电气专业外文翻译 - 负载运行的变压器及直流电机导论

The Transformer on load﹠Introduction to DC Machines

The Transformer on load

It has been shown that a primary input voltage V1 can be transformed to any desired open-circuit secondary voltage E2by a suitable choice of turn’s ratio. E2 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

I2N2 will change the flux, tending to demagnetize the core, reduce ?m and with it

E1. Because the primary leakage impedance drop is so low, a small alteration to E1

will cause an appreciable increase of primary current from I0 to a new value of I1 equal to ?V1?E1?/?R1?jXi?. 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

I0N1 as on no load. The total primary ampere-turns are increased by an amount

I2N2 necessary to neutralize the same amount of secondary ampere-turns. In the

vector equation,I1N1?I2N2?I0N1; alternatively, I1N1?I0N1?I2N2. At full load, the current I0 is only about 5% of the full-load current and so I1 is nearly equal toI2N2/N1. Because in mind that E1?E2N1/N2, the input kVA which is approximately E1I1 is also approximately equal to the output kVA, E2I2.

The physical current has increased, and with in the primary leakage flux to which it is proportional. The total flux linking the primary,?p??m??1??11 is shown unchanged because the total back e.m.f., （E1?N1d?1/dt）is still equal and

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opposite to V1. However, there has been a redistribution of flux and the mutual component has fallen due to the increase of ?1 with I1. 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 I2, and this opposes ?m. Although ?m and ?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 V2??N2d?S/dt which can be considered in two components, i.e.

V2??N2d?m/dt?N2d?2/dtor vectorially

V2?E2?jX2I2. As for the primary, ?2 is responsible for a substantially constant

2?2. It will be noticed that the primary secondary leakage inductance N2?2/i2?N2leakage 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 ?m has 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.

?p is unchanged in magnitude from the no load condition since, neglecting

resistance, it still has to provide a total back e.m.f. equal to V1. 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 E1 and permit more primary current to flow. E1 has increased this time

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but due to the vector combination with V1 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 E1?E2'. Secondly, the physical picture is drawn for a different instant of time from the vector diagrams which show

?m?0, 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 turn’s 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

N1?N2 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

I2 is large and N2 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 N1 as the primary.

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With N2 changes to N1, since the e.m.f.s are proportional to turns,

E2'?(N1/N2)E2 which is the same as E1.

For current, since the reaction ampere turns must be unchanged I2'N2'?I2'N1 must be equal to I2N2.i.e. I2?(N2/N1)I2.

For impedance, since any secondary voltage V becomes (N1/N2)V, and secondary current Ibecomes (N2/N1)I, then any secondary impedance, including load

impedance,

must

become

V'/I'?(N1/N2)2V/I. Consequently,

R2'?(N1/N2)2R2 andX2'?(N1/N2)2X2 .

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.

22I2'2R2' Must be equal to

2I2R2.

2(I2?N2/N1)2(R2?N1/N2）R2. does in fact reduce to I2Similarly the stored magnetic energy in the leakage field (1/2LI2) which is proportional to I2'X2 will be found to check as I2'X2'. The referred secondary

kVA?E2'I2'?E2(N1/N2)?I2(N2/N1)?E2I2.

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 N1,R2',X2'and

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I2', 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 1’s are interchanged for the subscript 2’s, the necessary referring constants are easily found; e.g.

R1?R2,X1'?X2; similarlyR2?R1 and X2'?X1.

''The equivalent circuit for the general case where N1?N2 except that rm has been added to allow for iron loss and an ideal lossless transformation has been included before the secondary terminals to return V2' to V2.All calculations of internal voltage and power losses are made before this ideal transformation is applied. The behavior of a transformer as detected at both sets of terminals is the same as the behavior detected at the corresponding terminals of this circuit when the appropriate parameters are inserted. The slightly different representation showing the coils

N1and N2 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 magnetizing 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 I0 is usually such a small fraction ofI1. 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:

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Re1?R1?R2(N1/N2)2 And Xe1?X1?X2(N1/N2)2

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,Ic?CdV/dt. 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 behavior.

