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Article(id=1207271185709093067, tenantId=1146029695717560320, journalId=1205116964453384197, issueId=1207271180105499439, articleNumber=null, orderNo=null, doi=10.20040/j.cnki.1000-7709.2025.20241621, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1724860800000, receivedDateStr=2024-08-29, revisedDate=1730217600000, revisedDateStr=2024-10-30, acceptedDate=null, acceptedDateStr=null, onlineDate=1765765480687, onlineDateStr=2025-12-15, pubDate=1758729600000, pubDateStr=2025-09-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1765765480687, onlineIssueDateStr=2025-12-15, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1765765480687, creator=13701087609, updateTime=1765765480687, updator=13701087609, issue=Issue{id=1207271180105499439, tenantId=1146029695717560320, journalId=1205116964453384197, year='2025', volume='43', issue='9', pageStart='1', pageEnd='220', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1765765479351, creator=13701087609, updateTime=1765765681303, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1207272027254247478, tenantId=1146029695717560320, journalId=1205116964453384197, issueId=1207271180105499439, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1207272027254247479, tenantId=1146029695717560320, journalId=1205116964453384197, issueId=1207271180105499439, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=197, endPage=202, ext={EN=ArticleExt(id=1207271186384376035, articleId=1207271185709093067, tenantId=1146029695717560320, journalId=1205116964453384197, language=EN, title=Design Optimization of Magnetic-geared Speed Regulator for Energy Storage System with Synchronous Condenser and Flywheel, columnId=null, journalTitle=Water Resources and Power, columnName=null, runingTitle=null, highlight=null, articleAbstract=

With the increasing proportion of new energy, the inertia support, voltage support, and frequency regulation ability are obviously weakened in current power system. The development of energy storage system with synchronous condenser and flywheel (ESSSCF) is of great significance to improve the regulation capability of new energy power generation and enhance the stability of new power systems. This article briefly describes the principle and different operation states of the magnetic-geared speed regulator (MGSR) for ESSSCF, and focuses on the design optimization of its electromagnetic structure. The electromagnetic finite element model of the MGSR is established. The shape of the flux barrier is selected for the inner rotor with V-shaped permanent magnet by calculating and analyzing the no-load leakage flux factor. The geometric parameters of the V-shaped permanent magnets and stator slots and the pole-arc coefficient of the modulating ring are optimized for multiple objectives, respectively, using genetic algorithm, under the conditions of a constant amount of permanent magnet and a constant area of stator slot. In addition, the correlation of the target performances with the geometric parameters is analyzed. The results of the design optimization and correlation analysis can direct the structural design of the magnetic-geared speed regulator for improvement of the torque and efficiency performances.

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随着新能源占比的提高，电力系统的惯量支撑、电压支撑以及调频能力明显减弱。同步调相机—飞轮储能系统的研发，对于提高新能源场站的调节能力、增强新型电力系统的稳定性具有重要意义。简要阐述了用于同步调相机—飞轮储能系统的磁齿轮调速器的工作原理和不同的运行状态，着重对其电磁结构进行了优化设计。建立了磁齿轮调速器的电磁有限元模型，通过计算和分析空载漏磁系数选定了V形永磁体内转子的磁障形状，进而采用遗传算法，在一定的永磁体用量和定子槽面积条件下，对V形永磁体和定子槽的形状参数及调制环的极弧系数进行了多目标优化，并分析了目标性能与结构形状参数的相关性。优化设计和相关性分析结果从结构设计上为磁齿轮调速器转矩和效率性能的提升指明了方向。

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詹阳（1978-），男，博士、副教授、硕导，研究方向为磁齿轮和磁场调制电机，E-mail：
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常可（1999-），女，硕士研究生，研究方向为磁场调制永磁电机，E-mail：

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常可（1999-），女，硕士研究生，研究方向为磁场调制永磁电机，E-mail：

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常可（1999-），女，硕士研究生，研究方向为磁场调制永磁电机，E-mail：

