Voltage source equivalent model of offshore direct current wind turbine based on LLC resonant converter

doi:10.11930/j.issn.1004-9649.202501008

Abstract

Abstract:

Offshore wind farms adopting a DC collection scheme can avoid overvoltage problems caused by the capacitive charging effect of undersea cables, and also eliminate the need for bulky power-frequency transformers, representing an important direction for future development. This paper firstly establishes a detailed model of an offshore direct current (DC) wind turbine based on the LLC resonant converter and designs an integrated control strategy for the turbine unit. Then, based on the averaging model and the operating principles of the LLC resonant converter, the detailed model is simplified to obtain an equivalent voltage source model. Finally, a comparative analysis of the dynamic characteristics is conducted under various operating conditions among the equivalent voltage source model, the detailed model, and the existing current source equivalent model established in previous studies, verifying the accuracy of the former. The established model holds practical reference value for conducting stability analysis on the integration of offshore DC wind farms into the main power grid.

Key words: DC collection, LLC resonant converter, DC wind power turbines, control strategy, voltage source equivalent model

NING Yujie, HU Shuju, CHEN Yijing, LI Chunhua, LI Fenglin, ZHAO Dawei. Voltage source equivalent model of offshore direct current wind turbine based on LLC resonant converter[J]. Electric Power, 2026, 59(1): 143-152.

Add to citation manager EndNote|Ris|BibTeX

URL: https://www.electricpower.com.cn/EN/10.11930/j.issn.1004-9649.202501008

https://www.electricpower.com.cn/EN/Y2026/V59/I1/143

Figures/Tables 16

Fig.1 Parallel two-stage boost-type configuration for offshore wind farms

Fig.2 Permanent-magnet direct-drive offshore DC wind turbine structure

Fig.3 Generator-side AC/DC converter control block diagram

Fig.4 LLC resonant converter topology

Fig.5 DC gain curves

Fig.6 Grid-side DC/DC converter control block diagram

Fig.7 Generator-side AC/DC converter equivalent model

Fig.8 Grid-side DC/DC converter equivalent model

Fig.9 Example system of DC wind turbine integrated into DC power grid

Table 1 Main parameters of the 5 MW offshore DC wind turbine

参数	取值
风机容量/MW	5
风轮直径/m	126
切入风速/(m·s^–1)	4
额定风速/(m·s^–1)	11.5
定子线电压/kV	3.3
直流母线电压/kV	5.2
极对数	72
直轴电感/mH	9.3
交轴电感/mH	9.3
电枢电阻/$ \mathrm{\Omega } $	0.065
永磁体磁链/Wb	26.48
发电机惯性时间常数/s	0.84
风力机等效惯性时间常数/s	5.54

Table 2 Main parameters of the DC/DC converter

参数	取值
输入电压/kV	5.2
输出电压/kV	10.5
输入功率/MW	0.12~2.5
工作频率/kHz	3.1~5.7
变压器变比	1∶2
谐振电感/μH	76.2
励磁电感/μH	381.1
谐振电容/μF	9.2
子模块数量	2

Fig.10 Random wind speed at an average value of 10 m/s

Fig.11 Comparison of simulation results from the three models under wind speed fluctuations

Table 3 MAPE of the simplified model under wind speed fluctuations 单位：%

变量	电流源模型	电压源模型
${\omega _{\text{r}}}$	0.08	0.05
${V_{{\text{dc}}}}$	0.52	0.31
${P_{{\text{wt}}}}$	0.05	0.04
${V_{{\text{wt}}}}$	0.43	0.06
$ i_{\text{wt}} $	0.19	0.27

Fig.12 Comparison of simulation results among three models under grid voltage fluctuations

Table 4 MAPE of the simplified model under voltage fluctuations 单位：%

变量	电流源模型	电压源模型
${V_{{\text{dc}}}}$	6.40	0.41
${V_{{\text{wt}}}}$	0.40	0.02
$ i_{\text{wt}} $	0.49	0.22
${P_{{\text{wt}}}}$	0.41	0.05

