The Transformer on load Introduction to DC Machines The Transformer on load It has been shown that a primary input voltage 1V can be transformed to any desired open-circuit secondary voltage 2E by a suitable choice of turns ratio. 2E is available for circulating a load current impedance. For the moment, a lagging power factor will be considered. The secondary current and the resulting ampere-turns 22NI will change the flux, tending to demagnetize the core, reduce mand with it 1E . Because the primary leakage impedance drop is so low, a small alteration to 1E will cause an appreciable increase of primary current from 0Ito a new value of 1I equal to ijXREV 111 / . The extra primary current and ampere-turns nearly cancel the whole of the secondary ampere-turns. This being so , the mutual flux suffers only a slight modification and requires practically the same net ampere-turns 10NIas on no load. The total primary ampere-turns are increased by an amount 22NI necessary to neutralize the same amount of secondary ampere-turns. In the vector equation , 102211 NININI ； alternatively, 221011 NININI . At full load, the current 0Iis only about 5% of the full-load current and so 1I is nearly equal to 122 / NNI . Because in mind that 2121 / NNEE , the input kVA which is approximately 11IE is also approximately equal to the output kVA, 22IE . The physical current has increased, and with in the primary leakage flux to which it is proportional. The total flux linking the primary ,111 mp, is shown unchanged because the total back e.m.f.,（ dtdNE /111 ） is still equal and opposite to 1V . However, there has been a redistribution of flux and the mutual component has fallen due to the increase of 1 with 1I . Although the change is small, the secondary demand could not be met without a mutual flux and e.m.f. alteration to permit primary current to change. The net flux slinking the secondary winding has been further reduced by the establishment of secondary leakage flux due to 2I , and this opposes m. Although mand 2 are indicated separately , they combine to one resultant in the core which will be downwards at the instant shown. Thus the secondary terminal voltage is reduced to dtdNVS /22 which can be considered in two components, i.e. dtdNdtdNVm / 2222 or vectorially 2222 IjXEV . As for the primary, 2 is responsible for a substantially constant secondary leakage inductance 222222 / NiN . It will be noticed that the primary leakage flux is responsible for part of the change in the secondary terminal voltage due to its effects on the mutual flux. The two leakage fluxes are closely related； 2 , for example, by its demagnetizing action on mhas caused the changes on the primary side which led to the establishment of primary leakage flux. If a low enough leading power factor is considered, the total secondary flux and the mutual flux are increased causing the secondary terminal voltage to rise with load. pis unchanged in magnitude from the no load condition since, neglecting resistance, it still has to provide a total back e.m.f. equal to 1V . It is virtually the same as 11 , though now produced by the combined effect of primary and secondary ampere-turns. The mutual flux must still change with load to give a change of 1E and permit more primary current to flow. 1E has increased this time but due to the vector combination with 1V there is still an increase of primary current. Two more points