. ntroduction to Tranformer. DKT 3 CHAPTER Tranformer By Roemizi Abd Rahim Tranformer i a device that change ac electrical ower at one voltage level to ac electric ower at another voltage level through the action of magnetic field. Figure.: Block Diagram of Tranformer.. Alication of Tranformer. Why do we need tranformer?. Alication of Tranformer. Why do we need tranformer? The Tranmiion Tower The Power Grid (a) Ste U. n modern ower ytem, electrical ower i generated at voltage of k to 5k. Tranformer will te u the voltage to between 0k to 000k for tranmiion over long ditance at very low lot. The Subtation The Power Grid The Utility ole (b) Ste Down. The tranformer will teed down the voltage to the k to 34.5k range for local Ditribution. n home, office and factorie teed down to 40..3 Tye and Contruction of Tranformer. Power tranformer are contructed on two tye of core; (i) Core form. (ii) Shell form. A) Core tye B) Shell tye Figure.: Core Form and Shell Form. Core form. A) Core tye B) Shell tye The core form contruction conit of a imle rectangular laminated iece of teel with the tranform winding wraed around the two ide of the rectangle. Shell form. The hell form contruction conit of a three-legged laminated core with the winding wraed around the center leg.
Figure.3: A Simle Tranformer. Contruction. Tranformer conit of two or more coil of wire wraed around a common ferromagnetic core. The coil are uually not directly connected. The common magnetic flux reent within the coil connect the coil. There are two winding; (i) Primary winding (inut winding); the winding that i connected to the ower ource. (ii) Secondary winding (ut winding); the winding connected to the load. Oeration. When AC voltage i alied to the rimary winding of the tranformer, an AC current will reult i L or i (current at load). The AC rimary current i et u time varying magnetic flux φ in the core. The flux link the econdary winding of the tranformer. Oeration. From the Faraday law, the emf will be induced in the econdary winding. Thi i known a tranformer action. The current i will flow in the econdary winding and electric ower will be tranfer to the load. The direction of the current in the econdary winding i determined by Len z law. The econdary current direction i uch that the flux roduced by thi current ooe the change in the original flux with reect to time..4 General Theory of Tranformer Oeration. FARADAY S LAW Michael Faraday f current roduce a magnetic field, why can't a magnetic field roduce a current? n 83 two eole, Michael Faraday in the UK and Joeh Henry in the US erformed exeriment that clearly demontrated that a changing magnetic field roduce an induced EMF (voltage) that would roduce a current if the circuit wa comlete. When the witch wa cloed, a momentary deflection wa noticed in the galvanometer after which the current returned to zero. When the witch wa oened, the galvanometer deflected again momentarily, in the other direction. Current wa not detected in the econdary circuit when the witch wa left cloed. An e.m.f. i made to haen (or induced) in a conductor (like a iece of metal) whenever it 'cut' magnetic field line by moving acro them. Thi doe not work when it i tationary. f the conductor i art of a comlete circuit a current i alo roduced. Faraday found that the induced e.m.f. increae if (i) the eed of motion of the magnet or coil increae. (ii) the number of turn on the coil i made larger. (iii) the trength of the magnet i increaed.
