翻译--变压器

附录A 译文变压器1. 介绍要从远端发电厂送出电能，必须应用高压输电。

因为最终的负荷，在一些点高电压必须降低。

变压器能使电力系统各个部分运行在电压不同的等级。

本文我们讨论的原则和电力变压器的应用。

2. 双绕组变压器变压器的最简单形式包括两个磁通相互耦合的固定线圈。

两个线圈之所以相互耦合，是因为它们连接着共同的磁通。

在电力应用中，使用层式铁芯变压器(本文中提到的)。

变压器是高效率的，因为它没有旋转损失，因此在电压等级转换的过程中，能量损失比较少。

典型的效率范围在92到99%，上限值适用于大功率变压器。

从交流电源流入电流的一侧被称为变压器的一次侧绕组或者是原边。

它在铁圈中建立了磁通φ，它的幅值和方向都会发生周期性的变化。

磁通连接的第二个绕组被称为变压器的二次侧绕组或者是副边。

磁通是变化的；因此依据楞次定律，电磁感应在二次侧产生了电压。

变压器在原边接收电能的同时也在向副边所带的负荷输送电能。

这就是变压器的作用。

3. 变压器的工作原理当二次侧电路开路是，即使原边被施以正弦电压V p，也是没有能量转移的。

外加电压在一次侧绕组中产生一个小电流Iθ。

这个空载电流有两项功能：（1）在铁芯中产生电磁通，该磁通在零和 φm之间做正弦变化，φm是铁芯磁通的最大值；（2）它的一个分量说明了铁芯中的涡流和磁滞损耗。

这两种相关的损耗被称为铁芯损耗。

变压器空载电流Iθ一般大约只有满载电流的2%—5%。

因为在空载时，原边绕组中的铁芯相当于一个很大的电抗，空载电流的相位大约将滞后于原边电压相位90º。

显然可见电流分量I m= I0sinθ0，被称做励磁电流，它在相位上滞后于原边电压V P 90º。

就是这个分量在铁芯中建立了磁通；因此磁通φ与I m 同相。

第二个分量I e =I 0sin θ0，与原边电压同相。

这个电流分量向铁芯提供用于损耗的电流。

两个相量的分量和代表空载电流，即I 0 = I m + I e应注意的是空载电流是畸变和非正弦形的。

这种情况是非线性铁芯材料造成的。

如果假定变压器中没有其他的电能损耗一次侧的感应电动势E p 和二次侧的感应电压E s 可以表示出来。

因为一次侧绕组中的磁通会通过二次绕组，依据法拉第电磁感应定律，二次侧绕组中将产生一个电动势E ，即E=N Δφ/Δt 。

相同的磁通会通过原边自身，产生一个电动势E p 。

正如前文中讨论到的，所产生的电压必定滞后于磁通90º，因此，它于施加的电压有180º的相位差。

因为没有电流流过二次侧绕组，E s =V s 。

一次侧空载电流很小，仅为满载电流的百分之几。

因此原边电压很小，并且V p 的值近乎等于E p 。

原边的电压和它产生的磁通波形是正弦形的；因此产生电动势E p 和E s 的值是做正弦变化的。

产生电压的平均值如下E avg = turns×给定时间内磁通变化量给定时间即是法拉第定律在瞬时时间里的应用。

它遵循E avg = N 21/(2)m f = 4fN φm其中N 是指线圈的匝数。

从交流电原理可知，有效值是一个正弦波，其值为平均电压的1.11倍；因此E = 4.44fN φm因为一次侧绕组和二次侧绕组的磁通相等，所以绕组中每匝的电压也相同。

因此E p = 4.44fN p φm并且E s = 4.44fN s φm其中N p 和E s 是一次侧绕组和二次侧绕组的匝数。

一次侧和二次侧电压增长的比率称做变比。

用字母a 来表示这个比率，如下式a = ps E E = p s N N假设变压器输出电能等于其输入电能——这个假设适用于高效率的变压器。

实际上我们是考虑一台理想状态下的变压器；这意味着它没有任何损耗。

因此P m = P out或者V p I p × primary PF = V s I s × secondary PF这里PF 代表功率因素。

在上面公式中一次侧和二次侧的功率因素是相等的；因此V p I p = V s I s从上式我们可以得知ps V V = p s I I ≌ p s E E ≌ a它表明端电压比等于匝数比，换句话说，一次侧和二次侧电流比与匝数比成反比。