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2D获得永磁电机空载漏磁系数的方法[J]. 防爆电机, 2010, 45(5): 24-26, 28., articleTitle=一种利用Maxwell 2D获得永磁电机空载漏磁系数的方法, refAbstract=null), Reference(id=1207271202905740277, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, doi=null, pmid=null, pmcid=null, year=2015, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[8], rfOrder=7, authorNames=蹇林旎, journalName=同轴磁性齿轮的原理及应用, refType=null, unstructuredReference=蹇林旎. 同轴磁性齿轮的原理及应用[M]. 北京: 科学出版社, 2015., articleTitle=null, refAbstract=null)], funds=[Fund(id=1207271202054296524, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, awardId=null, language=CN, fundingSource=中国电科院自有基金项目, fundOrder=null, country=null)], companyList=[AuthorCompany(id=1207271192856187370, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, xref=1., ext=[AuthorCompanyExt(id=1207271192864575979, tenantId=1146029695717560320, 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tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=EN, label=Tab. 1, caption=

Basic parameters of initial design

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参数数值参数数值
定子极对数10定子槽数21
定子铁心内径/mm770定子铁心外径/mm1 071
额定电流密度/(A·mm-2)2.33电流最高频率/Hz170
调制块个数17调制环内径/mm620
调制环外径/mm750内转子极对数7
内转子直径/mm600永磁体型号N35EH
轴向有效长度/mm2 470内转子额定转速/(r·min-1)7 285.7
内转子最高转速/(r·min-1)8 742.9内转子最低转速/(r·min-1)5 828.6
), ArticleFig(id=1207271199701291918, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=CN, label=表1, caption=

初步设计的基本参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值参数数值
定子极对数10定子槽数21
定子铁心内径/mm770定子铁心外径/mm1 071
额定电流密度/(A·mm-2)2.33电流最高频率/Hz170
调制块个数17调制环内径/mm620
调制环外径/mm750内转子极对数7
内转子直径/mm600永磁体型号N35EH
轴向有效长度/mm2 470内转子额定转速/(r·min-1)7 285.7
内转子最高转速/(r·min-1)8 742.9内转子最低转速/(r·min-1)5 828.6
), ArticleFig(id=1207271199780983697, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=EN, label=Tab. 2, caption=

Typical operations of magnetic-geared speed regulator

, figureFileSmall=null, figureFileBig=null, tableContent=
运行参数数值
Ωr>Ωr0状态Ωr=Ωr0状态Ωr<Ωr0状态
内转子/飞轮转速/(r∙min-1)8 742.97 285.75 828.6
定子电流频率/Hz-1700170
定子基波磁场转速/(r∙min-1)-1 02001 020
), ArticleFig(id=1207271199957144473, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=CN, label=表2, caption=

磁齿轮调速器的典型工作状态

, figureFileSmall=null, figureFileBig=null, tableContent=
运行参数数值
Ωr>Ωr0状态Ωr=Ωr0状态Ωr<Ωr0状态
内转子/飞轮转速/(r∙min-1)8 742.97 285.75 828.6
定子电流频率/Hz-1700170
定子基波磁场转速/(r∙min-1)-1 02001 020
), ArticleFig(id=1207271200049419165, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=EN, label=Tab. 3, caption=

Electromagnetic performances of initial design

, figureFileSmall=null, figureFileBig=null, tableContent=
性能数值
Ωr>Ωr0加速Ωr>Ωr0减速Ωr=Ωr0加速Ωr=Ωr0减速Ωr<Ωr0加速Ωr<Ωr0减速
内转子电磁转矩/(kN·m)19.147-19.85919.227-19.69818.954-19.977
调制环电磁转矩/(kN·m)-47.10947.417-47.01247.235-47.11447.165
定子电磁转矩/(kN·m)-27.96227.558-27.78527.537-28.16027.187
内转子电磁功率/MW17.530-18.18214.669-15.02911.569-12.193
调制环电磁功率/MW-14.80014.896-14.66915.029-14.80114.817
定子电磁功率/MW2.730-3.28500-3.2322.624
永磁体损耗/kW281.231307.021209.671227.027232.223233.999
铁耗/kW211.734207.066236.832233.206208.886208.440
铜耗/kW68.80068.80068.80068.80068.80068.800
不计摩擦的效率/%96.79596.79496.48796.48096.55596.550
内转子转矩脉动/%24.30325.12323.06125.42423.80124.282
调制环转矩脉动/%4.2125.5103.5224.6415.0035.220
), ArticleFig(id=1207271200145888163, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=CN, label=表3, caption=