Faraday Law Δφ E Δt E Electromotive force (emf) Φ Flux umber of turn t time Any change in the magnetic environment of a coil of wire will caue a voltage (emf) to be "induced" in the coil. o matter how the change i roduced, the voltage will be generated. The change could be roduced by changing the magnetic field trength, moving a magnet toward or away from the coil, moving the coil into or of the magnetic field, rotating the coil relative to the magnet, etc. nerting a magnet into a coil alo roduce an induced voltage or current. The fater eed of inertion/ retraction, the higher the induced voltage. Figure.4: Baic Tranformer Comonent. According to the Faraday law of electromagnetic induction, electromagnetic force (emf ) are induced in and due to a time rate of change of φ M, dλ dφ dφ dφ e ± ± e ; e Where, (.) e intantaneou voltage induced by magnetic field (emf), λ number of flux linkage between the magnetic field and the electric circuit. φ effective flux Lenz Law tate that the direction of e i uch to roduce a current that ooe the flux change. f the winding reitance i neglected, then equation (.) become; v dφ e ( ); dφφ v e ( ) Taking the voltage ratio in equation (.) reult in, e e (.) (.3) eglecting loe mean that the intantaneou ower i the ame on both ide of the tranformer; (.4) e i ei According to Lenz a Law, the direction of e i ooe the flux change, and the flux varie inuoidally uch that φ m ax φ φ max in ωt (.6) Combining i all the above equation we get the equation (.5) where a i the turn ratio of the tranformer. v i a v i a > Ste down tranformer a < Ste u tranformer a olation Tranformer (.5) Subtitute eqn(.6) into eqn(.) dφ d e ( φ max in πft) The rm value of the induce voltage i; ωφ max E 4.44 fφ max (.7) (.8) 3
Loe are comoed of two art; (a) The Eddy-Current lot. Eddy current lot i baically lo due to the induced current in the magnetic material. To reduce thi lot, the magnetic circuit i uually made of a tack of thin lamination. (b) The Hyterei lo. Hyterei lot i caued by the energy ued in orienting the magnetic domain of the material along the field. The lot deend on the material ued..5 The deal Tranformer. An deal tranformer i a lole device with an inut winding and an ut winding. Zero reitance reult in zero voltage dro between the terminal voltage and induced voltage Figure.6 how the relationhi of inut voltage and ut voltage of the ideal tranformer. An deal Tranformer and the Schematic Symbol. The relationhi between voltage and the number of turn., number of turn of wire on it rimary ide., number of turn of wire on it econdary ide. (t), voltage alied to the rimary ide. (t), voltage alied to the econdary ide. v ( t) v ( t) a where a i defined to be the turn ratio of the tranformer. The relationhi between current into the rimary ide, (t), of tranformer veru the econdary ide, (t), of the tranformer; ( t) ( t) ( t) ( t) a n term of haor quantitie; -ote that and are in the ame hae angle. and are in the ame hae angle too. - the turn ratio, a, of the ideal tranformer affect the magnitude only but not the their angle. a a The dot convention aearing at one end of each winding tell the olarity of the voltage and current on the econdary ide of the tranformer. f the rimary voltage i oitive at the dotted end of the winding with reect to the undotted end, then the econdary voltage will be oitive at the dotted end alo. oltage olaritie are the ame with reect to the doted on each ide of the core. f the rimary current of the tranformer flow into the dotted end of the rimary winding, the econdary current will flow of the dotted end of the econdary winding. Examle : Tranformer. How many turn mut the rimary and the econdary winding of a 0-0, 60 Hz ideal tranformer have if the core flux i not allowed to exceed 5mWb? Solution: For an ideal tranformer with no loe, E 0 E 0 From the emf equation, we have E 4.* f * φ max 0 83turn. 3 (4.)(60)(5X0 ) 0 66turn. 3 (4.)(60)(5X0 ) 4
.5. Power in an deal Tranformer. Power ulied to the tranformer by the rimary circuit i given by ; Pin coθ where, θ i the angle between the rimary voltage and the rimary current. The ower ulied by the tranformer econdary circuit to it load i given by the equation; P where, θ i the angle between the econdary voltage and the econdary current. oltage and current angle are unaffected by an ideal tranformer, θ θ θ. Τhe rimary and econdary winding of an ideal tranformer have the ame ower factor. coθ The ower of a tranformer; P coθ - aly /a and a into the above equation give, P ( a )coθ a P coθ P - The ut ower of an ideal tranformer i equal to the inut ower. in The reactive ower, Q, and the aarent ower, S; Q S in in inθ inθ Q S n term of haor quantitie; -ote that and are in the ame hae angle. and are in the ame hae angle too. - the turn ratio, a, of the ideal tranformer affect the magnitude only but not the their angle. Examle : deal Tranformer. Conider an ideal, ingle-hae 400-40 tranformer. The rimary i connected to a 00 ource and the econdary i connected to an imedance of Ω < 36.9 ο, find, (a) The econdary ut current and voltage. (b) The rimary inut current. (c)the load imedance a een from the rimary ide. (d) The inut and ut aarent ower. (e) The ut ower factor. Examle : deal Tranformer. Conider an ideal, ingle-hae 400-40 tranformer. The rimary i connected to a 00 ource and the econdary i connected to an imedance of Ω < 36.9 ο, find, Solution: Examle. 5
