陳 濤，王 蝶，苑 鋒

(河南工程學(xué)院 電氣信息工程學(xué)院，河南 鄭州 451191)

轉(zhuǎn)子失磁永磁同步電機(jī)驅(qū)動(dòng)系統(tǒng)建模

陳 濤，王 蝶，苑 鋒

(河南工程學(xué)院 電氣信息工程學(xué)院，河南 鄭州 451191)

轉(zhuǎn)子失磁故障會(huì)降低永磁同步電機(jī)(PMSM)驅(qū)動(dòng)系統(tǒng)的控制性能與運(yùn)行可靠性，精確的轉(zhuǎn)子失磁PMSM驅(qū)動(dòng)系統(tǒng)數(shù)學(xué)模型是進(jìn)行轉(zhuǎn)子狀態(tài)監(jiān)控及失磁故障診斷研究的前提.建立轉(zhuǎn)子失磁PMSM物理模型并進(jìn)行有限元分析，獲得永磁體空載氣隙磁密，經(jīng)傅里葉變換獲得其傅里葉頻譜并據(jù)此建立轉(zhuǎn)子失磁PMSM及其驅(qū)動(dòng)系統(tǒng)的數(shù)學(xué)模型，仿真結(jié)果證實(shí)了所建模型的正確性.

永磁同步電機(jī)；轉(zhuǎn)子失磁；數(shù)學(xué)模型；有限元分析

永磁同步電機(jī)(PMSM)由于具有維護(hù)率低、功率密度高等優(yōu)勢(shì)，在電動(dòng)汽車等新能源技術(shù)領(lǐng)域得到了廣泛應(yīng)用[1-2].然而，上述領(lǐng)域多受安裝空間限制且散熱條件有限、電機(jī)運(yùn)行工況復(fù)雜，易導(dǎo)致較高工作溫度及較強(qiáng)電樞反應(yīng)而引起轉(zhuǎn)子局部或均勻失磁，而其驅(qū)動(dòng)系統(tǒng)常用的最大轉(zhuǎn)矩電流比(MTPA)及弱磁控制均需要準(zhǔn)確的轉(zhuǎn)子磁鏈，轉(zhuǎn)子失磁故障的出現(xiàn)勢(shì)必降低系統(tǒng)運(yùn)行可靠性及控制性能.因此，為確保PMSM驅(qū)動(dòng)系統(tǒng)的可靠運(yùn)行并實(shí)現(xiàn)高性能控制，必須對(duì)轉(zhuǎn)子失磁故障進(jìn)行可靠診斷.

精確建立轉(zhuǎn)子失磁的PMSM數(shù)學(xué)模型是進(jìn)行故障診斷研究的前提.既有文獻(xiàn)中，多采用有限元軟件建立考慮轉(zhuǎn)子失磁的PMSM物理模型[3-4]，分析其轉(zhuǎn)子磁場(chǎng)特性及由其導(dǎo)致的電氣特征信號(hào)，并將其作為實(shí)際系統(tǒng)運(yùn)行中的PMSM轉(zhuǎn)子失磁故障的定性診斷依據(jù)，亦有基于等效分析模型描述PMSM轉(zhuǎn)子失磁的文獻(xiàn)報(bào)道[5].但上述模型計(jì)算量大，多進(jìn)行PMSM轉(zhuǎn)子失磁的離線分析，無法實(shí)現(xiàn)其在線描述且難以實(shí)現(xiàn)與實(shí)際系統(tǒng)的銜接.為此，本研究首先通過有限元分析建立轉(zhuǎn)子失磁PMSM物理模型，獲得永磁體空載氣隙磁密并對(duì)其進(jìn)行傅里葉分析，在此基礎(chǔ)上建立轉(zhuǎn)子失磁PMSM驅(qū)動(dòng)系統(tǒng)數(shù)學(xué)模型與仿真模型，驗(yàn)證所建數(shù)學(xué)模型的正確性，為實(shí)現(xiàn)PMSM轉(zhuǎn)子失磁故障的有效描述及診斷方法的在線研究奠定了基礎(chǔ).

1 轉(zhuǎn)子失磁PMSM有限元模型

基于數(shù)值近似的有限元分析方法在PMSM結(jié)構(gòu)設(shè)計(jì)及其電磁場(chǎng)分析中得到了廣泛應(yīng)用[6]，以普銳斯車用PMSM為研究對(duì)象，根據(jù)橡樹嶺國家實(shí)驗(yàn)室公布的物理結(jié)構(gòu)及設(shè)計(jì)參數(shù)[7]，采用MAXWELL12軟件建立該電機(jī)轉(zhuǎn)子失磁時(shí)的物理模型并獲取其永磁體空載氣隙磁密.建模過程中，假定局部失磁集中在一個(gè)永磁體上，轉(zhuǎn)子失磁采用集中方式進(jìn)行描述.

