With the advantages of low loss and flexible control, direct-drive wave energy converter (WEC) based on oscillating body structure has become a research hotspot in wave energy. Through mooring system, two-body direct-drive WEC, which is independent of off-shore fixed platforms, is a promising solution to wave energy utilization. However, the two-body WEC utilizes relative motion between upper and lower float to generate electricity, which makes modelling and optimal energy extraction control more difficult. Through equivalent method, a two-body WEC can be regarded as two power sources with different voltages and resistance paralleled to output electricity, furthermore, this two paralleled power source can be equivalent to a single source model, which is similar to a single-body WEC. Therefore modelling and energy extraction characteristic of two-body WEC are simplified and it can be concluded that stiffness of mooring has a great effect on maximum wave energy extraction. The results show that the mooring should be as stiffness as possible to avoid energy extraction loss and in this case two-body WEC can be totally equivalent to a single-body WEC: the upper float plays the role of harnessing wave energy and the lower float along with mooring system acts as a fixed base. And the design of two-body WEC with pretension mooring system is put forward.
Model predictive control (MPC) is the state-of-art method for optimal energy extraction in wave energy. Based on the equivalent model, MPC problem for maximizing wave energy extraction considering generator force and float displacement constraints is formulated. For the need of wave excitation force prediction, Kalman filter is used to achieve excitation force identification and autoregressive model is used for excitation force prediction. Considering the computation complexity for MPC solution, a fast solution algorithm is put forward, the core idea of this algorithm is to use the solution from previous step as the initial iteration of current step, thus only one iteration is required. Compared with conventional MPC that requires 3-5 interactions, the proposed fast solution algorithm can save up to 80% computing time.
A two-body direct-drive WEC prototype with upper float of 1.5m diameter is designed for experimental test in the wave tank lab with dimension of 100mx18mx5m. This lab can generate waves with periods from 2-3m and 0.25m maximum wave height. Different power control methods are conducted including resistive control, damping control, latching control, conventional MPC and proposed MPC. The results show that MPC can extract 70% more energy compared with traditional methods and the proposed MPC with fast solution algorithm have the same energy extraction efficiency while only 50% CPU operation time required.
The following conclusions can be drawn: (1) pretension mooring has no negative effect on energy extraction and two-body WEC can be equivalent to one-body WEC through equivalent circuit method, which will simplify control modelling significantly, (2) compared with conventional methods, MPC has more energy extraction efficiency by injecting reactive power to increase the oscillation amplitude while limiting it within preset constraints simultaneously, (3) the experimental results indicate that the proposed MPC is stable considering there exists modelling errors in experiment, besides, excitation force prediction is achieved by software algorithms, and the proposed MPC method only requires 50% computation time, which means the proposed method is promising for practical implementation without need of additionally sensors and high-performance control system.
黄宣睿, 林泽川, 肖曦. 双浮体直驱波浪发电装置建模分析与基于模型预测控制的能量提取算法研究[J]. 电工技术学报, 0, (): 20235418-20235418.
Huang Xuanrui, Lin Zechuan, Xiao Xi. Modelling and Analysis of the Two-body Direct-drive Wave Energy Converter and Optimal Energy Extraction Method based on Model Predictive Control. Transactions of China Electrotechnical Society, 0, (): 20235418-20235418.
[1] 洪岳,潘剑飞,刘云,王璨,李灿,付鹏飞.直驱波浪能发电系统综述[J].中国电机工程学报,2019,39(07):1886-1900.
Hong Yue, Pan Jianfei, Liu Yun, Wang Can, Li Can, Fu Pengfei.A Review on Linear Generator Based Wave Energy Conversion Systems[J]. Proceedings of the CSEE,2019,39(07):1886-1900.
[2] Ahamed R, McKee K, Howard I. Advancements of wave energy converters based on power take off (PTO) systems: A review[J]. Ocean Engineering.2020 May 15;204:107248.
[3] 张家明,黎明,刘臻,史宏达.10kW组合型振荡浮子波浪发电装置的电力变换与控制系统[J].中国海洋大学学报(自然科学版),2018,48(04):126-133.