References 38

1	季湛洋, 胡阳, 孔令行, 等. 考虑多领域耦合特性的风电机组一次调频动态建模与仿真[J]. 中国电力, 2025, 58 (4): 56- 67.
	JI Zhanyang, HU Yang, KONG Lingxing, et al. Dynamic modeling and simulation of wind turbine unit primary frequency regulation considering multi-domain coupling characteristics[J]. Electric Power, 2025, 58 (4): 56- 67.
2	李国栋, 徐明扬. 基于KCR-Informer的长期风电功率预测研究[J]. 电力信息与通信技术, 2024, 22 (4): 55- 62.
	LI Guodong, XU Mingyang. Research on long-term wind power prediction based on KCR-informer[J]. Electric Power Information and Communication Technology, 2024, 22 (4): 55- 62.
3	陈小乾, 尹亮, 展宗辉, 等. 基于注意力机制和RCN-BiLSTM融合的风电机组故障识别[J]. 中国电力, 2025, 58 (8): 94- 102.
	CHEN Xiaoqian, YIN Liang, ZHAN Zonghui, et al. Fault identification for wind turbine based on attention mechanism and RCN-BiLSTM fusion[J]. Electric Power, 2025, 58 (8): 94- 102.
4	陈阅海, 彭乔, 刘天琪, 等. 考虑电压恢复的风电系统改进分段协调频率控制[J]. 电力工程技术, 2025, 44 (2): 160- 171,196.
	CHEN Yuehai, PENG Qiao, LIU Tianqi, et al. Improved piecewise coordinated frequency control of wind power generation system considering voltage restoration[J]. Electric Power Engineering Technology, 2025, 44 (2): 160- 171,196.
5	陶思钰, 江福庆. 集群化发展模式下风电场预测、规划及控制关键技术综述[J]. 电力工程技术, 2024, 43 (1): 86- 99.
	TAO Siyu, JIANG Fuqing. Review of the key technologies of wind farm cluster prediction, planning and control[J]. Electric Power Engineering Technology, 2024, 43 (1): 86- 99.
6	杨铎烔, 俞靖一, 葛俊, 等. 海上风电场自适应多目标无功优化控制策略[J]. 电力工程技术, 2024, 43 (3): 121- 129.
	YANG Duotong, YU Jingyi, GE Jun, et al. Adaptive multi-objective reactive power optimization control strategy for offshore wind farms[J]. Electric Power Engineering Technology, 2024, 43 (3): 121- 129.
7	黄冬梅, 牟宗凯, 时帅, 等. 考虑复杂海洋状况下的深远海风电场并网系统可靠性评估[J]. 电力科学与技术学报, 2024, 39 (6): 174- 183.
	HAUNG Dongmei, MOU Zongkai, SHI Shuai, et al. Reliability assessment of grid-connected systems in deep-sea offshore wind farmsunder complex oceanic conditions[J]. Journal of Electric Power Science and Technology, 2024, 39 (6): 174- 183.
8	姜文瑾, 刘巧妹, 杨晓东, 等. 计及气固两相储氢特性的海上风电-多元储能系统优化配置[J]. 中国电力, 2024, 57 (9): 103- 112.
	JIANG Wenjin, LIU Qiaomei, YANG Xiaodong, et al. Optimal allocation of offshore wind power-multiple energy storage system considering gas-solid two-phase hydrogen storage characteristics[J]. Electric Power, 2024, 57 (9): 103- 112.
9	孙均磊, 贾科, 李再男, 等. 基于故障分量时频突变特征的海上风电直流升压送出线路纵联保护[J]. 电力系统保护与控制, 2024, 52 (18): 1- 11.
	SUN Junlei, JIA Ke, LI Zainan, et al. Pilot protection for offshore wind power DC transmission lines based on the time-frequencymutation characteristics of fault components[J]. Power System Protection and Control, 2024, 52 (18): 1- 11.
10	刘钟淇, 刘耀, 侯金鸣. 以深远海风电为核心的能源岛能源外送经济性分析[J]. 中国电力, 2024, 57 (9): 94- 102.
	LIU Zhongqi, LIU Yao, HOU Jinming. Economic analysis of energy transmission for energy island based on deep-sea offshore wind farms[J]. Electric Power, 2024, 57 (9): 94- 102.
11	边晓燕, 左轩泽, 潘汀莹, 等. 基于编码规划矩阵的海上风电基地送出系统规划方法[J]. 电力系统保护与控制, 2025, 53 (10): 130- 141.
	BIAN Xiaoyan, ZUO Xuanze, PAN Tingying, et al. A planning method for transmission system of offshore wind power base based on a coded planning matrix[J]. Power System Protection and Control, 2025, 53 (10): 130- 141.