初步设计的电磁性能

, figureFileSmall=null, figureFileBig=null, tableContent=
性能数值
Ωr>Ωr0加速Ωr>Ωr0减速Ωr=Ωr0加速Ωr=Ωr0减速Ωr<Ωr0加速Ωr<Ωr0减速
内转子电磁转矩/(kN·m)19.147-19.85919.227-19.69818.954-19.977
调制环电磁转矩/(kN·m)-47.10947.417-47.01247.235-47.11447.165
定子电磁转矩/(kN·m)-27.96227.558-27.78527.537-28.16027.187
内转子电磁功率/MW17.530-18.18214.669-15.02911.569-12.193
调制环电磁功率/MW-14.80014.896-14.66915.029-14.80114.817
定子电磁功率/MW2.730-3.28500-3.2322.624
永磁体损耗/kW281.231307.021209.671227.027232.223233.999
铁耗/kW211.734207.066236.832233.206208.886208.440
铜耗/kW68.80068.80068.80068.80068.80068.800
不计摩擦的效率/%96.79596.79496.48796.48096.55596.550
内转子转矩脉动/%24.30325.12323.06125.42423.80124.282
调制环转矩脉动/%4.2125.5103.5224.6415.0035.220
), ArticleFig(id=1207271201341264806, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=EN, label=Tab. 4, caption=

Geometric parameter values of flux barrier

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磁障设计参数数值磁障设计参数数值
b10RT/mm15
b20  
), ArticleFig(id=1207271201412567980, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=CN, label=表4, caption=

磁障形状设计参数值

, figureFileSmall=null, figureFileBig=null, tableContent=
磁障设计参数数值磁障设计参数数值
b10RT/mm15
b20  
), ArticleFig(id=1207271201492259762, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=EN, label=Tab. 5, caption=

Value ranges of optimization variables

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优化变量取值范围优化变量取值范围
l/mm80~100k0.7~0.8
α/（°）42~46e0.5~0.7
), ArticleFig(id=1207271201559368628, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=CN, label=表5, caption=

优化变量取值范围

, figureFileSmall=null, figureFileBig=null, tableContent=
优化变量取值范围优化变量取值范围
l/mm80~100k0.7~0.8
α/（°）42~46e0.5~0.7
), ArticleFig(id=1207271201643254714, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=EN, label=Tab. 6, caption=

Designs of highest efficiency and lowest torque ripple on Pareto front

, figureFileSmall=null, figureFileBig=null, tableContent=
结构变量和电磁性能效率最高设计内转子转矩脉动最低设计
l/mm98.497.6
α/（°）46.046.0
k0.7530.800
e0.5000.503
内转子电磁转矩/（kN·m）20.44520.847
调制环电磁转矩/（kN·m）-49.686-51.005
不计摩擦的效率/%97.4997.41
内转子转矩脉动/%24.3923.79
调制环转矩脉动/%3.283.34
), ArticleFig(id=1207271201710363581, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=CN, label=表6, caption=

Pareto前沿上的效率和转矩脉动指标最优设计

, figureFileSmall=null, figureFileBig=null, tableContent=
结构变量和电磁性能效率最高设计内转子转矩脉动最低设计
l/mm98.497.6
α/（°）46.046.0
k0.7530.800
e0.5000.503
内转子电磁转矩/（kN·m）20.44520.847
调制环电磁转矩/（kN·m）-49.686-51.005
不计摩擦的效率/%97.4997.41
内转子转矩脉动/%24.3923.79
调制环转矩脉动/%3.283.34
), ArticleFig(id=1207271201815221187, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=EN, label=Tab. 7, caption=

Spearman's correlation coefficients of electromagnetic performances to structural variables in multi-objective optimization

