Research of Power Take-off System for “Sharp Eagle II” Wave Energy Converter

The “Sharp Eagle” device is a wave energy converter of a hinged double floating body. The wave-absorbing floating body hinges on the semi-submerged floating body structure. Under the action of wave, the wave-absorbing floating body rotates around the hinge point, and the wave energy can be converted into kinetic energy. In this paper, the power take-off system of “Sharp Eagle II” wave energy converter (the second generation of “Sharp Eagle”) was studied, which adopts the hydraulic type power take-off system. The 0–1 power generation mode was applied in this system to make the “Sharp Eagle II” operate under various wave conditions. The principle of power generation was introduced in detail, and the power take-off system was simulated. Three groups of different movement period inputs were used to simulate three kinds of wave conditions, and the simulation results were obtained under three different working conditions. In addition, the prototype of “Sharp Eagle II” wave energy converter was tested on land and in real sea conditions. The experimental data have been collected, and the experimental data and simulation results were compared and validated. This work has laid a foundation for the design and application of the following “Sharp Eagle” series of devices.


Introduction
Ocean wave energy is a kind of marine renewable energy, which is rich in reserves and widely distributed (Cuadra et al., 2016). The available wave energy around the globe is approximately 3×10 9 kW (Liu et al., 2017), the theoretical amount of wave energy in China's offshore is about 1.6× 10 7 kW, and the technically available amount is about 1.47×10 7 kW (Han, 2015). Compared with other forms of renewable energies, the wave energy density is relatively large. The average density of wave energy can reach 2− 4 kW/m 2 , which is significantly higher than that of solar energy (100−200 W/m 2 ) and wind energy (400−600 W/m 2 ) (Zheng and Li, 2016). Moreover, there is almost no secondary pollution during the utilization of wave energy. Therefore, the development and utilization of ocean wave energy are significant in improving the structure of energy utilization and alleviating the environmental pollution caused by the use of traditional fossil energy.
To promote the development of marine renewable energy, the State Oceanic Administration of China launched the National Marine Renewable Energy special project in 2010. With the financial support, the project undertakers developed and built a "Sharp Eagle" wave energy converter (WEC) with independent intellectual property rights (Sheng et al., 2015). As one of the few devices in China, which has experienced the operation under the real sea conditions, the "Sharp Eagle" WECs have some unique advantages. Firstly, the wave-electricity conversion efficiency η w-e is relatively high. The maximum wave-electricity conversion efficiency of "Sharp Eagle" can reach 37.7% in real sea state experiments. Under most wave conditions, it can reach 20%, and the system can also start power generation when wave height is 0.4 m . Secondly, the Semisubmersible barge has been used as the base of the WEC, which increases the stability of the device and makes the transportation and maintenance of the device very conveni-ent (Sheng et al., 2015). In December 2012, the first prototype "Sharp Eagle Ι" started the sea trial, which verified the related functions of "Sharp Eagle" series, and this sea trial of the device achieved satisfactory results. The second generation with a larger capacity of "Sharp Eagle II" was built in 2013, and sea trials were conducted in 2016. The third generation "Wan Shan" of the "Sharp Eagle" series was built in 2014, and the real sea test was carried out in 2015. Figs. 1a−1c are "Sharp Eagle Ι", "Sharp Eagle II" and "Sharp Eagle Wan Shan". "Sharp Eagle Ι", "Sharp Eagle II" and "Sharp Eagle Wan Shan" have the same power generation principles. Their differences are mainly as follows. (1) The primary size and weight of the three are different. (2) The number of suction floats and the arrangement of the three are different.
(3) The installation of the hydraulic cylinders is different. The hydraulic cylinders of "Sharp Eagle Ι" are installed at the bottom of the absorbing floating body and parallel to the three evenly distributed wave front hydraulic cylinders. For "Sharp Eagle II", the hydraulic cylinders are installed at the bottom of the absorbing floating body and perpendicular to the four wave direction distributed hydraulic cylinders. The hydraulic cylinders of "Sharp Eagle Wan Shan" are installed at the upper part of the absorbing floating body and parallel to the four evenly distributed wave front hydraulic cylinders. (4) The power of the generator is different. The main parameters of the Eagle series are shown in Table 1. "Sharp Eagle" WECs can achieve high conversion efficiency. The special design work of the Power Take-Off (PTO) system is indispensable. In this paper, the simulation, land testing and real sea state testing of "Sharp Eagle II" PTO system are studied.