12	丰力, 张莲梅, 韦家佳, 等. 基于全生命周期经济评估的海上风电发展与思考[J]. 中国电力, 2024, 57 (9): 80- 93.
	FENG Li, ZHANG Lianmei, WEI Jiajia, et al. Development & thinking of offshore wind power based on life cycle economic evaluation[J]. Electric Power, 2024, 57 (9): 80- 93.
13	蔡旭, 杨仁炘, 周剑桥, 等. 海上风电直流送出与并网技术综述[J]. 电力系统自动化, 2021, 45 (21): 2- 22.
	CAI Xu, YANG Renxin, ZHOU Jianqiao, et al. Review on offshore wind power integration via DC transmission[J]. Automation of Electric Power Systems, 2021, 45 (21): 2- 22.
14	MEYER C, HÖING M, PETERSON A, et al. Control and design of DC grids for offshore wind farms[J]. IEEE Transactions on Industry Applications, 2007, 43 (6): 1475- 1482.
15	TIMMERS V, EGEA-ÀLVAREZ A, GKOUNTARAS A, et al. All-DC offshore wind farms: when are they more cost-effective than AC designs?[J]. IET Renewable Power Generation, 2023, 17 (10): 2458- 2470.
16	赵彪, 安峰, 屈鲁, 等. 多功能直流集电器概念及其全直流海上风电系统[J]. 中国电机工程学报, 2021, 41 (18): 6169- 6180.
	ZHAO Biao, AN Feng, QU Lu, et al. Multi-function DC-collector concept and its all-DC offshore wind power system[J]. Proceedings of the CSEE, 2021, 41 (18): 6169- 6180.
17	蔡旭, 施刚, 迟永宁, 等. 海上全直流型风电场的研究现状与未来发展[J]. 中国电机工程学报, 2016, 36 (8): 2036- 2048.
	CAI Xu, SHI Gang, CHI Yongning, et al. Present status and future development of offshore all-DC wind farm[J]. Proceedings of the CSEE, 2016, 36 (8): 2036- 2048.
18	AN F, ZHAO B, CUI B, et al. Multi-functional DC collector for future all-DC offshore wind power system: concept, scheme, and implement[J]. IEEE Transactions on Industrial Electronics, 2022, 69 (8): 8134- 8145.
19	GUO G P, SONG Q, ZHAO B, et al. Series-connected-based offshore wind farms with full-bridge modular multilevel converter as grid- and generator-side converters[J]. IEEE Transactions on Industrial Electronics, 2020, 67 (4): 2798- 2809.
20	ZHANG H B, GRUSON F, RODRIGUEZ D M F, et al. Overvoltage limitation method of an offshore wind farm with DC series-parallel collection grid[J]. IEEE Transactions on Sustainable Energy, 2019, 10 (1): 204- 213.
21	江道灼, 谷泓杰, 尹瑞, 等. 海上直流风电场研究现状及发展前景[J]. 电网技术, 2015, 39 (9): 2424- 2431.
	JIANG Daozhuo, GU Hongjie, YIN Rui, et al. Research status and developing prospect of offshore wind farm with pure DC systems[J]. Power System Technology, 2015, 39 (9): 2424- 2431.
22	王新颖, 汤广福, 贺之渊, 等. 远海风电场直流汇集用DC/DC变换器拓扑研究[J]. 中国电机工程学报, 2017, 37 (3): 837- 847.
	WANG Xinying, TANG Guangfu, HE Zhiyuan, et al. Topology research of DC/DC converters for offshore wind farm DC collection systems[J]. Proceedings of the CSEE, 2017, 37 (3): 837- 847.
23	刘云波, 胡书举, 李丰林, 等. 海上风电直流汇集DC-DC变换器拓扑与控制策略分析[J]. 电测与仪表, 2023, 60 (12): 77- 81.
	LIU Yunbo, HU Shuju, LI Fenglin, et al. Topology and control strategy analysis of offshore wind power DC converters[J]. Electrical Measurement & Instrumentation, 2023, 60 (12): 77- 81.
24	ZHANG J, MA K, LEI E, et al. Modeling and controller design of a hybrid input-parallel output-serial modular DC-DC converter for high efficiency and wide output range[J]. IEEE Transactions on Industry Applications, 2023, 59 (3): 3425- 3437.
