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1、 The Transformer on loadIntroduction to DC MachinesThe Transformer on loadIt has been shown that a primary input voltage can be transformed to any desired open-circuit secondary voltage by a suitable choice of turns ratio. is available for circulating a load current impedance. For the moment, a lagg
2、ing power factor will be considered. The secondary current and the resulting ampere-turns will change the flux, tending to demagnetize the core, reduce and with it . Because the primary leakage impedance drop is so low, a small alteration to will cause an appreciable increase of primary current from
3、 to a new value of equal to . 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 as on no load. The total primary ampere-turns are incr
4、eased by an amount necessary to neutralize the same amount of secondary ampere-turns. In the vector equation , ; alternatively, . At full load, the current is only about 5% of the full-load current and so is nearly equal to. Because in mind that , the input kVA which is approximately is also approxi
5、mately equal to the output kVA, .The physical current has increased, and with in the primary leakage flux to which it is proportional. The total flux linking the primary , is shown unchanged because the total back e.m.f.,（）is still equal and opposite to . However, there has been a redistribution of
6、flux and the mutual component has fallen due to the increase of with . 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 linking the secondary winding has been further reduced by the estab
7、lishment of secondary leakage flux due to , and this opposes . Although and 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 which can be considered in two components, i.e. or vectoria
8、lly . As for the primary, is responsible for a substantially constant secondary leakage inductance . 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 rela
9、ted; , for example, by its demagnetizing action on 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 t
10、o rise with load. 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 . It is virtually the same as , though now produced by the combined effect of primary and secondary ampere-turns. The mutual flux must still chang
11、e with load to give a change of and permit more primary current to flow. has increased this time but due to the vector combination with 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 tha
12、t . Secondly, the physical picture is drawn for a different instant of time from the vector diagrams which show , 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 w
13、hen 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 resi
14、stance 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 the reaction of the second
15、ary 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 is large and small or vice versa, it is the product of current and turns which causes the reac
16、tion. 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 as
17、the primary. With changes to , since the e.m.f.s are proportional to turns, which is the same as .For current, since the reaction ampere turns must be unchanged must be equal to .i.e. .For impedance , since any secondary voltage becomes , and secondary current becomes , then any secondary impedance,
18、 including load impedance, must become . Consequently, and .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
19、 winding must be the same as in the original secondary otherwise the primary would have to supply a different loss power. must be equal to . does in fact reduce to .Similarly the stored magnetic energy in the leakage field which is proportional to will be found to check as . The referred secondary .
20、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 ,and , measurements from the primary terminals would be unable to d
21、etect any difference in secondary ampere-turns, 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,
22、if all the subscript 1s are interchanged for the subscript 2s, the necessary referring constants are easily found; e.g. ,; similarly and .The equivalent circuit for the general case where except that has been added to allow for iron loss and an ideal lossless transformation has been included before
23、the secondary terminals to return to .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
24、when the appropriate parameters are inserted. The slightly different representation showing the coils and 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 magnetis
25、ing 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 is usually such a small fraction of . Slightly different answers may
26、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: and It should be pointed out that the equivalent circuit as derived here is only valid for normal operat
27、ion at power frequencies; capacitance effects must be taken into account whenever the rate of change of voltage would give rise to appreciable capacitance currents, . They are important at high voltages and at frequencies much beyond 100 cycles/sec. A further point is not the only possible equivalen
28、t 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.
29、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
30、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 ,or(b) viewed from the secondary as a source of constant voltage with internal drops due to and . The magnetizing branch is sometimes omitted in t
31、his representation and so the circuit reduces to a generator producing a constant voltage (actually equal to ) and having an internal impedance (actually equal to ).In either case, the parameters could be referred to the secondary winding and this may save calculation time .The resistances and react
32、ances can be obtained from two simple light load tests.Introduction to DC MachinesDC 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
33、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 schemat
34、ically. 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
35、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
36、 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 schemat
37、ic 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 t
38、heir 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-den
39、sity 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 and the space-fundamental component of the armature m.m.f. wave . With the brushes in the quadrature axis, the an
40、gle between these fields is 90 electrical degrees, and its sine equals unity. For a P pole machine In which the minus sign has been dropped because the positive direction of the torque can be determined from physical reasoning. The space fundamental of the sawtooth armature m.m.f. wave is 8/ times i
41、ts peak. Substitution in above equation then gives Where =current in external armature circuit; =total number of conductors in armature winding; =number of parallel paths through winding;And Is a constant fixed by the design of the winding.The rectified voltage generated in the armature has already
42、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 neut
43、ral 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 in figure. With a dozen or so commutator segments per pole, the ripple becomes very small and the average generated v
44、oltage observed from the brushes equals the sum of the average values of the rectified coil voltages. The rectified voltage between brushes, known also as the speed voltage, is Where is the design constant. The rectified voltage of a distributed winding has the same average value as that of a concen
45、trated coil. The difference is that the ripple is greatly reduced. From the above equations, with all variable expressed in SI units: This equation simply says that the instantaneous electric power associated with the speed voltage equals the instantaneous mechanical power associated with the magnet
46、ic 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. of the field windings, the flux-m.m.f. characteristic being the magnetization curve for the particular iron geometry of th
47、e 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 proportiona
48、l to flux times speed, it is usually more convenient to express the magnetization curve in terms of the armature e.m.f. at a constant speed . The voltage for a given flux at any other speed is proportional to the speed,i.e. 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