远海岛礁供电系统外转子聚磁式永磁游标电机电磁特性解析

doi:10.12382/bgxb.2025.0691

摘要/Abstract

摘要：

茫茫大洋上，部分岛礁分布分散，彼此间距较远。传统能源发电方式面临供电保障困难、运维成本高昂等突出难题。为充分开发海洋可再生能源，构建可持续的海上能源供应体系，海上风力发电技术正逐步成为解决远海岛礁供电难题的战略选择。永磁游标电机(Permanent Magnet Vernier Motor，PMVM)作为一种基于先进磁场调制理论的新型电磁能量转换装置，凭借其低速大转矩的优异特性，在船舶推进和海上风电等领域展现出独特优势，尤其适合作为远海岛礁微电网的核心发电单元。针对切向励磁PMVM，创新性构建了多节点磁路解析模型体系。通过严谨的数学建模，获得了该结构下气隙磁场的精确解析解，并基于磁场调制理论及机电能量转换原理，系统化地建立了气隙磁场、空载反电势、电磁转矩及电枢电感等核心电磁参数与电机几何尺寸的量化关系。在考虑双边开槽效应的情况下，核心电气参数的误差控制在了2%以内。特别地，采用直流电流衰减法实现了电机电感参数的高精度实验标定，解析模型预测值与实测数据误差控制在3%以内，充分验证了理论模型的有效性。该研究为切向励磁结构PMVM的快速设计优化提供了完整的理论分析框架与工程实践指导，研究通过有限元仿真和样机实验的对比验证，证实了解析模型的准确性和工程适用性。

关键词: PMVM, 磁路法, 解析法, 磁场分布, 电感计算

Abstract:

On the vast ocean，some islands and reefs are scattered and far apart from each other.The traditional energy power generation mode is facing prominent problems such as difficulties in power supply guarantee，and high operation and maintenance costs，etc.In order to fully develop renewable energy in the ocean and build a sustainable offshore energy supply system，the offshore wind power generation technology is gradually becoming a strategic choice to solve the problem of power supply in remote islands and reefs.As a new type of electromagnetic energy conversion device based on advanced magnetic field modulation theory，the permanent magnet vernier motor (PMVM) has demonstrated unique advantages in the fields of ship propulsion and offshore wind power generation due to its excellent low-speed and high torque characteristics，and is particularly suitable for use as the core power generation unit of offshore island microgrids.A multi-node magnetic circuit analytical model system is structured for tangential excitation PMVM.An accurate analytical solution for the air gap magnetic field in this structure is obtained through rigorous mathematical modeling.Based on the theory of magnetic field modulation and the principle of electromechanical energy conversion，the quantitative relationship among the core electromagnetic parameters such as air gap magnetic field，no-load back electromotive force，electromagnetic torque and armature inductance with the size of motor are systematically established.Taking into account the bilateral slotting effect，the error of the core electrical parameters is controlled within 2%.Specifically，the direct current attenuation method is used to achieve the high-precision experimental calibration of motor inductance parameters.The error between the predicted values of the analytical model and the measured data is controlled within 3%，fully verifying the effectiveness of the theoretical model.This study provides a complete theoretical analysis framework and engineering practice guidance for the rapid design and optimization of tangential excitation structure PMVM.The accuracy and engineering applicability of the analytical model are confirmed through the comparative verification of finite element simulation and prototype experiments.

Key words: PMVM, magnetic circuit method, analytic method, magnetic field distribution, inductance calculation

吴波, 乔鸣忠, 夏益辉, 赵世遥, 王康宁, 邱泓铭, 姚宇杰, 杨科科. 远海岛礁供电系统外转子聚磁式永磁游标电机电磁特性解析[J]. 兵工学报, 2025, 46(S1): 250691-.

WU Bo, QIAO Mingzhong, XIA Yihui, ZHAO Shiyao, WANG Kangning, QIU Hongming, YAO Yujie, YANG Keke. Electromagnetic Characteristics of an Outer-rotor Magnetic-Concentrating PMVM for Power Supply System on Offshore Islands and Reefs[J]. Acta Armamentarii, 2025, 46(S1): 250691-.

