Edited by: Shaowei Zhang, Institute of DeepSea Science and Engineering, Chinese Academy of Sciences (CAS), China
Reviewed by: Chengbin Zhang, Southeast University, China; Song Ruiyin, Zhejiang University, China
*Correspondence: Qingchao Xia,
This article was submitted to Ocean Observation, a section of the journal Frontiers in Marine Science
This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
With the increasing scarcity of energy in the world, energy has become an important part of restricting the development and application of traditional ocean profilers. The method of converting ocean thermal energy (OTE) into electrical energy through an energy conversion system is a solution. The model establishment and performance analysis of the energy conversion system are the basis of the ocean thermal profiler (OTP) design. The model and performance are affected by the coupling of multiple parameters, especially rotational speed and pressure. In this study, a universal parameterized model for multiparameter coupling was proposed. System performance analysis based on experiments including load current, speed, mechanical efficiency and total efficiency was presented. After model parameter identification, the error of mechanical efficiency was within 5%; the total efficiency error was less than 12.8%, and the maximum efficiency point error didn’t exceed 2.21%. The results indicated that the parameterized model was satisfactory for the engineering applications and could guide the design of OTP.
Profiler used for monitoring ocean profile elements are important platforms for marine scientific research. Traditional ocean profilers, such as ARGO buoys and underwater gliders, usually include many batteries. Owing to the limitations of battery capacity, they can only perform simple and shortterm missions, which greatly restricts their longterm and complex applications in the ocean. In the face of energy constraints, harnessing marine renewable energy with energy conversion system is an effective solution (
An ocean thermal profiler (OTP) can capture and utilize OTE. Compared with direct driving by OTE, the method of converting OTE into electrical energy through an energy conversion system to drive is safer and more reliable. Two categories of energy conversion system can be classified according to the power generation principles. (1) Using thermoelectric generators (TEGs) to convert OTE into electrical energy directly (
The performance study of the energy conversion system through modelling can provide important support for the design, motion control, and energy optimization of the OTP. Currently, most studies have concentrated on the conversion system of wind energy, wave energy, tidal energy, and hydraulic energy (
However, research on the modelling of energy conversion systems for the OTP has been scarce. Owing to the nonlinear characteristics, Xia et al. applied the neural network method to identify and model the energy conversion system of the OTP and obtained the curved surface of the efficiency on the inlet pressure of the hydraulic motor and the load current of the generator (
Above research has mostly ignored the actual working conditions of energy conversion systems for OTP, especially the change in the mechanical efficiency and the total efficiency with the rotation speed and pressure; thus, performance study is not comprehensive. In this paper, the factors affecting the performance of energy conversion system are analyzed according to the operation principle of OTP. A universal parameterized model of the total efficiency for the energy conversion system are proposed. The performance analysis is presented by establishing an experimental platform. Simultaneously, experimental data are used to identify parameters of the parameterized model and verify the accuracy.
The remainder of this paper is organized as follows. Section 2 introduces the operation principle of OTP, analyses the affecting factors of performance and presents an experimental platform. In Section 3, the parameterized model of the energy conversion system is established. In Section 4, performance analysis and experimental verification are presented. Section 5 provides a brief conclusion.
The OTP collects data of the ocean’s vertical profile by moving up and down while capturing OTE and generating electricity to power sensors, controllers, GPS, and other electronic equipment. The OTP is mainly composed of a thermal engine, energy conversion system, buoyancy adjustment system, data acquisition and communication systems, control system, and a pressure hull. The thermal engine, buoyancy adjustment system, and energy conversion system jointly realize OTP movement and power generation. The thermal engine was encapsulated with PCM to capture the OTE. When the OTP is in warm water, the volume of the PCM increases and external work is performed to convert OTE into potential energy and store it in the accumulator. The energy conversion system is mainly composed of a hydraulic motor, generator, and battery, which can convert the potential energy of the accumulator into electrical energy.
The principle of the operation and the energy conversion for the OTP.
The energy conversion system adopts an energy storage power generation mode. According to the operation principle of the OTP, the energy conversion system is characterized by the following. (1) In a single profile, the total amount of OTE stored by the accumulator is certain; (2) the hydraulic motor inlet pressure follows the accumulator pressure and gradually decreases; and (3) the outlet pressure of the hydraulic motor changes with the pressure of the external bladder, which is the water pressure during power generation. Therefore, the performance of energy conversion system is affected by the coupling of multiple parameters. The parameters of the hydraulic motor include inlet pressure, outlet pressure, displacement, and speed. The parameters of the generator include the power, voltage, armature resistance, speed constant, torque constant, and reducer. In practical applications, it was found that the mechanical efficiency of the hydraulic motor was significantly affected by the speed, and the traditional mechanical efficiency model was not suitable for the energy conversion system of the OTP. When the hydraulic motor and generator are determined, the performance of energy conversion system is mainly affected by the pressure, speed and load current.
According to system overview of the OTP, the experimental platform for the energy conversion system is designed and shown in
The experimental platform of the energy conversion system.
The component parameters used in the experimental platform of the energy conversion system are listed in
The component parameters used in the experimental platform of energy conversion system.
Item  Parameter  Value 