.6 Real Single-Phae Tranformer. The ideal tranformer in Section.5 can never been made. The real tranformer ha many imerfection. The real tranformer conit of two or more coil of wire hyically wraed around the ferromagnetic core. The real tranformer aroximate the characteritic of the ideal tranformer. Oeration if the real tranformer; (i) t conit of two coil of wire wraed around a tranformer core. (ii) The rimary of the tranformer i connected to an ac ower ource, and the econdary winding i an oencircuited. (iii) Figure.5 i the hyterei of the tranformer. (iv) Baic oeration from the faraday law, e ind dλ λ i the flux linkage in the coil acro which the voltage i being induced. The um of the flux aing through each turn in the coil added over all the turn of the coil i; λ The average flux er turn i given by ; And Faraday law can be written a, e ind i φ φ i λ dφ.7 The Exact Equivalent Circuit of a Real Tranformer. Coer loe are reitive loe in the rimary and the econdary winding of the tranformer core. Coer loe are modeled by lacing a reitor R in the rimary circuit of the tranformer and a reitor R in the econdary circuit. The leakage flux in the rimary winding i, di e ( t) L LP e di ( t) L LS.7 The Exact Equivalent Circuit of a Real Tranformer. Figure below i an exact model of a tranformer. Model of a Real Tranformer To analyze the tranformer it i neceary to convert the entire circuit to an equivalent circuit at a ingle voltage level a in Figure.8..7 The Exact Equivalent Circuit of a Real Tranformer. To analyze the tranformer it i neceary to convert the entire circuit to an equivalent circuit at a ingle voltage level. Symbol ued for the Exact Equivalent Circuit above; (a) The Tranformer Model Referred to it Primary Winding. (b) The Tranformer Model Referred to it Secondary Winding. 6
The major ue of the exact equivalent circuit of a tranformer i to determine the characteritic uch a voltage regulation and efficiency. A haor diagram for the circuit of the tranformer model referred to it rimary winding, for lagging ower factor can be obtained by uing the following equation: Baed on the above equation and auming a zero degree reference angle for, the haor diagram in the tranformer model referred to it rimary winding for the exact equivalent circuit model of a tranformer. RMS Phaor Diagram for the Exact Equivalent Circuit Model of a Tranformer..8 The Aroximate Equivalent Circuit of a Tranformer. The Exact tranformer in reviou ection i comlex for a ractical engineering alication. n the Aroximate model the voltage dro in R and X i negligible becaue the current i very mall. Figure below i the Aroximate equivalent circuit referred to the rimary ide. The voltage in the rimary erie imedance (r + jx ) i mall, even at full load. Alo, the no load current ( 0 ) i o mall that it effect on the voltage dro in the rimary erie imedance i negligible. Therefore, it matter little if the hunt branch of R c in arallel with X m i connected before the rimary erie imedance or after it. The core lo and magnetizing current are not greatly affected by the move. Connecting the hunt comonent right at the inut terminal ha the great advantage of ermitting the two erie imedance to be combined into one comlex imedance. The equivalent imedance for the circuit i; Aroximate Tranformer Model Referred to the Primary Side. The value of thi equivalent imedance of a articular tranformer deend, of coure, on whether the model ued i referred to the rimary or econdary. Figure below how the aroximate equivalent circuit of tranformer referred to the econdary ide..9 Tranformer oltage Regulation and Efficiency. oltage regulation i a meaure of the change in the terminal voltage of the tranformer with reect to loading. Therefore the voltage regulation i defined a:, nl R, fl, fl 00% Aroximate Circuit Model of a Tranformer Referred to the Secondary. The equivalent imedance for the circuit i; At no load, /a and the voltage regulation can alo be exre a; R a, fl, fl 00% 7
.9 Tranformer oltage Regulation and Efficiency. n the er-unit ytem;, u R, f, ul, fl, u 00% For ideal tranformer R0. t i a good ractice to have a mall voltage regulator a oible. Examle of Tranformer oltage Regulation. Tranformer Efficiency, efficiency of a tranformer i defined a follow; Outut Power P η Outut Power P For on-deal tranformer, the ut ower i le than the inut ower becaue of loe. Thee loe are the winding or R lo (coer loe) and the core lo (hyterei and eddy-current loe). