脈寬調(diào)制技術(shù)外文翻譯

1、<p><b>　　附錄A 譯文</b></p><p><b>　　脈寬調(diào)制技術(shù)</b></p><p>　　前面討論的三相6階梯逆變器既有其優(yōu)點也有其局限性。由于在基波頻率的每個周期僅開關(guān)六次，因此逆變器的控制簡單而且開關(guān)損耗低。但是6階梯波電壓中的低次諧波會導(dǎo)致電流波形產(chǎn)生極大的畸變，除非使用笨重龐大的不經(jīng)濟的低通濾波器濾波。另外

2、，輸出電壓靠整流器控制，也不可避免的帶有整流器所具有的通常的缺點[16]。</p><p>　　脈寬調(diào)制（PWM）工作原理</p><p>　　由于逆變器中電子開關(guān)的存在，在恒定的直流輸入電壓作用下，逆變器可以通過自身的多次開關(guān)控制輸出電壓并優(yōu)化輸出諧波。圖5-18解釋了通過PWM控制輸出電壓的工作原理?；妷涸诜讲üぷ髂Ｊ较戮哂凶畲蟮姆担?）。如圖示，通過產(chǎn)生倆個凹口，的幅值可以被減

3、小，隨著凹口寬度的增加，基波電壓將隨之減小。</p><p>　　圖5-18 PWM控制輸出電壓的工作原理</p><p><b>　　PWM分類</b></p><p>　　在過去的文獻中已提出了很多的PWM技術(shù)，下面是對這些PWM技術(shù)的分類。</p><p>　　正弦PWM（SPWM）；</p>&l

4、t;p>　　特定諧波消除PWM（SHEPWM）；</p><p>　　最小紋波電流PWM；</p><p>　　空間矢量PWM（SVW）；</p><p><b>　　隨機PWM；</b></p><p>　　滯環(huán)電流控制PWM；</p><p>　　瞬時電流控制正弦PWM；</p&g

5、t;<p>　　Delta調(diào)制PWM；</p><p>　　Sigma Delta調(diào)制PWM</p><p>　　通常PWM技術(shù)可以按電壓控制或電流控制來分類，或按前饋方式或反饋方式來分類，也可以按基于斬波或不基于斬波來分類。注意，前面討論的移相控制PWM也是一種PWM技術(shù)。在這一節(jié)中，將對主要的PWM技術(shù)做一簡單的回顧。</p><p>　　5.5.

6、1正弦PWM</p><p>　　正弦PWM技術(shù)在實際的工業(yè)變流器的應(yīng)用中非常普及。這項技術(shù)在文獻中已經(jīng)得到了廣泛的討論。圖5-19解釋了SPWM的基本工作原理。圖中頻率為的等腰三角載波與頻率f的正弦調(diào)制波相比較，兩者的焦點確定了電力電子器件的開關(guān)時刻。例如，圖中給出了開關(guān)半橋逆變器中的構(gòu)成的波形，為防止的同時導(dǎo)通而設(shè)計的之間的死區(qū)時間在圖中被忽略了。上述方法也被稱為三角波法，次諧波法或次震蕩法。波形的脈沖及凹口

7、寬度按正弦規(guī)律變化，從而使其基波成分的頻率等于f且幅值正比于指令調(diào)制電壓。如圖5-20給出了負載無中線連接的典型的線電壓的相電壓波形。波形的傅立葉分析可以由下式給出:</p><p>　　(5-33) </p><p>　　圖5-19 三相橋式逆變器正弦PWM的工作原理</p><p>　　式中，m為調(diào)制指數(shù)；w為基波頻率（rad/s），（與調(diào)制頻率相同）

8、；為輸出相位移，取決于調(diào)制波的實際位置。</p><p>　　圖5-20 PWM逆變器的線電壓和相電壓的波形</p><p>　　a）線電壓 b）相電壓</p><p>　　調(diào)制指數(shù)m被定義 (5-34)</p><p>　　式中，為調(diào)制波的峰值；為載波的峰值。理想

