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黄河科技学院毕业设计（外文翻译） 第 1 页 T R A N S F O R M E R 1 . I N T R O D U C T I O N The high- voltage transmission is requied in the case that electrical power is to be provided at considerable distance from a generating station. At some point this high voltage must be reduced, because it ultimately is must supplied to a load. The transformer makes it possible for various parts of a power system to operate at different voltage levels. In this paper we discuss the principles and applications of power transformer. 2 . T O W - W I N D I N G T R A N S F O R M E R S A simplest transformer consists of two stationary coils coupled by a mutual magnetic flux. The coils are said to be mutually coupled because they link a common flux. In power applications, laminated steel core transformers (to which this paper is restricted) are used. Transformers are efficient because the rotational losses normally associated with rotating machine are absent, so relatively little power is lost when transforming power from one voltage level to another. Typical efficiencies are in the range 92 to 99%, the higher values applying to the larger power transformers. The current flowing in the coil connected to the ac source is called the primary winding or simply the primary. It sets up the flux f in the core, which varies periodically both in magnitude and direction. The flux links the second coil, called the secondary winding or simply secondary. The flux is changing; therefore, it induces a voltage in the secondary by electromagnetic induction in accordance with Lenz s law. Thus the primary receives its power from the source while the secondary supplies this power to the load. This action is known as transformer action. 黄河科技学院毕业设计（外文翻译） 第 2 页 3 . T R A N S F O R M E R P R I N C I P L E S When a sinusoidal voltage Vp is applied to the primary with the secondary open- circuited, there will be no energy transfer. The impressed voltage causes a small current I? to flow in the primary winding. This no- load current has two functions: (1) it produces the magnetic flux in the core, which varies sinusoidally between zero and fm, where fm is the maximum value of the core flux; and (2) it provides a component to account for the hysteresis and eddy current losses in the core. There combined losses are normally referred to as the core losses. The no- load current I? is usually few percent of the rated full- load current of the transformer (about 2 to 5%). Since at no- load the primary winding acts as a large reactance due to the iron core, the no- load current will lag the primary voltage by nearly 90 . It is readily seen that the current component Im= I0sin?0, called the magnetizing current, is 90 in phase behind the primary voltage VP. It is this component that sets up the flux in the core; f is therefore in phase with Im. The second component, Ie=I0sin?0, is in phase with the primary voltage. It is the current component that supplies the core losses. The phasor sum of these two components represents the no- load current, or I0 = Im+ Ie It should be noted that the no- load current is distortes and nonsinusoidal. This is the result of the nonlinear behavior of the core material. If it is assumed that there are no other losses in the transformer, the induced voltage In the primary, Ep and that in the secondary, Es can be shown. Since the magnetic flux set up by the primary winding， there will be an induced EMF E in the secondary winding in accordance with Faraday s law, namely, E=N?f/?t. This same flux also links the primary itself, inducing in it an EMF, Ep. As discussed earlier, the induced voltage must lag the flux by 90 , therefore, they are 180 out of phase with the applied voltage. Since no current flows in the secondary winding, Es=Vs. The no- load primary current I0 is small, a few percent of full- load current. Thus the voltage in the primary is small and Vp is nearly equal to Ep. The primary voltage and the resulting flux are sinusoidal; thus the induced quantities Ep and Es vary as a sine function. 黄河科技学院毕业设计（外文翻译） 第 3 页 The average value of the induced voltage given by Eavg = turns change influxinagiventime given time which is Faraday s law applied to a finite time interval. It follows that Eavg = N 2 1/(2 ) m f = 4fNfm which N is the number of turns on the winding. Form ac circuit theory, the effective or root- mean- square (rms) voltage for a sine wave is 1.11 times the average voltage; thus E = 4.44fNfm Since the same flux links with the primary and secondary windings, the voltage per turn in each winding is the same. Hence Ep = 4.44fNpfm and Es = 4.44fNsfm where Ep and Es are the number of turn on the primary and secondary windings, respectively. The ratio of primary to secondary induced voltage is called the transformation ratio. Denoting this ratio by a, it is seen that a = p s E E = p s N N Assume that the output power of a transformer equals its input power, not a bad sumption in practice considering the high efficiencies. What we really are saying is that we are dealing with an ideal transformer; that is, it has no losses. Thus Pm = Pout or VpIp primary PF = VsIs secondary PF where PF is the power factor. For the above- stated assumption it means that the power factor on primary and secondary sides are equal; therefore VpIp = VsIs from which is obtained 黄河科技学院毕业设计（外文翻译） 第 4 页 p s V V = p s I I p s E E a It shows that as an approximation the terminal voltage ratio equals the turns ratio. The primary and secondary current, on the other hand, are inversely related to the turns ratio. The turns ratio gives a measure of how much the secondary voltage is raised or lowered in relation to the primary voltage. To calculate the voltage regulation, we need more information. The ratio of the terminal voltage varies somewhat depending on the load and its power factor. In practice, the transformation ratio is obtained from the nameplate data, which list the primary and secondary voltage under full- load condition. When the secondary voltage Vs is reduced compared to the primary voltage, the transformation is said to be a step- down transformer: conversely, if this voltage is raised, it is called a step- up transformer. In a step- down transformer the transformation ratio a is greater than unity (a1.0), while for a step- up transformer it is smaller than unity (a1.0). In the event that a=1, the transformer secondary voltage equals the primary voltage. This is a special type of transformer used in instances where electrical isolation is required between the primary and secondary circuit while maintaining the same voltage level. Therefore, this transformer is generally knows as an isolation transformer. As is apparent, it is the magnetic flux in the core that forms the connecting link between primary and secondary circuit. In section 4 it is shown how the primary winding current adjusts itself to the secondary load current when the transformer supplies a load. Looking into the transformer terminals from the source, an impedance is seen which by definition equals Vp / Ip. From p s V V = p s I I p s E E a , we have Vp = aVs and Ip = Is/a.In terms of Vs and Is the ratio of Vp to Ip is p p V I = / s s aV Ia = 2 s s a V I But Vs / Is is the load impedance ZL thus we can say that Zm (primary) = a2ZL This equation tells us that when an impedance is connected to the secondary side, it appears from the source as an impedance having a magnitude that is a2 times its actual value. We say 黄河科技学院毕业设计（外文翻译） 第 5 页 that the load impedance is reflected or referred to the primary. It is this property of transformers that is used in impedance- matching applications. 4 . T R A N S F O R M E R S U N D E R L O A D The primary and secondary voltages shown have similar polarities, as indicated by the “ dot- making” convention. The dots near the upper ends of the windings have the same meaning as in circuit theory; the marked terminals have the same polarity. Thus when a load is connected to the secondary, the instantaneous load current is in the direction shown. In other words, the polarity markings signify that when positive current enters both windings at the marked terminals, the MMFs of the two windings add. Since the secondary voltage depends on the core flux f0, it must be clear that the flux should not change appreciably if Es is to remain essentially constant under normal loading conditions. With the load connected, a current Is will flow in the secondary circuit, because the induced EMF Es will act as a voltage source. The secondary current produces an MMF NsIs that creates a flux. This flux has such a direction that at any instant in time it opposes the main flux that created it in the first place. Of course, this is Lenz s law in action. Thus the MMF represented by NsIs tends to reduce the core flux f0. This means that the flux linking the primary winding reduces and consequently the primary induced voltage Ep, This reduction in induced voltage causes a greater difference between the impressed voltage and the counter induced EMF, thereby allowing more current to flow in the primary. The fact that primary current Ip increases means that the two conditions stated earlier are fulfilled: (1) the power input increases to match the power output, and (2) the primary MMF increases to offset the tendency of the secondary MMF to reduce the flux. In general, it will be found that the transformer reacts almost instantaneously to keep the resultant core flux essentially constant. Moreover, the core flux f0 drops very slightly between no load and full load (about 1 to 3%), a necessary condition if Ep is to fall sufficiently to allow an increase in Ip. On the primary side, Ip is the current that flows in the primary to balance the demagnetizing effect of Is. Its MMF NpIp sets up a flux linking the primary only. Since the 黄河科技学院毕业设计（外文翻译） 第 6 页 core flux f0 remains constant. I0 must be the same current that energizes the transformer at no load. The primary current Ip is therefore the sum of the current Ip and I0. Because the no- load current is relatively small, it is correct to assume that the primary ampere- turns equal the secondary ampere- turns, since it is under this condition that the core flux is essentially constant. Thus we will assume that I0 is negligible, as it is only a small component of the full- load current. When a current flows in the secondary winding, the resulting MMF (NsIs) creates a separate flux, apart from the flux f 0 produced by I0, which links the secondary winding only. This flux does no link with the primary winding and is therefore not a mutual flux. In addition, the load current t