学术讨论

TRANSFORMER
Abstract：The transformer is the transformer substation major installation, the function realizes the network voltage rank transformation, the key job principle is the electromagnetic induction.Changes the substation is realizes the voltage class transformation and the electrical energy assignment place. Carries on the voltage class transformation to the electric power supply, deals with the place which the electrical energy carries on redistributes to be called the transformer substation. Constructs the transformer substation is for electrical power distribution system's key position, the electric power supply directs the transformer substation from the electrical network, completes the voltage dropping in the transformer substation, functions and so on electrical energy assignment.
Key-words: substation；transformer；Relay protection；
1. INTRODUCTION
The 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 TRANSFORMERS
A 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 PRINCIPLES
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 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 Iθ 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 90o. It is readily seen that the current component Im= I0sinθ0, called the magnetizing current, is 90o in phase behind the primary voltage VP. It is this component that sets up the flux in the core; φ is therefore in phase with Im.
The second component, Ie=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, 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=NΔφ/Δt. 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 90o, therefore, they are 180o 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. The average value of the induced voltage given by
Eavg = turns×change in flux in a given time/given time
which is Faraday’s law applied to a finite time interval. It follows that
Eavg = N 2φm/1/2f = 4fNφm
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 = 4.44fNφm
Since the same flux links with the primary and secondary windings, the voltage per turn in each winding is the same. Hence
Ep = 4.44fNpφm
and
Es = 4.44fNsφm
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 =Ep/Ei =Np/Ni
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
Vp/Vi =Ip/Ii ≌Ep/Ei ≌ 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 (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 Vp / Ip. From Vp/Vi =Ip/Ii ≌ Ep/Ei ≌ a , we have Vp = aVs and Ip = Is/a.In terms of Vs and Is the ratio of Vp to Ip is
Vp/Ip =aVi/Ii/a = a2Vi/Ii
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 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 LOAD
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.
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 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 core flux φ0 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 φ0 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 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 voltage 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.