9、情況下，m可以從0變化到1，并且調(diào)制波與輸出波形之間將保持著線性關(guān)系。逆變器基本上可以被看作是一個線性放大器，根據(jù)（5-33）和式（5-34）可以得出這個放大器的增益G為：</p><p><b>　　(5-35)</b></p><p>　　當(dāng)m=1時，可以得到最大的基波電壓峰值0.5，這個數(shù)值是方波電壓輸出時基波電壓峰值（4）的78.55%。事實上，通過將某些三次

10、諧波成分加入到調(diào)制波中，線性工作范圍的最大輸出基波電壓峰值可以增加到方波輸出時的90.7%。當(dāng)m=0時，是一個頻率與載波頻率相同，脈沖和凹口寬度上下對稱的方波。PWM輸出波形中，含有與載波頻率相關(guān)且邊（頻）帶與調(diào)制波頻率相關(guān)的諧波成分。這些頻率成分可以表示為，如式（5-33）所示。式中，M和N均為整數(shù)；M+N為一個奇整數(shù)。表5-1給出了當(dāng)載波頻率與調(diào)制波頻率的比值時的輸出諧波。</p><p>　　表5-1 SP

11、WM在時的輸出諧波</p><p>　　由上述的輸出諧波成分可以推導(dǎo)出，其幅值與載波比P無關(guān)，并將隨著M和N的增大而減小。隨著載波比的P的增大，逆變器輸出線電流諧波將通過電機的漏電感得到更好的濾波，并接近于正弦波。選擇載波頻率需要折中考慮逆變器損耗和點擊損耗。高的載波頻率（與開關(guān)頻率相同）將使逆變的開關(guān)損耗增加，但會減少電機的諧波損耗。最有的載波頻率選擇應(yīng)使系統(tǒng)的總損耗減小。PWM開關(guān)頻率的一個重要影響是當(dāng)逆變器

12、向電機提供功率時由磁滯效應(yīng)產(chǎn)生的噪聲（也稱為磁噪聲）。這種噪聲可以通過隨機的改變PWM開關(guān)頻率而減輕（隨機SPWM）,通過吧開關(guān)頻率增加到高于音頻范圍，也可以把這種噪聲完全消除?，F(xiàn)代高速IGBT可以很容易的實現(xiàn)這種無音頻噪聲的變頻傳動。逆變器輸出端的低通濾波器也可以消除這種噪聲。</p><p>　　1.過調(diào)制區(qū)操作 當(dāng)調(diào)制指數(shù)m接近于1時，在正，負半周期中間位置附近的凹口和脈沖將趨于消失。為了使器件能有一

13、個完整的開關(guān)操作，應(yīng)保持一個最小的凹口和脈沖寬度。當(dāng)這個最小脈寬的凹口和脈沖消失時，負載電流會有一個瞬態(tài)跳變。對IGBT逆變器，這個跳變可能是比較小的；但對于電力GTO晶閘管逆變器，由于器件變速的開關(guān)，這個跳變會很大。m的數(shù)值可以增加到大于1進入準(zhǔn)PWM區(qū)域，圖5-21所示為正半周期操作。圖中在正半周期中間附近脈沖向下的凹口不見了，從而給出了一個具有較高的基波成分的準(zhǔn)方波輸出。如圖5-22所示，在過調(diào)區(qū)，傳遞特性是非線性的，波形中重新出

14、現(xiàn)了5次和7次諧波成分。隨著m數(shù)值的增加，即調(diào)制信號的增大，最終逆變器將給出一個方波輸出，器件在方波的上升沿開關(guān)一次，在下降沿開關(guān)一次。在這種情況下，輸出基波相電壓峰值達到4（0.5）/，即達到100%的輸出，如圖5-22所示。</p><p>　　圖5-21 過調(diào)制區(qū)的波形 圖5-22 SPWM過調(diào)制輸出傳遞特性</p><p>　　2.載波與調(diào)制波頻率的關(guān)系 對