25	HU P, YIN R, WEI B, et al. Modular isolated LLC DC/DC conversion system for offshore wind farm collection and integration[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9 (6): 6713- 6725.
26	GUAN M Y. A series-connected offshore wind farm based on modular Dual-Active-Bridge (DAB) isolated DC-DC converter[J]. IEEE Transactions on Energy Conversion, 2019, 34 (3): 1422- 1431.
27	肖寒冰, 马建军, 朱淼, 等. 面向海上风电直流升压汇集的非对称双向有源桥DC-DC变换器[J]. 中国电机工程学报, 2025, 45 (7): 2719- 2731.
	XIAO Hanbing, MA Jianjun, ZHU Miao, et al. Asymmetrical bidirectional active bridge DC-DC converter for DC voltage step-up collection in offshore wind farm[J]. Proceedings of the CSEE, 2025, 45 (7): 2719- 2731.
28	刘其辉, 洪诚程, 樊双婕, 等. 一种基于二重移相变换的大容量海上直流风机及控制技术[J]. 中国电机工程学报, 2023, 43 (2): 507- 518.
	LIU Qihui, HONG Chengcheng, FAN Shuangjie, et al. One kind of large-scale DC wind turbine and its control technology based on dual phase-shift power conversion[J]. Proceedings of the CSEE, 2023, 43 (2): 507- 518.
29	ZENG J, ZHANG G, YU S S, et al. LLC resonant converter topologies and industrial applications—A review[J]. Chinese Journal of Electrical Engineering, 2020, 6 (3): 73- 84.
30	ROBINSON J, JOVCIC D, JOÓS G. Analysis and design of an offshore wind farm using a MVDC grid[J]. IEEE Transactions on Power Delivery, 2010, 25 (4): 2164- 2173.
31	姚良忠, 施刚, 蔡旭, 等. 适用于风场级研究的含机电暂态直流风电机组动态模型[J]. 电网技术, 2016, 40 (2): 465- 470.
	YAO Liangzhong, SHI Gang, CAI Xu, et al. Dynamic modeling of DC wind turbine with electromechanical transients for wind farm studies[J]. Power System Technology, 2016, 40 (2): 465- 470.
32	WANG Y, MENG J, ZHANG X, et al. Control of PMSG-based wind turbines for system inertial response and power oscillation damping[J]. IEEE Transactions on Sustainable Energy, 2015, 6 (2): 565- 574.
33	陈载宇, 殷明慧, 蔡晨晓, 等. 一种实现风力机MPPT控制的加速最优转矩法[J]. 自动化学报, 2015, 41 (12): 2047- 2057.
	CHEN Zaiyu, YIN Minghui, CAI Chenxiao, et al. An accelerated optimal torque control of wind turbines for maximum power point tracking[J]. Acta Automatica Sinica, 2015, 41 (12): 2047- 2057.
34	胡海兵, 王万宝, 孙文进, 等. LLC谐振变换器效率优化设计[J]. 中国电机工程学报, 2013, 33 (18): 48- 56.
	HU Haibing, WANG Wanbao, SUN Wenjin, et al. Optimal efficiency design of LLC resonant converters[J]. Proceedings of the CSEE, 2013, 33 (18): 48- 56.
35	ZHAO S, KEMPITIYA A, CHOU W T, et al. Variable DC-link voltage LLC resonant DC/DC converter with wide bandgap power devices[J]. IEEE Transactions on Industry Applications, 2022, 58 (3): 2965- 2977.
36	戈现勉. 高效率LLC谐振变换器研究[D]. 杭州: 浙江大学, 2015.
	GE Xianmian. Research on high efficiency LLC resonant converter[D]. Hangzhou: Zhejiang University, 2015.
37	姚良忠, 施刚, 曹远志, 等. 海上直流风电场内网中串联直流风机的变速控制[J]. 电网技术, 2014, 38 (9): 2410- 2415.
	YAO Liangzhong, SHI Gang, CAO Yuanzhi, et al. Variable speed control of series-connected DC wind turbines in the internal grid of offshore DC wind farm[J]. Power System Technology, 2014, 38 (9): 2410- 2415.
38	TIMMERS V, EGEA-ÀLVAREZ A, GKOUNTARAS A. Frequency optimisation for DC/DC converters in DC-connected offshore wind turbines[C]. 2023 25th European Conference on Power Electronics and Applications (EPE'23 ECCE Europe). IEEE, 2023: 1–8.