Overview of the PTO system
The WECs can be generally divided into two parts: the energy capture system and the PTO system (Wang et al., 2018). The function of the PTO system is to convert the captured wave energy into electrical energy through the intermediate transition link. There are two common classifications of WECs (de O Falcão, 2010). According to different energy capture systems, it can be divided into the following types: oscillating water column, overtopping, oscillating buoy and so on. According to different PTO systems, it can be divided into the following types: air turbine (or pneumatic) type, water turbine type, hydraulic type, linear generator and so on (Mei, 2012;López et al., 2013).
The principle of WEC using the pneumatic PTO system is as follows: The waves promote the air reciprocating movement, and then the reciprocating airflow drives the air turbine. Finally, the air turbine operates the generator. Its energy conversion process goes from wave energy to air kinetic energy to rotating mechanical energy to electric energy. The pneumatic type PTO system usually matches with oscillating water column (OWC) energy capture system. The typical pneumatic WEC is the LIMPET power station (Heath et al., 2000).
The principle of water turbine type PTO system is similar to that of hydroelectric power generation. It transforms the wave energy into the potential energy of seawater and then drives the turbine to rotate. The water turbine type PTO system usually matches with the overtopping energy capture system. Wave-dragon is a kind of typical WEC with a water turbine type PTO system (Kofoed et al., 2006). The hydraulic PTO system generally matches with the oscillating floating type energy capture system, and the wave energy is converted to mechanical energy by using the relative motion between the two bodies. Then the hydraulic elements are used to transform the mechanical energy into pressure energy of hydraulic oil and finally turned into electrical energy. The characteristics of waves are of low frequency and high torque, which is suitable for hydraulic energy transmission (Lasa et al., 2012). Also, several main parameters of the wave (including period, direction and wave height) are random, so the power of the wave is unstable. The accumulators in hydraulic energy transmission system can realize short-term energy storage and smooth output of energy. Therefore, the hydraulic type PTO system has become the mainstream choice of WEC. For example, Pelamis (Henderson, 2006), Wavestar (Kramer et al., 2011), etc. "Sharp Eagle II" WEC is no exception as one kind of oscillating buoy wave energy device. The principle of the linear generator PTO system is relatively simple. The linear generator is directly driven to generate electricity by using the relative motion of the float. The stator of the linear generator is connected to the seabed or the underwater floating body, and the actuator is mounted on the absorbing float. Under the drive of the wave, the absorbing floating body vibrates up and down, driving the actuator up and down, thus generating electrical energy.

"Sharp Eagle II" PTO system
3.1 Principle of the PTO system "Sharp Eagle II" PTO system consists mainly of the following components: hydraulic cylinder, check valve1, check valve2, accumulators, hydraulic automatic controller1, hydraulic automatic controller2, hydraulic control valve1, hydraulic control valve2, hydraulic motor1, hydraulic motor2, permanent magnet generator1, permanent magnet generat-or2, oil tank and so on. Fig. 2 shows the principle of the "Sharp Eagle II" PTO system.
The principle of power generation for "Sharp Eagle II" WEC is as follows: The eagle pose float is hinged on the main deck of WEC. It rotates around the hinge point under wave actions, which drives the hydraulic cylinder connected below the eagle pose buoy to make reciprocating motion. The upper chamber of the hydraulic cylinder pumps the oil from the tank into the accumulators in the process of reciprocating movement. With the increase of the oil entering the accumulators, the pressure in the accumulators increases gradually. When the pressure reaches the set opening value, the hydraulic automatic controller transmits the pressure signal to the hydraulic control valve and then opens the hydraulic control valve. The high-pressure hydraulic oil flows into the hydraulic motor through the control valve, which rotates the hydraulic motor and the generator. In Fig. 2, two sets of hydraulic autonomous control valves' control modes are the same, just set the opening pressure value different, the hydraulic autonomous control valve 1 control motor 1 opening and closing, the hydraulic autonomous Control valve 2 control Motor 2 opening and closing. The bottom chamber of the hydraulic cylinder directly exposes to the air in the cabin.