15、于變速傳動，逆變器輸出電壓和頻率應(yīng)按圖2-14所示關(guān)系變化。在恒功率區(qū)，逆變器以方波模式工作從而可以獲得最大電壓。在恒轉(zhuǎn)矩區(qū)，逆變器輸出電壓可以采用PWM控制。通常希望逆變器工作時載波與調(diào)制波頻率比P為一整數(shù)，即在整個工作范圍內(nèi)調(diào)制波與載波保持同步。但當(dāng)P保持為一定值，在基波頻率下降時，會使載波頻率也隨之變得很低，就電機的諧波損耗而言，這通常是不希望的。圖5-23給出了一個GTO晶閘管逆變器實際的載波與基波頻率的關(guān)系。當(dāng)基波頻率很低時，

16、載波頻率保持恒定。逆變器以自由運行方式或稱一部模式工作。在這個區(qū)域，載波比P可以是一個非整數(shù)，相位可能連續(xù)的移動，這將會產(chǎn)生諧波問題以及變化的直流偏移（差拍效應(yīng)）。隨著數(shù)值的下降，這個問題會變得越發(fā)的嚴(yán)重。在這里應(yīng)該提及的是，與基波頻率變化范圍相比，現(xiàn)代IGBT器件的開關(guān)頻率是非常高的，這使得PWM逆變器可以在整個異步范圍內(nèi)得到滿意的操作。如圖5-23所示，在異步運行區(qū)后是同步區(qū)，在這個區(qū)，P以一種階梯的方式變化，這使得最大和最小頻率保

17、持在設(shè)定邊界值內(nèi)的一個特定區(qū)域。P的數(shù)值總是保持為三的倍數(shù)，這是因為對無中線連接的負</p><p>　　5-23 載波頻率f/f的關(guān)系 </p><p>　　3.死區(qū)時間效應(yīng)及補償 由于死區(qū)（或封鎖）效應(yīng)，實際的PWM逆變器的相電壓（）波形會在某種程度上偏離5-19所示的理想波形。這種效應(yīng)可以用圖5-24中三相逆變橋中的a相橋臂來解釋。電壓源型逆變器的一個基本控制原則是要導(dǎo)通的器

18、件應(yīng)滯后于要關(guān)斷的器件一個死區(qū)時間t（典型值為幾微妙）以防止峭壁的直通。這是因為器件的導(dǎo)通是非?？斓模鄬碚f關(guān)斷是比較慢的。死區(qū)效應(yīng)會導(dǎo)致輸出電壓的畸變并減小其幅值。</p><p>　　考慮圖5-24所示PWM操作，如圖示，a相電流i的方向為正。初始狀態(tài)Q為導(dǎo)通，的幅值為+0.5V。Q在理想的開關(guān)點關(guān)斷后，在Q導(dǎo)通前有一個時間間隔t，在這個間隔，Q和Q都處于關(guān)斷狀態(tài)，但+ i的流通使得在理想開關(guān)點自然的切換

19、到-0.5 V?，F(xiàn)在考慮在理想開關(guān)點從Q到Q的帶有延遲時間t的開關(guān)轉(zhuǎn)換。當(dāng)QQ兩個器件都關(guān)斷時，+i繼續(xù)通過D流通，從而造成了如圖所示陰影面積的脈沖伏-秒（Vt）面積損失。下面再考慮電流i的極性為負時的情況。仔細的觀察圖示波形可以看到Q導(dǎo)通的前沿有一個類似的伏-秒面積的增加。注意，上述伏-秒面積的損失或增加僅僅取決于電流的極性，而與電流的幅值無關(guān)。圖5-25給出了在每一個載波周期T分別對應(yīng)于+i和-i的伏-秒面</p>&

20、lt;p>　　圖5-24 半橋逆變器死區(qū)效應(yīng)的波形</p><p>　　積（Vt）損失和增加的積累效應(yīng)對基波電壓波形的影響。圖中基波電流i滯后于基波電壓一個相位角。圖5-25中最下面的圖解釋了死區(qū)效應(yīng)。把由Vt構(gòu)成的這些面積累加起來并在基波頻率的半周期內(nèi)加以平均可得出方波偏移電壓V為</p><p><b>　?。?-36）</b></p><

21、;p>　　式中，P=，f為基波頻率，圖5-25中最上端的波形給出了V波對理想波的影響。在較低的基波頻率下，這種基波電壓的損失以及低頻諧波畸變會變得很嚴(yán)重。死區(qū)效應(yīng)可以很容易的通過電流反饋或電壓反饋方法進行補償。對于點一種方法，通過對相電流極性的檢測，將一個固定量的補償偏移電壓加到調(diào)制波上；對后一種方法，將檢測的輸出相電壓與PWM電壓參數(shù)信號相對比，延后把偏差用于補償PWM參考調(diào)制波。</p><p>　　5

22、.5.2 特定諧波消除PWM（SHEPWM）</p><p>　　應(yīng)用特定諧波消除PWM（SHEPWM）可以將方波中不希望有的低次諧波消除，并控制輸出基波電壓的大小，如圖5-26所示。在這種方法中，要在方波電壓中開出一些預(yù)先確</p><p>　　圖5-25 輸出相電壓波形的死區(qū)效應(yīng)</p><p>　　定好角度的凹槽。圖中所示為四分之一波對稱的正半周波形，可以通過

23、控制圖中四個凹槽角，，和消除三個特定的諧波成分，同時控制輸出基波電壓。如果圖示波形中有更多的凹槽角，責(zé)可以消除更多的諧波成分。</p><p>　　圖5-26 特定諧波消除PWM的相電壓波形</p><p>　　任何波形均可用如下傅立葉級數(shù)展開形似表示：</p><p>　　v（t）= （5-37）<

24、/p><p><b>　　式中</b></p><p><b>　?。?-38）</b></p><p><b>　?。?-39）</b></p><p>　　對于四分之一周期對稱的波形，波形中將只含有正弦項，并且只含有幾次諧波成分。因此有 </p><p>

25、;　　a=0 （5-40）</p><p>　　v（t）= （5-41）</p><p><b>　　式中 </b></p><p><b>　?。?-42）

26、 </b></p><p>　　假設(shè)圖示波形具有單位幅值，即v（t）=，則b可以求出如下：</p><p><b>　?。?-43）</b></p><p><b>　　根據(jù)表達式</b></p><p><b>　?。?-44）</b></p>&

27、lt;p>　　可以得出式（5-43）中的第一項和最后一項為</p><p><b>　?。?-45）</b></p><p><b>　?。?-46）</b></p><p>　　將式（5-45），式（5-46）代入式（5-43）并求出式中其它的積分項，可得</p><p><b>

28、　?。?-47）</b></p><p>　　注意在（5-47）中有k個變量（即，，，…，），因此需要有k個方程式去解出這k個變量的數(shù)值。通過求解出這k個角度，可以使基波電壓得到控制并且消除k-1個頻率的特定諧波。</p><p>　　圖5-37 消除5次和6次諧波時凹槽角與基波輸出電壓關(guān)系</p><p>　　考慮下面的例子，消除5次和7次諧波（最低次

29、的特定諧波）并控制基波電壓，3次諧波以及三的倍數(shù)次諧波在無中線連接的電機負載中不可以不考慮。在這種情況下，k=3.根據(jù)式（5-47），可以得到如下方程：</p><p>　　基波： （5-48）</p><p>　　5次諧波： （5-49）</p><p>　

30、　7次諧波： （5-50）</p><p>　　對于一個指定的基波電壓幅值，可以通過計算機程序用數(shù)值算法求解上面這組非線性超越方程組，算出、和的數(shù)值，如圖5-27所示。例如，給定50%的基波電壓（=0.5），可得到數(shù)值為</p><p>　　=20.9° =35.8° =51.2°</p><p

31、>　　從圖5-27還可以看到由于低次諧波的消除，較低次的其他特定諧波（如11次和13次）被顯著的增加了，但由于這些特定諧波的頻率比基波頻率高出很多，因此他們的影響不大。從圖5-27還可以看出，在輸出基波電壓幅值從0變化到93.34%時（100%對應(yīng)于方波電壓輸出），5次和7次諧波都可以完全消除。在輸出電壓為93.34%時，=0后，在半周期外側(cè)的單一凹槽可以通過減小角度而對稱的變窄，最后跳變?yōu)橥暾姆讲ā１?-2給出了輸出基波電壓以

32、1%步距變化時的角度的變化。圖5-28給出了輸出電壓為98%時的典型波形。注意，基波電壓的方向與角的整個變化范圍無關(guān)，輸出基波電壓在93.3%～100%的范圍內(nèi)變化時，會有某種程度的5次和7次諧波成分重新出現(xiàn)，但與限制電壓跳變所得的益處相比這是微不足道的。</p><p>　　表5-2 電壓在93.3%～100%范圍內(nèi)變化時的角變化</p><p>　　通過預(yù)先設(shè)置凹槽角的查尋表格，特定的

33、諧波消除法可以很方便的用微機實現(xiàn)。圖5-29所示簡單框圖給出了這種方法的而實現(xiàn)策略。對于一個給定的指令電壓,可以在查尋表格中得到相應(yīng)的凹槽角度，然后在時域里應(yīng)用一個減法計算器就可以產(chǎn)生相應(yīng)的電壓脈沖寬度。這里，計算器的脈沖為。例如，k=360，則可以產(chǎn)生分辨率為1的波形。</p><p>　　圖5-28 輸出電壓為98%時的典型波形</p><p>　　隨著基波頻率的下降，可以使凹槽的數(shù)量

34、增多，這樣就可以消除更多的特定諧波，但是如前所述，每周期凹槽角的數(shù)量或者開關(guān)頻率本身是受到逆變器的開關(guān)損耗限制的。這種方法的一個明顯缺點就是當(dāng)基波頻率比較低時，查尋表會變得非常的大，因此，一種混合PWM方法成為一種非常具有吸引力的選擇，在這種方法中，在低頻、低電壓區(qū)域中使用SPWM方法；而在高頻區(qū)，使用特定諧波消除法。</p><p>　　圖5-29 特定諧波消除法的實現(xiàn)框圖</p><p&g

35、t;<b>　　最小紋波電流PWM</b></p><p>　　特定諧波消除PWM法的一個明顯缺點是當(dāng)較低次的諧波被消除時，與其相鄰的下一個較高次的諧波卻被增值了，如圖5-27所示。由于電機中諧波損耗是由紋波電流的有效值確定的，因此，應(yīng)該減小的是紋波電流有效值而不是某些個別的諧波。在前面已指出，與各次諧波電壓相對應(yīng)的諧波電壓值本質(zhì)上取決于斷崖的有效漏電感。因此紋波電流有效值可以表示如下：&l

36、t;/p><p><b>　?。?-51）</b></p><p>　　式中，，…為諧波電流有效值；L為電機每相的等效漏感，,…為諧波電流的峰值；n為諧波次數(shù)；為n次諧波電壓峰值；為基波頻率。</p><p>　　相應(yīng)的諧波銅損為 （5-52）</p>

37、;<p>　　式中，R為電機每相的有效電阻。</p><p>　　對于一組確定的凹槽角，從式（5-47）可以得到的表達式，將此式代入到式（5-51）中，就可以得到作為角函數(shù)的。對于一個確定基波幅值，通過計算機程序?qū)堑\算可以求出最小化的。與諧波消除法相比，基于諧波損耗最小化修改的角查尋表是一種更理想的選擇。</p><p><b>　　附錄B 外文文獻</

38、b></p><p>　　5.5 PULSE WIDTH MODULATION TECHNIQUES</p><p>　　The three-phase, six-step inverter discussed before has several advantages and limitations. The inverter control is simple and the s

39、witching loss is low because there are only six switching per cycle of fundamental frequency .Unfortunately, the lower order harmonics of the six-step voltage wave will cause large distortions of the current wave unless

40、filtered by bulky and uneconomical low-pass filters. Besides, the voltage control by the line-side rectifier has the usual disadvantages[17].</p><p>　　5.5.1 PWM Principle</p><p>　　Because an inv

41、erter contains electronic switches ,it is possible to control the output voltage as well as optimize the harmonics by performing multiple switching within the inverter with the constant dc input voltage .The PWM principl

42、e to control the output voltage is explained in Figure 5.18.The fundamental voltage has the maximum amplitude（4/）at square wave, but by creating two notches as shown ,the magnitude can be reduced. If the notch widths are