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 V2',or

(b) Viewed from the secondary as a source of constant voltage V1 with internal drops due to Re1 andXe1. The magnetizing branch is sometimes omitted in this representation and so the circuit reduces to a generator producing a constant voltage

E1(actually equal to V1) and having an internal impedance R?jX (actually equal

to Re1?jXe1).

In either case, the parameters could be referred to the secondary winding and this may save calculation time.

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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 steady state 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 quadrature 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

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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 ?d and the space-fundamental component Fa1 of 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

T??P()2?dFa1 22In which the minus sign has been dropped because the positive direction of the torque can be determined from physical reasoning. The space fundamental Fa1 of the saw tooth armature m.m.f. wave is 8/?2 times its peak. Substitution in above equation then gives

T?PCa?dia?Ka?dia 2?mWhere ia=current in external armature circuit;

Ca=total number of conductors in armature winding; m=number of parallel paths through winding; And

Ka?PCa 2?mIs 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

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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 ea in 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 ea between brushes, known also as the speed voltage, is

ea?PCa?dWm?Ka?dWm 2?mWhere Ka is 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: eaia?Twm

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. ?Nfif of 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

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times speed, it is usually more convenient to express the magnetization curve in terms of the armature e.m.f. ea0at a constant speedwm0. The voltage ea for a given flux at any other speed wm is proportional to the speed,i.e.

ea?wmea0 wm0Figure 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

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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. Ea and the terminal voltage Vtis

Vt?Ea?IaRa

Where Iathe armature is current output and Ra is the armature circuit resistance. In a generator, Ea is large than Vt; and the electromagnetic torque T is a counter torque 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

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terminals are supplied from a constant-voltage source. In a motor the relation between the e.m.f. Ea generated in the armature and the terminal voltage Vt is

Vt?Ea?IaRa

Where Ia is now the armature current input. The generated e.m.f. Ea is now smaller than the terminal voltage Vt, 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

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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.

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负载运行的变压器及直流电机导论

负载运行的变压器

通过选择合适的匝数比，一次侧输入电压V1可任意转换成所希望的二次侧开路电压E2。E2可用于产生负载电流，该电流的幅值和功率因数将由而次侧电路的阻抗决定。现在，我们要讨论一种滞后功率因数。二次侧电流及其总安匝

I2N2将影响磁通，有一种对铁芯产生去磁、减小?m和E1的趋向。因为一次侧

漏阻抗压降如此之小，所以E1的微小变化都将导致一次侧电流增加很大，从I0增大至一个新值I1??V1?E1?/?R1?jXi?。增加的一次侧电流和磁势近似平衡了全部二次侧磁势。这样的话，互感磁通只经历很小的变化，并且实际上只需要与空载时相同的净磁势I0N1。一次侧总磁势增加了I2N2，它是平衡同量的二次侧磁势所必需的。在向量方程中，I1N1?I2N2?I0N1，上式也可变换成

I1N1?I0N1?I2N2。满载时，电流I0只约占满载电流的5%，因而I1近似等于

I2N2/N1。记住E1?E2N1/N2，近似等于E1I1的输入容量也就近似等于输出容

量E2I2。

一次侧电流已增大，随之与之成正比的一次侧漏磁通也增大。交链一次绕组的总磁通?p??m??1??11没有变化，这是因为总反电动势E1?N1d?1/dt仍然与V1相等且反向。然而此时却存在磁通的重新分配，由于?1随I1的增加而增加，互感磁通分量已经减小。尽管变化很小，但是如果没有互感磁通和电动势的变化来允许一次侧电流变化，那么二次侧的需求就无法满足。交链二次绕组的净磁通?s由于I2产生的二次侧漏磁通（其与?m反相）的建立而被进一步

