藍(lán)建宇，唐厚君，陸亭華

(上海交通大學(xué) 電力傳輸與功率變換控制教育部重點(diǎn)實(shí)驗(yàn)室,上海 200240)

導(dǎo)抗變換器在感應(yīng)耦合電能傳輸中的應(yīng)用

藍(lán)建宇，唐厚君，陸亭華

(上海交通大學(xué) 電力傳輸與功率變換控制教育部重點(diǎn)實(shí)驗(yàn)室,上海 200240)

對于低階補(bǔ)償?shù)母袘?yīng)耦合電能傳輸系統(tǒng),松耦合變壓器原邊電流對負(fù)載變化敏感,這使得輸出功率不穩(wěn)定。針對這一問題提出一種基于導(dǎo)抗變換器原理的補(bǔ)償拓?fù)洹．?dāng)系統(tǒng)工作頻率為副邊自然諧振頻率時(shí),松耦合變壓器的原邊繞組電流在負(fù)載變化時(shí)能夠保持恒定。這使得感應(yīng)耦合電能傳輸系統(tǒng)能較好應(yīng)用于電流型負(fù)載。首先,介紹感應(yīng)耦合系統(tǒng)工作原理并運(yùn)用互感耦合理論建立了系統(tǒng)的阻抗模型。在此基礎(chǔ)上,推導(dǎo)感應(yīng)耦合電能傳輸系統(tǒng)工作于電流源特性的條件,然后討論主要參數(shù)變化對松耦合變壓器原邊電流及電壓增益的影響;并以體積最小為優(yōu)化目標(biāo),介紹基于導(dǎo)抗變換器的感應(yīng)耦合電能傳輸系統(tǒng)的優(yōu)化設(shè)計(jì)過程。最后,仿真結(jié)果和實(shí)驗(yàn)數(shù)據(jù)驗(yàn)證了理論分析的正確性。

感應(yīng)耦合;電能傳輸;松耦合變壓器;導(dǎo)抗變換器;諧振頻率

0 引 言

感應(yīng)耦合電能傳輸(inductively coupled power transfer,ICPT)是一種根據(jù)電磁感應(yīng)原理通過氣隙把電能傳輸給用電設(shè)備的技術(shù)[1-5]。與傳統(tǒng)的通過導(dǎo)線和插座的傳輸方式相比,ICPT更具靈活性和安全性。因此,ICPT在生物醫(yī)療、礦下作業(yè)及電動汽車充電等領(lǐng)域具有廣泛的應(yīng)用[6-10]。

ICPT是通過松耦合變壓器來傳遞能量的,而松耦合變壓器的耦合系數(shù)非常低,這使得ICPT的效率很低。通常采用電容補(bǔ)償?shù)姆绞絹硖岣逫CPT中松耦合變壓器的功率因數(shù),從而提高其功率傳輸能力和效率。傳統(tǒng)的補(bǔ)償拓?fù)洳捎脝渭夒娙蓠詈涎a(bǔ)償方式。對電壓源型逆變系統(tǒng)采用原邊串聯(lián)副邊串聯(lián)(primary-series-secondary-series,PSSS)或原邊串聯(lián)副邊并聯(lián)(primary-series-secondary-parallel,PSSP)的方式;對于電流源型逆變器采用原邊并聯(lián)副邊串聯(lián)(primary-parallel-secondary-series,PPSS)或原邊并聯(lián)副邊并聯(lián)(primary-parallel-secondary-parallel,PPSP)的方式[11]。文獻(xiàn)[12-13]對單級補(bǔ)償?shù)母袘?yīng)耦合電能傳輸系統(tǒng)參數(shù)進(jìn)行了最優(yōu)化設(shè)計(jì),提高了系統(tǒng)的輸出效率。然而,負(fù)載變化對單級電容補(bǔ)償拓?fù)涞挠绊戄^大;負(fù)載的輕微變化會引起原邊零電壓開關(guān)工作頻率的較大漂移,導(dǎo)致系統(tǒng)工作能力和傳輸效率的下降[14]。另外,單級電容補(bǔ)償拓?fù)錈o法解決系統(tǒng)頻率分叉問題[15-17],這給系統(tǒng)的穩(wěn)定運(yùn)行帶來隱患。文獻(xiàn)[18]提出阻抗變換的方法來穩(wěn)定輸出電壓,但是在副邊要加上DC/DC變換電路,這增加了系統(tǒng)的復(fù)雜性。針對低階補(bǔ)償拓?fù)湟陨洗嬖诘膯栴},文獻(xiàn)[19]提出多級補(bǔ)償拓?fù)涞母拍?針對電流源供電的ICPT系統(tǒng)采用電容—電感—電容(capacitanceinductance-capacitance,CLC)型諧振補(bǔ)償,并論述了其可行性及設(shè)計(jì)方法。文獻(xiàn)[20]對CLC型諧振電路進(jìn)行廣義狀態(tài)空間平均(generalized state-space averaging,GSSA)建模,提出魯棒控制的方法。文獻(xiàn)[21]對斷續(xù)電流模式的三階補(bǔ)償拓?fù)銲CPT系統(tǒng)展開分析，并確定其穩(wěn)定運(yùn)行條件;文獻(xiàn)[22]對電感—電容—電容(inductance-capacitance-capacitance,LCC)補(bǔ)償型拓?fù)涞腎CPT系統(tǒng)數(shù)學(xué)建模及優(yōu)化設(shè)計(jì)方面做了相關(guān)分析。