匝数比可以衡量二次侧电压相对于一次恻电压是升高或者是降低。

为了计算电压，我们需要更多数据。

终端电压的比率变化有些根据负载和它的功率因素。

实际上, 变比从标识牌数据获得, 列出在满载情况下原边和副边电压。

当副边电压V s 相对于原边电压减小时，这个变压器就叫做降压变压器。

如果这个电压是升高的，它就是一个升压变压器。

在一个降压变压器中传输变比a 远大于1(a>1.0)，同样的，一个升压变压器的变比小于1(a<1.0)。

当a=1时，变压器的二次侧电压就等于起一次侧电压。

这是一种特殊类型的变压器，可被应用于当一次侧和二次侧需要相互绝缘以维持相同的电压等级的状况下。

因此，我们把这种类型的变压器称为绝缘型变压器。

显然，铁芯中的电磁通形成了连接原边和副边的回路。

在第四部分我们会了解到当变压器带负荷运行时一次侧绕组电流是如何随着二次侧负荷电流变化而变化的。

从电源侧来看变压器，其阻抗可认为等于V p / I p 。

从等式 ps V V = p s I I ≌ p s E E ≌a 中我们可知V p = aV s并且I p = I s /a 。

根据V s 和I s ，可得V p 和I p 的比例是pp V I = /s s aV I a = 2s s a V I但是V s / I s 负荷阻抗Z L ，因此我们可以这样表示Z m (primary) = a 2Z L这个等式表明二次侧连接的阻抗折算到电源侧，其值为原来的a 2倍。

我们把这种折算方式称为负载阻抗向一次侧的折算。

这个公式应用于变压器的阻抗匹配。

4. 有载情况下的变压器一次侧电压和二次侧电压有着相同的极性，一般习惯上用点记号表示。

如果点号同在线圈的上端，就意味着它们的极性相同。

因此当二次侧连接着一个负载时，在瞬间就有一个负荷电流沿着这个方向产生。

换句话说，极性的标注可以表明当电流流过两侧的线圈时，线圈中的磁动势会增加。

因为二次侧电压的大小取决于铁芯磁通大小φ0，所以很显然当正常情况下负载电势E s 没有变化时，二次侧电压也不会有明显的变化。

当变压器带负荷运行时，将有电流I s 流过二次侧，因为E s 产生的感应电动势相当于一个电压源。

二次侧电流产生的磁动势N s I s 会产生一个励磁。

这个磁通的方向在任何一个时刻都和主磁通反向。

当然，这是楞次定律的体现。

因此，N s I s 所产生的磁动势会使主磁通φ0减小。

这意味着一次侧线圈中的磁通减少，因而它的电压E p 将会增大。

感应电压的减小将使外施电压和感应电动势之间的差值更大，它将使初级线圈中流过更大的电流。

初级线圈中的电流I p 的增大，意味着前面所说明的两个条件都满足：（1）输出功率将随着输出功率的增加而增加（2）初级线圈中的磁动势将增加，以此来抵消二次侧中的磁动势减小磁通的趋势。

