外文翻譯--風力發(fā)電中的自我激勵與諧波（節(jié)選）

1、<p><b>　　中文3880字</b></p><p>　　出處：Muljadi E, Butterfield C P, Romanowitz H, et al. Self-excitation and harmonics in wind power generation[J]. Journal of solar energy engineering, 2005, 127(4)

2、: 581-587.</p><p>　　Self-Excitation and Harmonics in Wind Power Generation</p><p>　　E. Muljadi ， C. P. Butterfield</p><p>　　National Renewable Energy Laboratory, Golden, Colorado 80

3、401</p><p>　　H. Romanowitz</p><p>　　Oak Creek Energy Systems Inc.,Mojave, California 93501</p><p><b>　　R. Yinger</b></p><p>　　Southern California Edison,Ros

4、emead, California 91770</p><p>　　Traditional wind turbines are commonly equipped with induction generators because they are inexpensive, rugged, and require very little maintenance. Unfortunately, induction

5、generators require reactive power from the grid to operate，capacitor compensation is often used. Because the level of required reactive power varies with the output power, the capacitor compensation must be adjusted as t

6、he output power varies. The interactions among the wind turbine, the power network, and the capacitor comp</p><p>　　1．Introduction </p><p>　　Many of today’s operating wind turbines have fixed sp

7、eed induction generators that are very reliable, rugged, and low cost. During normal operation, an induction machine requires reactive power from the grid at all times. The most commonly used reactive power compensation

8、is capacitor compensation. It is static, low cost. Different sizes of capacitors are generally needed for different levels of generation.</p><p>　　Although reactive power compensation can be beneficial to th

9、e overall operation of wind turbines, we should be sure the compensation is the proper size and provides proper control. Two important aspects of capacitor compensation, self-excitation and harmonics ,are the subjects o

10、f this paper.</p><p>　　2．Power System Network Description </p><p>　　A diagram representing this system is shown in Fig(1). The power system components analyzed include the following:</p>

11、<p>　　? An infinite bus and a long line connecting the wind turbine to the substation</p><p>　　? A transformer at the pad mount</p><p>　　? Capacitors connected in the low voltage side of th

12、e transformer</p><p>　　? An induction generator</p><p>　　For the self-excitation, we focus on the turbine and the capacitor compensation only the right half of Fig. For harmonic analysis, we con

13、sider the entire network shown in Fig.</p><p>　　3. Self-Excitation</p><p>　　3.1 The Nature of Self-Excitation in an Induction Generator. Self-excitation is a result of the interactions among the

14、 induction generator, capacitor compensation, electrical load, and magnetic saturation. This section investigates the self-excitation process in an off-grid induction generator, knowing the limits and the boundaries of s

15、elf-excitation operation will help us to either utilize or to avoid self-excitation.</p><p>　　Fixed capacitors are the most commonly used method of reactive power compensation in a fixed-speed wind turbine.

16、An induction generator alone cannot generate its own reactive power; it requires reactive power from the grid to operate normally, and the grid dictates the voltage and frequency of the induction generator.</p>&l

17、t;p>　　One potential problem arising from self-excitation is the safety aspect. Because the generator is still generating voltage, it may compromise the safety of the personnel inspecting or repairing the line or gener

18、ator. Another potential problem is that the generator’s operating voltage and frequency may vary. Thus, if sensitive equipment is connected to the generator during self-excitation, that equipment may be damaged by over/u

19、nder voltage and over/ under frequency operation. In spite of the dis</p><p>　　3.2 Steady-State Representation. </p><p>　　The steady-state analysis is important to understand the conditions requ

20、ired to sustain or to diminish self-excitation. As explained above, self-excitation can be a good thing or a bad thing, depending on how we encounter the situation. Figure 2 shows an equivalent circuit of a capacitor com

21、pensated induction generator. As mentioned above, self-excitation operation requires that the balance of both real and reactive power must be maintained. Equation （1）gives the total admittance of the system s</p>

22、<p>　　++=0 （1）</p><p><b>　　where</b></p><p>　　= effective admittance representing the stator winding, the capacitor, and the load seen by node M</p>

23、;<p>　　= effective admittance representing the magnetizing branch as seen by node M,referred to the stator side</p><p>　　= effective admittance representing the rotor winding as seen by node M, referr

24、ed to the stator side</p><p>　　Equation 1 can be expanded into the equations for imaginary and real parts as shown in Eqs.2and3:</p><p><b>　?。?）</b></p><p>　　Fig. 2 Per

25、phase equivalent circuit of an induction generator under self-excitation mode</p><p>　　Fig.3 A typical magnetization characteristic</p><p>　　= stator winding resistance</p><p>　　= s

26、tator winding leakage inductance</p><p>　　= rotor winding resistance</p><p>　　= rotor winding leakage inductance</p><p>　　= stator winding resistance</p><p>　　S = oper

27、ating slip</p><p>　　= operating frequency</p><p>　　= load resistance connected to the terminals</p><p>　　C = capacitor compensation</p><p><b>　　=阻抗</b></

28、p><p>　　One important aspect of self-excitation is the magnetizing characteristic of the induction generator. Figure 3 shows the relationship between the flux linkage and the magnetizing inductance for a typica

29、l generator; an increase in the flux linkage beyond a certain level reduces the effective magnetizing inductance . This graph can be derived from the experimentally determined no-load characteristic of the induction gene

30、rator. </p><p>　　The voltage at the terminals of the induction generator presented in Fig . （5） shows the impact of changes in the capacitance and load resistance. As shown in Fig. （5）, the load resistance

31、does not affect the terminal voltage, especially at the higher rpm （higher frequency）, but the capacitance has a significant impact on the voltage profile at the generator terminals. A larger capacitance yields less volt

32、age variation with rotor speed, while a smaller capacitance yields m ore voltage variation </p><p>　　These concepts of self-excitation can be exploited to provide dynamic braking for a wind turbine as menti

33、oned above to prevent the turbine from running away when it loses its connection to the grid; one simply needs to choose the correct values for capacitance （a high value） and load resistance to match the turbine power o

34、utput. Appropriate operation over a range of wind speeds can be achieved by incorporating a variable resistance and adjusting it depending on wind speed.</p><p>　　3.3 Dynamic Behavior. </p><p>　

35、　This section examines the transient behavior in self-excitation operation. We choose a value of 3.8 mF capacitance and a load resistance of 1.0 for this simulation. The constant driving torque is set to be 4500 Nm. Note

36、 that the wind turbine aerodynamic characteristic and the turbine control system are not included in this simulation because we are more interested in the self-excitation process itself. Thus, we focus on the electrical

37、side of the equations.</p><p>　　Figure 7 shows time series of the rotor speed and the electrical output power. In this case, the induction generator starts from rest. The speed increases until it reaches its

38、 rated speed. It is initially connected to the grid and at t=3.1 seconds （s）, the grid is disconnected and the induction generator enters self-excitation mode. At t=6.375 s, the generator is reconnected to the grid, term

39、inating the self-excitation. The rotor speed increases slightly during self-excitation, but, eventually, </p><p>　　Figure 8 (a) plots per phase stator voltage. It shows that the stator voltage is originally

40、the same as the voltage of the grid to which it is connected. During the self-excitation mode 3.1 s<t<6.375 s, when the rotor speed increases as shown in Fig. 7, the voltage increases and the frequency is a bit hig

41、her than 60 Hz. The voltage and the frequency then return to the rated values when the induction generator is reconnected to the grid. Figure 8(b) is an expansion of Fig. 8(a) between t=3.0 s an</p><p>　　4．H

42、armonic Analysis</p><p>　　4.1 Simplified Per Phase Higher Harmonics Representation. In order to model the harmonic behavior of the network, we replace the power network shown in Fig. 1 with the per phase equ

43、ivalent circuit shown in Fig. 9（a）. In this circuit representation, a higher harmonic or multiple of 60 Hz is denoted by h, where h is the integer multiple of 60 Hz. Thus h=5 indicates the fifth harmonic （300 Hz）. For wi

44、nd turbine applications, the induction generator, transformer, and capacitors are three phase and c</p><p>　　Fig.8 The terminal voltage versus the time.（a）Voltage during self-excitation.（b） Voltage before an

45、d during self-excitation , and after reconnection.</p><p>　　4.1.1 Infinite Bus and Line Feeder. The infinite bus and the line feeder connecting the wind turbine to the substation are represented by a simple

46、Thevenin representation of the larger power system network. Thus, we consider a simple RL line representation.</p><p>　　Fig.9 The per phase equivalent circuit of the simplified model for harmonic analysis<

47、;/p><p>　　4.1.2 Transformer.</p><p>　　We consider a three-phase transformer with leakage reactance （） of 6 percent. Because the magnetizing reactance of a large transformer is usually very large co