本文在引入導(dǎo)抗變換器原理的基礎(chǔ)上,研究了一種具有電流源特性的電感—電容—電感(inductance-capacitance-inductance,LCL)補(bǔ)償拓?fù)鋄23]。當(dāng)系統(tǒng)工作在松耦合變壓器副邊自然諧振頻率時(shí),松耦合變壓器原邊電流不隨負(fù)載的變化而變化。這種拓?fù)淇梢允笽CPT系統(tǒng)更好地應(yīng)用于電池充電、氬弧焊、發(fā)光二極管驅(qū)動等負(fù)載。論文首先介紹了基于導(dǎo)抗變換器的ICPT系統(tǒng)的組成,并根據(jù)導(dǎo)抗變換器原理推導(dǎo)了該系統(tǒng)具有恒流特性的條件;其次,分析了系統(tǒng)的電氣性能。然后,以最小化系統(tǒng)體積為目標(biāo)函數(shù),對系統(tǒng)的優(yōu)化設(shè)計(jì)方法進(jìn)行了說明。最后,對本文所提的理論和方法進(jìn)行了實(shí)驗(yàn)驗(yàn)證。

1 IC-ICPT系統(tǒng)

導(dǎo)抗變換器(immittance converter,IC)是導(dǎo)納–阻抗變換器的簡稱,在實(shí)現(xiàn)導(dǎo)納–阻抗變換特性的同時(shí),可以實(shí)現(xiàn)電壓源與電流源之間的轉(zhuǎn)換[23-26]。本文提出的利用導(dǎo)抗變換器得到具有電流源特性的ICPT系統(tǒng),稱為IC-ICPT系統(tǒng)。圖1所示為本文所研究的IC-ICPT系統(tǒng)，該系統(tǒng)應(yīng)用半橋逆變器作為諧振電路的輸入。如圖,虛線框中為導(dǎo)抗變換器,由T型電感—電容—電感(inductance-capacitanceinductance,LCL)結(jié)構(gòu)組成;M為松耦合變壓器原副之間的互感;RL為負(fù)載;L1、C1、L2和C2組成PSSP型諧振補(bǔ)償網(wǎng)絡(luò);T型導(dǎo)抗變換器與PSSP型諧振網(wǎng)絡(luò)串聯(lián)組成IC-ICPT系統(tǒng)。

圖1 IC-ICPT系統(tǒng)拓?fù)銯ig.1 IC-ICPT system topology

1.1 IC-ICPT系統(tǒng)恒流特性條件

采用基波分析法,可將圖1電路簡化為如圖2所示。

圖2 IC-ICPT系統(tǒng)簡化模型Fig.2 Simpli fi ed model of IC-ICPT system

假設(shè)系統(tǒng)的工作頻率為松耦合變壓器副邊繞組的自然諧振頻率,即

則副邊繞組折合到原邊的阻抗為

1.2 IC-ICPT系統(tǒng)性能分析

由于IC-ICPT系統(tǒng)儲能元件多,參數(shù)比較復(fù)雜,為便于分析將參數(shù)歸一化處理,定義以下參數(shù):歸一化角頻率ωn為

其中,ω0為自然諧振角頻率。定義導(dǎo)抗器電感與副邊電感比為

副邊諧振網(wǎng)絡(luò)品質(zhì)因數(shù)為

松耦合變壓器原副邊匝比為

輸出電壓增益為

設(shè)松耦合變壓器原邊電流I1=1,可得到各儲能元件電壓、電流參數(shù)以原邊電流歸一化后的表達(dá)式,如表1所示。表1中參數(shù)下標(biāo)N表示松耦合變壓器原邊電流歸一化以后的參數(shù)。

表1 IC-ICPT系統(tǒng)歸一化參數(shù)Tab.1 Normalized parameters of IC-ICPT system

下面分析IC-ICPT的電氣特性,圖3所示為k=0.3,n=1,m=0.3時(shí),原邊諧振電流歸一化值I1N隨副邊品質(zhì)因數(shù)變化曲線。

圖3 不同品質(zhì)因數(shù)下原邊繞組電流Fig.3 Primary winding current at different quality factor Q2

如圖,隨著副邊品質(zhì)因數(shù)的變化,在ωn=1及附近,I1N值與品質(zhì)因數(shù)無關(guān),即A點(diǎn)所示。這意味著在諧振頻率,IC-ICPT原邊諧振電流不隨負(fù)載變化而變化。

圖4為k=0.3,n=1,m=0.3時(shí),電壓增益隨副邊品質(zhì)因數(shù)變化曲線,從圖中可以看出,在ωn=1附近,品質(zhì)因數(shù)越大電壓增益越小。品質(zhì)因數(shù)越大，則增益曲線越陡,并且有兩個(gè)電壓增益峰值。

圖4 不同品質(zhì)因數(shù)下電壓增益Fig.4 Voltage gain at different quality factor Q2

2 IC-ICPT系統(tǒng)參數(shù)優(yōu)化

ICPT系統(tǒng)中,電感、電容元件體積所占比重較大,而IC-ICPT系統(tǒng)包含較多的電感、電容元件。因此,IC-ICPT參數(shù)設(shè)計(jì)的關(guān)鍵是在保證系統(tǒng)傳輸性能前提下,盡可能地減小系統(tǒng)的體積。在相同的輸出功率條件下,諧振電路的體積與視在功率和有功功率的比值成正比關(guān)系。定義視在功率與有功功率比值為

其中,S是視在功率,P是有功功率,由式(5)和(9)-(13)可得到λ的表達(dá)式,

參數(shù)優(yōu)化的目標(biāo)是,在滿足系統(tǒng)輸出功率及器件應(yīng)力的前提下盡可能使λ最小。因此,以參數(shù)λ為目標(biāo)函數(shù),品質(zhì)因數(shù)Q2和電感比m為變量,對參數(shù)λ的最小值為目標(biāo)進(jìn)行優(yōu)化。優(yōu)化模型方程為

約束條件為

約束條件由兩個(gè)等式約束條件及4個(gè)不等式約束條件組成,約束方程的邊界參數(shù)及初始條件如表2所示。

表2約束方程參數(shù)Tab.2 Parameters of constraint equations

約束條件表達(dá)式中,Uin是導(dǎo)抗變換器輸入端電壓基波分量的幅值,與直流電壓Udc的關(guān)系為

另外,Iinmax,I1max和Uoutmax分別表示導(dǎo)抗變換器最大允許輸入電流,原邊繞組最大允許輸入電流和系統(tǒng)最大允許輸出電壓。選取SIMULINK工具箱中內(nèi)點(diǎn)法為優(yōu)化工具,選取[Q2,m]的初始值為[1,1],收斂精確度ε=1e?6,得到最優(yōu)解為[2.979,0.283]。優(yōu)化算法在迭代11次后趨于穩(wěn)定,系統(tǒng)誤差小于10?5,目標(biāo)函數(shù)值8.857 2。由表1的換算關(guān)系可以得到優(yōu)化后的IC-ICPT電氣參數(shù)如表3所示。

表3 IC-ICPT系統(tǒng)優(yōu)化參數(shù)Tab.3 IC-ICPT system optimized parameters

3 IC-ICPT系統(tǒng)實(shí)驗(yàn)驗(yàn)證

根據(jù)圖1所示拓?fù)浣Y(jié)構(gòu)搭建實(shí)驗(yàn)平臺驗(yàn)證ICICPT恒流特性及設(shè)計(jì)方法,實(shí)驗(yàn)參數(shù)用表3數(shù)據(jù)。實(shí)驗(yàn)波形如圖5、6所示。圖5為松耦合變壓器原邊繞組電流和副邊繞組電流波形,圖6為副邊輸出電壓和原邊繞組電流波形。逆變橋輸出電流幅值Iin=5.6A,原邊繞組電流I1=3.7A,副邊繞組電流I2=3.8A,輸出電壓Uout=38V。

