided into “oscillating water column (OWC),” “oscillating body system” and “overtopping converter.” In terms of location, WECs can be classified as offshore, nearshore, and onshore systems (Curto et al., 2021, Chybowski and Kuźniewski, 2015; Falcao, 2010). However, special precautions must be taken to ensure that WECs do not harm marine ecosystems (Riefolo et al., 2015). Further, they must be able to withstand various environmental impacts such as seawater corrosion, earthquakes, and typhoons, and should not cause environmental pollution in the event of an accident (Chakraborty and Majumder, 2019).

Our previously reported WEC applications (Halder et al., 2020; Shintake et al., 2017) were located in the breaking wave zone and harnessed energy from incoming breaking waves for electrical energy generation. Shintake (2016) reported that breaking waves can release large amounts of energy and create a strong flow towards the shore, thereby necessitating the use of screw-like turbines. Such WECs are susceptible to standstill periods if waves of sufficient strength no longer hit them owing to changes in weather conditions. If there are frequent standstill periods during the day, effectiveness decreases drastically (Arena et al., 2015). To increase the daily operational time, it is necessary to find alternative cost-effective methods for converting energy into electricity. In recent years, various new approaches have emerged, each with its advantages and disadvantages (Guo and Ringwood, 2021; Koca et al., 2013). We introduced a new design with a 2-turbine concept that requires less energy to maintain turbine rotation. A horizontally oriented, straight-bladed Darrieus turbine was adopted, which utilizes a horizontally oscillating underwater flow (Fig. 1(a)) for energy generation (Abusannuga and Özkaymak, 2022; Batista et al., 2018). Darrieus turbines are characterized by the use the energy generated by both forward and backward horizontal oscillating currents in coastal waves that are transverse to the turbine axis, allowing a greater amount of energy to be harnessed (Li et al., 2023). Although the Darrieus turbine has an advantage over other types of turbines in terms of daily operating time, it lacks the ability to self-start and has high starting power requirements; however, once in rotation, the Darrieus turbine does not require much energy to maintain the rotation (Batista et al., 2011; Kirke and Lazauskas, 2008). Therefore, it is necessary to design a generator with a low cogging torque because the energy of the water oscillation may not be sufficient to turn the turbine, resulting in a reduction in the daily operating time (Darjazini et al., 2023). There are several ways to reduce the cogging torque of permanent magnet generators. One way is to change the magnet to a bread shape; however, this method only applies to the surface and internal magnet rotors. Other possible methods include changing the pole-to-slot ratio, diameter, length, and gap size. However, such changes also affect performance and efficiency (Chung & You, 2015; Muljadi and Green, m p2002). To ensure safe operation and increase the daily operational time, the WEC must be mounted on a height-adjustable platform before the breaking wave zone. This allows the WEC to be moved into deeper water under adverse weather conditions to avoid potential damage and set the correct height at low and high tide. Thus, breaking and post-breaking waves that can generate destructive forces and damage the WEC can be avoided. To withstand underwater loads, the connection between the shaft and blades was chosen to be at the center of the blades. The blade ends were reinforced with a guide ring that protects the blades from bending and maintains them in the correct position.

Fig. 1.

(a) Schematic representation of the working principle; (b) 1:4 model; and (c) 3D model in sectional view

The potential for harnessing solar energy is low across a large number of marine regions worldwide because of local climate and weather conditions, including cloudy and rainy weather with low average number of sunshine hours per day and long periods of low sunlight (Halkos and Gkampoura, 2020; Malinowski, 2021). Wind turbines, on the other hand, are not suitable for construction near the coastline of small islands because they require tall cranes and substantial space for installation and maintenance, which can drastically increase the cost (Desalegn et al., 2023). A small WEC near the breaking zone allows easier and more cost-effective installation and maintenance, requiring only a small mobile crane. The expected output power of our conceptual WEC is >10 kW, and it is suitable for small power systems in small island regions. The cost of electricity on these islands is usually higher than that in other regions, mainly owing to the transportation cost of fossil fuels, such as coal and diesel, and the limited space available for a variety of energy systems (Filho et al., 2022; Weisser, 2004). However, several WECs can solve this problem as they can generate a sufficient amount of energy at a low cost without occupying large spaces.