, figureFileSmall=null, figureFileBig=null, tableContent=
结构变量与调制环电磁转矩的相关系数与不计摩擦的效率的相关系数与内转子转矩脉动的相关系数
l0.4050.82-0.133
α0.2120.672-0.103
k0.838-0.162-0.444
e0.346-0.3150.096
), ArticleFig(id=1207271201911690182, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271185709093067, language=CN, label=表7, caption=

多目标优化中电磁性能与结构变量的Spearman相关系数

, figureFileSmall=null, figureFileBig=null, tableContent=
结构变量与调制环电磁转矩的相关系数与不计摩擦的效率的相关系数与内转子转矩脉动的相关系数
l0.4050.82-0.133
α0.2120.672-0.103
k0.838-0.162-0.444
e0.346-0.3150.096
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用于同步调相机—飞轮储能系统的磁齿轮调速器优化设计
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常可 1 , 詹阳 1 , 李志强 2
水电能源科学 | 水能利用及水电站工程 2025,43(9): 197-202
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水电能源科学 | 水能利用及水电站工程 2025, 43(9): 197-202
用于同步调相机—飞轮储能系统的磁齿轮调速器优化设计
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常可1 , 詹阳1 , 李志强2
作者信息
  • 1.华北电力大学电气与电子工程学院，北京 102206
  • 2.中国电力科学研究院有限公司，北京 100192

    • 常可（1999-），女，硕士研究生，研究方向为磁场调制永磁电机，E-mail：

通讯作者:

詹阳（1978-），男，博士、副教授、硕导，研究方向为磁齿轮和磁场调制电机，E-mail：
Design Optimization of Magnetic-geared Speed Regulator for Energy Storage System with Synchronous Condenser and Flywheel
Ke CHANG1 , Yang ZHAN1 , Zhi-qiang LI2
Affiliations
  • 1.School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, China
  • 2.China Electric Power Research Institute, Beijing 100192, China
出版时间: 2025-09-25 doi: 10.20040/j.cnki.1000-7709.2025.20241621
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摘要
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随着新能源占比的提高，电力系统的惯量支撑、电压支撑以及调频能力明显减弱。同步调相机—飞轮储能系统的研发，对于提高新能源场站的调节能力、增强新型电力系统的稳定性具有重要意义。简要阐述了用于同步调相机—飞轮储能系统的磁齿轮调速器的工作原理和不同的运行状态，着重对其电磁结构进行了优化设计。建立了磁齿轮调速器的电磁有限元模型，通过计算和分析空载漏磁系数选定了V形永磁体内转子的磁障形状，进而采用遗传算法，在一定的永磁体用量和定子槽面积条件下，对V形永磁体和定子槽的形状参数及调制环的极弧系数进行了多目标优化，并分析了目标性能与结构形状参数的相关性。优化设计和相关性分析结果从结构设计上为磁齿轮调速器转矩和效率性能的提升指明了方向。

同步调相机—飞轮储能系统  /  磁齿轮调速器  /  转矩  /  效率  /  多目标优化

With the increasing proportion of new energy, the inertia support, voltage support, and frequency regulation ability are obviously weakened in current power system. The development of energy storage system with synchronous condenser and flywheel (ESSSCF) is of great significance to improve the regulation capability of new energy power generation and enhance the stability of new power systems. This article briefly describes the principle and different operation states of the magnetic-geared speed regulator (MGSR) for ESSSCF, and focuses on the design optimization of its electromagnetic structure. The electromagnetic finite element model of the MGSR is established. The shape of the flux barrier is selected for the inner rotor with V-shaped permanent magnet by calculating and analyzing the no-load leakage flux factor. The geometric parameters of the V-shaped permanent magnets and stator slots and the pole-arc coefficient of the modulating ring are optimized for multiple objectives, respectively, using genetic algorithm, under the conditions of a constant amount of permanent magnet and a constant area of stator slot. In addition, the correlation of the target performances with the geometric parameters is analyzed. The results of the design optimization and correlation analysis can direct the structural design of the magnetic-geared speed regulator for improvement of the torque and efficiency performances.

