BASIC THEORY OF TRANSFORMERS

INTRODUCTION

The invention of the power transformer in the latter part of the nineteenth century made possible the development of the modern constant voltage AC supply system, with power stations often located many miles from the centers of electrical load. Before that, in the early days, the supplies were DC systems with generation, of necessity close to the point of loading.

The amount of auxiliary plant needing electrical supply in a large power station requires five or possibly six different voltage levels, requiring 60 or more transformers to provide the interconnections.

The transformer interconnects and transfers power between systems at different voltages. It does this at very high efficiency, at 99% or higher.

Transformers in power stations are generally three phase and double wound, i.e. they have electrically separate primary and secondary windings

BASIC THEORY OF TRANSFORMERS

 In figure 1, an ac generator connected to circuit 1 , referred to as PRIMARY, transfers energy to the magnetic circuit, which in turn transfers this energy to circuit 2, referred to as SECONDARY. The flux in the core   φM  is common to both circuits, and is responsible for this transfer of energy.

Fig. 1.1. Ideal transformer

In an ideal transformer, there are no losses in the core and the windings have no resistance or leakage reactance.

Consequently, the voltage V1 applied at the primary terminals will be used to circulate the primary current I1 against the opposing emf induced by the main flux. This INDUCED EMF e1 can be calculated by the following equation:

e1 = N1 x change in flux

or e1  =  N1  x change in flux /  change in t    ( 1 )


where N1 is the number of primary turns.
Similarly, the secondary winding is linked by the same flux as the primary winding and will have an emf e2 induced in it,

e2 = N2 x change in flux  ( 2 )

where N2 is the number of secondary turns.

In the above e1 and e2 are instantaneous values of induced voltage. However it is usual and more convenient to use rms ( root mean square) values. It can be shown that, as a general formula
E  =  4.44 N φM f     ( 3 )

where    

E = rms induced voltage
N = number of turns
φM = rms value of flux
f = system frequency ( 60 cps)

In an ideal transformers, the losses which are normally small are ignored, and then

V1 / V2  =  N1 / N2 = I2 / I1      ( 4 )

This important relationship must be clearly understood and memorized.

The operation of the transformer can be summarized as follows:

1.    When an alternating voltage V1 is applied to a primary coil of N1 turns linking a suitable iron core as shown in figure 1. A magnetizing reactive current flows in the coil, establishing flux φM in the core (and small additional fluxes elsewhere, neglected for a first consideration).

2.    The flux φM, is such that it induces in the primary coil an emf E1, by self induction to counter the applied voltage V1 and establish electrical balance. If a secondary coil of N2 turns is linked by the same flux, then by mutual induction, an emf E2, is developed in this coil. If a load is connected to the secondary coil, a current I2 will flow in the secondary circuit under the influence of induced voltage E2. This induced voltage E2 appears across the secondary terminals as V2.

السبت، 25 ديسمبر، 2010 justaneng