should be made about the figures. Firstly, a unity turns ratio has been assumed for convenience so that 21 EE . Secondly, the physical picture is drawn for a different instant of time from the vector diagrams which show 0m, if the horizontal axis is taken as usual, to be the zero time reference. There are instants in the cycle when primary leakage flux is zero, when the secondary leakage flux is zero, and when primary and secondary leakage flux is zero, and when primary and secondary leakage fluxes are in the same sense. The equivalent circuit already derived for the transformer with the secondary terminals open, can easily be extended to cover the loaded secondary by the addition of the secondary resistance and leakage reactance. Practically all transformers have a turns ratio different from unity although such an arrangement is sometimes employed for the purposes of electrically isolating one circuit from another operating at the same voltage. To explain the case where 21 NN the reaction of the secondary will be viewed from the primary winding. The reaction is experienced only in terms of the magnetizing force due to the secondary ampere-turns. There is no way of detecting from the primary side whether 2I is large and 2N small or vice versa, it is the product of current and turns which causes the reaction. Consequently, a secondary winding can be replaced by any number of different equivalent windings and load circuits which will give rise to an identical reaction on the primary .It is clearly convenient to change the secondary winding to an equivalent winding having the same number of turns 1N as the primary. With 2N changes to 1N , since the e.m.f.s are proportional to turns, 2212 )/( ENNE which is the same as 1E . For current, since the reaction ampere turns must be unchanged 1222 NINI must be equal to 22NI .i.e. 2122 )/( INNI . For impedance , since any secondary voltage V becomes VNN )/( 21 , and secondary current I becomes INN )/( 12 , then any secondary impedance, including load impedance, must become IVNNIV /)/(/ 221 . Consequently, 22212 )/( RNNR and 22212 )/( XNNX . If the primary turns are taken as reference turns, the process is called referring to the primary side. There are a few checks which can be made to see if the procedure outlined is valid. For example, the copper loss in the referred secondary winding must be the same as in the original secondary otherwise the primary would have to supply a different loss power. 222 RI must be equal to 222RI . ）222122122 /()/( NNRNNI does in fact reduce to 222RI . Similarly the stored magnetic energy in the leakage field )2/1( 2LI which is proportional to 22XI will be found to check as 22 XI . The referred secondary 2212221222 )/()/( IENNINNEIEk V A . The argument is sound, though at first it may have seemed suspect. In fact, if the actual secondary winding was removed physically from the core and replaced by the equivalent winding and load circuit designed to give the parameters 1N , 2R , 2X and 2I , measurements from the primary terminals would be unable to detect any difference in secondary ampere-turns, kVA demand or copper loss, under normal power frequency operation. There is no point in choosing any basis other than equal turns on primary and referred secondary, but it is sometimes convenient to refer the primary to the secondary winding. In this case, if all the subscript 1s are interchanged for the subscript 2s, the necessary referring constants are easily found； e.g. 21 RR , 21 XX ； similarly 12 RR and 12 XX . The equivalent circuit for the general case where 21 NN except that mrhas been added to allow for iron loss and an ideal lossless transformation has been included before the secondary terminals to return 2V to 2V .All calculations of internal voltage and power losses are made before this ideal transformation is applied. The behaviour of a transformer as detected at both sets of terminals is the same as the behaviour detected at the corresponding terminals of this circuit when the appropriate parameters are inserted. The slightly different representation showing the coils 1N and 2N side by side with a core in between is only used for convenience. On the transformer itself, the coils are , of course , wound round the same core. Very little error is introduced if the magnetising branch is transferred to the primary terminals, but a few anomalies will arise. For example ,the current shown flowing through the primary impedance is no longer the whole of the primary current. The error is quite small since 0Iis usually such a small fraction of 1I . Slightly different answers may be obtained to a particular problem depending on whether or not allowance is made for this error. With this simplified circuit, the primary and referred secondary impedances can be added to give: 221211 )/(Re NNRR and 221211 )/( NNXXXe It should be pointed out that the equivalent circuit as derived here is only valid for normal operation at power frequencies； capacitance effects must be taken into account whenever the rate of change of voltage would give rise to appreciable capacitance currents, dtCdVIc /. They are important at high voltages and at frequencies much beyond 100 cycles/sec. A further point is not the only possible equivalent circuit even for power frequencies .An alternative , treating the transformer as a three-or four-terminal network, gives rise to a representation which is just as accurate and has some advantages for the circuit engineer who treats all devices as circuit elements with certain transfer properties. The circuit on this basis would have a turns ratio having a phase shift as well as a magnitude change, and the impedances would not be the same as those of the windings. The circuit would not explain the phenomena within the device like the effects of saturation, so for an understanding of internal behaviour . There are two ways of looking at the equivalent circuit: (a) viewed from the primary as a sink but the referred load impedance connected across 2V ,or (b) viewed from the secondary as a source of constant voltage 1V with internal drops due to 1Re and 1Xe . The magnetizing branch is sometimes omitted in this representation and so the circuit reduces to a generator producing a constant voltage 1E (actually equal to 1V ) and having an internal impedance jXR (actually equal to 11Re jXe ). In either case, the parameters could be referred to the secondary winding and this may save calculation time . The resistances and reactances can be obtained from two simple light load tests. Introduction to DC Machines DC machines are characterized by their versatility. By means of various combination of shunt, series, and separately excited field windings they can be designed to display a wide variety of volt-ampere or speed-torque characteristics for both dynamic and