2. Principle of Hardware Design

Several technical issues must be addressed while designing operational WECs. As these issues are related to the high energy density of waves on turbines and generators and the effects of seawater on materials, we investigated a generator and platform design to address them. A 1:4 conceptual design of the WEC device is shown in Fig. 1(b) and a sectional 3D model is shown in Fig. 1(c). The boundary conditions for hardware were established by considering the following points.

3. Hardware Design and Simulation Evaluation

3.1 Design of the Full-Scale and Scaled-Down Generator

The electrical generator was driven by the up-and-down rhythm of the oscillating water near the breaking wave zone. This requires the use of a permanent magnet (PM) generator coupled with energy storage and a DC/AC inverter system to supply alternating current to the grid. Cogging noise from the generator is not a major problem because of presence of the background noise caused by nearby waves. As a result, the design of the generator and permanent magnets can be simplified, maximizing the efficiency of power generation and minimizing costs. As mentioned in the Introduction, the main goal is to achieve the lowest possible cogging torque, which would increase the number of operating hours per day. The cogging torque T_cog in a generator can be described by the following equation (Wang et al., 2019):

(1) Tcog(α)=−∂W(α)∂α

where W is the magnetic energy and α is the rotor angle. The magnetic energy is the sum of the magnetic energies of the air gap W_airgap and the permanent magnet W_PM and can be described as follows:

(2) W(α)=Wairgap+WPM=12μ0∫VB2dV

where B is the magnetic field density and μ₀ is the magnetic permeability. When the gap size g and stator stack length L_i are separated from the rotor angle, it can be expressed with the following equation (Gieras, 2004):

(3) W(α)=Lig2μ0∫B2(θ,α)dθ

where B (θ, α) describes the air-gap magnetic field density. Let us assume that the energy change with the permanent magnets and iron core is negligible compared with the energy change with the air-gap magnetic field. This can be expressed as follows (Zhang et al., 2022):

(4) W(α)=14μ0(R22−R12)∫0Li[∫02πK2(θ,z)B2(θ,α)dθ]dz

where R₂ is the inner diameter of the stator core, and R₁ is its outer diameter of the rotor core. Therefore ( R22−R12) corresponds to the gap size g and K²(θ, z) is the stator core slotting adjustment function. Now, Eq. (1) becomes.

(5) Tcog(α)=−2LiBr2μ0πNsNPNL(R22−R12)∑n=1∞[Ksknsin(nNLb02)sin(nNLαP′πNP)sin(nNLα)]

where B_r is the remanence density of the permanent magnets, K_sk is the slot skew factor, b₀ is the slot opening width, α_P′′ is the polar arc factor of the magnets, N_S is the number of slots, N_P is the number of poles, and N_L is the least common multiple (LCM) of N_S and N_P. Eq. (5) demonstrates that the skew factor, stack length, slot width, gap size, pole arc factor, and numbers of slots and poles mainly influence the cogging torque.

To determine the required characteristics for low cogging torque, Eq. (5) can be used. In addition, as the design process had to be carried out considering cost efficiency, it was necessary to develop a generator in which the stator and rotor core lengths were approximately the same as the diameter. If the differences between these are too large, production costs will increase significantly. Therefore, for testing and weight reduction, the shaft of the scaled-down generator was designed with a significantly smaller diameter. The final specified dimensions of the full-scale and small-scale generators are listed in Table 1.

Table 1.

Dimensions and expected values of the conceptual full-scale and scaled-down generator

Figs. 2(a) and (b) show the generator configurations tested by numerical simulations using the current version of JMAG-Designer 22.0 from JSOL Corporation (JSOL Corporation, 2023). A 36-slot design with a three-phase output, a 2-star concept (Fig. 2(c)), and 20 permanent magnets were selected for the final configuration. Our design was planned to be fabricated with two different lengths: one for a full-scale WEC and the other for a scaled-down test generator. The stack lengths were 400 and 60 mm, with expected output powers of >10 and >1 kW at 180 rpm, respectively. The selected neodymium (NdFeB) permanent magnets have a remanence field of Br 13.8–14.4 kG and a coercive force Hcb of 1035 kA/m. Each slot was wrapped with 84 turns of 0.75 a thick copper wire. To prevent a short circuit from the magnet wire to the stator core, a thin insulating paper was inserted into each slot before the winding process. The dimensions of the magnets were 30 mm × 8 mm × 400 mm. In practice, the magnets were fabricated as small 50 mm long pieces and then positioned in groups of eight in the rotor to allow thermal expansion. To facilitate the assembly of the magnets and rotor core on the shaft, the rotor cores were also fabricated with a stack length of 50 mm and arranged in a row of eight pieces. For the scaled-down generator, permanent magnets and a rotor core were fabricated with a length of 60 mm. The outer diameter of the stator core was set to 290 mm; along with the minimum thickness of the aluminum housing required for safe underwater use, overall width, and height were 350 mm × 350 mm. This size also represents the limit at which extruded aluminum can be custom-engineered in a cost-effective manner to allow for low-cost manufacturing.