48、mpared to the leakage reactance （→open circuit）, only the leakage reactance is considered. Assuming the efficiency of the transformer is about 98 percent at full load, and the copper loss is equal to the core loss （a gen

49、eral assumption for an efficient, large Transformer）, the copper loss and core loss are each approximately 1 percent or 0</p><p>　　4.1.3 Capacitor Compensation. Switched capacitors represent the compensation

50、 of the wind turbine. The wind turbine we consider is equipped with an additional 1.9 MVAR reactive power compensation（1.5 MVAR above the 400 kVAR supplied by the manufacturer）. The wind turbine is compensated at differe

51、nt levels of compensation depending on the level of generation. The capacitor is represented by the capacitance C in series with the parasitic resistance（Rc）, representing the losses in the capacitor. Thi</p><

52、p>　　4.1.4 Induction Generator. The induction generator （1.5 MW,480 V,60 Hz）used for this wind turbine can be represented as the per phase equivalent circuit shown Fig. 9（a）. The slip of an induction generator at any h

53、armonic frequency h can be modeled as</p><p><b>　　where</b></p><p>　　= slip for th harmonic</p><p>　　H = harmonic order</p><p>　　= synchronous speed of the

54、generator</p><p>　　= rotor speed of the generator</p><p>　　Thus for higher harmonics ( fifth and higher) the slip is close to 1 (=1) and for practical purposes is assumed to be 1.</p>&l

55、t;p>　　4.2 Steady State Analysis. Figure 9(b) shows the simplified equivalent circuit of the interconnected system representing higher harmonics. Note that the magnetizing inductance of the transformers and the inducti

56、on generator are assumed to be much larger than the leakages and are not included for high harmonic calculations. In this section, we describe the characteristics of the equivalent circuit shown in Fig. 9, examine the im

57、pact of varying the capacitor size on the harmonic admittance, and us</p><p>　　From the superposition theorem, we can analyze a circuit with only one source at a time while the other sources are turned off.

58、For harmonics analysis, the fundamental frequency voltage source can be turned off. In this case, the fundamental frequency voltage source(infinite bus), Vs, is short circuited.</p><p>　　Fig. 10(a) The total

59、 admittance for higher harmonics as a function of reactive compensation. (b) Total harmonic distortion of the current as a function of the reactive compensation in per unit.</p><p><b>　　where</b>

60、</p><p>　　= + j= line impedance</p><p>　　= + j = transformer leakage impedance</p><p>　　= += capacitor impedance</p><p>　　= + j= generator impedance</p><p&g

61、t;　　The admittance at any capacitance and harmonic frequency can be found from the impedance:</p><p>　　For a given harmonic, the harmonic current is proportional to the admittance shown in Eq. (6) multiplied

62、 by the corresponding harmonic voltage. Because the field data only consist of the total harmonic distortion of the capacitor current, and do not provide information about individual harmonics, we can only compare the tr

63、ends from the admittance calculation to the measured data. </p><p>　　Fig. 11 (a) Per-phase equivalent circuit of a transformer. (b) Phasor diagram for P>0,Q>0. (c) Phasor diagram for P>0,Q <0.<

64、;/p><p>　　From Fig. 10, we can say that the circuit will resonate at different frequencies as the capacitor C is varied. Two harmonic components must exist to generate harmonics currents in the systems—a harmon

65、ic source (due to magnetic saturation as shown in Fig. 3) and a circuit that will resonate at certain levels of capacitance compensation.</p><p>　　4.3 Dynamic Simulation. Now consider how the harmonic source

66、s are generated in the transformer. Most utility-size wind turbines are equipped with a pad-mount step-up transformer that connects them to the utility. When the transformer is saturated, the nonlinear characteristic of

67、the magnetic circuit generates a nonsinusoidal current.</p><p>　　Figure 11(a) shows the per-phase equivalent circuit of a transformer. The iron core loss of a transformer is usually represented as an equival

68、ent resistance,, in parallel with the magnetizing reactance . In this study, the core loss is small enough to be neglected (i.e., the value of = represents an open circuit; thus, the equivalent resistance is not drawn i

69、n the equivalent circuit). The magnetizing flux linkage is proportional to the ratio of the voltage and the frequency:</p><p><b>　　where</b></p><p>　　= the magnetizing voltage </p

70、><p>　　= flux linkage</p><p>　　= the base frequency</p><p><b>　　= 磁化的電壓</b></p><p>　　The flux linkage of the transformer can be found from Eq.(7). The relation