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削弱。尽管图中?m和?2是分开表示的，但它们在铁芯中是一个合成量，该合成量在图示中的瞬时是向下的。这样，二次侧端电压降至V2??N2d?S/dt，它可被看成两个分量，即V2??N2d?m/dt?N2d?2/dt，或者向量形式

V2?E2?jX2I2。与一次侧漏磁通一样，?2的作用也用一个大体为常数的漏电

2?2来表征。要注意的是，由于它对互感磁通的作用，一次侧漏感N2?2/i2?N2磁通对于二次侧端电压的变化产生部分影响。这两种漏磁通，紧密相关；例如，

?2对?m的去磁作用引起了一次侧的变化，从而导致了一次侧漏磁通的产生。

如果我们讨论一个足够低的超前功率因数，二次侧总磁通和互感磁通都会增加，从而使得二次侧端电压随负载增加而升高。在空载情形下，如果忽略电阻，?p幅值大小不变，因为它仍提供一个等于V1的反总电动势。尽管现在?p是一次侧和二次侧磁势的共同作用产生的，但它实际上与?11相同。互感磁通必须仍随负载变化而变化以改变E1，从而产生更大的一次侧电流。此时E1的幅值已经增大，但由于E1与V1是向量合成，因此一次侧电流仍然是增大的。

从上述图中，还应得出两点：首先，为方便起见已假设匝数比为1，这样可使E1?E2'。其次，如果横轴像通常取的话，那么向量图是以?m?0为参数的，图中各物理量时间方向并不是该瞬时的。在周期性交变中，有一次侧漏磁通为零的瞬时，也有二次侧漏磁通为零的瞬时，还有它们处于同一方向的瞬时。

已经推出的变压器二次侧绕组端开路的等效电路，通过加上二次侧电阻和漏抗便可很容易扩展成二次侧负载时的等效电路。

实际中所有的变压器的匝数比都不等于1，尽管有时使其为1也是为了使一个电路与另一个在相同电压下运行的电路实现电气隔离。为了分析N1?N2时的

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情况，二次侧的反应得从一次侧来看，这种反应只有通过由二次侧的磁势产生磁场力来反应。我们从一次侧无法判断是I2大，N2小，还是I2小，N2大，正是电流和匝数的乘积在产生作用。因此，二次侧绕组可用任意个在一次侧产生相同匝数N1的等效绕组是方便的。

当N2变换成N1，由于电动势与匝数成正比，所以E2'?(N1/N2)E2，与E1相等。

对于电流，由于对一次侧作用的安匝数必须保持不变，因此

I2'N2'?I2'N1?I2N2，即I2?(N2/N1)I2。

对于阻抗，由于二次侧电压V变成(N1/N2)V，电流I变为(N2/N1)I，因此阻抗值，包括负载阻抗必然变为V'/I'?(N1/N2)2V/I。因此，

R2'?(N1/N2)2R2，X2'?(N1/N2)2X2。

如果将一次侧匝数作为参考匝数，那么这种过程称为往一次侧的折算。 我们可以用一些方法来验证上述折算过程是否正确。

例如，折算后的二次绕组的铜耗必须与原二次绕组铜耗相等，否则一次侧

2R2，而提供给其损耗的功率就变了。I2'2R2'必须等于I22(I2?N2/N1)2(R2?N1/N2）R2。 事实上确实简化成了I22X2成比例的漏磁场的磁场储能(1/2LI2)，求出后验证与类似地，与I222I2'X2'成正比。折算后的二次侧kVA?E2'I2'?E2(N1/N2)?I2(N2/N1)?E2I2。

尽管看起来似乎不可理解，事实上这种论点是可靠的。实际上，如果我们将实际的二次绕组当真从铁芯上移开，并用一个参数设计成N1，R2'，X2'，I2'的等效绕组和负载电路替换，在正常电网频率运行时，从一次侧两端无法判断二次侧的磁势、所需容量及铜耗与前有何差别。

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在选择折算基准时，无非是将一次侧与折算后的二次侧匝数设为相等，除此之外再没有什么更要紧的了。但有时将一次侧折算到二次侧倒是方便的，在这种情况下，如果所有下标“1”的量都变换成了下标“2”的量，那么很容易得到必需的折算系数，例如。值得注意的是，对于一台实际的变压器，R1?R2，

X1'?X2；同样地R2?R1，X2'?X1。

''它除了为了考虑铁耗而引入了rm，且为N1?N2的通常情形时的等效电路，

了将V2'折算回V2而在二次侧两端引入了一理想的无损耗转换外，其他方面是一样的。在运用这种理想转换之前，内部电压和功率损耗已进行了计算。当在电路中选择了适当的参数时，在一、二次侧两端测得的变压器运行情况与在该电路相应端所测得的请况是完全一致的。将N1线圈和N2线圈并排放置在一个铁芯的两边，这一点与实际情况之间的差别仅仅是为了方便。当然，就变压器本身来说，两线圈是绕在同一铁芯柱上的。

如果将激磁支路移至一次绕组端口，引起的误差很小，但一些不合理的现象又会发生。例如，流过一次侧阻抗的电流不再是整个一次侧电流。由于I0通常只是I1的很小一部分，所有误差相当小。对一个具体问题可否允许有细微差别的回答取决于是否允许这种误差的存在。对于这种简化电路，一次侧和折算后二次侧阻抗可相加，得Re1?R1?R2(N1/N2)2和Xe1?X1?X2(N1/N2)2

需要指出的是，在此得到的等效电路仅仅适用于电网频率下的正常运行；一旦电压变化率产生相当大的电容电流Ic?CdV/dt时必须考虑电容效应。这对于高电压和频率超过100Hz的情形是很重要的。其次，即使是对于电网频率也并非唯一可行的等效电路。另一种形式是将变压器看成一个三端或四端网络，这样便产生一个准确的表达，它对于那些把所有装置看成是具有某种传递性能的电路元件的工程师来说是方便的。以此为分析基础的电路会拥有一个既产生

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电压大小的变化，也产生相位移的匝比，其阻抗也会与绕组的阻抗不同。这种电路无法解释变压器内类似饱和效应等现象。

等效电路有两个入端口形式：

（a） 从一次侧看为一个U形电路，其折合后的负载阻抗的端电压为V2'； （b） 从二次侧看为一其值为V1，且伴有由Re1和Xe1引起内压降的恒压源。在这种电路中有时可省略激磁支路，这样电路简化为一台产生恒值电压E1（实际上等于V1）并带有阻抗R?jX（实际上等于Re1?jXe1）的发电机。

在上述两种情况下，参数都可折算到二次绕组，这样可减小计算时间。 其电阻和电抗值可通过两种简单的轻载试验获得。 直流电机导论

直流电机以其多功用性而形成了鲜明的特征。通过并励、串励和特励绕组的各种不同组合，直流电机可设计成在动态和稳态运行时呈现出宽广范围变化的伏-安或速度-转矩特性。由于直流电机易于控制，因此该系统用于要求电动机转速变化范围宽或能精确控制电机输出的场合。

定子上有凸极，由一个或一个以上励磁线圈励磁。励磁绕组产生的气隙通以磁极中心线为轴线对称分布，这条轴线称为磁场轴线或直轴。

我们知道，每个旋转的电枢绕组中产生的交流电压，经由一与电枢连接的旋转的换向器和静止的电刷，在电枢绕组出线端转换成直流电压。换向器一电刷的组合构成机械整流器，它产生一直流电枢电压和一在空间固定的电枢磁势波形。电刷的放置应使换向线圈也处于磁极中性区，即两磁极之间。这样，电枢磁势波形的轴线与磁极轴线相差90°电角度，即位于交轴上。在示意图中，电刷位于交轴上，因为此处正是与其相连的线圈的位置。这样，如图所示电枢磁势波的轴线也是沿着电刷轴线的。（在实际电机中，电刷的几何位置大约偏移图例中所示位置90°电角度，这是因为元件的末端形状构成图示结果与换向器相连。）