43、 increased, the fundamental voltage will be re</p><p>　　PWM Classification</p><p>　　There are many possible PWM techniques proposed in the literature. The classification of PWM techniques can be

44、 given as follows：</p><p>　　Sinusoidal PWM (SPMW)</p><p>　　Selected harmonic elimination (SHE）PWM</p><p>　　Minimum ripple current PWM</p><p>　　Space-Vector PWM（SVM）<

45、/p><p>　　Random PWM</p><p>　　Hysteresis band current control PWM</p><p>　　Sinusoidal PWM with instantaneous current control</p><p>　　Delta modulation</p><p>　

46、　Sigma-delta modulation</p><p>　　Figure 5.17 PWM principle to control output voltage</p><p>　　Often, PWM techniques are classified on the basis of voltage or current control, feed-forward or fee

47、dback methods, carrier-or non-carrier-based control, etc. Note that the phase-shirt PWM discussed before can also be classified as a PWM technique. In this section, we will briefly review the principle PWM techniques.<

48、;/p><p>　　Sinusoidal PWM</p><p>　　The sinusoidal PWM technique is very popular for industrial converters and is discussed extensively in the literate. Figure 5.19 explains the general principle of

49、SPWM, where an isosceles triangle carrier wave of frequency is compared with the fundamental frequency sinusodal modulating wave, and the points of intersection determine the switching points of power devices. For examp

50、le, fabrication by switching and of half-bridge inverter, is shown in the figure. The lock-out time between and t</p><p><b>　　(5-33)</b></p><p>　　Where m=modulation index,=fundam

51、ental frequency in r/s（same as the modulating frequency）and =phase shift of output, depending on the position of the modulating wave. The modulating index m is defined as </p><p><b>　　(5-34)</b>&

52、lt;/p><p>　　Figure 5.18 Principle of sinusoidal PWM for three-phase bridge inverter</p><p>　　Figure 5.19 Line and phase voltage waves of PWM inverter</p><p>　　Where =peck value of th

53、e modulating wave and = peck value of the carrier wave. Ideally, m can be varied between 0 and 1 to give a linear relation between the modulating and output wave. The inverter basically acts as a linear amplifier. Combin

54、ing Equations（5.33）and（5.34）,the amplifier gain G is given as</p><p><b>　　(5-35)</b></p><p>　　At m=1,the maximum value of fundamental peak voltage is 0.5 ,which is 78.55</p>&

55、lt;p>　　percent of the peak voltage（4/2）of the square wave. In fact, the maximum value in the linear range can be increased to 90.7 percent of that of the square wave by mixing the appropriate values of triplen harmoni

56、cs with the modulating wave. At m=0, is a square wave at carrier frequency with symmetrical pulse and notch widths. The PWM output wave contains carrier frequency-related harmonics with modulating frequency-related sideb

57、ands in the form,which are shown in Equation（5.33）,where M and N are i</p><p>　　Table 5.1 Family of Output Harmonics for Sinusoidal PWM with </p><p>　　It can be shown that the amplitude of the

58、harmonics is independent of P and diminishes with higher values of M and N. With higher carrier frequency ratio P, the inverter line current harmonics will be well-filter by nominal leakage inductance of the machine and

59、will practically approach a sine wave. The selection of a carrier frequency depends on the trade-off between the inverter loss and the machine loss. Higher carrier frequency（same as switching frequency）increases inverter

60、 switching loss bu</p><p>　　Overmodulation Region</p><p>　　As the modulation index m approaches 1,the notch and pulse widths near the center of positive and negative half-cycles,respectively, te

61、nd to vanish. To complete switching operation of device, minimum notch and pulse widths must be maintained. When minimum-width notches and pulses are dropped, there will be some transient jump of load current. The jump m

62、ay be small for IGBT inverters, but it is substantial for high-power GTO inverter because of the slow switching of the devices. The value of m ca</p><p>　　Frequency Relation</p><p>　　For variabl

63、e-speed drive applications, the inverter output voltage and frequency are to be varied in the relation shown in Figure2.14.In the constant power region, the maximum voltage can be obtained by operating the inverter in sq

