電氣類外文文獻及其翻譯--正弦脈寬調制

1、<p>　　24.437 Power Electronics</p><p>　　Sinusoidal Pulse width modulation</p><p>　　The switches in the voltage source inverter(See Fig.1)can be turned on and off as required.In the</p>

2、;<p>　　simplest approach,the top switch is turned on If turned on and off only once in each cycle,a</p><p>　　square wave waveform results.However,if turned on several times in a cycle an improved har-

3、</p><p>　　monic profile may be achieved.</p><p>　　Fig 1:Simple Voltage Sourced</p><p>　　In the most straightforward implementation,generation of the desired output voltage is achiev

4、ed</p><p>　　by comparing the desired reference waveform(modulating signal)with a high-frequency triangu-</p><p>　　lar‘carrier’wave as depicted schematically in Fig.2.Depending on whether the sig

5、nal voltage is</p><p>　　larger or smaller than the carrier waveform,either the positive or negative dc bus voltage is</p><p>　　applied at the output.Note that over the period of one triangle wav

6、e,the average voltage applied</p><p>　　to the load is proportional to the amplitude of the signal(assumed constant)during this period.</p><p>　　The resulting chopped square waveform contains a r

7、eplica of the desired waveform in its low fre-</p><p>　　quency components,with the higher frequency components being at frequencies of an close to the</p><p>　　carrier frequency.Notice that the

8、root mean square value of the ac voltage waveform is still equal</p><p>　　to the dc bus voltage,and hence the total harmonic distortion is not affected by the PWM process.</p><p>　　The harmonic

9、components are merely shifted into the higher frequency range and are automati-</p><p>　　cally filtered due to inductances in the ac system.</p><p>　　When the modulating signal is a sinusoid of

10、amplitude Am,and the amplitude of the triangular</p><p>　　carrier is Ac,the ratio m=Am/Ac is known as the modulation index.Note that controlling the</p><p>　　modulation index therefor controls t

11、he amplitude of the applied output voltage.With a sufficiently</p><p>　　high carrier frequency(see Fig.3 drawn for fc/fm=21 and t=L/R=T/3;T=period of funda-</p><p>　　mental),the high frequency c

12、omponents do not propagate significantly in the ac network(or load) due the presence of the inductive elements.However,a higher carrier frequency does result in a</p><p>　　larger number of switchings per cyc

13、le and hence in an increased power loss.Typically switching</p><p>　　frequencies in the 2-15 kHz range are considered adequate for power systems applications.Also</p><p>　　in three-phase systems

14、 it is advisable to use sso that all three waveforms are</p><p>　　symmetric.</p><p>　　Fig 2:Principal of Pulse Width Modulation</p><p>　　Fig.3:SPWM with fc/fm=48,L/R=T/3</p>

15、<p>　　Note that the process works well for m ≤1.For m >1,there are periods of the triangle wave in</p><p>　　which there is no intersection of the carrier and the signal as in Fig.4.However,a certain

16、amount</p><p>　　of this“overmodulation”is often allowed in the interest of obtaining a larger ac voltage magni-</p><p>　　tude even though the spectral content of the voltage is rendered somewhat

17、 poorer.</p><p>　　Note that with an odd ratio for fc/fm,the waveform is anti-symmetric over a 360 degree cycle.</p><p>　　With an even number,there are harmonics of even order,but in particular a

18、lso a small dc compo- nent.Hence an even number is not recommended for single phase inverters,particularly for smal</p><p>　　ratios of fc/fm.</p><p>　　SPWM Spectra:</p><p>　　Althoug

19、h the SPWM waveform has harmonics of several orders in the phase voltage waveform,</p><p>　　the dominant ones other than the fundamental are of order n and n±2 where n=fc/fm.This is evi-</p><

20、p>　　dent for the spectrum for n=15 and m=0.8 shown in Fig.5.Note that if the other two phases are</p><p>　　identically generated but 120o apart in phase,the line-line voltage will not have any triplen har

21、-monics.Hence it is advisable to choose,as then the dominant harmonic will</p><p>　　be eliminated.It is evident from Fig 5b,that the dominant 15th harmonic in Fig.5a is effectively</p><p>　　elim

22、inated in the line voltage.Choosing a multiple of 3 is also convenient as then the same trian-</p><p>　　gular waveform can be used as the carrier in all three phases,leading to some simplification in</p&g

23、t;<p><b>　　hardware.</b></p><p>　　It is readily seen that as the where E is the dc bus voltage,that the rms value</p><p>　　of the output voltage signal is unaffected by the PW