总的来说，变压器为了保持磁通是常数，对磁通变化的响应是瞬时的。

更重要的是，在空载和满载时，主磁通φ0的降落是很少的（一般在）1至3%。

其需要的条件是E 降落很多来使电流I p 增加。

在一次侧，电流I p ’在一次侧流过以平衡I s 产生的影响。

它的磁动势N p I p ’只停留在一次侧。

因为铁芯的磁通φ0保持不变，变压器空载时空载电流I0必定会为其提供能量。

故一次侧电流I p是电流I p’与I0’的和。

因为空载电流相对较小，那么一次侧的安匝数与二次侧的安匝数相等的假设是成立的。

因为在这种状况下铁芯的磁通是恒定的。

因此我们仍旧可以认定空载电流I0相对于满载电流是极其小的。

当一个电流流过二次侧绕组，它的磁动势（N s I s）将产生一个磁通，于空载电流I0产生的磁通φ0不同，它只停留在二次侧绕组中。

因为这个磁通不流过一次侧绕组，所以它不是一个公共磁通。

另外，流过一次侧绕组的负载电流只在一次侧绕组中产生磁通，这个磁通被称为一次侧的漏磁。

二次侧漏磁将使电压增大以保持两侧电压的平衡。

一次侧漏磁也一样。

因此，这两个增大的电压具有电压降的性质，总称为漏电抗电压降。

另外，两侧绕组同样具有阻抗，这也将产生一个电阻压降。

把这些附加的电压降也考虑在内，这样一个实际的变压器的等值电路图就完成了。

由于分支励磁体现在电流里，为了分析我们可以将它忽略。

这就符我们前面计算中可以忽略空载电流的假设。

这证明了它对我们分析变压器时所产生的影响微乎其微。

因为电压降与负载电流成比例关系，这就意味着空载情况下一次侧和二次侧绕组的电压降都为零。

附录B 外文原文TRANSFORMER1. INTRODUCTIONThe high-voltage transmission was need for the case electrical power is to be provided at considerable distance from a generating station. At some point this high voltage must be reduced, because ultimately is must supply 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 power transformer principles and applications.2. TOW-WINDING TRANSFORMERSA transformer in its simplest form 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 φ 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.3. TRANSFORMER PRINCIPLESWhen a sinusoidal voltage V p is applied to the primary with the secondary open-circuited, there will be no energy transfer. The impressed voltage causes a small current Iθ 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 φm, where φm 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 Iθis 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 90º. It is readily seen that the current component I m= I0sinθ0, called the magnetizing current, is 90ºin phase behind the primary voltage V P. It is this component that sets up the flux in the core; φ is therefore in phase with I m.The second component, I e=I0sinθ0, 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, orI0 = I m+ I eIt 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 , E p and that in the secondary , E s 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=NΔφ/Δt. This same flux also links the primary itself, inducing in it an EMF, E p . As discussed earlier, the induced voltage must lag the flux by 90º, therefore, they are 180º out of phase with the applied voltage. Since no current flows in the secondary winding, E s =V s . The no-load primary current I 0 is small, a few percent of full-load current. Thus the voltage in the primary is small and V p is nearly equal to E p . The primary voltage and the resulting flux are sinusoidal; thus the induced quantities E p and E s vary as a sine function. The average value of the induced voltage given byE avg = turns× change in flux in a given timegiven timewhich is Faraday’s law applied to a finite time interval. It follows thatE avg = N 21/(2)mf = 4fNφmwhich 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; thusE = 4.44fNφmSince the same flux links with the primary and secondary windings, the voltage per turn in each winding is the same. HenceE p = 4.44fN p φmandE s = 4.44fN s φmwhere E p 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 thata = ps E E = p s N NAssume 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. ThusP m = P outorV p I p × primary PF = V s I s × secondary PFwhere PF is the power factor. For the above-stated assumption it means that the power factor on primary and secondary sides are equal; thereforeV p I p = V s I s from which is obtainedps V V = p s I I ≌ p s E E ≌ aIt 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 V s 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 (a>1.0), while for a step-up transformer it is smaller than unity (a<1.0). 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 V p / I p . From ps V V = p s I I ≌ p s E E ≌ a , we have V p = aV sand I p = I s /a.In terms of V s and I s the ratio of V p to I p ispp V I = /s s aV I a = 2s s a V IBut V s / I s is the load impedance Z L thus we can say thatZ m (primary) = a 2Z LThis 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 a 2 times its actual value. We say 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. TRANSFORMERS UNDER LOADThe primary and secondary voltages shown have similar polarities, as indicated by the “dot -making” convention. The dots near the upper ends of t he 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 φ0, it must be clear that the flux should not change appreciably if E s is to remain essentially constant under normal loading conditions. With the load connected, a current I s will flow in the secondary circuit, because the induced EMF E s will act as a voltage source. The secondary current produces an MMF N s I s 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 firstplace. Of course, this is Lenz’s law in action. Thus the MMF represented by N s I s tends to reduce the core flux φ0. This means that the flux linking the primary winding reduces and consequently the primary induced voltage E p, 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 I p 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 φ0 drops very slightly between n o load and full load (about 1 to 3%), a necessary condition if E p is to fall sufficiently to allow an increase in I p.On the primary side, I p’is the current that flows in the primary to balance the demagnetizing effect of I s. Its MMF N p I p’sets up a flux linking the primary only. Since the core flux φ0 remains constant. I0 must be the same current that energizes the transformer at no load. The primary current I p is therefore the sum of the current I p’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 I0is negligible, as it is only a small component of the full-load current.When a current flows in the secondary winding, the resulting MMF (N s I s) creates a separate flux, apart from the flux φ0produced 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 that flows through the primary winding creates a flux that links with the primary winding only; it is called the primary leakage flux. The secondary- leakage flux gives rise to an induced voltage that is not counter balanced by an equivalent induced voltage in the primary. Similarly, the volta ge induced in the primary is not counterbalanced in the secondary winding. Consequently,these two induced voltages behave like voltage drops, generally called leakage reactance voltage drops. Furthermore, each winding has some resistance, which produces a resistive voltage drop. When taken into account, these additional voltage drops would complete the equivalent circuit diagram of a practical transformer. Note that the magnetizing branch is shown in this circuit, which for our purposes will be disregarded. This follows our earlier assumption that the no-load current is assumed negligible in our calculations. This is further justified in that it is rarely necessary to predict transformer performance to such accuracies. Since the voltage drops are all directly proportional to the load current, it means that at no-load conditions there will be no voltage drops in either winding.。