Hydraulic motor 

0.4 cc/rev 

5 MPa  
Reducer 

4 
DC generator  Max. speed  8000 rpm 

0.0292 N▪m/A  

328 rpm/V  
Δ 
0.013 N▪m  

0.583 Ω  
Δ 
0.47 Ω 
A hydraulic motor is a hydraulic actuator that converts hydraulic energy into rotational mechanical energy. It is one of the core components of energy conversion systems. The swashplate axial piston hydraulic motor has the advantages of a high working pressure, high working speed, and compact structure. It is suitable for the highly integrated energy conversion system of the OTP.
The working principle and force analysis of the swashplate axial piston hydraulic motor are shown in
The working principle and force analysis of the swashplate axial piston hydraulic motor.
The number of plungers
where φ is the rotation angle of the deepest plunger embedded in the cylinder block relative to the bottom dead centre and α is the angle between two adjacent plungers.
Mechanical efficiency is a parameter used to evaluate the degree of mechanical loss in a hydraulic motor. The friction loss of the swashplate axial piston hydraulic motor is mainly caused by the relative motion of the friction pair between the bottom surface of the cylinder block and port plate, between the slippers and swashplate, and between the plunger and plunger cavity. The mechanical efficiency of the hydraulic motor is expressed as follows:
where
According to the force analysis shown in
(1) The force of the inlet and outlet pressure oil is transmitted to the swash plate through the plunger and slipper, and the average torque is produced by the reaction force generated by the swash plate on the output shaft. The average torque is
where
(2) Average friction torque
where
(3) The average friction torque
where
(4) The average friction torque
where
(5) The average friction torque
where
(6) The average friction torque
where
Therefore,
From equations (5)–(9), it can be seen that the friction loss of the hydraulic motor is related to the inlet pressure
Thus,
where
The power loss caused by the internal and external leakage of the liquid, including the internal leakage of the working chamber volume due to the compressibility of the liquid, is expressed in terms of volumetric efficiency as follows.
where
Substituting Equation (16) into Equation (15) to obtain the volumetric efficiency model of the hydraulic motor, we obtain
where
where
The hydraulic motor was connected to the DC generator through the reducer. The mechanical resistance torque Δ
where
The output voltage of the DC generator
where
The efficiency model of energy conversion system
The performance analysis of the energy conversion system based on the experiment complements the parameterized model. Due to the nonlinearity of the parameterized model, the relationships of the intermediate variables after parameter identification are difficult to obtain directly, such as the load current. However, the speed is controlled by the load current. Therefore, analyzing the performances of load current, speed, and efficiency contributes to the original design of the OTP.
Load current varies with inlet pressure of hydraulic motor.
The speed and load current are not independent.
The relationship between speed and load current.
The mechanical efficiency of hydraulic motor in the energy conversion system.
The total efficiency of the energy conversion system.
The mathematical model of the mechanical efficiency of a hydraulic motor contains three undetermined parameters, and Equation (13) can be simplified as follows.
where
The pressure difference ΔP was 10–15 MPa, and the pressure difference increment was 1 MPa. The mechanical efficiency data at different speeds under these six working conditions were obtained experimentally, and the LevenbergMarquardt method in the nonlinear leastsquares problem was used to fit Equation (25). The experimental data and fitting results are shown in
The experimental data and fitting results for mechanical efficiency of hydraulic motor.
Experiments with differential pressures of 19, 21, and 23 MPa were performed to verify the accuracy of Equation (26) for other pressure and speed ranges of the hydraulic motor. A comparison between the simulation and experimental results of mechanical efficiency is shown in
The comparison between the simulation and experimental results of the mechanical efficiency model.
During the experiment, there was less leakage of the hydraulic motor. Therefore, to simplify the model and calculation, it is considered that the volumetric efficiency of the hydraulic motor does not change with the pressure difference and speed.
The total efficiency of energy conversion system can be derived using two methods based on the mechanical efficiency model of the hydraulic motor: (1) indirect method based on the mechanical efficiency model after parameter identification and (2) direct method based on the mechanical efficiency model before parameter identification. The indirect method can identify the unknown parameters of the intermediate variables and can be applied in the fields of dynamic modeling and control algorithm design of energy conversion system. The direct method implicitly includes unknown parameters of intermediate variables and can be applied in static modeling and energy efficiency analysis of energy conversion system.
The indirect method involves substituting Equations (26) and (21) into Equation (24).
The simulation and experimental comparison of indirect method.
The direct method involves bringing Equations (25) and (21) into Equation (24) and simplifying them to obtain a parameterized model of the total efficiency as follows.
where
b_{1}, b_{2} and b_{3} should be separated by three lines. "ΔP2" is modified to "^{△P2}". "D2" is modified to "D^{2}".
Here,
where
Parameter identification in the total efficiency was similar to the mechanical efficiency of the hydraulic motor. The experimental data and fitting results are shown in
The experimental data and fitting results for the total efficiency of energy conversion system.
The parameters in parameterized model of total efficiency.
Undetermined parameters  Fitting value  Standard error 


