Introduction:
The transformer is a static device for transferring electrical energy from one alternating current to another alternating current without changing in frequency. A transformer may receive energy at one voltage and deliver it at higher voltage, in which case it is called a step-up transformer. When the energy is received at a higher voltage and delivered at a lower voltage, it is called a step-down transformer.
Operating Principle of transformer:
The transformer is a based on the principle that energy may be efficiently transferred by induction from one set of coils to another by means of a varying magnetic flux, provided that both sets of coils are on a combined magnetic circuit. Electromotive force are induced by change in flux linkages.
In the transformer, coils and magnetic circuit are all stationary with respect to one another. The emfs are induced by the change in the magnitude of the flux with time. This is called 'transformer emf' . This is illustrated in figure.
Referring to figure , an a.c. voltage is applied to the primary winding 'P'. As this winding is linked with an iron core, its m.m.f. produces an alternating flux ɸ in the core. This alternating flux links the turns of the winding 'S'. As this flux is alternating, it induces in the winding 'S' an e.m.f. of the same frequency as the flux. Because of this induced e.m.f. the secondary winding 'S' is capable of delivering current and energy. The energy therefore, is transferred from 'P', the primary to 'S' , the secondary by means of magnetic flux. In a transformer, either winding may be the primary, the other being the secondary, depending upon which winding receives and which delivers energy.
primary and secondary:
the more closely the primary circuits are mutually linked, the more direct becomes the exchange of energy between them. if the two circuits link a common iron core in figure. the effects are:
Linked electric and magnetic circuit in power transformer:
The power transformer is required to pass electrical energy from one circuit to another, via the medium of the pulsating mutual magnetic field, as efficiently and economically as possible. Our knowledge of magnetic material indicates the use of iron or steel for the conveyance of the flux with much greater ease than any other known material. the coils are therefore made to embrace an iron core, which serves as a good conducting path for the mutual magnetic flux, ensuring that flux links each coil fairly completely.
The elementary linked circuits are shown diagrammatically in figure. The use of an iron core permits of much greater freedom in the shape and arrangement of the primary and secondary coils, since the majority of the flux will be conveyed by the core almost regardless of the relative position of coil primary and secondary that link it. In practice, two general forms are usual these are obtained from the simple linked circuit of figure(a) by splitting either the coils (b)or the core (c) to give the core and shell types, of which the elementary forms are shown for single-phase transformer.
In core type, to avoid undue leakage flux, it is usual to have half the primary and half the secondary winding side-by-side or concentrically on each limb. not primary on one limb and secondary on the other. The forms of the transformer constructional methods employed ans by the control of leakage flux.
Three-phase transformers are developed from 1-phase types as in figure 2.4(a)and 2.4(b). The three- phase shell arrangement is merely three single-phase transformers assembled together. The three-phase core type, on the other hand, embodies the principle that the sum of the fluxes in each phase in a given direction along the cores is zero, i.e. the flux going up one limb can be returned down the other two. Thus only one-half of complete magnetic circuit is necessary for each phase. Each set of phase windings occupies one limb only.
The core type id more easily repaired on site, by removing the yoke, which permits the inspection of the coils and cores. The shell type is more robust mechanically since the coils are more readily braced. The radial shell type employs simple round coils, and the cooling is good, particularly for the iron.
E.M.F. Equation of Transformer:
Referring of figure. the mutual flux ɸ, is passing through the magnetic circuit formed by the iron core, links both the primary winding 'P' and the secondary winding 'S'. Hence, it must induce the same e.m.f. per turn in each winding. The total induced e.m.f. in each winding then must be proportional to the number of turns in that winding that is.
This change of flux occurs in a half cycle or in a time T/2 sec, where T is the period, or the time required for the wave to complete one cycle. The time T/2 is equal to 1/2f seconds.
Method-1: The average induced e.m.f. in the primary winding is equal to the total change of flux divided by the time i.e.
e1= -N1 2ɸm/(T/2)=-4fN1 ɸm Volts
Since, the forn=m factor for a sine wave is 1.11, the r.m.s induced e.m.f. is
E1 = - 4.44fN1 ɸm Volt
Method-2: ɸ =ɸm sin wt
e1
The transformer is a static device for transferring electrical energy from one alternating current to another alternating current without changing in frequency. A transformer may receive energy at one voltage and deliver it at higher voltage, in which case it is called a step-up transformer. When the energy is received at a higher voltage and delivered at a lower voltage, it is called a step-down transformer.