steadystate operation. Because of the ease with which they can be controlled , systems of DC machines are often used in applications requiring a wide range of motor speeds or precise control of motor output. The essential features of a DC machine are shown schematically. The stator has salient poles and is excited by one or more field coils. The air-gap flux distribution created by the field winding is symmetrical about the centerline of the field poles. This axis is called the field axis or direct axis. As we know , the AC voltage generated in each rotating armature coil is converted to DC in the external armature terminals by means of a rotating commutator and stationary brushes to which the armature leads are connected. The commutator-brush combination forms a mechanical rectifier, resulting in a DC armature voltage as well as an armature m.m.f. wave which is fixed in space. The brushes are located so that commutation occurs when the coil sides are in the neutral zone , midway between the field poles. The axis of the armature m.m.f. wave then in 90 electrical degrees from the axis of the field poles, i.e., in the quadrature axis. In the schematic representation the brushes are shown in quarature axis because this is the position of the coils to which they are connected. The armature m.m.f. wave then is along the brush axis as shown. (The geometrical position of the brushes in an actual machine is approximately 90 electrical degrees from their position in the schematic diagram because of the shape of the end connections to the commutator.) The magnetic torque and the speed voltage appearing at the brushes are independent of the spatial waveform of the flux distribution； for convenience we shall continue to assume a sinusoidal flux-density wave in the air gap. The torque can then be found from the magnetic field viewpoint. The torque can be expressed in terms of the interaction of the direct-axis air-gap flux per pole dand the space-fundamental component 1aFof the armature m.m.f. wave . With the brushes in the quadrature axis, the angle between these fields is 90 electrical degrees, and its sine equals unity. For a P pole machine 12)2(2 ad FPT In which the minus sign has been dropped because the positive direction of the torque can be determined from physical reasoning. The space fundamental 1aFof the sawtooth armature m.m.f. wave is 8/ 2 times its peak. Substitution in above equation then gives adaada iKimPCT 2 Where ai=current in external armature circuit； aC=total number of conductors in armature winding； m =number of parallel paths through winding； And mPCK aa 2Is a constant fixed by the design of the winding. The rectified voltage generated in the armature has already been discussed before for an elementary single-coil armature. The effect of distributing the winding in several slots is shown in figure ,in which each of the rectified sine waves is the voltage generated in one of the coils, commutation taking place at the moment when the coil sides are in the neutral zone. The generated voltage as observed from the brushes is the sum of the rectified voltages of all the coils in series between brushes and is shown by the rippling line labeled aein figure. With a dozen or so commutator segments per pole, the ripple becomes very small and the average generated voltage observed from the brushes equals the sum of the average values of the rectified coil