energy storage system with synchronous condenser and flywheel  /  magnetic-geared speed regulator  /  torque  /  efficiency  /  multi-objective optimization
常可, 詹阳, 李志强. 用于同步调相机—飞轮储能系统的磁齿轮调速器优化设计. 水电能源科学, 2025 , 43 (9) : 197 -202 . DOI: 10.20040/j.cnki.1000-7709.2025.20241621
Ke CHANG, Yang ZHAN, Zhi-qiang LI. Design Optimization of Magnetic-geared Speed Regulator for Energy Storage System with Synchronous Condenser and Flywheel[J]. Water Resources and Power, 2025 , 43 (9) : 197 -202 . DOI: 10.20040/j.cnki.1000-7709.2025.20241621
正文
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1 引言
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为实现“双碳”目标，我国提出建立以新能源为主体的新型电力系统[1]，而大规模新能源融入引起的惯性支撑不足、频率和电压稳定性减弱是当前新型电力系统建设迫切需要解决的问题[2]。增加储能和无功调节设备[3]分别是提高新型电力系统频率和电压稳定性常用的技术措施。磁齿轮调速器是基于同心式磁齿轮工作原理[4-5]的一种无级变速装置，它具有单电气端口和双机械端口。利用磁齿轮调速器的双机械端口将同步调相机与飞轮的转轴耦合，通过改变调速器定子电流的频率，可以在调相机转速固定、飞轮转速连续变化的条件下，实现飞轮与调相机之间能量的双向传递。该系统将同步调相机的无功支撑和飞轮的有功支撑功能集于一体，通过同步电机与电网交换其产生的全部无功功率和大部分有功功率，可以充分发挥同步电机短路容量大、对电网故障穿越能力强、可靠性高的优势，成为提升新能源消纳能力的新技术途径。本文针对用于同步调相机—飞轮储能系统的具有V形内置永磁体内转子的磁齿轮调速器，建立了电磁有限元分析模型，分析了内转子不同隔磁结构形状对空载漏磁系数的影响，并通过选择合适的几何参数降低了空载漏磁系数，有效增加了永磁体的利用率；以此为基础，为提高最大转矩和效率、降低转矩脉动，在额定电流条件下，保持永磁体用量和定子槽面积恒定，采用遗传算法对磁齿轮调速器的V形永磁体、调制环和定子槽的形状参数进行多目标优化设计，得到了Pareto前沿最优解集，并通过相关性分析揭示了各结构形状参数对各优化目标的影响及不同目标之间存在的冲突或协同关系。
2 同步调相机—飞轮储能系统及其磁齿轮调速器的基本结构和运行行为
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2.1 同步调相机—飞轮储能系统及其磁齿轮调速器的基本结构
磁齿轮调速器由定子、调制环转子和内转子三个基本结构组成，见图1。定子绕组极对数pc、内转子极对数pr和调制块的个数N应满足[5]：
此结构设计利用调制块与磁阻块形成的交变磁导对定子和内转子磁场的调制作用，将不同极对数和转速的定子和内转子磁场耦合，使定子绕组、调制环转子和内转子之间形成稳定的功率传递。
将磁齿轮调速器的调制环转子与同步调相机连接，内转子与飞轮连接，定子三相绕组通过变流器与电网连接，并将同步调相机的定子绕组通过变压器接入电网，形成如图2所示的同步调相机—飞轮储能系统。
2.2 同步调相机—飞轮储能系统及其磁齿轮调速器的基本运行行为
在满足式（1）所示结构参数关系的调制环作用下，若磁齿轮调速器的内转子转速Ωr、定子基波磁场转速Ωc和调制环转速Ωm满足[5]：