图/表 16

图1 磁场调制过程

Fig.1 Schematic diagram of magnetic field modulation process

图2 聚磁式PMVM拓扑结构

Fig.2 Aggregation-based PMVM topology structure

图3 电机气隙结构

Fig.3 Motor air gap structure

图4 磁路模型

Fig.4 Magnetic circuit model

表1 样机参数

Table 1 Prototype parameters

参数	数值	参数	数值
定子内径/mm	150	永磁体极对数	23
定子外径/mm	300	永磁体宽度/mm	12
转子内径/mm	304	永磁体长度/mm	32.5
转子外径/mm	370	绕组串联匝数	290
铁芯轴向长度/mm	323	额定转速/(r·min^-1)	65
定子槽数	30	额定频率/Hz	25

图5 电机气隙空载磁场对比分析

Fig.5 Comparative analysis diagram of no-load magnetic field in motor air gap

图6 空载反电势对比分析

Fig.6 Comparison and analysis diagram of no-load reverse electromotive force

图7 有限元分析转矩

Fig.7 Finite element analysis of torque

图8 PMVM电势相位图

Fig.8 PMVM potential phase diagram

表2 静态求解法下电机电感计算结果

Table 2 Calculated results of motor inductance obtained by static solution method /mH

绕组	绕组
绕组	A	B	C
A	25.59	0.064	0.061
B	0.064	25.23	0.065
C	0.061	0.065	25.58

图9 瞬态求解法下电机电感计算结果

Fig.9 Calculation results of motor inductance obtained by transient solution method