Zhang Jiaming, Li Ming, Liu Zhen, Shi Hongda.Power Conversion and Control System for 10kW Oscillating Buoy Array Wave Energy Converter[J]. Periodical of Ocean Engineering of China, 2018,48(4):126-133.
[4] 路晴,史宏达.中国波浪能技术进展与未来趋势[J].海岸工程,2022,41(01):1-12.
Lu Qing, Shi Hongda.Progress and Future Trend of Wave Energy Technology in China[J].Coastal Engineering,2022,41(01):1-12.
[5] 刘娜,谭亦旻,莫伟强,韩欢庆,李琳.基于模拟退火算法的Halbach直线发电机优化设计[J].电工技术学报,2021,36(06):1210-1218.
Liu Na, Tan Yihao, Mo Wei, Han Huanqing, Li Lin.Optimization Design of Halbach Linear Generator with Simulated Annealing Algorithm[J]. Transactions of China Electrotechnical Society, 2021,36(06):1210-1218.
[6] 张静,余海涛,施振川.一种波浪发电装置用低速双动子永磁直线电机运行机理研究[J].电工技术学报,2018,33(19):4553-4562.
Zhang Jing, Yu Haitao, Shi Zhenchuan.Research on a Tubular Linear Permanent Magnet Machines with Dual Translators for Low Speed Wave Energy Conversion[J]. Transactions of China Electrotechnical Society,2018,33(19):4553-4562.
[7] FALNES J.Ocean waves and oscillating systems: linear interactions including wave-energy extraction[M]. Cambridge university press, 2020.
[8] 康庆,肖曦,聂赞相,黄立培.直驱型海浪发电系统输出功率优化控制策略[J].电力系统自动化,2013,37(03):24-29.
Kang Qing, Xiao Xi, Nie Zanxiang, Huang Lipei.An Optimal Control Strategy for Output Power of the Directly Driven Wave Power Generation System[J]. Automation of Electric Power Systems,2013,37(03):24-29.
[9] Temiz I, Leijon J, Ekergård B, Boström C. Economic aspects of latching control for a wave energy converter with a direct drive linear generator power take-off[J]. Renewable energy.2018 Dec 1;128:57-67.
[10] Xiao Xi, Huang Xuanrui, Kang Qing. A hill-climbing-method-based maximum-power-point-tracking strategy for direct-drive wave energy converters[J]. IEEE Transactions on Industrial Electronics.2015 Aug 7;63(1):257-267.
[11] LI G, BELMONT M R.Model predictive control of sea wave energy converters - Part I: A convex approach for the case of a single device[J]. Renewable Energy, 2014, 69:453-63.
[12] Zhan, Siyuan, Jing Na, Guang Li, and Bin Wang. Adaptive model predictive control of wave energy converters[J]. IEEE Transactions on Sustainable Energy,2018,11(01): 229-238.
[13] Haider AS, Brekken TK, McCall A. Application of real‐time nonlinear model predictive control for wave energy conversion[J]. IET Renewable Power Generation.2021 Oct;15(14):3331-40.
[14] Sheng W, Alcorn R, Lewis A. On improving wave energy conversion, part II: Development of latching control technologies[J]. Renewable Energy.2015 Mar 1;75:935-44.
[15] 方红伟,宋如楠,姜茹,胡玉洁.振荡浮子式波浪能转换装置的全电气化模拟研究[J].电工技术学报,2019,34(14):3059-3065.
Fang Hongwei, Song Runan, Jiang Ru, Hu Yujie.An Oscillating Buoy Type Wave Energy Converter with All-Electrical Analogue Method[J]. Transactions of China Electrotechnical Society, 2019,34(14):3059-3065.
[16] Sahraoui M, Cardoso AJ, Ghoggal A. The use of a modified prony method to track the broken rotor bar characteristic frequencies and amplitudes in three-phase induction motors[J]. IEEE Transactions on Industry Applications.2014 Dec 2;51(3):2136-2147.