定子绕组、内转子和调制环转子之间就可以形成稳定的转矩传递和机电功率交换。同步调相机—飞轮储能系统的运行过程中，由于磁齿轮调速器的调制环转子与同步调相机转子相连，Ωm的方向与电网的相序一致，保持不变，Ωm的大小与电网频率关联，基本保持不变。飞轮的转向始终与同步调相机保持一致，即Ωr、Ωm方向相同。假设二者恒为正，并以此方向作为本文所有转速和转矩的参考方向，即与Ωr、Ωm方向相同的转矩和转速为正，反之为负。当磁齿轮调速器的机械转矩/电磁转矩方向与相应的转子/旋转磁场转向相同（起驱动作用）时，对应的机械功率/电磁功率为正；当机械转矩/电磁转矩方向与相应的转子/旋转磁场转向相反（起制动作用）时，对应的机械功率/电磁功率为负。
若定子电流的频率为fc，则由式（2）得到：
式（3）说明，通过调节定子电流的频率，就可以实现内转子/飞轮的无级差转速调节，从而控制飞轮能量的存储和释放。规定fc的符号与Ωc的符号一致，对应不同符号的fc，内转子/飞轮的转速存在以下不同的状态：①当fc=0时，定子绕组通入直流电，Ωc=0，内转子/飞轮的转速为Ωr0=NΩm/pr；②当fc>0时，Ωc与Ωm同方向，Ωr<Ωr0；③当fc<0时，Ωc与Ωm反方向，Ωr>Ωr0。
以Pr、Pm、Pc分别表示内转子的机械功率、调制环转子的机械功率、定子绕组的电磁功率，根据内转子/飞轮的转速和加速度，忽略一切损耗的条件下，磁齿轮调速器和同步调相机—飞储能系统存在以下不同的功率流动状态[6]：①当dΩr/d t=0时，飞轮处于待机状态，fc保持不变，Pr=Pm=Pc=0。②当dΩr/d t>0时，飞轮增加储能（Pr<0），调制环转子经调相机从电网吸收功率（Pm>0），变流器向负方向调整电流频率（d fc/d t<0）：若Ωr>Ωr0，则磁齿轮调速器定子从电网吸收功率（Pc>0）；若Ωr= Ωr0，磁齿轮调速器定子与电网无功率交换（Pc=0）；若Ωr<Ωr0，则磁齿轮调速器定子向电网发出功率（Pc<0）。③当dΩr/d t<0时，飞轮释放储能（Pr>0），调制环转子通过调相机向电网发出功率（Pm<0），变流器向正方向调整电流频率（d fc/d t>0）：若Ωr>Ωr0，则磁齿轮调速器定子向电网发出功率（Pc<0）；若Ωr=Ωr0，则磁齿轮调速器定子与电网无功率交换（Pc=0）；若Ωr<Ωr0，则磁齿轮调速器定子从电网吸收功率（Pc>0）。
3 磁齿轮调速器的初步设计及其电磁性能
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用于同步调相机—飞轮储能系统的磁齿轮调速器在运行过程中，与同步调相机转子直连的调制环转子的转速基本保持在3 000 r/min左右，在电网频率出现波动时，通过变流器调节磁齿轮变速器的电流频率，从而控制飞轮增速/减速（增加/释放储能），起到稳定电网频率的作用。为实现上述功能，以与电网交换的最大总功率达到15 MW以上为目标，本文初步设计了一台用于同步调相机—飞轮储能系统的磁齿轮调速器，其基本结构及设计参数见图3、表1。
综合考虑电磁性能和机械强度的需要，本文给出的磁齿轮调速器初步设计采用10对极定子绕组和7对极内置V形永磁体的内转子。将定子绕组通入直流电并且调制环转速为3 000 r/min时的内转子转速规定为内转子的额定转速，即7 285.7 r/min，内转子/飞轮的工作转速在额定转速的±20%范围内，即5 828.6~8 742.9 r/min，最低工作转速和最高工作转速对应的定子电流频率fc分别为170、-170 Hz。
采用动态电磁有限元模型，在额定电流条件下，分别计算初步设计的磁齿轮调速器内转子达到最高转速、额定转速和最低转速，并以最大转矩使飞轮存储和释放能量时的动态电磁性能。表2归纳了磁齿轮调速器的上述典型工作状态，表3给出了这些工作状态下的电磁转矩和转矩脉动、电磁功率、电磁损耗、效率等计算结果。
4 内转子磁障结构的设计
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4.1 空载漏磁系数及其计算方法
磁齿轮调速器的定子电磁转矩与永磁体在定子侧产生的工作谐波磁通成正比，而永磁体产生的总磁通中未交链到定子侧的比例（即漏磁通的占比）是影响磁齿轮调速器电磁性能的主要因素之一。漏磁通大会导致永磁体的磁能利用率降低，使磁齿轮调速器的转矩/功率密度降低。本文磁齿轮调速器具有远比普通永磁电机复杂的磁路结构，形成三类比较大的漏磁场（图4）：①调制环的空间交变磁导使相邻的调制块之间存在较大的漏磁场；②为保证匹配高转速飞轮所需的结构强度，磁齿轮调速器的直径不能过大，而在这种限制下还要设计足够多的定子极数，不得不采用近极槽配合，造成较大的槽漏磁场；③V形永磁体布置造成较大的内转子漏磁场。
采用空载漏磁系数来量化磁齿轮调速器中漏磁通在永磁体总磁通中的占比。定义空载漏磁系数σ为：
式中，ϕM、ϕσ分别为永磁体的总磁通、永磁体交链到定子侧的主磁通；LM、Lσ分别为永磁体总磁通和定子侧主磁通的积分路径（图4）；BM、Bσ分别为LM、Lσ路径上的径向磁密；L为积分所沿闭合路径。
空载漏磁系数在普通永磁电机的设计中已有应用[7]，由于普通永磁电机仅依靠基波磁场工作，空载漏磁系数计算中的积分路径取一个极距即可；而本文磁齿轮调速器具有10对极和7对极两个工作谐波磁场，为计及所有工作谐波磁场，空载漏磁系数计算的积分路径必须取完整的圆周。
4.2 基于空载漏磁系数的内转子磁障设计
磁齿轮调速器设计中需抑制三类主要漏磁场，其中内转子漏磁场一般通过在V形永磁体顶部设置磁障结构加以抑制。采用图5所示梯形磁障结构，梯形磁障下底和上底的长度分别为RT、0.5RT，上底到V形永磁体内侧边的距离为w1，下底到V形永磁体外侧边的距离为w2，梯形倒角半径和斜边到内转子外圆最窄处的厚度均为3 mm。定义b1=w1/w，b2=w2/w，其中w为永磁体的厚度。
通过计算不同b1、b2、RT取值条件下的σ值，总结磁障形状设计影响空载漏磁系数的规律，并最终确定适当的形状设计参数值。逐个选取单个形状设计变量，采用有限元方法计算此变量不同取值条件下的磁密分布，并根据式（4）计算空载漏磁系数，在此过程中保持其余形状变量和磁障与内转子外圆之间3 mm的最窄厚度不变，得到σ随b1、b2、RT变化的曲线（图6）。由图6可知，随着b1、b2的增大，永磁体产生的漏磁比例增大；而随着RT的增大，永磁体产生的漏磁比例减小。
分析发现，梯形磁障形状设计参数影响空载漏磁系数的规律非常明确，梯形的高与V形永磁体的厚度相等且底边尽可能大，最有利于降低内转子漏磁和提高转矩密度，但确定磁障形状参数值还需综合考虑连接飞轮的高速内转子的结构强度和制造工艺的难度。磁齿轮调速器最终确定的磁障形状设计参数值见表3。梯形磁障形状设计参数影响空载漏磁系数的规律不受其他结构形状设计的影响，故后续对其他结构的优化设计中，保持表4中所示的磁障形状设计参数值不变。
5 永磁体、调制环、定子槽形状多目标优化设计
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为提升磁齿轮调速器的电磁性能，在完成内转子磁障结构设计的基础上，采用非支配排序遗传算法（NSGA-Ⅱ）对关键结构形状的设计进行优化。以转矩和效率最大、转矩脉动最小为多重目标，对结构形状变量l、α、k、e进行优化，得到Pareto最优解集，从而在多个性能指标间取得平衡。
根据文献[6，8]中的经验，对磁齿轮调速器转矩性能影响较大的关键结构形状参数包括V形永磁体的宽度l、开合角度α、定子槽的高度hs1占定子铁心厚度hs2的比例k（即k=hs1/hs2）、调制环的极弧系数e=β2/（β1+β2）（β1、β2分别为调制环中磁阻块和调制块的角度），如图7所示。在优化过程中，内环子直径、调制环径向厚度、定子内外径、气隙厚度、轴向有效长度等其他结构的变量保持不变；永磁体宽度l作为优化变量的同时保持永磁体总用量不变，故永磁体的厚度w不作为独立的优化变量；定子采用矩形开口槽，槽高占比k作为优化变量的同时保持槽面积不变，故槽宽不作为独立的优化变量。
为确保优化计算的准确性与效率，在表5的优化变量取值范围内，通过均匀拉丁超立方抽样方法设置10个设计样本作为优化过程的初始集合，设计样本总数迭代到1 400个时终止优化过程。
图8为多目标优化过程中调制环电磁转矩、不计摩擦损耗的效率（以内转子达到最大转速并且处于加速状态时的效率计）和内转子转矩脉动（以内转子达到最大转速并且处于加速状态时的转矩脉动计）的变化趋势。在多目标优化过程中，调制环电磁转矩会提升到最高值附近后，开始在一定范围内浮动，这是多目标协同优化的结果；同理，不计摩擦损耗的效率和内转子转矩脉动在优化过程后期也在特定范围内波动。图8结果表明，采用非支配排序遗传算法进行磁齿轮调速器多目标优化的有效性，优化过程整体上提升了转矩和效率，并降低了转矩脉动。