Fig. 2.

2D-Model of the Generator with 36 Slots and 20 Poles: (a) in complete view; (b) in partial view; and (c) 3-phase winding diagram

First, simulations were performed to evaluate the conceptual design at 180 rpm. In each simulation, a cycle consisting of one positively oriented magnet and one negatively oriented magnet was used. These two magnets can be considered a pair, and owing to the speed, the cycle of a pair takes exactly 0.033 s. Fig. 3(a) shows the simulated cogging torque, a peak-to-peak cogging torque of −2.6 Nm to 1.9 Nm and −0.4 Nm to 0.3 Nm was achieved for the full-scale and scaled-down generator, respectively. The effective cogging torque was 1.4 Nm for a 400 mm stack length and 0.21 Nm of 60 mm stack length. Fig. 3(b) shows the induced voltage over one cycle: the effective value for a 400 mm stack length was 1123.16 V for U-V, 1119.17 V for V-W, and 1122.83 V for V-W. However, because of the high induced voltage, it is possible to change the 2-star concept to a 4-star concept to adjust the induced voltage according to the cable characteristics and location conditions. If a 4-star concept is used, the effective values of the induced voltage are halved and the current is doubled. On the other hand, the effective value for the scaled-down generator is 168.47 V for U-V, 167.88 V for V-W, and 168.43 V for W-U. Fig. 3(c) shows the circuit voltages for lead lines U, V, and W. Since the curves of U, V, and W are shifted exactly 120 degrees each in the order U→V→W, we can assume that the angle structure and position of the winding have been designed correctly. Fig. 4(a) shows the magnetic flux density based on the 60 mm stack length results. A maximum density of approximately 2 T was achieved in the stator core. A magnetic-field plot is shown in Fig. 4(b), which shows the correct behavior of the magnetic-field lines. These results are comparable to the expected values and magnetic behavior obtained from the numerical calculations, which led to an accurate design concept and the start of manufacturing the scaled-down generator. The simulation results also show that a low cogging torque was achieved, which was the main objective of the design concept. The generator development process, including the manufacturing and testing of the scaled-down and full-size generators, and further detailed analysis, was conducted by Ichinomiya Denki Co., Ltd.

Fig. 3.

Simulation results for the 400 mm and 60 mm stack length with (a) cogging torque, (b) induced voltage and (c) circuit voltage, for one cycle of one positively and one negatively poled magnet at 180 rpm.

Fig. 4.

Simulation results of the stator with 60 mm stack length (a) magnetic flux density and (b) magnetic field plot

3.2 Mechanical Seal and Protection from Seawater

Although the WEC is located near the breaking wave zone, seawater can enter the generator housing and damage and/or rust the permanent magnets, ball bearings, rotor core, and stator core, which may result in malfunction. The circumferential bushing, which seals the rotating shaft, was the most difficult part to seal. We chose a mechanical seal instead of an oil seal because the latter uses a rubber lip structure that cannot withstand the grinding effect of salt crystals when the turbine rotates for long periods. The mechanical seal chosen was HA211 from EKK Eagle Industry Co., Ltd. This seal uses SiC rings pressed by a coiled spring. We plan to fill the generator with environmentally friendly silicone oil and provide positive static pressure (1 kg/cm²) through a reservoir mechanism. The oil provides lubrication for the mechanical seal and ball bearings, as well as heat transfer between the winding coil and the generator frame. The expected oil leakage is less than 100 ml after ten years of operation. The housing was cooled by water circulation, which was expected to be available at the location. One of the weaknesses of most waterproof generators is the cable connection. Therefore, a cable cover must be designed to protect the cable connection with the stator core. A shielded cable gland was designed to connect the inside of the cable cover to the outside. We filled the cover with silicone oil and applied a static pressure of 1 kg/cm² to prevent seawater ingress. The oil from the cable cover and generator is completely separated so that in the event of seawater ingress, it will not spread throughout the system. An additional outer cable cover was fitted over the shielded cable gland to protect it from incoming waves. However, the interior of the outer cable cover was not waterproof.

The NdFeB magnets were protected by an epoxy resin coating that is resistant to external influences and was sufficiently strong to prevent damage during the assembly process when the magnet was inserted into the rotor core. If any damage occurred during the assembly, it can initiate a corrosion process or affect the magnetic properties. Fig. 5 shows a magnet after assembly in the rotor core of the scaled-down generator. It can be seen that the epoxy coating remained stable and undamaged, which is well suited to our application.

Fig. 5.

Permanent magnet after the assembly process

3.3 Adjustable Platform

The WEC is mounted on a height-adjustable platform so that it can be moved into deeper water as weather conditions change to protect it from the strong forces experienced during stormy weather. This platform was also designed to correct the height in relation to high and low tides to maximize the operational time per day. However, the position of the cable connection is an important factor. The cable must move up and down with the WEC to prevent damage, pinching, or disconnection. Fig. 6(a) shows the conceptual design and Fig. 6(b) shows a schematic illustration of the functional method. The platform consists of a base plate attached to the WEC. Other components include the main hydraulic foot installed between the base plate and the seabed. The second part is the supporting hydraulic foot, which is installed between the connecting rod of the main hydraulic foot and the seabed. Both hydraulic feet were designed to be filled with the same silicone oil as the generator and maintain a minimum static pressure to prevent seawater from entering. The cable entry point into the cover is designed to be located on the frame structure between the turbines. Before the connection point, the cable was laid along the supporting hydraulic foot, down to the seabed. An S-FREE submarine cable with an outer diameter of 25 mm was used as the power cable. This type is characterized by good seawater resistance, stability, and flexibility.

Fig. 6.

(a) View on the full-scale 3D-WEC mounted on the platform and (b) schematic concept of the adjustable platform

Owing to its location immediately below the waterline, a warning light should be installed on top of the WEC housing, which should be located above or near the waterline. Because the WEC is positioned just below the waterline, passing boats must be warned to avoid damage to the WEC and boats. The platform will be designed, tested, and manufactured by the Mitsubishi Heavy Industries Machinery Systems. The cable connection and position were planned and designed by Ichinomiya Denki Co., Ltd.

4. Fabrication Process and Experimental Details

To reduce weight, the frame was fabricated from aluminum A5052. Good corrosion resistance to seawater make aluminum alloy A5052 a preferred material for marine applications (Bhowmik and Mishra, 2016). The frame was fabricated using extrusion molding. A cast material would also be suitable, but any air entrapment during casting could cause the top layers to flake off and the thickness would decrease significantly over a long period of time. The frame of the scaled-down generator was made of A5052, and to reduce cost and weight, brackets were also made of this material. This served as a test run for the manufacturer to determine whether a frame of this size could be fabricated without large air pockets. However, the brackets, shield covers, cable covers, and shafts of the full-scale generator are planned to be made from a block or round material of SUS316L. This type of stainless steel has excellent resistance to seawater, and all the components must be machined using a digitally controlled milling machine (Thirumalai Kumaran et al., 2021). Because only a small number of generators were initially fabricated, the winding process was carried out by hand. Once the coils were connected, the stator core and magnetic wire were coated with a waterproof varnish to protect them from seawater ingress. To reduce costs, the material thickness of the scaled-down generator was adjusted to the test conditions. Therefore, the thickness was reduced to about 1/4 of the expected minimum thickness of the full-scale frame; however, it was still designed to be waterproof.

The inductance was measured using a HIOKI 3522-50 LCR HiTESTER, and the resistance was measured using a TSURUGA BT3563 Digital OHM Meter. For a series of tests in which the load voltage, load current strength, torque, output power, and efficiency were tested, the generator was mounted on a holder (Fig. 7(a)). A star-connected three-phase load resistor was connected to the generator to simulate the different load conditions (Fig. 7(b)). The test series was conducted using a SMACH-MCAT system equipped with a speed-controllable motor with a maximum power of 37 kW. A YOKOGAWA DL350 oscilloscope was used to verify that all 3 phases U-V-W were in the correct order. The assembly and generator tests were performed at the Engine Design Technology Department of Ichinomiya Denki Co., Ltd. First, the cogging torque was measured using an ONO SOKKI torque detector (MT Series). However, owing to the large size and weight of the scaled-down generator (∼60 kg), the cogging torque could not be measured.