voltages. The rectified voltage aebetween brushes, known also as the speed voltage, is mdamdaa WKWmPCe 2 Where aKis the design constant. The rectified voltage of a distributed winding has the same average value as that of a concentrated coil. The difference is that the ripple is greatly reduced. From the above equations, with all variable expressed in SI units: maa Twie This equation simply says that the instantaneous electric power associated with the speed voltage equals the instantaneous mechanical power associated with the magnetic torque , the direction of power flow being determined by whether the machine is acting as a motor or generator. The direct-axis air-gap flux is produced by the combined m.m.f. ffiNof the field windings, the flux-m.m.f. characteristic being the magnetization curve for the particular iron geometry of the machine. In the magnetization curve, it is assumed that the armature m.m.f. wave is perpendicular to the field axis. It will be necessary to reexamine this assumption later in this chapter, where the effects of saturation are investigated more thoroughly. Because the armature e.m.f. is proportional to flux times speed, it is usually more convenient to express the magnetization curve in terms of the armature e.m.f. 0aeat a constant speed 0mw. The voltage aefor a given flux at any other speed mwis proportional to the speed,i.e. 00 amma ewwe Figure shows the magnetization curve with only one field winding excited. This curve can easily be obtained by test methods, no knowledge of any design details being required. Over a fairly wide range of excitation the reluctance of the iron is negligible compared with that of the air gap. In this region the flux is linearly proportional to the total m.m.f. of the field windings, the constant of proportionality being the direct-axis air-gap permeance. The outstanding advantages of DC machines arise from the wide variety of operating characteristics which can be obtained by selection of the method of excitation of the field windings. The field windings may be separately excited from an external DC source, or they may be self-excited； i.e., the machine may supply its own excitation. The method of excitation profoundly influences not only the steady-state characteristics, but also the dynamic behavior of the machine in control systems. The connection diagram of a separately excited generator is given. The required field current is a very small fraction of the rated armature current. A small amount of power in the field circuit may control a relatively large amount of power in the armature circuit； i.e., the generator is a power amplifier. Separately excited generators are often used in feedback control systems when control of the armature voltage over a wide range is required. The field windings of self-excited generators may be supplied in three different ways. The field may be connected in series with the armature, resulting in a shunt generator, or the field may be in two sections, one of which is connected in series and the other in shunt with the armature, resulting in a compound generator. With self-excited generators residual magnetism must be present in the machine iron to get the self-excitation process started. In the typical steady-state volt-ampere characteristics, constant-speed prime movers being assumed. The relation between the steady-state generated e.m.f. aEand the terminal voltage tVis aaat