Control scheme of the PTO system
From the second section, we can see that the PTO system has undergone two conversions. The first conversion is to convert the mechanical energy made by the reciprocating motion of the hydraulic cylinder into the pressure energy of high-pressure hydraulic oil in the accumulators, and the second conversion is to convert the pressure energy into electrical energy according to the hydraulic motor and permanent magnet generator. In the process of energy conversion, the latter energy form in each conversion can be regarded as the load of the previous energy form. That is to say, the load connected to the hydraulic cylinder is the highpressure hydraulic oil in the accumulators, which is called the hydraulic load. The load of the pressure energy in the accumulators is the electrical load connected to the generator end. To enable the WECs to work efficiently and stably under various wave conditions, the wave force must match with the hydraulic load force F PTO . Otherwise, the WECs can only be efficient under certain wave conditions, but inefficient or even deactivated under other wave conditions. Here, the expression F PTO is: (1) As can be seen from Eq. (1), three parameters can be adjusted to change F PTO , namely, p ac , the working pressure of the accumulators. S is the effective working area of the hydraulic cylinder. mis the number of the hydraulic cylinders. Hansen et al. (2013) adjusted the F PTO by changing the effective working area of the hydraulic cylinder. They proposed a discrete displacement cylinder (DDC), which has multiple chambers, and the effective working area of each chamber is different, thus achieving the changes to the F PTO (Hansen et al., 2013). The "Sharp Eagle II" WEC changes F PTO by adjusting the pressure to adapt to different wave conditions. The method adopted is 0−1 power generation mode .
The principle of 0−1 power generation mode is as follows: an automatic hydraulic controller is added to the hydraulic system to control the opening and closing of the hydraulic motor. When the pressure of the accumulators reaches the set opening pressure p 1o , the automatic hydraulic controller opens the hydraulic valve. Then, the hydraulic motor and the generator began to rotate. The hydraulic motor is of constant displacement, without real-time adjustment. The rotation speed of the motor changes with the pressure of the accumulators. When the pressure of the accumulators drops to the set closing pressure p 1c , the automatic hydraulic controller shuts down the hydraulic valve, the hydraulic motor stops rotating, and the generator stops generating electricity. For 0−1 control, 1 means that the system generates electricity, and 0 means the system stops generating electricity. This control mode is similar to the relay function in electrical control.
After the hydraulic valve is opened, the pressure of the accumulators may appear in three kinds of situations. The first one, in the case of small waves, the speed of the hydraulic cylinder is relatively low, the flow of the hydraulic cylinder is relatively tiny, and the pressure of the accumulators will drop down to the set closing pressure p 1c of the hydraulic valve. At this point, the hydraulic valve is closed under the action of the automatic hydraulic controller, and the accumulators will start the next energy storage process.
The second one, when the waves become slightly larger, the hydraulic cylinder speed is somewhat faster, the flow increased. The pressure of the accumulators will also be reduced, but cannot be reduced to the set-closing pressure, then the pressure p ac is roughly stable. The flow rate into and out of the accumulators is roughly equal. The hydraulic valve keeps open.
The third one, as the wave continues to grow, and the speed of hydraulic cylinder continues to increase, the inflow to the accumulators is higher than the outflow. The pressure will not fall, but rise. When the inflow and outflow of the accumulators are roughly balanced, the pressure ceases to increase. The hydraulic valve will remain open in this process. Fig. 3 shows the logic sketch of 0−1 control. Q m1,1o represents the flow rate of No.1 hydraulic motor when accumulator pressure is p 1o . Q m1,1c represents the flow rate of No.1 hydraulic motor when accumulator pressure is p 1c . Q ahy is the average flow rate of the hydraulic cylinder.