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电刷上的电磁转矩和速度电压与磁通分布的空间波形无关；为了方便起见，我们假设气隙中仍然是正弦磁密波，这样便可以从磁场分析着手求得转矩。

转矩可以用直轴每极气隙磁通?d和电枢磁势波的空间基波分量Fa1相互作用的结果来表示。电刷处于交轴时，磁场间的角度为90°电角度，其正弦值等于1，则对于一台P极电机

T??P()2?dFa1

22式中由于转矩的正方向可以根据物理概念的推断确定，因此负号已经去掉。电枢磁势锯齿波的空间基波Fa1是峰值的8/?2。上式变换后有

T?PCa?dia?Ka?dia 2?m式中 ia=电枢外部电路中的电流； Ca=电枢绕组中的总导体数； m=通过绕组的并联支路数； 且

Ka?PCa 2?m其为一个由绕组设计而确定的常数。

简单的单个线圈的电枢中的整流电压前面已经讨论过了。将绕组分散在几个槽中的效果可用图形表示，图中每一条整流的正弦波形是一个线圈产生的电压，换向线圈边处于磁中性区。从电刷端观察到的电压是电刷间所有串联线圈中整流电压的总和，在图中由标以ea的波线表示。当每极有十几个换向器片，波线的波动变得非常小，从电刷端观察到的平均电压等于线圈整流电压平均值之和。电刷间的整流电压ea即速度电压，为

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ea?PCa?dWm?Ka?dWm 2?m式中Ka为设计常数。分布绕组的整流电压与集中线圈有着相同的平均值，其差别只是分布绕组的波形脉动大大减小。

将上述几式中的所有变量用SI单位制表达，有 eaia?Twm

这个等式简单地说明与速度电压有关的瞬时功率等于与磁场转矩有关的瞬时机械功率，能量的流向取决于这台电机是电动机还是发电机。

直轴气隙通由励磁绕组的合成磁势?Nfif产生，其磁通-磁势曲线就是电机的具体铁磁材料的几何尺寸决定的磁化曲线。在磁化曲线中，因为电枢磁势波的轴线与磁场轴线垂直，因此假定电枢磁势对直轴磁通不产生作用。这种假设有必要在后述部分加以验证，届时饱和效应会深入研究。因为电枢电势与磁通成正比，所以通常用恒定转速wm0下的电枢电势ea0来表示磁化曲线更为方便。任意转速wm时，任一给定磁通下的电压ea与转速成正比，即

ea?wmea0 wm0图中表示只有一个励磁绕组的磁化曲线，这条曲线可以很容易通过实验方法得到，不需要任何设计步骤的知识。

在一个相当宽的励磁范围内，铁磁材料部分的磁阻与气隙磁阻相比可以忽略不计，在此范围内磁通与励磁绕组总磁势呈线性比例，比例常数便是直轴气隙磁导率。

直流电机的突出优点是通过选择磁场绕组不同的励磁方法，可以获得变化范围很大的运行特性。励磁绕组可以由外部直流电源单独激磁，或者也可自励，即电机提供自身的励磁。励磁防哪个法不仅极大地影响控制系统中电机的静态特性，而且影响其动态运行。

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他励发电机的连接图已经给出，所需励磁电流是额定电枢电流的很小一部分。励磁电路中很小数量的功率可以控制电枢电路中相对很大数量的功率，也就是说发电机是一种功率放大器。当需要在很大范围内控制电枢电压时，他励发电机常常用于反馈控制系统中。自励发电机的励磁绕组可以有三种不同的供电方式。励磁绕组可以与电枢串联起来，这便形成了串励发电机；励磁绕组可以与电枢并联在一起，这便形成了并励发电机；或者励磁绕组分成两部分，其中一部分与电枢串联，另一部分与电枢并联，这便形成复励发电机。为了引起自励过程，在自励发电机中必须存在剩磁。