9.18156E12  2.92082E12 

6.27942E8  1.4227E8 

2.62316E6  1.74247E7 

1.15067E4  2.40286E5 

0.00953  4.57568E4 

0.018  0.01656 

0.34921  0.0078 

4.60104  0.36058 

21.62071  4.62731 
The experimental data for differential pressures of 19, 21, and 23 MPa were selected to verify the parameterized model of total efficiency established by the direct method.
The simulation and experimental comparison of direct method.
The accuracy of maximum efficiency point prediction of energy conversion system is a significant criterion for judging the rationality of the proposed parameterized model. The maximum efficiency point is the optimal load current and optimal speed when the total efficiency is maximum. The load current in the direct method is an intermediate variable, which is difficult to obtain accurate parameters; therefore, the simulation and experimental comparison of the optimal load current only applies to the indirect method, while the direct method can be explained by the optimal speed indirectly.
The simulation and experimental comparison of the optimal load current.
The simulation and experimental comparison of the optimal speed.
In this study, the factors affecting the performance of energy conversion system are analyzed according to the operation principle of OTP. A force analysis of a swashplate axial piston hydraulic motor was performed, and a parameterized model for establishing the mechanical efficiency of the hydraulic motor was established. Direct method and indirect method were proposed for establishing the universal parameterized model of total efficiency for energy conversion system. An experimental platform was established to study system performance and verify the accuracy of the proposed parameterized model.
In the energy conversion system of OTP, the maximum and minimum load current increased with the inlet pressure, but the variation range decreased. The load current was inversely related to the speed, while positively related to the inlet pressure. The mechanical efficiency of hydraulic motor increased with inlet pressure, but decreased with speed. The total efficiency increased with the load current, and decreased after reaching the maximum point at low inlet pressure, whereas the total efficiency decreased with the load current at high inlet pressure. The maximum efficiency point showed a rising trend with inlet pressure.
In the parameterized model identification, the average relative error between the simulation and experiment for the mechanical efficiency of the hydraulic motor was less than 5%, and the maximum relative error was 5.6%, verifying the validity and accuracy of the established mechanical efficiency parameterized model. For the total efficiency model established by the indirect method, the minimum average relative error was 4%, and the maximum average relative error was 12.8%. For the direct method, except for the large error at the initial speed, the average relative error in the other speed ranges was within 10%, the maximum was 9%, and the minimum was 0.41%. In the prediction of optimal load current, the average relative error of the indirect method was 2.21%. In predicting the optimal speed, the average relative errors of the indirect method and the direct method were 0.45% and 0.8%, respectively. The parameterized model of energy conversion system met the engineering application.
The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding authors.
YC, BC, QX, and CY contributed to conception and design of the study. YC provided methodology and performed the statistical analysis. BC conducted experiments, organized the database, and wrote the first draft of the manuscript. MH provided data visualization. LZ carried out the preliminary investigation. QX provided resources and supervision. CY provided project administration and funding acquisition. All authors contributed to manuscript revision, read, and approved the submitted version.
This work was supported by the National Natural Science Foundation of China (No. 51979246), National Key Research and Development Program of China (No. 2021YFC2800202), and Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA22000000).
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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