Fig. 7.

(a) Experimental setup for the scaled-down generator; (b) wiring diagram of the star-connected three-phase load resistor; and (c) measured values obtained from the experiment at 180 rpm

5. Results and Discussion

The calculated line-induced voltage (168.48 V) was almost identical to the measured value of 168.12 V. In addition, the line inductance and resistance were significantly reduced compared to the expected values. However, the measured line inductance was 0.0593 H compared to the calculated 0.0647 H, and the line resistance was reduced from 7.08 Ω to 5.58 Ω from our first expectation. This reduction resulted from the more compact winding of the stator core, which reduced the average length of each turn by approximately 23 mm. The output power increased from 1222 W to 1356 W (approximately 10 %). Based on this information from the initial measurements, we adjusted the new length for further calculations (Table 1) and compared the results with the experimental results.

Fig. 7(c) shows the measured values at 180 rpm. Measurements were performed at two points: one at an output power of 315 W and the other at 693 W. At 315 W, we obtained an induced voltage of 162.99 V and a current of 2.571 A, yielding an efficiency of 90.18%. At 693 W, we obtained an induced voltage of 155.60 V and a current of 1.115 A, yielding an efficiency of 89.57%. These measured results are close to or directly on the lines of the calculated values, as shown in Figs. 8 (a)–(e). In terms of the current, efficiency, power, torque, and voltage, the generator has characteristics that are almost identical to the expected values, depending on the specified load resistance. Based on these results, the scaled-down generator achieved the desired characteristics at a load resistance of 12 Ω with an output power of 1356.16 W, a load voltage of 127.57 V, a torque of 89.88 Nm, and an efficiency of 80.1%. This meets output power requirements >1 kW, load voltage AC 100 V ± 30%, and efficiency >65% at 180 rpm. As the measured values from the simulations were almost identical to the results of the experimental tests, we assumed that the cogging torque roughly corresponded to the simulation results. Therefore, we conclude that a very low cogging torque was achieved, which is well suited for use as a WEC.

Fig. 8.

Comparison of the calculated values with the measured results for (a) power per load resistance, (b) voltage per load resistance, (c) torque per load resistance, (d) efficiency per load resistance, and (e) current per load resistance

6. Conclusions

In this study, we developed a new generator design that harnesses energy using two horizontally oriented Darrieus turbines, and verified the expected performance with a scaled-down generator. Based on the results, we determined that the design met the desired requirements and provided even better results than expected and calculated, mainly achieved by a more compact winding of the stator core. Therefore, we believe that it is possible to design and build an optimized generator that is well suited for a WEC operating with horizontal-axis-oriented Darrieus turbines. However, our 2-turbine concept represents a new approach for using Darrieus turbines for underwater energy harnessing, with the advantages of increased output power, extended daily operating time, and maintaining of rotation, even when the available energy is low owing to weather conditions. This concept has also led to challenges in the platform and sealing design. As a result, a new platform concept was developed that can adjust the height of the WEC according to the tides and move the WEC to deep water regions to avoid destructive forces experienced during bad weather. Sealing is provided by mechanical seals mounted at each shaft location, where the shaft exits the housing and is held in position by specially designed shield covers. The generator was also designed to be filled with silicone oil under positive static pressure, which provided a higher pressure inside the housing than the seawater pressure from the outside, thus preventing seawater ingress, pressurizing the mechanical seal, and preventing the mechanical seal from being pushed into the housing by seawater pressure.

Once the results of the experimental tests on the small turbines are satisfactory and the final site has been selected, the manufacturing of full-scale WEC systems is planned in the near future. The development, manufacturing, and experimental testing of the Darrieus turbines will be conducted by Mitsubishi Heavy Industries Machinery Systems. To determine a location where waves are sufficiently strong to enable and sustain turbine rotation, the Institute of Computational Fluid Dynamics (iCFD) conducted wave and seabed profile simulations for several regions in Japan.

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