64、uare-wave mode, but in the constant torque region, the voltage can be controlled using the PWM principle. It is usually desirable to operate the inverter with an integral ratio P of carrier-to-modulating frequency, where

65、 the modulating wave remains synchronized with th</p><p>　　Figure 5.20 Waveforms in overmodulation region</p><p>　　to be the same as the fundamental frequency. The control should be designed car

66、efully so that at the jump of carrier frequency, there is no voltage jump problem, and chattering between adjacent s should be avoided by providing a narrow hysteresis band at the critical points.</p><p>　　D

67、ead Time Effect and Compensation </p><p>　　The actual phase voltage () wave in a PWM inverter deviates to some extent from the ideal wave shown in Figure5.19 because of the dead-time (or lock-out ) effect. T

68、his effect is explained in Figure5.24 for the phase leg a of a three-phase bridge inverter. A fundamental control principle of a voltage-fed inverter is that the incoming device should be delayed by a</p><p>

69、;　　Figure 5.21 SPWM overmodulation output transfer characteristics</p><p>　　dead-time t(typically a few) from the outgoing device to prevent a shoot-through fault. This is because the turn-on of a device is

70、very fast, but the turn-off is slow. The dead-time effect causes distortion of the output voltage and reduces its magnitude.</p><p>　　Consider the sinusoidal PWM operation in Figure 5.24. The direction of ph

71、ase a current is positive, as shown. With Q conducting initially, magnitude is +0.5V,as indicated. When Qis turned off at the ideal transition point, there is a time gap t before Q is turned on. During this gap, this ga

72、p, both Q and Q are off, but + i causes switching of to -0.5 V naturally at the ideal transition point. Consider the switching from Q to Qwith a delay tfrom the ideal transition point. When both devices are</p>&

73、lt;p>　　Figure5.22 Relation of carrier frequency with ratio</p><p>　　and -i, respectively, on the fundamental voltage wave is explained in Figure 5.25. The fundamental current i is shown to lag the fundam

74、ental voltage by phase angle. The dead-time effect is indicated in the lowest part of the figure. The areas contributed by Vt can be accumulated and averaged in the half-circle of fundamental frequency to calculate the s

75、quare-wave offset V as </p><p><b>　　（5-36）</b></p><p>　　where , P= and f=fundamental frequency. The effect of the Vwave on the ideal wave is shown at the top of the figure. The loss

76、 of fundamental voltage and low-frequency harmonic distortion become serious at low fundamental frequency. The dead-time effect can be compensated easily by the current or voltage feedback method [20]. In the former meth

77、od, the polarity of the phase current is detected and a fixed amount of compensating bias voltage is added with the modulating wave. In the latter method,</p><p>　　5.5.1.1.2 Selected Harmonic Elimination PWM

78、</p><p>　　The undesirable lower order harmonics of a square wave can be eliminated and fundamental voltage can be controlled as well by what is known as selected harmonics </p><p>　　Figure5.23 W

79、aveforms of half-bridge inverter explaining dead-time effect</p><p>　　Figure5.24 Dead-time effect on output phase voltage wave</p><p>　　elimination (SHE) PWM. In this method, notches are created

80、 on the square wave at predetermined angles, as shown in Figure5.26. In the figure, positive half-circle output is shown with quarter-wave symmetry. It can be shown that the notch angles ,,and can be control the fundame

81、ntal voltage. A large number of harmonic components can be eliminated if waveform can accommodate additional notch angles.</p><p>　　The general Fourier series of the wave can be given as </p><p>

82、;　　v（t）= （5-37）</p><p><b>　　where </b></p><p><b>　　（5-38）</b></p><p><b>　?。?-39）</b></p><p>　　For a wav

83、eform with quarter-circle symmetry, only the odd harmonics with sine components will be present. Therefore </p><p>　　a=0 （5-40）</p><p>　　v（t）=

84、 （5-41）</p><p>　　Figure5.25 Phase voltage wave for selected harmonic elimination PWM</p><p><b>　　where</b></p><p><b>　　（5-42）