圖1為上述PMSM轉(zhuǎn)子健康時(shí)經(jīng)有限元分析獲得的永磁體空載氣隙磁密及其傅里葉頻譜，圖2為轉(zhuǎn)子局部失磁50%的空載氣隙磁密及其傅里葉頻譜，圖3則為轉(zhuǎn)子均勻失磁50%的永磁體空載氣隙磁密及其傅里葉頻譜.由于電機(jī)極對(duì)數(shù)為4，故圖1(b)、圖2(b)、圖3(b)中的4次諧波為空載氣隙磁密基波，其余頻率則為整數(shù)或非整數(shù)次諧波(4的整數(shù)倍或非整數(shù)倍頻率).

圖1 轉(zhuǎn)子健康時(shí)空載氣隙磁密及其傅里葉頻譜Fig.1 The no load flux density and its fourier spectrum with healthy rotor

圖2 局部失磁50%時(shí)空載氣隙磁密及其傅里葉頻譜Fig.2 The no load flux density and its fourier spectrum with 50% local demagnetization fault

圖3 均勻失磁50%時(shí)空載氣隙磁密及其傅里葉頻譜Fig.3 The no load flux density and its fourier spectrum with 50% uniform demagnetization

2 轉(zhuǎn)子失磁PMSM數(shù)學(xué)模型

2.1 失磁時(shí)永磁體定子繞組磁鏈

由圖2(b)可知，PMSM轉(zhuǎn)子局部失磁時(shí)，永磁體空載氣隙磁密中出現(xiàn)如式(1)所示非整數(shù)次諧波：

(1)

式中：k取正整數(shù)；np表示電機(jī)極對(duì)數(shù)；θ為永磁體氣隙磁場(chǎng)軸線(d軸)與電機(jī)A相軸線的夾角.因此，永磁體空載氣隙磁密在PMSM三相繞組中產(chǎn)生的磁鏈可表示為

(2)

(3)

2.2 轉(zhuǎn)子失磁PMSM數(shù)學(xué)模型

PMSM的dq軸定子電壓方程、磁鏈方程、電磁轉(zhuǎn)矩及機(jī)電運(yùn)動(dòng)方程分別如式(4)至式(7)所示[9].

(4)

(5)

Te=np(ψdiq-ψqid)，

(6)

(7)

式中：ud,q為dq軸定子電壓；id,q為dq軸定子電流；ψd,q表示dq軸定子磁鏈；Ld,q表示dq軸定子電感；ψf為永磁體磁密在定子繞組中產(chǎn)生的磁鏈；Rs為定子電阻；ωe表示轉(zhuǎn)子電氣角速度；np表示電機(jī)極對(duì)數(shù).

(8)

根據(jù)式(8)獲得轉(zhuǎn)子失磁PMSM磁鏈方程:

(9)

式中：ψrd,ψrq為轉(zhuǎn)子失磁的dq軸永磁體磁鏈;ψfd,ψfq為轉(zhuǎn)子失磁的dq軸定子磁鏈.

將式(9)代入式(4)和式(6)，可獲得轉(zhuǎn)子失磁PMSM的dq軸定子電壓方程和電磁轉(zhuǎn)矩方程，如式(10)至式(11)所示:

(10)

Te=np(ψfdiq-ψfqid).

(11)

聯(lián)立式(7)、(9)、(10)、(11)即可獲得dq軸系上的轉(zhuǎn)子失磁PMSM數(shù)學(xué)模型.盡管上述建模過程建立在轉(zhuǎn)子局部失磁基礎(chǔ)之上，但由于轉(zhuǎn)子失磁通過電機(jī)磁鏈方程來描述，故所建模型可作為表征PMSM轉(zhuǎn)子健康、局部失磁及均勻失磁的統(tǒng)一數(shù)學(xué)模型.