24、M process.This is strictly true for the phase</p><p>　　voltage as triplen harmonic orders are cancelled in the line voltage.However,the problematic har-</p><p>　　monics are shifted to higher ord

25、ers,thereby making filtering much easier.Often,the filtering is</p><p>　　carried out via the natural high-impedance characteristic of the load.</p><p>　　Fig.5:SPWM Harmonic Spectra:n=15,m=0.<

26、/p><p>　　Selective Harmonic Elimination</p><p>　　(also called Optimal PWM)</p><p>　　Notice that in the SPWM strategy developed above,a large number of switchings are required,</p>

27、;<p>　　with the consequent associated switching losses.With the method of Selective Harmonic Elimina-</p><p>　　tion,only selected harmonics are eliminated with the smallest number of switchings.This m

28、ethod</p><p>　　however can be difficult to implement on-line due to computation and memory requirements.</p><p>　　For a two level PWM waveform with odd and halfwave symmetries and n chops per qu

29、arter cycle</p><p>　　as shown in Fig 4,the peak magnitude of the harmonic components including the fundamental,</p><p>　　are given byEqn.1:</p><p>　　Hereis the magnitude of theharmo

30、nic andis theprimary switching angle.Even har-</p><p>　　monics do not show up because of the half-wave symmetry.</p><p>　　The n chops in the waveform afford n degrees of freedom.Several control

31、options are thus possi-</p><p>　　ble.For example n selected harmonics can be eliminated.Another option which is used here is to</p><p>　　eliminate n-1 selected harmonics and use the remaining de

32、gree of freedom to control the funda-</p><p>　　mental frequency ac voltage.To find theα’s required to achieve this objective,it is sufficient to</p><p>　　set the corresponding h’s in the above e

33、quations to the desired values(0 for the n-1 harmonics to</p><p>　　be eliminated and the desired per-unit ac magnitude for the fundamental)and solve for theα’s.</p><p>　　Fig 4:A two-level PWM wa

34、veform with odd and halfwave symm</p><p>　　Equation 1 can be readily proved by finding the fourier coefficients of the waveform shown inFig.4.In general,for a periodic waveform with period,the Fourier Cosine

35、 and Sine Coeffi-</p><p>　　cients are given by:</p><p>　　Because of the half-cycle symmetry of the waveform of Fig.4,only odd order harmonics exist.</p><p>　　Also,it is easy to see

36、that the Fourier Cosine coefficients disappear with the choice of coordinate</p><p>　　axes used.Utilizing the quarter cycle symmetry,the Fourier Sine coefficients become:</p><p>　　Substituting t

37、he two-valued pwm waveform for,one obtains(see Fig.4):</p><p>　　The following example illustrates the use of three chops per quarter cycle which allow for three</p><p>　　degrees of freedom.We ma

38、y use these to eliminate two harmonics and control the magnitude of</p><p>　　the fundamental to any desired value:</p><p><b>　　Example:</b></p><p>　　Selective Harmonic E

39、limination is applied with a view to controlling the fundamental component</p><p>　　of voltage to 50V(rms)and eliminating the 3rd and 5th harmonics.The source voltage is 100 V.</p><p>　　Calculat

40、e the required chopping angles.</p><p>　　As three objectives are to be achieved,we need 3 chops.The fundamental,3rd and 5th harmonic</p><p>　　magnitudes are given by:</p><p>　　We re

41、quire:</p><p><b>　　翻譯</b></p><p>　　24.437電力電子</p><p><b>　　正弦脈寬調制</b></p><p>　　電壓源逆變器的開關（見圖1）可以按要求打開和關閉。用最簡單的方法，頂部的開關打開，如果每個周期打開和關閉，方波的波形結果只有一次。但

42、是，如果改進諧波的數(shù)據(jù)則在一個周期內可以形成多次打開關閉。</p><p>　　圖1：簡單的電壓源逆變器</p><p>　　在最直接的實現(xiàn)方式，所期望的輸出電壓生成是通過比較預期的參考波形與高頻率三角’載體’波（調制信號）所描述的圖2.根據(jù)信號電壓是否大于或小于載體波波形，無論是正還是負的直流母線電壓施加在輸出。注意，在此期間一個三角波周期的平均電壓加到負載型成正比（假定不變），信號的振