71、ship between the flux linkage and the magnetizing inductance due to the magnetizing current is nonlinear. When the magnetizing current is low, the flux (and flux linkage) varies linearly with the magnetizing current, bu

72、t eventually saturation is reached and the nonlinear characteristic starts; further increases in magnetizing current will produce smaller increases in the flux linkage. In the saturation region, the resulti</p>&l

73、t;p>　　Fig. 12 The output voltage and current of a transformer under light load condition</p><p>　　There are two types of operation that can cause saturation. The first one occurs when the transformer oper

74、ates at a higher voltage level. One example of this operation is when the transformer is lightly loaded. As a result, the magnetizing branch is exposed to a high voltage , producing a large magnetizing current in the ma

75、gnetizing branch.</p><p>　　The second type of operation that can result in high saturation is when the transformer is operated with a leading power factor (supplying reactive power to the grid Vs).</p>

76、<p>　　The voltage across the magnetizing reactance (referred to the primary side) can be expressed as</p><p><b>　　where</b></p><p>　　=+ j= line impedance connecting the trans

77、former to the voltage source VS</p><p>　　= + j = primary winding impedance of the transformer</p><p>　　== = resistance of the primary and secondary winding of the transformer</p><p>

78、;　　== = leakage reactance of the primary and secondary winding of the transformer</p><p>　　= voltage at the infinite bus</p><p>　　= current flowing in the primary winding</p><p>　　=

79、 reactance of the line</p><p>　　= line resistance</p><p>　　As an illustration, we can use the phasor diagrams shown in Figs. 11(b) and 11(c). For the case of simplicity in the phasor diagram ill

80、ustrations, we can simplify the equivalent circuit shown in Fig. 11(a) as an ideal transformer with only its leakage reactance represented. In Fig. 11(a), the real power P and reactive power Q are considered to be flowin

81、g from the right to the left (positive values flow from the turbine to the grid). When P >0, Q<0 (the turbine generates real power but absorbs re</p><p>　　風力發(fā)電中的自我激勵與諧波</p><p><b>　　1

82、．介紹</b></p><p>　　傳統(tǒng)的風力渦輪機通常安裝的是感應發(fā)電機，因為它廉價，耐用，而且只需要很少的維護。然而，電感應發(fā)電機需要的無功功率通常通過電容器補償來得到。因為輸出功率各不相同，所以電容補償必須隨之調整。風力發(fā)電機組的電力網絡中，相互的電容補償作用是導致輸出電流中產生自我激勵和高次諧波的一個重要原因。這篇文章探討產生這些現(xiàn)象的原因，并對如何控制或消除這些現(xiàn)象提出一些方法。</p

83、><p>　　現(xiàn)在大部份風力發(fā)電機的性能是非?？煽康?，并且維修簡單，費用低。一臺感應發(fā)電機在正常工作期間始終需要得到無功功率。使用最普遍的無功功率補償是電容器補償，因為它是靜態(tài)的, 而且成本低。不同型號的電容器可以提供不同的電容補償。</p><p>　　雖然無功的動力補償可能對風輪機總的操作有利，但是我們必須確保補償是恰當?shù)?，并且不影響控制。自我激勵和諧波是電容器補償?shù)膬蓚€重要部分也是這篇文

84、章的主題。</p><p>　　2．動力系統(tǒng)網絡描述</p><p>　　如圖1所示描述的這個系統(tǒng)。動力系統(tǒng)的部件分析包括如下內容：</p><p>　　? 連接風機各部分的總線和輸入線路。</p><p>　　? 一臺安裝在襯墊上的變壓器</p><p>　　? 連結在變壓器低電壓的電容器</p>&l

85、t;p>　　? 一臺電感應發(fā)電機</p><p>　　圖1. 系統(tǒng)各部件圖</p><p>　　對于自我激勵，我們關注的是在渦輪上的電容補償。對于諧波分析，我們用圖表來表示整個網絡。</p><p><b>　　3．自我激勵</b></p><p>　　3.1感應發(fā)電機的自我激勵。 </p>&l

86、t;p>　　自激是在感應發(fā)電機和電容器補償之中負電荷和磁性浸透交互作用的一個結果。自我激勵過程這部分是在一臺離柵欄的電感應發(fā)電機里進行研究的，知道極限和自激操作的邊界將會幫助我們去利用或者避免自激。</p><p>　　在固定速度的風輪機中應用最普遍的是固定電容器無功的動力補償方法。只有一臺電感應發(fā)電機是不能得到它自己需要的無功動力的，它要求來自電網正常操作的無功動力，并且柵欄口接電感應發(fā)電機的電壓和頻率。