RIEV Where aIis the armature current output and aRis the armature circuit resistance. In a generator, aEis large than tV； and the electromagnetic torque T is a countertorque opposing rotation. The terminal voltage of a separately excited generator decreases slightly with increase in the load current, principally because of the voltage drop in the armature resistance. The field current of a series generator is the same as the load current, so that the air-gap flux and hence the voltage vary widely with load. As a consequence, series generators are not often used. The voltage of shunt generators drops off somewhat with load. Compound generators are normally connected so that the m.m.f. of the series winding aids that of the shunt winding. The advantage is that through the action of the series winding the flux per pole can increase with load, resulting in a voltage output which is nearly constant. Usually, shunt winding contains many turns of comparatively heavy conductor because it must carry the full armature current of the machine. The voltage of both shunt and compound generators can be controlled over reasonable limits by means of rheostats in the shunt field. Any of the methods of excitation used for generators can also be used for motors. In the typical steady-state speed-torque characteristics, it is assumed that the motor terminals are supplied from a constant-voltage source. In a motor the relation between the e.m.f. aEgenerated in the armature and the terminal voltage tVis aaat RIEV Where aIis now the armature current input. The generated e.m.f. aEis now smaller than the terminal voltage tV, the armature current is in the opposite direction to that in a motor, and the electromagnetic torque is in the direction to sustain rotation of the armature. In shunt and separately excited motors the field flux is nearly constant. Consequently, increased torque must be accompanied by a very nearly proportional increase in armature current and hence by a small decrease in counter e.m.f. to allow this increased current through the small armature resistance. Since counter e.m.f. is determined by flux and speed, the speed must drop slightly. Like the squirrel-cage induction motor ,the shunt motor is substantially a constant-speed motor having about 5 percent drop in speed from no load to full load. Starting torque and maximum torque are limited by the armature current that can be commutated successfully. An outstanding advantage of the shunt motor is ease of speed control. With a rheostat in the shunt-field circuit, the field current and flux per pole can be varied at will, and variation of flux causes the inverse variation of speed to maintain counter e.m.f. approximately equal to the impressed terminal voltage. A maximum speed range of about 4 or 5 to 1 can be obtained by this method, the limitation again being commutating conditions. By variation of the impressed armature voltage, very wide speed ranges can be obtained. In the series motor, increase in load is accompanied by increase in the armature current and m.m.f. and the stator field flux (provided the iron is not completely saturated). Because flux increases with load, speed must drop in order to maintain the balance between impressed voltage and counter e.m.f.