3 轉(zhuǎn)子失磁PMSM驅(qū)動(dòng)系統(tǒng)仿真

圖4 矢量控制的PMSM驅(qū)動(dòng)系統(tǒng)Fig.4 The vector controlled PMSM drive system

基于Matlab平臺(tái)建立轉(zhuǎn)子失磁PMSM驅(qū)動(dòng)系統(tǒng)仿真模型，設(shè)定轉(zhuǎn)速為750 r/min、負(fù)載轉(zhuǎn)矩為50 N·m.圖5至圖7分別為轉(zhuǎn)子健康、局部失磁50%及均勻失磁50%時(shí)PMSM穩(wěn)態(tài)定子電流及穩(wěn)態(tài)電磁轉(zhuǎn)矩的傅里葉頻譜.由圖5可見，PMSM轉(zhuǎn)子健康時(shí)，定子相電流中僅存在由于電機(jī)結(jié)構(gòu)不對(duì)稱所致的5次及7次微弱諧波，并且在電磁轉(zhuǎn)矩中形成定子電流基波的6倍頻脈動(dòng)轉(zhuǎn)矩.而在轉(zhuǎn)子局部失磁時(shí)，除上述5次及7次諧波電流外，PMSM定子電流中亦出現(xiàn)了如文獻(xiàn)[10-11]實(shí)驗(yàn)結(jié)果所示的非整數(shù)次諧波，如圖6(b)所示.PMSM轉(zhuǎn)子均勻失磁時(shí)，圖7所示電機(jī)定子基波電流因轉(zhuǎn)子磁鏈降低而出現(xiàn)一定程度的增加，以確保電磁轉(zhuǎn)矩與負(fù)載轉(zhuǎn)矩的平衡，但其定子電流中并沒有出現(xiàn)圖6(b)所示表征PMSM轉(zhuǎn)子局部失磁的特征諧波.這是因?yàn)檗D(zhuǎn)子局部失磁破壞了PMSM永磁體等效物理結(jié)構(gòu)的對(duì)稱性，導(dǎo)致永磁體空間氣隙磁密及PMSM定子繞組磁鏈中出現(xiàn)特定諧波并導(dǎo)致PMSM定子中出現(xiàn)特定諧波電流.轉(zhuǎn)子均勻失磁的出現(xiàn)并不會(huì)破壞PMSM永磁體等效物理結(jié)構(gòu)的對(duì)稱性，故不會(huì)在PMSM定子電流和電磁轉(zhuǎn)矩中出現(xiàn)類似圖6所示的特征諧波.上述仿真結(jié)果和理論分析與既有文獻(xiàn)[7-8]的實(shí)驗(yàn)結(jié)論一致，證實(shí)了所建轉(zhuǎn)子失磁PMSM驅(qū)動(dòng)系統(tǒng)數(shù)學(xué)模型的正確性.

圖5 轉(zhuǎn)子健康時(shí)定子電流、電磁轉(zhuǎn)矩傅里葉頻譜及其局部放大圖Fig.5 The fourier frequency spectrum of stator current，electromagnetic torque and their tail view with healthy rotor

圖6 50%局部退磁時(shí)定子電流、電磁轉(zhuǎn)矩傅里葉頻譜及其局部放大圖Fig.6 The fourier frequency spectrum of stator current, electromagnetic torque and their detail view with 50% local demagnetization

圖7 50%均勻退磁時(shí)定子電流、電磁轉(zhuǎn)矩傅里葉頻譜及其局部放大圖Fig.7 The fourier frequency spectrum of stator current, electromagnetic torque and its detail view with 50% uniform demagnetization

4 結(jié)語

精確的轉(zhuǎn)子失磁PMSM驅(qū)動(dòng)系統(tǒng)數(shù)學(xué)模型是開展轉(zhuǎn)子失磁故障診斷研究的前提.基于轉(zhuǎn)子失磁的PMSM物理模型及其有限元分析與傅里葉變換結(jié)果，建立了轉(zhuǎn)子失磁PMSM驅(qū)動(dòng)系統(tǒng)數(shù)學(xué)模型及仿真模型并進(jìn)行了仿真研究，結(jié)果證實(shí)了所建轉(zhuǎn)子失磁PMSM及其驅(qū)動(dòng)系統(tǒng)數(shù)學(xué)模型能夠?qū)崿F(xiàn)轉(zhuǎn)子健康、局部失磁及均勻失磁3種轉(zhuǎn)子狀態(tài)的有效描述，可作為表征PMSM轉(zhuǎn)子健康、局部失磁及均勻失磁故障的統(tǒng)一數(shù)學(xué)模型，為開展PMSM轉(zhuǎn)子失磁故障診斷研究奠定了基礎(chǔ).

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Modelingthepermanentmagnetsynchronousmotordrivesystemwithrotordemagnetization

CHENTao,WANGDie,YUANFeng

(CollegeofElectricalInformationEngineering,HenanUniversityofEngineering,Zhengzhou451191,China)

Rotor demagnetization fault degrades the control performance and operational reliability of permanent magnet synchronous motor (PMSM) drive system, and an accurate mathematical model of PMSM drive system with rotor demagnetization fault is the precondition to realize rotor working condition monitor and demagnetization fault diagnosis. Therefore, the physical model of PMSM with rotor demagnetization fault is firstly developed, and its Fourier frequency spectrum is also achieved based on finite element analysis and Fourier transformation. Then, the mathematical model of PMSM with rotor demagnetization fault and its drive system is built, and the simulation results verified the validity of the proposed mathematic model.

permanent magnet synchronous motor; rotor demagnetization; mathematical model; finite element analysis

TM351

A

1674-330X(2017)04-0053-05

2017-08-05

河南省高等學(xué)校重點(diǎn)科研項(xiàng)目(18B470002) ；河南省科技發(fā)展計(jì)劃項(xiàng)目(172102210104)；2016國家級(jí)大學(xué)生創(chuàng)新創(chuàng)業(yè)訓(xùn)練計(jì)劃項(xiàng)目(201611517032)

陳濤(1981-)，男，河南淮陽人，副教授，博士，主要從事電機(jī)控制及其系統(tǒng)方面的研究.