图10 电机实验平台

Fig.10 Motor experimental platform

图11 实验测得电机输出电压曲线

Fig.11 Measured output voltage of motor

图12 直流衰减法实验电路图

Fig.12 Experimental circuit diagram of DC attenuation method

图13 电流衰减波形图

Fig.13 Current attenuation waveform

图14 电流衰减拟合曲线

Fig.14 Current attenuation fitting curve

参考文献 23

[1]	蔡博峰, 李亚飞, 鲁玺, 等. 中国风电和太阳能发电潜力评估(2024)[R]. 北京: 生态环境部环境规划院, 2024.
	CAI B F, LI Y F, LU X, et al. Assessment of wind and solar power potential in China (2024)[R]. Beijing: Environmental Planning Institute of the Ministry of Ecology and Environment, 2024. (in Chinese)
[2]	赵琳, 魏澈, 王阳, 等. 海上风电场宏观选址与风能资源储量估算[J]. 太阳能学报, 2024, 45(5):1-8.
	ZHAO L, WEI C, WANG Y, et al. Macroscopical site selection and estimation of wind energy reserves for offshore wind farms[J]. Acta Energiaesolaris Sinica, 2024, 45(5):1-8. (in Chinese)
[3]	李大伟. 磁场调制永磁电机研究[D]. 武汉: 华中科技大学, 2015.
	LI D W. Research on magnetic field modulation permanent magnet machines[D]. Wuhan: Huazhong University of Science and Technology, 2015. (in Chinese)
[4]	TLALI P M, WANG R J, Gerber S, et al. Design and performance comparison of vernier and conventional PM synchronous wind generators[J]. IEEE Transactions on Industry Applications, 2020, 56(3):2570-2579.
[5]	LI J G, WU D Y, ZHANG X D, et al. A new permanent-magnet vernier in-wheel motor for electric vehicles[C]// Proceedings of 2010 IEEE Vehicle Power and Propulsion Conference.Lille, France:IEEE,2010:1-6.
[6]	Li D W, QU R H, LI J, et al. Analysis of torque capability and quality in vernier permanent-magnet machines[J]. IEEE Transactions on Industry Applications, 2016, 52(1):125-134.
[7]	CHEN Q S, FAN Y, LEI Y T, et al. Multi-objective optimization design of unequal halbach array permanent magnet vernier motor based on optimization algorithm[J]. IEEE Transactions on Industry Applications, 2022, 58(5):6014-6023.
[8]	YU Y L, CHAI F, PEI Y L, et al. Investigation of PM loss in spoke-type permanent magnet vernier motors with different stator topologies for in-wheel direct drive[J]. IEEE Transactions on Industry Applications, 2022, 58(4):4562-4574.
[9]	李祥林. 基于磁齿轮原理的场调制永磁风力发电机及其控制系统研究[D]. 南京: 东南大学, 2015.
	Li X L. Research on field modulated permanent magnet machine and its control system for direct drive wind power generation[D]. Nanjing: Southeast University, 2015. (in Chinese)
[10]	KIM B, LIPO T A. Operation and design principles of a pm vernier motor[J]. IEEE Transactions on Industry Applications, 2014, 50(6):3565-3663.
[11]	张远志. 切向励磁型游标永磁直驱风力发电机技术研究[D]. 武汉: 华中科技大学, 2022.
	ZHANG Y Z. Research on spoke-type vernier oermanent magnet direct-drive wind turbine generator[D]. Wuhan: Huazhong University of Science and Technology, 2022. (in Chinese)
[12]	杨帆. 新型内置马鞍型永磁体游标电机研究[D]. 哈尔滨: 哈尔滨理工大学, 2024.
	YANG F. Research on novel built-in saddle-shaped permanent magnet vernier machine[D].Harbin: Harbin University of Science and Technology, 2024. (in Chinese)
[13]	UPPALAPATI K K, BOMELA W, BIRD J Z, et al. Construction of a low speed flux focusing magnetic gear[C]// Proceedings of 2013 IEEE Energy Conversion Congress and Exposition.Denver,CO, US:IEEE,2013:2178-2184.
[14]	秦语缘, 樊英, 陈秋蒴, 等. 高转矩密度永磁游标伺服电机磁通屏障效应分析及抑制[J]. 中国电机工程学报, 2025, 45(4):1237-1248.
	QIN Y Y, FAN Y, CHEN Q S, et al. Analysis and suppression of flux barrier effect of high torque density permanent magnet vernier servo motor[J]. Proceedings of the CSEE, 2025, 45(4):1237-1248. (in Chinese)
[15]	赵志刚, 郑宇萱, 陈天缘, 等. 基于镜像法的高频圆导线变压器漏感计算模型[J]. 中国电机工程学报, 2024, 44(16):6697-6706.
	ZHAO Z G, ZHENG Y H, CHEN T Y, et al. Leakage inductance calculation model of high-frequency round conductor transformer based on image method[J]. Proceedings of the CSEE, 2024, 44(16):6697-6706. (in Chinese)
[16]	SHARMA A, KIMBALL J W. Evaluation of transformer leakage inductance using magnetic image method[J]. IEEE Transactions on Magnetics, 2021, 57(11):8401912.
[17]	LI D W, QU R H, LI J, et al. Analysis of torque capability and quality in vernier permanent-magnet machines[J]. IEEE Transactions on Industry Applications, 2015, 52(1):125-135.
[18]	李仕豪, 狄冲, 刘佶炜, 等. 考虑交叉耦合影响的内置式永磁同步电机电感计算及转矩分析[J]. 电工技术学报, 2023, 38(18):4889-4899,4931.
	LI S H, DI C, LIU J Y, et al. Inductance calculation and torque analysis of interior permanent magnet synchronous machine considering cross-coupling effects[J]. Transactions of China Electrotechnical Society, 2023, 38(18):4889-4899,4931. (in Chinese)
[19]	康皓宇, 马一鸣, 孙鲁, 等. 基于场路耦合模型的大型交流励磁电机电感参数计算[J/OL]. 电工技术学报, 2025 (2025-01-24).[2025-05-21]https://doi.org/10.19595/j.cnki.1000-6753.tces.241378.
	KANG H Y, MA Y M, SUN L, et al. Calculation of inductance parameters for large ac excitation machine based on field-circuit coupled model[J/OL]. Transactions of China Electrotechnical Society, 2025 (2025-01-24)[2025-05-21].https://doi.org/10.19595/j.cnki.1000-6753.tces.241378. in Chinese)
[20]	曲荣海, 李大伟, 赵钰. 磁场调制电机的由来、发展与挑战[J]. 中国电机工程学报, 2024, 44(18):7361-7381.
	QU R H, LI D H, ZHAO Y. The origin,development and challenge of flux modulation machine[J]. Proceedings of the CSEE, 2024, 44(18):7361-7381. (in Chinese)
[21]	KIM B, LIPO T A. Analysis of a PM vernier motor with spoke structure[J]. IEEE Transactions on Industry Applications, 2015, 52(1):217-225.
[22]	张洋. 新型永磁游标风力发电机设计与分析研究[D]. 南京: 东南大学, 2016.
	ZHANG Y. Study on design and analysis of novel permanent magnet vernier wind generator[D]. Nanjing: Southeast University, 2016. (in Chinese)
[23]	李彦飞, 李子欣, 张航, 等. 单层双列背绕式直线感应电机反相供电下电感参数特性研究[J/OL]. 电工技术学报, 2025(2025-05-23)[2025-6-13].https://doi.org/10.19595/j.cnki.1000-6753.tces.242084.
	LI Y F, LI Z X, ZHANG H, et al. Characteristics of inductance oarameters in single-layer double-row linear induction motors with gramme-ring windings under anti-phase power supply[J/OL]. Transactions of China Electrotechnical Society, 2025(2025-05-23)[2025-6-13].https://doi.org/10.19595/j.cnki.1000-6753.tces.242084. in Chinese)