In the PTO system of "Sharp Eagle II" WEC, the accumulator outlet is connected to two generating sets, 30 kW and 70 kW respectively. When the waves are enormous, even if the liquid control valve 1 is turned on, the pressure is still rising. When the pressure increases to the set open pressure p 2o of the No.2 hydraulic motor, the liquid control valve 2 will open, and the 70 kW generator will run. At this time, the power of the PTO system can reach 100 kW and will run the full load. The 70 kW generator also adopts the 0−1 control. When the accumulator pressure drops to the set close pressure p 2c of the No.2 hydraulic motor, the 70 kW generator will stop. Table 2 shows the operating status of two motors under different flow rates, where, Q m1,2o represents the flow rate of No.1 hydraulic motor when the accumulator pressure is p 2o , Q m1,2c represents the flow rate of No.1 hydraulic motor when the accumulator pressure is p 2c , Q ahy <Q m1,1c 0−1−0 0−0−0 2 Q m1,1c < Q ahy <Q m1,1o 0−1−1 0−0−0 3 Q m1,1o < Q ahy <Q m1,2c 0−1−1 0−0−0 4 Q m1,2c < Q ahy <Q m1,2c + Q m2,2c 0−1−1 0−1−0 5 Q m1,2c + Q m2,2c < Q ahy < Q m1,2o + Q m2,2o 0−1−1 0−1−1 6 Q m1,2o + Q m2,2o >Q ahy 0−1−1 0−1−1 Notes: 0−0−0 means no power generation, 0−1−0 means intermittent power generation, and 0−1−1 means continuous power generation Q m2,2o represents the flow rate of No.2 hydraulic motor when the accumulator pressure is p 2o , and Q m2,2c represents the flow rate of No.2 hydraulic motor when the accumulator pressure is p 2c . To realize the above control logic, the "Sharp Eagle II" WEC adopts a multi-level automatic hydraulic controller. As the electrical components are prone to malfunction in the high-temperature, high-salt, and high-humidity ocean environment, the multi-level automatic hydraulic controller is composed of all hydraulic parts without any electrical components, which ensures that the controller can work safely in the ocean. As shown in Fig. 4, the multi-level automatic hydraulic controller was tested in the laboratory.

Mathematical models
The PTO system of "Sharp Eagle II" WEC mainly includes hydraulic cylinders, accumulators, hydraulic motors, and generators. Friction losses in piping and hydraulic valves can be ignored here. The primary parameter of the hydraulic cylinder is the flow rate. The average flow rate can be expressed as: where, h is the effective stroke of hydraulic cylinder, and T is the motion period of hydraulic cylinder.
where d 1 and d 2 represent the diameter of the hydraulic cylinder inner cylinder and hydraulic cylinder rod, respectively. The mathematical model of the accumulator pressure stabilization system can be expressed as follows: where, V ac and Q ac are the volume and flow of the accumulator, respectively.
γ where is the gas index.
The mathematical model of the hydraulic motor can be expressed as: where, Q m is the flow rate of the hydraulic motor; q m , n m and k leak are the displacement, rotation speed and leakage coefficient of the hydraulic motor, respectively; Δp and T m are the inlet and outlet pressure difference and torque of the hydraulic motor, respectively; is the mechanical efficiency of the hydraulic motor; is the volumetric efficiency of the.hydraulic motor; P m is the power of the hydraulic motor.
The mathematical model of the permanent magnet generator with resistive load can be expressed as: where, J, and B m are the inertia moment, angular velocity and viscous damping coefficient of the hydraulic motor, respectively; T g , P g and are the torque, power and efficiency of the generator, respectively; E is the phase electromotive force; R is the load resistance; N is the number of series turns per phase winding of the generator; K, u and are the electromotive force winding factor, pole logarithm and magnetic flux of the generator, respectively.

Simulation
In order to study the characteristics of the PTO system, the simulation of the PTO system is carried out by using the MATLAB/SIMULINK software to simulate the system. Both 30 kW generator and 70 kW generator adopt the 0−1 control, and the characteristics of them are roughly the same, so only the 30 kW generator is simulated.
The parameters of the main hydraulic components are as follows: the maximum stroke of the hydraulic cylinder is about 4.5 m, the effective stroke of the hydraulic cylinder is about 2 m (The stroke of the hydraulic cylinder is set during the experiment and simulation), the piston diameter of the hydraulic cylinder is 200 mm, and the piston rod diameter is 185 mm, the accumulator capacity is 500 L, the generator load resistance is 6.47 Ω, and the motor displacement is 107 ml/r. The parameters of the simulation are as follows: the effective stroke of the hydraulic cylinder is about 2 m, the gas index is set to 1, the system opening pressure of the liquid control valve is 17.5 MPa, and the closing pressure of the liquid control valve is 8 MPa.