圖5 導(dǎo)抗變換器電流和原邊電流Fig.5 Immittance converter current and primary winding current

圖6 輸出電壓和副邊電流Fig.6 Output voltage and secondary winding current

圖7為導(dǎo)抗變換器電流Iin及松耦合變壓器原邊繞組電流I1隨負(fù)載變化曲線。從圖中可以看出,原邊繞組電流隨著負(fù)載變化基本保持恒定,在負(fù)載率從0.2變化到1的情況下,原邊繞組電流由3.8A變化到3.4A,變化了0.4A,而逆變橋電流由3.2A變化到8.1A,變化了4.9A,驗(yàn)證了IC-ICPT的恒流源特性。

圖7 不同負(fù)載率時(shí)Iin和I1Fig.7 Iinand I1at different load rate

為分析IC-ICPT系統(tǒng)的傳輸效率特性,對不同負(fù)載情況下的效率進(jìn)行了測量。圖8為效率曲線,由圖可知,當(dāng)負(fù)載率較高時(shí),系統(tǒng)效率也較高,當(dāng)負(fù)載率低于0.5時(shí),其效率較低且低于0.5。這是因?yàn)橄到y(tǒng)環(huán)流的存在使得系統(tǒng)效率有所下降,特別是在輕載時(shí)效率下降尤其明顯。

圖8 不同負(fù)載率時(shí)系統(tǒng)效率Fig.8 Ef fi ciency at different load rate

由上述分析可知,由無源器件組成的導(dǎo)抗變換器與變壓器串聯(lián),在電源與變壓器之間起緩沖的作用,使得變壓器的原邊電流能在負(fù)載變化時(shí)保持基本不變。但值得指出的是,引入導(dǎo)抗變換器同時(shí)也使得系統(tǒng)的環(huán)流較大,由于寄生參數(shù)的存在,IC-ICPT系統(tǒng)的效率有所下降。

4 結(jié)論

本文利用導(dǎo)抗變換器原理,提出在一定條件下可實(shí)現(xiàn)原邊諧振回路電流恒定的IC-ICPT系統(tǒng)及設(shè)計(jì)方法。給出了滿足恒流特性的條件并分析了IC-ICPT的電氣特性。以系統(tǒng)功率密度最大為目標(biāo)對IC-ICPT系統(tǒng)進(jìn)行了優(yōu)化設(shè)計(jì)。最后,通過實(shí)驗(yàn)數(shù)據(jù)驗(yàn)證了理論分析的正確性。

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(編輯：劉素菊)

Application of immittance converter on inductively coupled power transfer system

LAN Jian-yu,TANG Hou-jun,LU Ting-hua
(Key Laboratory of Control of Power Transmission and Conversion,Ministry of Education,Shanghai Jiao Tong University,Shanghai 200240,China)

For an inductively coupled power transfer system with low order compensated topology,the primary current of contactless transformer is sensitive to the variety of load.This causes the output power to be unstable.Aiming at solving this problem,an inductively coupled power transfer system with immittance converter was proposed.When the inductively coupled system operates at the nature resonant frequency of the secondary side,the primary side winding current will be constant at different loads with immittance converter.This is helpful for loads which need the current source.At fi rst,the principle of inductively coupled power transfer system was introduced,and the impedance model was established by means of mutual inductance theory as well.Based on this,the condition of operation with constant current was deduced.Then,main parameters about the primary side current and the voltage gain was discussed.Furthermore,an optimization design method for achieving maximum power density of this system was proposed.Finally,simulation and experiment results veri fi ed the theoretical analysis.

inductively coupled;power transfer;contactless transformer;immittance converter;resonant frequency

TM 74

A

1007–449X(2013)10–0007–06

2012–10–08

國際熱核聚變實(shí)驗(yàn)堆計(jì)劃專項(xiàng)(2011GB113005);國家自然科學(xué)基金(51277120)

藍(lán)建宇(1980—),男,博士研究生,研究方向?yàn)闊o線電能傳輸,諧振變換器;

唐厚君(1957—),男,博士,教授,博士生導(dǎo)師,研究方向?yàn)闊o線電能傳輸,諧振變換器;

陸亭華(1989—),男,碩士研究生,研究方向?yàn)闊o線電能傳輸,諧振變換器。

藍(lán)建宇