87、</p><p>　　安全是自我激勵的一個潛在問題。因為發(fā)電機可以產生電壓，它可能傷害檢查或者修理這臺發(fā)電機的人員。另一個潛在的問題是發(fā)電機的工作電壓和頻率可能變化。因此，在自我激勵期間連接在發(fā)電機上的易損設備可能在過高或過低的電壓和頻率下被損壞。盡管這是自我激勵過程中電感應發(fā)電機的缺點，然而一些人把這種方式應用于動態(tài)的剎車系統(tǒng)中，幫助在柵欄損失的緊急情況時控制轉子速度。因此，適當?shù)倪x擇電容和電阻器可以在柵欄損失

88、和機械剎車故障期間控制風輪機速度。</p><p><b>　　3.2 穩(wěn)態(tài)表現(xiàn)。</b></p><p>　　穩(wěn)態(tài)分析中關鍵是理解哪些條件對自我激勵有增強或削弱作用。如上面解釋的那樣，自我激勵可能是一件好事情也可能是一件壞事情，這取決于我們遇到什么樣的形勢。圖2為一個電容器補償電感應發(fā)電機。如上所述，自我激勵操作要求必須保持完全的無功平衡。</p>&

89、lt;p>　　++=0 （1）</p><p>　　=電容器節(jié)點的有效輸入</p><p>　　=磁化部分的有效輸入</p><p>　　=轉子節(jié)點的有效輸入</p><p>　　方程式1的實部和虛步可以被擴展為方程式2 和3。</p><p><b>

90、　　（2）</b></p><p>　　圖2.自我激勵方式下的等效電路</p><p>　　圖3. 典型的磁化特性</p><p><b>　?。?）</b></p><p><b>　　=阻抗</b></p><p><b>　　=滲漏電感</b

91、></p><p><b>　　=轉子阻抗</b></p><p><b>　　=轉子滲漏電感</b></p><p><b>　　= 阻抗</b></p><p><b>　　S =操作損失</b></p><p><

92、;b>　　=操作頻率</b></p><p><b>　　=終端負載電阻</b></p><p><b>　　C =電容器補償</b></p><p>　　自我激勵的一個重要方面是電感應發(fā)電機的磁化特性。圖3所示為一臺典型的勵磁電感發(fā)電機和輸出電流之間的關系；這圖由實驗得來反映了發(fā)電機的特性。</

93、p><p>　　圖5為電感應發(fā)電機的終端電壓受電容和負載電阻變化的影響而變化的示意圖。如圖5所示，負載電阻不影響終端電壓， 特別是在發(fā)電機轉速很高時，但是電容對發(fā)電機的輸出電壓有顯著影響。一個大的電容在轉子轉動過程中產生較少的電容變化，而較小的電容在轉子轉動過程會產生很大的電容變化。如圖6所示，對規(guī)定的電容來說，改變負載電阻的有效值能調節(jié)力矩速度。</p><p>　　自我激勵這個概念可以被利

94、用在渦輪機上，如上所述，當它失去對柵欄連接時可以提供動態(tài)剎車從而防止飛車現(xiàn)象發(fā)生。只要正確選擇電容和負載電阻使其與渦輪機輸出電源相匹配，就能在一定的風速范圍內來調節(jié)阻抗。</p><p><b>　　3.3 動態(tài)反應。</b></p><p>　　這部分可以在自我激勵過程中檢查瞬時的變化。對于這次模擬來說我們選擇3.8毫法電容和1.0歐的負載電阻。驅動力矩的常量被調整

95、為4500納米。但是，空氣動力學的風輪機特性控制系統(tǒng)不包括在這個模擬中，我們關注的是自我激勵的過程。因此，我們重視方程式電的方面。</p><p>　　圖7顯示連續(xù)時間內轉子速度和輸出功率的關系。在這種情況下，電感應發(fā)電機由靜止啟動，速度逐漸增加，直到達到它自身的額定速度。最初連接柵欄在開始的t = 3.1秒s，柵欄被斷開，電感應發(fā)電機進入自我激勵方式。在t = 6.375 s時，發(fā)電機被再接通到柵欄，終止自我激