图9为多目标优化过程中3个性能指标的变化集中展示在一起。多目标优化形成的成熟设计样本构成一个最优解集，即Pareto前沿，它揭示了这些设计样本在多重目标性能上的平衡。由图9可知，磁齿轮调速器多目标优化形成的Pareto前沿在转矩、效率、转矩脉动等方面表现优异，形成一个综合性能较为平衡的设计集合。Pareto前沿上的设计样本转矩脉动区别很小，而转矩与效率之间呈现负相关性，即转矩的增加会牺牲部分效率，这说明选取综合性能较高的设计关键是平衡转矩和效率。具体来说，就是寻求Pareto前沿上转矩随着效率变化较为缓的部分，在确保最大转矩满足要求的前提下，尽可能少的牺牲效率。
表6分别给出了Pareto前沿最优解集中效率最高和内转子转矩脉动最低设计的优化变量取值和电磁性能（以内转子达到最高转速并处在加速的状态为例）。对比表7的结果发现，由于效率作为优化目标之一，这两个典型设计的效率均达到97.4%以上，明显高于单目标最优设计，其中内转子转矩脉动最低设计不但转矩脉动有一定幅度下降，效率还提高0.53个百分点，而调制环电磁转矩仅有很小损失。这充分说明了多目标设计优化在平衡最大转矩、效率和转矩脉动上的有效性。
表7为多目标优化过程中3个电磁性能指标与4个优化变量之间的Spearman相关系数，在结构设计方面为提升磁齿轮调速器的综合性能指明了方向。可以看到，在多目标优化中，调制环电磁转矩与k具有极强的相关性，而与l具有中等程度的相关性，与α、e的相关性较弱；效率与l具有极强的相关性，与α具有较强的相关性，而与k、e相关性较弱；内转子转矩脉动仅与k具有中等程度的相关性，与其他结构变量相关性均非常弱，这说明还需要通过调整定子与内转子的极对数配比和极槽配合等其他方法更大幅度地抑制转矩脉动。
6 结论
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a. 采用空载漏磁系数方法确定了内转子磁障结构设计，能够有效降低内转子漏磁。
b. 采用遗传算法能够实现对永磁体、调制环和定子槽形状的多目标优化设计，利用优化过程获得的Pareto前沿可以均衡最大转矩、效率和转矩脉动等多个性能指标，为提升综合性能提供多种参考设计方案。
基金
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  • 中国电科院自有基金项目
文献
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2025年第43卷第9期
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doi: 10.20040/j.cnki.1000-7709.2025.20241621
  • 接收时间：2024-08-29
  • 首发时间：2025-12-15
  • 出版时间：2025-09-25
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  • 收稿日期：2024-08-29
  • 修回日期：2024-10-30
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    1.华北电力大学电气与电子工程学院，北京 102206
    2.中国电力科学研究院有限公司，北京 100192

通讯作者:

詹阳（1978-），男，博士、副教授、硕导，研究方向为磁齿轮和磁场调制电机，E-mail：
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
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红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
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