； moreover, the increase in armature current caused by increased torque is smaller than in the shunt motor because of the increased flux. The series motor is therefore a varying-speed motor with a markedly drooping speed-load characteristic. For applications requiring heavy torque overloads, this characteristic is particularly advantageous because the corresponding power overloads are held to more reasonable values by the associated speed drops. Very favorable starting characteristics also result from the increase in flux with increased armature current. In the compound motor the series field may be connected either cumulatively, so that its.m.m.f.adds to that of the shunt field, or differentially, so that it opposes. The differential connection is very rarely used. A cumulatively compounded motor has speed-load characteristic intermediate between those of a shunt and a series motor, the drop of speed with load depending on the relative number of ampere-turns in the shunt and series fields. It does not have the disadvantage of very high light-load speed associated with a series motor, but it retains to a considerable degree the advantages of series excitation. The application advantages of DC machines lie in the variety of performance characteristics offered by the possibilities of shunt, series, and compound excitation. Some of these characteristics have been touched upon briefly in this article. Still greater possibilities exist if additional sets of brushes are added so that other voltages can be obtained from the commutator. Thus the versatility of DC machine systems and their adaptability to control, both manual and automatic, are their outstanding features. 負(fù)載運(yùn)行的變壓器 及 直流電機(jī)導(dǎo)論 負(fù)載運(yùn)行的變壓器 通過選擇合適的匝數(shù)比，一次側(cè)輸入電壓 1V 可任意轉(zhuǎn)換成所希望的二次側(cè)開路電壓 2E 。 2E可用于產(chǎn)生負(fù)載電流， 該電流的幅值和功率因數(shù)將由而次側(cè)電路的阻抗決定。現(xiàn)在，我們要討論一種滯后功率因數(shù)。二次側(cè)電流及其總安匝 22NI 將影響磁通，有一種對(duì)鐵芯產(chǎn)生去磁、減小m和 1E 的趨向。因?yàn)橐淮蝹?cè)漏阻抗壓降如此之小，所以 1E 的微小變化都將導(dǎo)致一次側(cè)電流增加很大，從0I增大至一個(gè)新值 ijXREVI 1111 /。增加的一次側(cè)電流和磁勢(shì)近似平衡了全部二次側(cè)磁勢(shì)。這樣的話，互感磁通只經(jīng)歷很小的變化，并且實(shí)際上只需要與空載時(shí)相同的凈磁勢(shì)10NI。一次側(cè)總磁勢(shì)增加了 22NI ，它是平衡同量的二次側(cè)磁勢(shì)所必需的。在向量方程中，102211 NININI ，上式也可變換成221011 NININI 。滿載時(shí)，電流0I只約占滿載電流的 5%，因而 1I 近似等于 122 / NNI 。記住 2121 / NNEE ，近似等于 11IE 的輸入容量也就近似等于輸出容量 22IE 。 一次側(cè)電流已增大，隨之與之成正比的一次側(cè)漏磁通也增大。交鏈一次繞組的總磁通111 mp沒有變化，這是因?yàn)榭偡措妱?dòng)勢(shì) dtdNE /111 仍然與 1V 相等且反向 。然而此時(shí)卻存在磁通的重新分配，由于 1 隨 1I 的增加而增加，互感磁通分量已經(jīng)減小。盡管變化很小，但是如果沒有互感磁通和電動(dòng)勢(shì)的變化來允許一次側(cè)電流變化，那么二次側(cè)的需求就無法滿足。交鏈二次繞組的凈磁通s由于 2I 產(chǎn)生的二次側(cè)漏磁通（其與m反相）的建立而被進(jìn)一步削弱。盡管圖中m和 2 是分開表示的，但它們?cè)阼F芯中是一個(gè)合成量，該合成量在圖示中的瞬時(shí)是向下的。這樣，二次側(cè)端電壓降至 dtdNVS /22 ，它可被看成兩個(gè)分量，即dtdNdtdNV m / 2222 ，或者向量形式 2222 IjXEV 。與一次側(cè)漏磁通一樣， 2的作用也用一個(gè)大體為常數(shù)的漏電感 222222 / NiN 來表征。要注意的是，由于它 對(duì)互感磁通的作用，一次側(cè)漏磁通對(duì)于二次側(cè)端電壓的變化產(chǎn)生部分影響。這兩種漏磁通，緊密相關(guān)；例如， 2 對(duì)m的去磁作用引起了一次側(cè)的變化，從而導(dǎo)致了一次側(cè)漏磁通的產(chǎn)生。 如果我們討論一個(gè)足夠低的超前功率因數(shù)，二次側(cè)總磁通和互感磁通都會(huì)增加，從而使得二次側(cè)端電壓隨負(fù)載增加而升高。在空載情形下，如果忽略電阻，p幅值大小不變，因?yàn)樗蕴峁┮粋€(gè)等于 1V 的反總電動(dòng)勢(shì)。盡管現(xiàn)在p是一次側(cè)和二次側(cè)磁勢(shì)的共同作用產(chǎn)生的，但它實(shí)際上與 11 相同?；ジ写磐ū仨毴噪S負(fù)載變化而變化以改變 1E ，從而產(chǎn)生更大的一次側(cè)電流。此時(shí)1E 的幅值已經(jīng)增大，但由于 1E 與 1V 是向量合成，因此一次側(cè)電流仍然是增大的。 從上述圖中，還應(yīng)得出兩 點(diǎn)：首先，為方便起見已假設(shè)匝數(shù)比為 1，這樣可使 21 EE 。其次，如果橫軸像通常取的話，那么向量圖是以 0m為零時(shí)間參數(shù)的，圖中各物理量時(shí)間方向并不是該瞬時(shí)的。在周期性交變中，有一次側(cè)漏磁通為零的瞬時(shí)，也有二次側(cè)漏磁通為零的瞬時(shí)，還有它們處于同一方向的瞬時(shí)。 已經(jīng)推出的變壓器二次側(cè)繞組端開路的等效電路，通過加上二次側(cè)電阻和漏抗便可很容易擴(kuò)展成二次側(cè)負(fù)載時(shí)的等效電路。 