[1]	CHEN Rui, ZHENG Tao, REN Xiang, SHEN Wentao, ZHANG Lu, QIANG Yuze, LIU Bo, WANG Yuxuan. Adaptability Analysis of Positive Sequence Fault Component Direction Element Under the Condition of Electrochemical Energy Storage System [J]. Electric Power, 2025, 58(8): 84-93, 138.
[2]	YUAN Song, GE Zhao, Tang Jiajie, MEI Jiabao. Longitudinal Protection of Grid-Forming New Energy Outgoing Lines Based on Composite Sequence Current Characteristics [J]. Electric Power, 2025, 58(8): 185-192.
[3]	ZHANG Ruixiao, LIANG Li, WANG Dingmei. Fast Frequency Response Analysis and Efficient Test Device Design of New Energy Station [J]. Electric Power, 2025, 58(5): 144-151.
[4]	Mingyuan WAN, Xin REN, Du WANG, Yafei JIN, Zhigang WANG, Tingju WANG, Changhong YANG, Haokun LIU. Study of Dynamic Characteristics of 100 MW Cascade S-CO₂ Cycle [J]. Electric Power, 2024, 57(12): 169-177.
[5]	Nuo CHENG, Dacai CHEN, Xue CHEN, Xiaofei RUAN, Shuqing WEI, Zheyu HAN. An Optimized Scheme for Active Distribution Network Current Speed Protection Setting Considering Tie Switch Operation [J]. Electric Power, 2024, 57(10): 90-101.
[6]	Zhihui DAI, Meiyuan LIU, Shuqing WEI, Weiping ZHU, Wenzhuo WANG. Distance Protection for Outgoing Line of Photovoltaic Station Based on Superconducting Magnetic Energy Storage [J]. Electric Power, 2024, 57(10): 102-114.
[7]	Baocheng FENG, Zhen JIN, Wei HOU, Guangfu XU. Research and Application of Control Strategy Optimization for Regional Standby Automatic Switching System of Petal-Type Distribution Network [J]. Electric Power, 2024, 57(1): 244-254.
[8]	SHI Wenzhe, LI Bingjie, YOU Peipei, ZHANG Ling. Optimization Strategy of Building Energy System Based on Deep Reinforcement Learning [J]. Electric Power, 2023, 56(6): 114-122.
[9]	ZHOU Wenjun, CAO Yi, LI Jie, JIN Tao, CHEN Wenjian, ZHOU Xia. Reactive Voltage Emergency Control Strategy of Wind-Thermal-Bundled DC Transmission System Considering Wind Farm Regulation Margin [J]. Electric Power, 2023, 56(4): 77-87.
[10]	LIU Liantao, LIU Fei, JI Ping, LIN Weifang, ZHANG Xiangcheng, TIAN Xu, GAO Fei. Research on Optimal Control Strategy of Energy Storage for Improving New Energy Consumption [J]. Electric Power, 2023, 56(3): 137-143.
[11]	HE Yanqiang, WANG Ying, CHEN Xiaoqiang, CHEN Jianxiao. Energy Storage Control Strategy of Railway Network Side Considering Characteristic Harmonic Control [J]. Electric Power, 2022, 55(7): 33-41.
[12]	ZHOU Shijia, YANG Guangyuan, PENG Guangqiang, WU Jiyang, XIN Qingming. Fault-Tolerant Control Strategy Based on Multi-Phase Wind Power System [J]. Electric Power, 2022, 55(7): 134-141.
[13]	ZHANG Guozhu, ZHANG Juntai, WEN Yu, YANG Kaixuan, LIU Ming, LIU Jiping. Study on Off-design Condition Characteristics and Control Strategy of Fluegas Waste Heat and Water Recovery System of Coal-Fired Power Plants [J]. Electric Power, 2022, 55(4): 214-220.
[14]	CAO Yaqi, ZHAO Bo, WANG Lijie, LI Xiangjun, GAO Binheng. Research on Operational Benefit Improvement Strategy of Optical Storage Power Station Based on Genetic Ant Colony Algorithm [J]. Electric Power, 2022, 55(2): 9-18.
[15]	YU Yongjun, XU Liguo, LIN Zijie, SUN Binghan, LIU Qiujiang, WU Zhensheng, REN Zhijie. Wide-Band Harmonic Impedance Measurement Device for Wind Grid Based on Cascaded H-Bridge Converter [J]. Electric Power, 2022, 55(11): 73-83.