串并聯(lián)等值電路-電力牽引交流傳動系統(tǒng)

1、vUnit2 Ideal Sources Series and Parallel Equivalent Circuitsv理想電源的串并聯(lián)等效電路理想電源的串并聯(lián)等效電路vConsider an elementary circuit containing a single source of e.m.f. E and of internal resistance Rs, and a single load R (Fig.1). The resistance of the conductors of this type of circuit may be neglected.New Words

2、& Expressions:internal resistance 內(nèi)阻內(nèi)阻如圖如圖1 1所示，考慮一個由電動勢為所示，考慮一個由電動勢為E E、內(nèi)、內(nèi)阻為阻為RsRs的電源和負載為的電源和負載為R R構(gòu)成的基本電路構(gòu)成的基本電路（此句將英語的祈使句翻譯成漢語的無（此句將英語的祈使句翻譯成漢語的無主句）主句）。在這種類型的電路中，導線的。在這種類型的電路中，導線的電阻一般可以忽略不計。電阻一般可以忽略不計。vIn the external portion of the circuit, that is, in the load R, the current is assumed to

3、flow from the junction a (which is at a higher potential such that a=1) to the junction b (which is at a lower potential such that b=2).v在電路的外部，即在負載在電路的外部，即在負載 R R 處，假定電流從端點處，假定電流從端點 a a（位于（位于 a = 1 a = 1的高電勢）的高電勢）流向端點流向端點 b b（位于（位于 b = 2 b = 2的低電勢）的低電勢）。vThe direction of current flow may be shown e

4、ither by a hollow arrowhead or by supplying the current symbol with a double subscript whose first digit identifies the junction at a higher potential and the second (identifies) the junction at a lower potential. Thus for the circuit of Fig.2.1, the current I=Iab.分析：分析：整句是一個具有定語從句的主從復合句。從句里有并列句，第整句

5、是一個具有定語從句的主從復合句。從句里有并列句，第二句省略謂語動詞。二句省略謂語動詞。翻譯：翻譯：電流的方向既可以用一個空心箭頭來表示，又可用帶雙下標的電流的方向既可以用一個空心箭頭來表示，又可用帶雙下標的電流符號來表示，且第一個下標表示高電位點，第二個下標表示低電電流符號來表示，且第一個下標表示高電位點，第二個下標表示低電位點。因此，對于圖位點。因此，對于圖2.12.1中的電路，電流表示為中的電路，電流表示為I=IabI=Iab。vWe shall show that the circuit of Fig.2.1 containing a source of known e.m.f. E a

6、nd source resistance Rs may be represented by two types of equivalent circuits.v分析：分析：that引導引導賓語從句。從句的主語又有定語修飾。賓語從句。從句的主語又有定語修飾。v下面將證明，對于圖下面將證明，對于圖2.1所示的含一個已知電動勢所示的含一個已知電動勢E和內(nèi)阻和內(nèi)阻Rs的電源的的電源的電路，可以用兩種類型的等效電路來表示。電路，可以用兩種類型的等效電路來表示。New Words & Expressions:source resistance 內(nèi)阻內(nèi)阻vAs (it is) already sta

7、rted, the terminal voltage of a loaded source is lower than the source e.m.f. by an amount equal to the voltage drop across the source resistancev如前所述，電源加負載后的端電壓要比電源電動勢低一個值，這個值等如前所述，電源加負載后的端電壓要比電源電動勢低一個值，這個值等于電源內(nèi)阻兩端的電壓降：于電源內(nèi)阻兩端的電壓降：IREVEVss21IREVEVss21vOn the other hand, the voltage across the load

8、resistance R isvSince and , from Eqs. (2.1) and (2.2) it follows that , or and .RIVbaa1b2RIIREsRIIREs)/(RREIs另外，負載電阻另外，負載電阻R兩端的電壓是兩端的電壓是由于由于 、 ，從公式（，從公式（2.1）和（和（2.2）可以得出）可以得出或者或者 和和RIVbaa1b2RIIREsRIIREs)/(RREIsFrom the last equation we conclude that the current through the source is controlled by bo