實(shí)際中所有的變壓器的匝 數(shù)比都不等于 1，盡管有時(shí)使其為 1 也是為了使一個(gè)電路與另一個(gè)在相同電壓下運(yùn)行的電路實(shí)現(xiàn)電氣隔離。為了分析 21 NN 時(shí)的情況，二次側(cè)的反應(yīng)得從一次側(cè)來看，這種反應(yīng)只有通過由二次側(cè)的磁勢(shì)產(chǎn)生磁場(chǎng)力來反應(yīng)。我們從一次側(cè)無法判斷是 2I 大， 2N小，還是 2I 小， 2N 大，正是電流和匝數(shù)的乘積在產(chǎn)生作用。因此，二次側(cè)繞組可用 任意個(gè)在一次側(cè)產(chǎn)生相同匝數(shù) 1N 的等效繞組是方便的。 當(dāng) 2N 變換成 1N ，由于電動(dòng)勢(shì)與匝數(shù)成正比，所以 2212 )/( ENNE ，與 1E 相等。 對(duì)于電流，由于對(duì)一次側(cè)作用的安匝數(shù)必須保持不變，因此 221222 NININI ，即2122 )/( INNI 。 對(duì)于阻抗，由于二次側(cè)電壓 V 變成 VNN )/( 21 ，電流 I 變?yōu)?INN )/( 12 ，因此阻抗值，包括負(fù)載阻抗必然變?yōu)?IVNNIV /)/(/ 221 。因此， 22212 )/( RNNR ， 22212 )/( XNNX 。 如果將一次側(cè)匝數(shù)作為參考匝數(shù)，那么這種過程稱為往一次側(cè)的折算。 我們可以用一些方法來驗(yàn)證上述折算過程是否正確。 例如，折算后的二次繞組的 銅耗必須與原二次繞組銅耗相等，否則一次側(cè)提供給其損耗的功率就變了。 222 RI 必須等于 222RI ，而 ）222122122 /()/( NNRNNI 事實(shí)上確實(shí)簡(jiǎn)化成了222RI 。 類似地，與 222XI 成比例的漏磁場(chǎng)的磁場(chǎng)儲(chǔ)能 )2/1( 2LI ，求出后驗(yàn)證與 22 XI 成正比。折算后的二次側(cè) 2212221222 )/()/( IENNINNEIEk V A 。 盡管看起來似乎不可理解，事實(shí)上這種論點(diǎn)是可靠的。實(shí)際上，如果我們將實(shí)際的二次繞組當(dāng)真從鐵芯上移開，并用一個(gè)參數(shù)設(shè)計(jì)成 1N ， 2R ， 2X ， 2I 的等效繞組和負(fù)載電路替換，在正常電網(wǎng)頻率運(yùn)行時(shí)，從一次側(cè)兩端無法判斷二次側(cè)的磁勢(shì)、所需容量及銅耗與前有何差別。 在選擇折算基準(zhǔn)時(shí)，無非是將一次側(cè)與折算后的二次側(cè)匝數(shù)設(shè)為相等，除 此之外再?zèng)]有什么更要緊的了。但有時(shí)將一次側(cè)折算到二次側(cè)倒是方便的，在這種情況下，如果所有下標(biāo)“ 1”的量都變換成了下標(biāo)“ 2”的量，那么很容易得到必需的折算系數(shù)，例如。值得注意的是，對(duì)于一臺(tái)實(shí)際的變壓器， 21 RR ， 21 XX ；同樣地 12 RR ， 12 XX 。 21 NN 的通常情形時(shí)的等效電路，它除了為了考慮鐵耗而引入了 mr ，且為了將 2V 折算回2V 而在二次側(cè)兩端引入了一理想的無損耗轉(zhuǎn)換外，其他方面是一樣的。在運(yùn)用這種理想轉(zhuǎn)換之前，內(nèi)部電壓和功率損耗已進(jìn)行了計(jì)算。當(dāng)在電路中選擇了適當(dāng)?shù)膮?shù)時(shí)，在一、二次側(cè)兩端測(cè)得的變壓器運(yùn)行情況與在該電路相應(yīng)端所測(cè)得的請(qǐng)況是完全一致的。將 1N 線圈和 2N 線圈并排放置在一個(gè)鐵芯的兩邊，這一點(diǎn)與實(shí)際情況之間 的差別僅僅是為了方便。當(dāng)然，就變壓器本身來說，兩線圈是繞在同一鐵芯柱上的。 如果將激磁支路移至一次繞組端口，引起的誤差很小，但一些不合理的現(xiàn)象又會(huì)發(fā)生。例如，流過一次側(cè)阻抗的電流不再是整個(gè)一次側(cè)電流。由于0I通常只是 1I 的很小一部分，所有誤差相當(dāng)小。對(duì)一個(gè)具體問題可否允許有細(xì)微差別的回答取決于是否允許這種誤差的存在。對(duì)于這種簡(jiǎn)化電路，一次側(cè)和折算后二次側(cè)阻抗可相加，得 221211 )/(Re NNRR 和221211 )/( NNXXXe 需要指出的是，在此得到的等效電路僅僅適用于電網(wǎng)頻率下的正常運(yùn)行；一旦電壓變化率產(chǎn)生相當(dāng)大的電容電流 dtCdVIc /時(shí)必須考慮電容效應(yīng)。這對(duì)于高電壓和頻率超過 100Hz 的情形是很重要的。其次，即使是對(duì)于電網(wǎng)頻率也并非唯一可行的等效電路。另一種形式是將變壓器看成一個(gè)三端或四端網(wǎng)絡(luò)，這樣便產(chǎn)生一個(gè)準(zhǔn)確的表達(dá)，它對(duì)于那些把所有裝置看成是具有某種傳遞性能的電路元件的工程師來說是方便的。以此為分析基礎(chǔ)的電路會(huì)擁有一個(gè)既產(chǎn)生電壓大小的變化，也產(chǎn)生相位移的 匝比，其阻抗也會(huì)與繞組的阻抗不同。這種電路無法解釋變壓器內(nèi)類似飽和效應(yīng)等現(xiàn)象。 等效電路有兩個(gè)入端口形式： （ a） 從一次側(cè)看為一個(gè) U 形電路，其折合后的負(fù)載阻抗的端電壓為 2V ； （ b） 從二次側(cè)看為一其值為 1V ，且伴有由 1Re 和 1Xe 引起內(nèi)壓降的恒壓源。在這種電路中有時(shí)可省略激磁支路，這樣電路簡(jiǎn)化為一臺(tái)產(chǎn)生恒值電壓 1E （ 實(shí)際上等于 1V ）并帶有阻抗jXR （實(shí)際上等于 11Re jXe ）的發(fā)電機(jī)。 在上述兩種情況下，參數(shù)都可折算到二次繞組，這樣可減小計(jì)算時(shí)間。 其電阻和電抗值可通過兩種簡(jiǎn)單的輕載試驗(yàn)獲得。 直流電機(jī)導(dǎo)論 直流電機(jī)以其多功用性而形成了鮮明的特征。通過并勵(lì)、串勵(lì)和特勵(lì)繞組的各種不同組合，直流電機(jī)可設(shè)計(jì)成在動(dòng)態(tài)和穩(wěn)態(tài)運(yùn)行時(shí)呈現(xiàn)出寬廣范圍變化的伏 -安或速度 -轉(zhuǎn)矩特性。由于直流電機(jī)易于控制，因此該系統(tǒng)用于要求電動(dòng) 機(jī)轉(zhuǎn)速變化范圍寬或能精確控制電機(jī)輸出的場(chǎng)合。 定子上有凸極，由一個(gè)或一個(gè)以上勵(lì)磁線圈勵(lì)磁。勵(lì)磁繞組產(chǎn)生的氣隙通以磁極中心線為軸線對(duì)稱分布，這條軸線稱為磁場(chǎng)軸線或直軸。 我們知道，每個(gè)旋轉(zhuǎn)的電樞繞組中產(chǎn)生的交流電壓，經(jīng)由一與電樞連接的旋轉(zhuǎn)的換向器和靜止的電刷，在電樞繞組出線端轉(zhuǎn)換成直流電壓。換向器一電刷的組合構(gòu)成機(jī)械整流器，它產(chǎn)生一直流電樞電壓和一在空間固定的電樞磁勢(shì)波形。電刷的放置應(yīng)使換向線圈也處于磁極中性區(qū)，即兩磁極之間。這樣，電樞磁勢(shì)波形的軸線與磁極軸線相差 90電角度，即位于交軸上。在示意圖中，電刷位 于交軸上，因?yàn)榇颂幷桥c其相連的線圈的位置。這樣，如圖所示電樞磁勢(shì)波的軸線也是沿著電刷軸線