The different wave conditions are simulated by changing the flow rate of the hydraulic cylinder. According to Eq. (2), the flow rate and movement period of the hydraulic cylinder are inversely proportional, because the effective working area and effective stroke of the hydraulic cylinder have been set, as long as the change of the movement period, different wave conditions can be simulated. There are three groups of working conditions, the motion periods of three sets of hydraulic cylinders are 10 s, 20 s, ad 30 s, respectively. The larger motion cycle means smaller frequency, which represents lower input energy. The SIM-ULINK model is shown in Fig. 5.
The simulation results are shown in Fig. 6. Figs. 6a, 6b, 6c and 6d are graphs of pressure, flow, voltage and electric power over time, respectively.
As shown in Fig. 6, when the movement period is 35 s, the pressure fluctuation ranges from 8 MPa to 17.5 MPa. Each power generation process can be divided into two parts. One is the pressure rising process, which represents the system in the energy storage process, and the other is the pressure drop process, which represents the system in the power generation process, namely 0−1−0 mode. When the movement frequency of the hydraulic cylinder slightly increases, the pressure rises first and then gradually decreases, and finally tends to stabilize. At this time, the pressure value is lower than the opening pressure and higher than the closing pressure, which indicates that the system starts to generate electricity after the energy storage process, and the power gradually reduces. Finally, the power declined to a stable value. The system is in the continuous power generation state after the energy storage process. That is the 0−1−1 process. When the movement frequency still increases, the system pressure rises to the opening pressure, and the system begins to generate electricity. Since then, the system pressure is still rising until it reaches a stable value, and the system pressure no longer rises. The system is always in the state of continuous power generation.

Land testing of "Sharp Eagle II" PTO system
After construction, the PTO system of "Sharp Eagle II" WEC was tested on land. The hydraulic pump was used as the power source to pull the floating body and drive the hydraulic cylinder. Here, the hydraulic pump simulates the waves. The PTO system was tested in the shipyard, as shown in Fig. 7.
The hydraulic pump pumps the oil into the bottom chamber of the hydraulic cylinder so that the hydraulic rod moves upward and pushes the wave-absorbing floating body upward. Meanwhile, the hydraulic oil in the upper chamber of the hydraulic cylinder was pushed into the accumulators. When the wave-absorbing floating body moves to the upper limit position, the hydraulic pump will stop working. Then, the wave-absorbing floating body uses its gravity to descend slowly, and the hydraulic rod moves downward under YE Yin et al. China Ocean Eng., 2019, Vol. 33, No. 5, P. 618-627 the drive of the wave-absorbing floating body. At the same time, the hydraulic oil was sucked into the upper chamber from the oil tank.
When tested on land, the movement period of the hydraulic cylinder is approximately 180 s. Due to the limitation of hydraulic pump power, it is difficult to simulate the giant waves. Therefore, only the experiment of 0−1−0 power generation mode was carried out. If the wave power is small, the 0−1−0 power generation mode can be approximately divided into two independent processes: the energy storage process (pressure rise) and the power generation process (pressure drop). The time of the power generation process is much shorter than that of the energy storage process. The experimental results of the power generation pro-cess were collected as shown in Fig. 8 and compared with the simulation results. Fig. 8a is the curve of pressure with time during the energy storage and the power generation process. In the energy storage process, the flow rate, voltage and electrical power are all zeros. Figs. 8b, 8c, and 8d are the curves of flow rate, voltage and electrical power changing over time during the power generation process, respectively. The hydraulic-electricity efficiency can be calculated from the data obtained. It can be expressed as Eq. (12). The calculated hydraulic-electricity efficiency is about 69%.
where, Δt is the data acquisition time step. E i , p i and Q i are the measured voltage, pressure and flow rate, respectively. By comparing the results of the simulation and the land testing in Fig. 8, it can be seen that under the same starting pressure and closing pressure, the power generation process time of simulation experiment and land testing is 193.7 s and 173.4 s respectively, and the relative error is about 10.48%. The average powers of power generation in the simulation and land testing are 8.4 kW and 7.5 kW respectively, and the relative error is 10.71%.
6 Real sea state testing of "Sharp Eagle II" PTO system "Sharp Eagle II" WEC was put into Wan Shan island  sea area on May 11, 2016, as shown in Fig. 9. The real sea state testing was carried out, and the experimental data recorded in the real sea state testing were from May 11, 2016 to May 27, 2016. Among which two groups of representative real sea state experimental data were selected, as shown in Fig. 10.
Under the real sea conditions, the opening pressure of the PTO system is set to 16 MPa, and the closing pressure is set to 8 MPa. Fig. 10a Shows the pressure data from 5: 00 a.m. to 8: 00 a.m. on May 21. The pressure remains fluctuating within the range of 8−16 MPa, and the PTO system is working in the 0−1−0 mode (intermittent power generation). Fig. 10b is the electricity power data at this time. This means that the waves were small at this time. Fig. 10c shows the pressure data from 11: 30 a.m. to 12: 30 a.m. on May 27. The pressure value was basically between 12.5−18 MPa. The PTO system was performing 0−1−1 mode (continuous power generation). Fig. 10d shows the electric power data during this period. This indicates that the wave power was larger than that of the previous time.
By comparing Fig. 6 with Fig. 10, it can be seen that the pressure curve of the real sea state testing was consistent with the simulated pressure curve of Fig. 6a. From Fig. 6a, when the flow was relatively small, the PTO system generated intermittent power. The pressure value will make Vshaped trend between the opening pressure and closing pressure, which is also reflected by the pressure data of the real sea state testing, as shown in Fig. 10a. When the flow rate was relatively large, the PTO system performed continuous power generation, and the pressure value was always higher than the closing pressure value as shown in Fig.10c.

Conclusions
In this paper, the PTO system of "Sharp Eagle II" WEC is studied. To make the WEC work effectively in most wave conditions, 0−1 power generation mode was proposed. The mathematical model was established and simulated. Moreover, the land testing and the real sea state testing of "Sharp Eagle II" WEC were carried out. The preliminary conclusions are shown as follows.
The characteristics of pressure, flow rate and voltage  YE Yin et al. China Ocean Eng., 2019, Vol. 33, No. 5, P. 618-627 curves of the simulation and the land testing are similar, which indicates that the simulation results in this paper are reliable. When the PTO system carries out 0−1−0 power generation mode (intermittent power generation) with the land testing, the hydraulic-electrical efficiency is about 69%. The efficiency value may continue to increase if the piping and the resistance values are optimized. For the 0−1−1 power generation mode (continuous power generation), the efficiency value will also be higher than that of the 0−1−0 power generation mode because the rotational speeds of the hydraulic motor and generator are relatively constant and close to the rated operating conditions. In the literature (Hansen et al., 2013), the PTO efficiency achieved 70% by simulation, which is close to the experimental data in this paper. There are few wave energy devices operating in real sea conditions, so the experimental data of the wave energy prototype device are difficult to be found in the literature, and the PTO data in the real sea conditions are rare.
In order to realize 0−1 power generation mode, the multi-level automatic hydraulic controller has been developed. This controller is a mechanical type and has no electrical components. Electrical components are prone to corrosion and failure in the marine environment. They cannot normally work without extra power in the system. Therefore, the multi-level automatic hydraulic controller can improve the reliability and safety of the PTO system.
Besides, "Sharp Eagle II" WEC has a difference from other WECs. It does not work bidirectionally; instead, it only uses the upper chamber of the hydraulic cylinder to do work, while the bottom chamber of the hydraulic cylinder directly exposes to the air in the cabin.
The reason is that the floating body rotates around the axis, the waves push the upward movement, and the downward movement is mainly caused by the gravity of the wave-absorbing floating body itself. If the bottom chamber of the hydraulic cylinder is also connected with the accumulators, with the increase of accumulator pressure, the downward movement resistance of the wave-absorbing floating body will increase, which leads to the movement of the wave-absorbing floating body unable to keep up with the movement frequency of waves, thus reducing the efficiency of the energy capture system.
In the future, the research on the PTO system of "Sharp Eagle II" WEC will mainly focus on two points. The first is to study the optimal resistance load on the generator side, matching the optimal resistance value for the generator, and making the performance of the PTO system reach the best. The second is to study the characteristics and the power generation efficiency when the generator is connected to the battery load.