43、幅。注意,經(jīng)過一段時期一個三角形波,平均電壓的負荷是成正比的幅值的信號(假定常數(shù))在這個時期。由此產(chǎn)生的方波包含在它的低頻率元件所需波形的復制，具有較高頻率分量在一個載波頻率接近的頻率的福祉。注意，均方根平方的交流電壓波形值仍相等的直流母線電壓，由于PWM使得總諧波不失真。諧波成分只是轉移到更高的頻率范圍，并且由于電感的交流系統(tǒng)自動地過濾。</p><p>　　當調制信號為正弦波的振幅Am，和三角載波的振幅Ac的

44、比 Am/Ac是已知的調制指數(shù)。注意，控制調制指數(shù)為施加控制輸出電壓幅值。具有足夠高的載波頻率（參見圖3得出fc/fm=21 and t=L/R=T/3；T=基礎時期），由于感性元件的存在高頻成分明顯不傳播到交流網(wǎng)絡（或負載）。然而，由于較高的載波頻率，開關較多從而在每個周期不增加功率損耗。電力系統(tǒng)的應用通常在2-15kHz的開關頻率范圍被認為是足夠的。此外，在三相系統(tǒng)中，建議使用使所有三個波形對稱。</p><p&

45、gt;　　圖2：主要的脈寬調制</p><p>　　圖3：SPWM的 fc/fm=48，L/R=T/3</p><p>　　注意，這個過程很適合。因為在圖4中有三角波其中有沒有交際的載體作為信號周期。然而，這種“過調制”在一定量往往是允許獲得更大的交流電壓，使電壓頻譜呈現(xiàn)稍差。</p><p>　　注意，fc/fm使用一個額外的比率，波形是反周期超過360度的對稱。

46、隨著偶數(shù)階諧波，特別小的直流元件。因此一個單相逆變器的不推薦用偶數(shù)，特別是fc/fm額外比率。</p><p><b>　　SPWM的頻譜：</b></p><p>　　雖然SPWM波形已在幾個數(shù)量相電壓波形的諧波，比其他有根本優(yōu)勢，是因為當n=fc/fm，n和n正負2 。這是經(jīng)濟脆弱性，在圖5削弱了頻譜對n=15和m=0.8 。請注意，如果其他兩個階段產(chǎn)生的，但除了

47、在相同階段120o，先電壓不會有任何。因此它選擇是明智的。正如當時占主導地位的諧波將被淘汰。它是由圖5b自明的，占主導地位的第15諧波，圖5a有效地消除了線路電壓。選擇3的倍數(shù)也方便，則相同的特里安奇異波形可作為承運的所有三個階段，可以使其在硬件上簡化。</p><p>　　這是容易看到的，當E是輸出電壓信號的均方根，(pwm(θ))^2=E^2是直流母線電壓。這是嚴格的相電壓諧波。然而，問題諧波的轉移較高，從而

48、使過濾更加容易。通常情況下，進行過濾通過自然高阻抗負載的特點。</p><p>　　圖5：SPWM的諧波譜：n=15，m=0.8</p><p><b>　　選擇性諧波消除</b></p><p>　　（也稱為最優(yōu)脈寬調制）</p><p>　　注意發(fā)展SPWM布局，大量的開關需要與相應的高消耗隨之而來。隨著選擇性諧波E

49、limina-tion的方法的使用，只有選擇諧波消除使開關最少。然而，由于計算和內存的需要這種方法可能很難實現(xiàn)。對于奇數(shù)的半波對稱二級PWM波形，如圖4，包括基礎諧波成分峰值幅度，由等式1給出：</p><p>　　在波形n負擔n個自由度。幾個可能的控制選項。例如選擇諧波可以被去除。這里使用的另一個選擇是n-1個選擇諧波和使用剩余的自由度，以控制頻率的交流電壓。找到a的要求達到這一目標，在上述方程以設置相應的h為

50、所需的值（0為n-1個被淘汰的諧波和所需的每單位的基本交流大?。┖徒鉀Qa。</p><p>　　圖4：奇二電平PWM波形和半</p><p>　　公式1可以很容易地證明了在圖中顯示的波形的傅立葉系數(shù)。圖4在一般情況下，周期波形，傅立葉余弦和正弦系數(shù)的計算公式如下：</p><p>　　由于波形圖的半周期對稱。圖4只有奇次諧波存在。此外，它很容易看到，利用季度周期對稱

51、性，傅立葉余弦系數(shù)隨著使用的坐標軸的選擇消除。</p><p>　　代入f（θ）可得二值PWM波形（見圖4）：</p><p>　　下面的例子說明了三個周期，每季度的三自由度允許使用條件。我們可能使用這些兩個諧波消除和控制的基本幅度作出任何所需的值：</p><p><b>　　例如：</b></p><p>　　應用選