85、 </b></p><p>　　Assuming that the wave has unit amplitude, that is,v（t）=,bcan be expanded as </p><p><b>　?。?-43）</b></p><p>　　Using the general relation </p>

86、<p><b>　　（5-44）</b></p><p>　　the first and last terms are </p><p><b>　?。?-45）</b></p><p><b>　?。?-46）</b></p><p>　　Integrating

87、the other components of Equation（5-43）and substituting（5-45）and（5-46）in it yields </p><p><b>　?。?-47）</b></p><p>　　Note that Equation（5-47）contain K number of variables （i.e.,,,,…,）,

88、and K number of simultaneous equations are required to solve their values. With K number of angles ,the fundamental voltage can be controlled and k-1 harmonics can be eliminated.</p><p>　　Consider, for examp

89、le, that the 5th and 7th harmonics (lowest significant harmonics) are to be eliminated and fundamental voltage is to be controlled. The 3rd and other triplen harmonics can be ignored if the machine has an isolated neutra

90、l. In this case, k=3 and the simultaneous equations can be written from Equation（5-47）as</p><p>　　Fundamental: </p><p><b>　　（5-48）</b></p><p>　　5th harmonic:</p>

91、<p><b>　　（5-49）</b></p><p>　　7th harmonic:</p><p><b>　?。?-50） </b></p><p>　　Figure5.26 Notch angle relation with fundamental output voltage for 5th and

92、 7th harmonic elimination</p><p>　　These nonlinear, transcendental equations can be solved numerically by a computer program for the specified fundamental amplitude and 、and can be determined, as shown in Fi

93、gure 5.27. As an example, for a fundamental voltage of 50 percent（=0.5）,the values are</p><p><b>　　=20.9° </b></p><p><b>　　=35.8° </b></p><p>&l

94、t;b>　　=51.2°</b></p><p>　　Figure 5.27 also indicates that the lower order, significant harmonics (i.e.,11th and 13th) have been considerably boosted as a result of lower order harmonics elimina

95、tion. The effect of these harmonics will possibly be small because of their large separation from the fundamental. Also note that in Figure 5.27,the 5th and 7th harmonics can be eliminated up to a voltage level of 93.34

96、percent (100 percent corresponds to the square wave) where =0. The single notch remaining on the outer side of th</p><p>　　The selected harmonic elimination method can be conveniently implemented with a micr

97、ocomputer using a lookup table of notch angles. The simple block diagram in Figure5.29 indicates the implementation strategy. At a certain command voltage,the angles are retrieved from the lookup table, and corresponding

98、ly, the phase voltage pulse width are generated in the time domain with the help of down-counters, where the counters are locked at . If ,for example, k=360,then 1.0-degree resolution waveforms c</p><p>　　A

99、s the fundamental frequency decreases, the number of notch angles can be increased so that a higher number of significant harmonics can be eliminated. Again, the number of notch angles/cycle, or the switching frequency,

100、is determined by the switching losses of the inverter. An obvious disadvantage of the scheme is that the lookup table at low fundamental frequency is unusually large. For this reason a hybrid PWM scheme where the low-fre

101、quency, low-voltage</p><p>　　region uses the SPWM method, and the high-frequency region uses the SHE method appears very attractive[8]. </p><p>　　Table5.2 Angle Table for Voltage from 93% to 10

102、0%</p><p>　　Figure5.27 Typical waveform at 98 percent output</p><p>　　Figure5.28 Block diagram for SHE implementation</p><p>　　5.5.1.1.3 Minimum Ripple Current PWM </p><p

103、>　　One disadvantage of the SHE PWM method is that the elimination of lower order harmonics considerably boosts the next higher level of harmonics, as shown in Figure 5.27. Since the harmonic loss in a machine is dicta

104、ted by the rms ripple current, it is this parameter that should be minimized instead of emphasizing the individual harmonics. In chapter 2,it was shown that the effective leakage inductance of a machine essentially deter

105、mines the harmonic current corresponding to any harmonic voltage. </p><p><b>　　（5-51）</b></p><p><b>　　where </b></p><p>　　,…=rms harmonic currents</p>