96、勵。在自我激勵期間轉子速度逐漸增加，但是，最后發(fā)電機力矩達到4500牛米，并且轉子速度變?yōu)榉€(wěn)定。當發(fā)電機沒有同步而被再接通到柵欄時，在發(fā)電機的力矩會突然發(fā)生簡短的瞬間變化。這種情況一旦發(fā)生，轉子速度會與柵欄之前有相同的速度。</p><p>　　圖8(a)顯示每個時期電壓的狀況。它顯示最初電壓與被連結柵欄后的電壓相同。如圖7所示，在自我激勵方式下3.1 s<t<6.375 s期間，轉子速度逐漸增加，電

97、壓逐漸增加，最終頻率比60赫茲高一點。當電感應發(fā)電機再次被接通到柵欄時，電壓和頻率返回額定值。圖8（b）是對圖8（a）中t=3.0s和t=3.5s的擴展，舉例說明在這期間電壓存在的瞬間的變化。</p><p>　　圖5. 終端電壓對轉子速度的影響</p><p>　　圖6. RL和C對發(fā)電機轉速的影響</p><p><b>　　4．諧波分析</b&

98、gt;</p><p>　　4.1 簡化每個時期的諧波。為了模擬諧波網絡的變化，我們用圖9（a）中顯示的每個時期的線路替換圖 1 中顯示等效電路。在這電路表現(xiàn)中，h 指示60赫茲或更高頻率的諧波，在這里h是60赫茲的整數(shù)倍。因此h = 5 表明第5 諧波（300赫茲），對于風輪機應用來說， 電感應發(fā)電機、變壓器和電容器是三相的字母Y型連接或三角形連接，因此，諧波和第3諧波不存在[5，6] ，即，只是h = 5，7

99、，11，13，17，… ， 等等存在 。</p><p>　　圖7. 發(fā)電機的輸出功率和轉子速度</p><p>　　圖8 終端電壓與時間(a)在自我激勵期間的電壓 (b)在自我激勵期間的電壓</p><p>　　4.1.1 總線和輸入線路。 用大型的動力網絡系統(tǒng)來描述連接風機各部分的總線和輸入線路。因此，我們用簡單的RL圖線來表示。</p><

100、p>　　圖9. 等效電路模型的簡單諧波分析</p><p><b>　　4.1.2 變壓器</b></p><p>　　我們認為三相變壓器有大約百分之6的電抗被泄露 。因為一臺大的變壓器的磁化電杭遠遠少于滲漏電抗，所以我們只考慮滲漏電抗。假定變壓器的效率在滿負荷時大約是百分之98，銅損與核心損失基本相等，銅損失和核心損失大約都占百分之1。在這個假設下，我們能計算

101、出銅損在全部負載電流占多大比例， 并且我們能確定主要和次級繞組的總電阻。</p><p>　　電容補償。變換電容代表風輪機的補償。我們考慮的風輪機裝有額外的1.9 MV無功動力補償。風輪機按不同的標準進行補償。電容器通過電容器里的損失串聯(lián)電容進行描述。質量好的電容器阻抗通常非常小。</p><p>　　4.1.4 電感應發(fā)電機。</p><p>　　應用1.5兆瓦，

102、 480 V，60赫茲的電感應發(fā)電機，這臺風輪機的情況可以被等效電路描述，如圖（a）所示。這臺電感應發(fā)電機在任何諧頻h時的諧波可以表示為</p><p><b>　　= h頻率時的諧波</b></p><p><b>　　= 假設諧波頻率</b></p><p><b>　　=發(fā)電機的同步速度</b>

103、</p><p><b>　　=發(fā)電機的轉子速度</b></p><p>　　因為都接近于1 ，所以在應用公式時按照=1計算。</p><p><b>　　4.2 穩(wěn)態(tài)分析。</b></p><p>　　連接系統(tǒng)等效電路的主要諧波通過圖9(b)描述。注意，假設變壓器和電感應發(fā)電機的勵磁電感遠遠大于損

104、失的電感，并且不對很高諧波情況進行計算。在這部分中，我們通過對圖9進行分析，檢查電容器尺寸的變化對等效電路諧波特性的影響, 并且通過計算來解釋為什么會出現(xiàn)這些變化。</p><p>　　在這個定理的基礎上，我們每次只分析一個因素，把其它的因素都關閉。對諧波分析來說，基本頻率的電壓源可以被關上。 在這種情況下，基本頻率電壓源頭是短路的。</p><p>　　圖10(a)無功功率的諧波 (b