9、th the load resistance and the source resistance. Therefore, in an equivalent circuit diagram the source resistance Rs may be shown connected in series with the load resistance R. This configuration may be called the series equivalent circuit (usually known as the Thevenin equivalent)從上式我們可以得出：流經(jīng)電源的

10、電流由負載電阻和電源內(nèi)阻共同決從上式我們可以得出：流經(jīng)電源的電流由負載電阻和電源內(nèi)阻共同決定。因此，在等效電路圖中，可以將內(nèi)阻定。因此，在等效電路圖中，可以將內(nèi)阻Rs表示成與負載電阻表示成與負載電阻R串聯(lián)，串聯(lián)，這種連接方式稱為串聯(lián)等效電路（即人們熟知的戴維南等效電路）這種連接方式稱為串聯(lián)等效電路（即人們熟知的戴維南等效電路）vDepending on the relative magnitude of the voltages across Rs and R, we can develop two modifications of the series equivalent circuit.

11、v根據(jù)根據(jù)Rs和和R兩端電壓的相對大小，我們可以推出兩種串聯(lián)等效電路的變兩端電壓的相對大小，我們可以推出兩種串聯(lián)等效電路的變換形式。換形式。New Words & Expressions:relative magnitude 相對值相對值 vIn the equivalent circuit of Fig.2.2(a), V is controlled by the load current and is decided by the difference between the source e.m.f. E and the voltage drop Vs.在圖在圖2.2所示的等效電

12、路中，所示的等效電路中，V由負載電由負載電流所控制，其值由電源電動勢流所控制，其值由電源電動勢E和電壓和電壓降降Vs之間的差值決定。之間的差值決定。vIf RsR and, for the same current, Vs is much greater than is much lesser than 如果如果RsR ，則對同一電流，則對同一電流，VsV (也就是電源工作在近似空載也就是電源工作在近似空載,即即開路狀態(tài)開路狀態(tài))，這樣可以忽略電源內(nèi)部的電壓降，令，這樣可以忽略電源內(nèi)部的電壓降，令Vs=RsI=0（非常近（非常近似），這樣就能得到圖似），這樣就能得到圖2.2(b)所示的等效電路

13、。所示的等效電路。vWhat we have got is a source whose internal resistance is zero (Rs=0). It is called an ideal voltage source. In diagrams it is symbolized by a circle with an arrow inside and the letter E beside it. When applied to a network, it is called a driving force or an impressed voltage source. v這時

14、我們得到一個內(nèi)阻為零這時我們得到一個內(nèi)阻為零(Rs=0)的電源，稱為理想電壓源。在電路圖的電源，稱為理想電壓源。在電路圖中用一個里面有一個箭頭，旁邊標有字母中用一個里面有一個箭頭，旁邊標有字母E的圓圈表示。當接入電路時，的圓圈表示。當接入電路時，稱為驅(qū)動勢或外加電壓源。稱為驅(qū)動勢或外加電壓源。New Words & Expressions:driving force 驅(qū)動勢驅(qū)動勢 impressed voltage source 外加電壓源外加電壓源vThe terminal voltage of an ideal voltage source is independent of th

15、e load resistance and is always equal to the e.m.f. E of the practical source it represents. Its external characteristic is a straight line parallel to the x-axis (the dotted line ab in Fig.1.3). New Words & Expressions:be independent of 與與無關(guān)無關(guān)理想電壓源的端電壓與負載電阻無關(guān)，理想電壓源的端電壓與負載電阻無關(guān)，其值恒等于它所表示的實際電源的電動其

16、值恒等于它所表示的實際電源的電動勢勢E。它的外特性是一條與。它的外特性是一條與x軸平行的直軸平行的直線（圖線（圖1.3中的虛線中的虛線ab）。）。vThe other equivalent circuit in Fig.2.3 may be called the parallel equivalent circuit (usually known as the Norton equivalent). It may also have two modifications. New Words & Expressions:parallel equivalent circuit 并聯(lián)等效電路

