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1、The 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 lagging power factor will be considered. The secondary
2、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 to a new value of equal to . The extra primary cur
3、rent 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 increased by an amount necessary to neutralize the same
4、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 approximately equal to the output kVA, .The physical current
5、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 flux and the mutual component has fallen due to the in
6、crease 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 establishment of secondary leakage flux due to , and this o
7、pposes . 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 vectorially . As for the primary, is responsible for a substant
8、ially 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 related;, for example, by its demagnetizing action on has c
9、aused 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. is unchanged in magnitude from the no
10、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 change with load to give a change of and permit more primary
11、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 that . Secondly, the physical picture is drawn for a differ
12、ent 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 when primary and secondary leakage flux is zero, and when
13、 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 transformer
14、s 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 secondary will be viewed from the primary winding. The reactio
15、n 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 reaction. Consequently, a secondary winding can be replaced
16、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 the primary. With changes to , since the e.m.f.s are pro
17、portional 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, including load impedance, must become . Consequently, an
18、d .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 ot
19、herwise 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 .The argument is sound, though at first it may have seemed
20、 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 detect any difference in secondary ampere-turns, demand or
21、 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 subscrip
22、t 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 the secondary terminals to return to .All calculations of
23、 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
24、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 magnetizing branch is transferred to the primary terminals, but a few
25、 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 be obtained to a particular problem depending on whether or no
26、t 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 operation at power frequencies; capacitance effects must be taken in
27、to 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 equivalent circuit even for power frequencies .An alternative , treating
28、 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 pha
29、se 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 circui
30、t:(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 this representation and so the circuit reduces to a generator produ
31、cing 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 reactances can be obtained from two simple light load tests.负载运行的变压器通过选择
32、合适的匝数比,一次侧输入电压可任意转换成所希望的二次侧开路电压。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将影响磁通,有一种对铁芯产生去磁、减小和的趋向。因为一次侧漏阻抗压降如此之小,所以的微小变化都将导致一次侧电流增加很大,从增大至一个新值。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。一次侧总磁势增加了,它是平衡同量的二次侧磁势所必需的。在向量方程中,上式也可变换成。满载时,电流只约占满载电流的5%,因而近似等于。记住,近似等于的输入容
33、量也就近似等于输出容量。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没有变化,这是因为总反电动势仍然与相等且反向。然而此时却存在磁通的重新分配,由于随的增加而增加,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由于产生的二次侧漏磁通(其与反相)的建立而被进一步削弱。尽管图中和是分开表示的,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,它可被看成两个分量,即,或者向量形式。与一次侧漏磁通一样,的作用也用一个大体为常数的漏电感来表征。要注
34、意的是,由于它对互感磁通的作用,一次侧漏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,对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,幅值大小不变,因为它仍提供一个等于的反总电动势。尽管现在是一次侧和二次侧磁势的共同作用产生的,但它实际上与相同。互感磁通必须仍随负载变化而变化以改变,从而产生更大的一次侧电流。此时的幅值已经增大,但由于与是向量合成,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
35、匝数比为1,这样可使。其次,如果横轴像通常取的话,那么向量图是以为零时间参数的,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。为了分析时的情况,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大,小,还是小,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的等效绕组是方便的。当变换成,由于电动势与匝数成正比,所以,与相等。对于电流,由于对一次侧作用的安匝数必须保持不变,因此,即。对于阻抗,由于二次侧电压变成,电流变为,因此阻抗值,包括负载阻抗必然变为。因此,。如果将一次侧匝数作为参考
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