Transformers1IntroductionMichael Faraday propounded the principle of electro-magnetic induction in 1831. Itstates that a voltage appears across the terminals of an electric coil when the fulin!ed with the same changes. The magnitude of the induced voltage isproportional to the rate of change of the fu lin!ages. This "nding forms the #asisfor many magneto electric machines. The earliest use of this phenomenon was inthe development of induction coils. These coils were used to generate high voltagepulses to ignite the eplosive charges in the mines.$s the d.c.%ower system wasin use at that time& very little of transformer principle was made use of.In the d.c.'upply system the generating station and the load center have to #e necessarilyclose to each other due to the re(uirement of economic transmission of power. $lsothe d.c. generators cannot #e scaled up due to the limitations of the commutator.This made the world loo! for other e)cient methods for #ul! power generation andtransmission. *uring the second half of the 1+th century the alternators&transformers and induction motors were invented. These machines wor! onalternatingpower supply. The roleof the transformers #ecame o#vious. Thetransformer which consisted of two electric circuits lin!ed #y a common magneticcircuit helpedthevoltageandcurrent levelsto#echanged!eepingthepowerinvariant. The e)ciency of such conversion was etremely high. Thus one couldchoose a moderate voltage for the generation of a.c. power& a high voltage for thetransmissionof thispoweroverlongdistancesand"nallyuseasmall andsafeoperating voltage at the user end. $llthese are made possi#le #y transformers.The a.c. power systems thus got well esta#lished.Transformers can lin! two or more electric circuits. In its simple form two electriccircuits can #e lin!ed #y a magnetic circuit& one of the electric coils is used for thecreation of a time varying magnetic "eld.The second coil which is made to lin! this"eld has an induced voltage in the same. The magnitude of the induced emf isdecided #y the num#er of turns used in each coil. Thus the voltage levelcan #eincreased or decreased #y changing the num#er of turns.This ecitation winding iscalledaprimaryandtheoutput windingiscalledasecondary. $samagneticmedium forms the lin! #etween the primary and the secondary windings there is noconductiveconnection#etweenthetwo electric circuits. Thetransformer thusprovides an electric isolation #etween the two circuits. The fre(uency on the twosideswill #ethesame. $sthereisnochangeinthenatureof thepower& theresulting machine is called a ,transformer- and not a ,converter-.The electric powerat one voltage.current level is only ,transformed- into electric power& at the samefre(uency& to an- other voltage.current level./venthoughmost of thelarge-power transformerscan#efoundinthepowersystems& the use of the transformers is not limited to the power systems. The useof the principle of transformers is universal. Transformers can #e found operatingin the fre(uency range starting from a few hert0 going up to severalmegahert0.%ower ratings vary from a few mill watts to several hundreds of megawatts. Theuse of the transformers is so wide spread that it is virtually impossi#le to thin! of alargepower system withouttransformers. *emand onelectric powergenerationdou#les every decade in a developing country. For every M1$ of generation theinstalledcapacityoftransformersgrows#ya#out2M1$. These"guresshowtheindispensa#le nature of power transformers.2Basic Principles$s mentioned earlier the transformer is a static device wor!ing on the principle ofFaraday-s law of induction.Faraday-s law states that a voltage appears across theterminals of anelectric coil whenthefulin!ages associatedwiththesamechanges. This emf is proportional to the rate of change of fu lin!ages. %uttingmathematically&e 3d4.dt5555555555555555555555555555555555555555555555555555556178here& e is the induced emf in volt and 4 is the flu lin!ages in 8e#er turn. Fig. 1shows a