17、并聯(lián)等效電路Norton equivalent 諾頓等效電路諾頓等效電路另一個等效電路另一個等效電路(如圖如圖2.3所示所示)可稱為并聯(lián)等效電路，也就是人們所可稱為并聯(lián)等效電路，也就是人們所熟知的諾頓等效電路。等效電路可有兩種變換形式。熟知的諾頓等效電路。等效電路可有兩種變換形式。vTo prove this, we divide the right-and left-hand sides of Eq.(2.3) by Rs ：(eq.) or (eq.). vWhere J- current with the source short-circuited (with R=0)；vIs- cu

18、rrent equal to the ratio of the terminal source voltage to the source resistance; vI- load current.v為了證明這一點，我們將式為了證明這一點，我們將式(2.3)的左右兩邊分別除以的左右兩邊分別除以Rs ，得出，得出(公式公式)或或(公式公式)。其中。其中J是電源短路時的電流值是電源短路時的電流值(即即R=0時時)； 電流電流Is等于電源端電等于電源端電壓與內(nèi)阻的比值；壓與內(nèi)阻的比值；I是負載電流。是負載電流。New Words & Expressions:short circuit 短路短

19、路vEq.(2.4) is satisfied by the equivalent circuit of Fig.2.3(a) in which the source resistance Rs is placed in parallel with the load resistance R.v J=I+Is (2.4)公式公式(2.4)與圖與圖2.3(a)所示的等效電路所示的等效電路相符，圖中電源內(nèi)阻相符，圖中電源內(nèi)阻Rs與負載電阻與負載電阻相并聯(lián)。相并聯(lián)。vIf gsR and, for the same voltage across Rs and R, the current IsI (

20、that is, if the source is operating under conditions approaching a short-circuit), we may put Is=Vgs=0 (very nearly) and get the equivalent circuit of Fig.2.3(b).假如假如gsR 且且Rs和和R上的上的電壓相同，則電流電壓相同，則電流IsI 。(也就也就是電源近乎工作在短路狀態(tài)是電源近乎工作在短路狀態(tài))，因，因此可以令此可以令I(lǐng)s=Vgs=0 (非常接近非常接近)，這樣便得到如圖這樣便得到如圖2.3(b)所示的等所示的等效電路。效電路。

21、vWhat we have got is a source of zero internal conductance, gs=0(Rs=). It is called an ideal current source. When applied to a circuit, it is called a driving force or an impressed current source. The current of an ideal current source is independent of the load resistance R and is equal to E/Rs. Th

22、e external characteristic of an ideal current source is a straight line parallel to the y-axis (the dotted line cd in Fig.1.3)這是一個內(nèi)部電導這是一個內(nèi)部電導gs=0(Rs=)為零的電源為零的電源，稱為理想電流源。當應用稱為理想電流源。當應用在電路中，稱為驅(qū)動勢或外加電流源。理想電流源的電流與負載電阻在電路中，稱為驅(qū)動勢或外加電流源。理想電流源的電流與負載電阻R無關(guān)，其值等于無關(guān)，其值等于E/Rs。理想電流源的外特性是一條平行于。理想電流源的外特性是一條平行于y軸的直線

23、軸的直線（圖（圖1.3中的虛線中的虛線cd）vThus whether a real energy source may be represented by an ideal voltage source or an ideal current source depends on the relative magnitude of Rs and R. v因此，一個實際的電源是用理想電壓源還是用理想電流源表示，取決于因此，一個實際的電源是用理想電壓源還是用理想電流源表示，取決于Rs和和R的相對大小。的相對大小。vA real source, though, may be represented

24、by an ideal voltage or current source also when Rs is comparable with R. In such a case, either Rs, or gs=1/Rs (Fig.2.2(a) and Fig.2.3(a), respectively) should be removed from the source and lumped with R or g=1/R.v然而，當然而，當Rs與與R的值可以比擬時，一個實際的電源既可以用理想電的值可以比擬時，一個實際的電源既可以用理想電壓源表示，也可以用理想電流源來表示。在這種情況下，應將壓