在典型的静态伏-安特性中，假定原动机恒速运行，稳态电势Ea和端电压Vt关系为：

Vt?Ea?IaRa

式中Ia为电枢输出电流，Ra为电枢回路电阻。在发电机中，Ea比Vt大，电磁转矩T是一种阻转矩。

他励发电机的端电压随着负载电流的增加稍有降低，这主要是由于电枢电阻上的压降。串励发电机中的励磁电流与负载电流相同，这样，气隙磁通和电压随负载变化很大，因此很少采用串励发电机。并励发电机电压随负载增加会有所下降，但在许多应用场合，这并不防碍使用。复励发电机的连接通常使串励绕组的磁势与并励绕组磁势相加，其优点是通过串励绕组的作用，每极磁通随着负载增加，从而产生一个随负载增加近似为常数的输出电压。通常，并励绕组匝数多，导线细；而绕在外部的串励绕组由于它必须承载电机的整个电枢电流，所以其构成的导线相对较粗。不论是并励还是复励发电机的电压都可借助并励磁场中的变阻器在适度的范围内得到调节。

任何用于发电机的励磁方法都可用于电动机。在电动机典型的静态转速-转矩特性中，假设电动机两端由一个恒压源供电。在电动机电枢中感应的电势与端电压Vt间的关系为

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Vt?Ea?IaRa

式中Ia此时为输入的电枢电流。电势Ea此时比端电压小，电枢电流与发电机中的方向相反，且电磁转矩与电枢旋转方向相同。

在并励和他励电动机中磁场磁通近似为常数，因此转矩的增加必须要求电枢电流近似成比例增大，同时为允许增大的电流通过小的电枢电阻，要求反电势稍有减少。由于反电势决定于磁通和转速，因此，转速必须稍稍降低。与鼠笼式感应电动机相类似，并励电动机实际上是一种从空载到满载速降仅约为5%的恒速电动机。起动转矩和最大转矩受到能成功换向的电枢电流的限制。

并励电动机的突出优点是易于调速。在并励绕组回路装上变阻器，励磁电流和每极磁通都可任意改变，而磁通的变化导致转速相反的变化以维持反电势大致等于外施端电压。通过这种方法得到最大调速范围为4或5比1，最高转速同样受到换向条件的限制。通过改变外施电枢电压，可以获得很宽的调速范围。

在串励电动机中，电枢电流、电枢电势和定子磁场磁通随负载增加而增加（假设铁芯不完全饱和）。因为磁通随负载增大，所以为了维持外施电压与反电势之间的平衡，速度必须下降，此外，由于磁通增加，所以转矩增大所引起的电枢电流的增大比并励电动机中的要小。因此串励电动机是一种具有明显下降的转速-负载特性的变速电动机。对于要求转矩过载很多的应用场合，由于对应的过载功率随相应的转速下降而维持在一个合理的范围内，因此，这种特性具有特别的优越性。磁通随着电枢电流的增大而增大，同时还带来非常有用的起动特性。

在复励电动机中，串励磁场可以连接成积复励式，使其磁势与并励磁场相加；也可以连接成差复励式，两磁场方向相反。差复励连接很少使用。积复励电动机具有界于并励和串励电动机之间的速度-负载特性，转速随负载的降低取决于并励磁场和串励磁场的相对安匝数。这种电动机没有像串励电动机那样轻载高转速的缺点，但它在相当的程度上保持着串励方式的优点。

直流电机的应用优势在于可接成并励、串励和复励等各种励磁方式，因而

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可提供多种性能各异的运行特性。其中有一些特性在本文中已大致提及。如果增加附加的电刷组以至于从换向器上另外可得到一些电压，那么还会存在更多的运用场合，因此直流电机系统的多用性，及其不论对人工还是自动控制的适应性，是它们的显著特性。

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