Operating Principle of transformer:
The transformer is a based on the principle that energy may be efficiently transferred by induction from one set of coils to another by means of a varying magnetic flux, provided that both sets of coils are on a combined magnetic circuit. Electromotive force are induced by change in flux linkages.
In the transformer, coils and magnetic circuit are all stationary with respect to one another. The emfs are induced by the change in the magnitude of the flux with time. This is called 'transformer emf' . This is illustrated in figure.
Referring to figure , an a.c. voltage is applied to the primary winding 'P'. As this winding is linked with an iron core, its m.m.f. produces an alternating flux ɸ in the core. This alternating flux links the turns of the winding 'S'. As this flux is alternating, it induces in the winding 'S' an e.m.f. of the same frequency as the flux. Because of this induced e.m.f. the secondary winding 'S' is capable of delivering current and energy. The energy therefore, is transferred from 'P', the primary to 'S' , the secondary by means of magnetic flux. In a transformer, either winding may be the primary, the other being the secondary, depending upon which winding receives and which delivers energy.
primary and secondary:
the more closely the primary circuits are mutually linked, the more direct becomes the exchange of energy between them. if the two circuits link a common iron core in figure. the effects are:
- A great increase in the total flux by virtue of the improved permeance of the the magnetic circuit.
- A smaller magnetizing current (i.e. primary current with secondary open- circuited), since the increased flux per ampere induces more primary e.m.f.
- A much greater proportion of mutual to non-mutual or leakage flux. the latter has paths where as the former occupies the permeable iron core.
- The introduction of losses in the core, so that the field can no longer be established without loss.
Linked electric and magnetic circuit in power transformer:
The power transformer is required to pass electrical energy from one circuit to another, via the medium of the pulsating mutual magnetic field, as efficiently and economically as possible. Our knowledge of magnetic material indicates the use of iron or steel for the conveyance of the flux with much greater ease than any other known material. the coils are therefore made to embrace an iron core, which serves as a good conducting path for the mutual magnetic flux, ensuring that flux links each coil fairly completely.
The elementary linked circuits are shown diagrammatically in figure. The use of an iron core permits of much greater freedom in the shape and arrangement of the primary and secondary coils, since the majority of the flux will be conveyed by the core almost regardless of the relative position of coil primary and secondary that link it. In practice, two general forms are usual these are obtained from the simple linked circuit of figure(a) by splitting either the coils (b)or the core (c) to give the core and shell types, of which the elementary forms are shown for single-phase transformer.
In core type, to avoid undue leakage flux, it is usual to have half the primary and half the secondary winding side-by-side or concentrically on each limb. not primary on one limb and secondary on the other. The forms of the transformer constructional methods employed ans by the control of leakage flux.
Three-phase transformers are developed from 1-phase types as in figure 2.4(a)and 2.4(b). The three- phase shell arrangement is merely three single-phase transformers assembled together. The three-phase core type, on the other hand, embodies the principle that the sum of the fluxes in each phase in a given direction along the cores is zero, i.e. the flux going up one limb can be returned down the other two. Thus only one-half of complete magnetic circuit is necessary for each phase. Each set of phase windings occupies one limb only.
The core type id more easily repaired on site, by removing the yoke, which permits the inspection of the coils and cores. The shell type is more robust mechanically since the coils are more readily braced. The radial shell type employs simple round coils, and the cooling is good, particularly for the iron.
E.M.F. Equation of Transformer:
Referring of figure. the mutual flux ɸ, is passing through the magnetic circuit formed by the iron core, links both the primary winding 'P' and the secondary winding 'S'. Hence, it must induce the same e.m.f. per turn in each winding. The total induced e.m.f. in each winding then must be proportional to the number of turns in that winding that is.
E1/E2 = N1/N2
where E1 and E2 are the primary and secondary induced e.m.f.s and N1 and N2are the number of turns in primary and secondary, respectively.
Figure shows the mutual flux, ɸ, varying sinusoidally with time. Between points a and b, the total change of flux is 2ɸm webers.
This change of flux occurs in a half cycle or in a time T/2 sec, where T is the period, or the time required for the wave to complete one cycle. The time T/2 is equal to 1/2f seconds.
Method-1: The average induced e.m.f. in the primary winding is equal to the total change of flux divided by the time i.e.
e1= -N1 2ɸm/(T/2)=-4fN1 ɸm Volts
Since, the forn=m factor for a sine wave is 1.11, the r.m.s induced e.m.f. is
E1 = - 4.44fN1 ɸm Volt
Method-2: ɸ =ɸm sin wt
e1