25、源表示，也可以用理想電流源來表示。在這種情況下，應將Rs或或gs=1/Rs (分別如圖分別如圖2.2(a)和圖和圖2.3(a)所示所示)從電源中移出并與從電源中移出并與R或或g=1/R進行合并。進行合并。vIdeal voltage and current sources are active circuit elements, while resistances and conductance are passive elements. v理想電壓源和理想電流源是有源電路元件，而電阻和電導是無源電路元理想電壓源和理想電流源是有源電路元件，而電阻和電導是無源電路元件。件。New Words &

26、amp; Expressions:active circuit elements 有源電路元件有源電路元件passive circuit elements 無源電路元件無源電路元件vIn developing an equivalent circuit, it is important to take into account, as much as practicable, the known properties of each device and of the circuit as a whole. v在推導等效電路時，重要的是盡可能把每一裝置和整個電路的已知特性在推導等效電路時，重要

27、的是盡可能把每一裝置和整個電路的已知特性都考慮到。都考慮到。vLet us develop an equivalent circuit for a two-wire power transmission line of length I, diagrammatically shown in Fig.2.4(a). There is a generator of e.m.f. E and of source resistance Rs at the sending end and a load of resistance R2 at the receiving end of the line.N

28、ew Words & Expressions:power transmission line 輸電線輸電線sending end 發(fā)送端發(fā)送端 receiving end 接收端接收端下面推導如圖下面推導如圖2.4(a)所示的長度為所示的長度為l的兩根輸電線的等效電路。在線路的兩根輸電線的等效電路。在線路中，發(fā)送端有電動勢為中，發(fā)送端有電動勢為E，內(nèi)阻為，內(nèi)阻為Rs的電源，接收端有一個負載電阻的電源，接收端有一個負載電阻R2。vIt is obvious that the receiving end voltage will be less than the sending end o

29、ne by an amount equal to the voltage drop across the resistance of the line conductors. The current at the receiving end will be smaller than that at the sending end by an amount equal to the leakage current (due to imperfect insulation).v很顯然，接收端的電壓比發(fā)出端的電壓小一個導線上的壓降，接收端的很顯然，接收端的電壓比發(fā)出端的電壓小一個導線上的壓降，接收端

30、的電流比發(fā)出端的電流小一個漏電流電流比發(fā)出端的電流小一個漏電流(由于不完全絕緣由于不完全絕緣)。New Words & Expressions:leakage current 漏電流漏電流vLet each line conductor have a resistance R0/2 and a conductance g0 per unit length of the line. We divide the line into length elements dx (Fig.2.4(a). Then each length element will have associated wi

31、th it the combined resistance of the “go” and “return” wires, and a conductance g0dx。v令每一根導體單位長度的電阻為令每一根導體單位長度的電阻為R0/2，電位長度的電導為，電位長度的電導為g0。v我們將輸電線分成長度元我們將輸電線分成長度元dx(如圖如圖2.4(a)所示所示)。這樣，每一長度元將有。這樣，每一長度元將有之其相關(guān)的之其相關(guān)的 “去去”與與“來來”兩段的組合電阻兩段的組合電阻(eq.)和電導和電導g0dx 。xRxRxRd)2(d)2(d000vAccordingly, the entire lin

32、e may be represented by a network of elements each of resistance R0dx and conductance g0dx (Fig.2.4(b). The sending end generator in this network is represented by a voltage source (of e.m.f. E and of source resistance Rs).v因此，整條輸電線可用單元組成的網(wǎng)絡來表示，每一單元分別包括電阻因此，整條輸電線可用單元組成的網(wǎng)絡來表示，每一單元分別包括電阻R0dx和電導和電導g0dx，如圖如圖2.4(b)所示。該網(wǎng)絡中的發(fā)送端的發(fā)電機用一個所示。該網(wǎng)絡中的發(fā)送端的發(fā)電機用一個電壓源來表示電壓源來表示 (電動勢為電動勢為E、內(nèi)阻為、內(nèi)阻為RS)。vFrom this equivalent circuit we can find the voltage and current at any point on the line in terms of specified voltage and current at the sending or receiving end.v從這個等效電路中，我們能求出以發(fā)送端或接收端的電壓或電流的形式從這個等效電路中，我們能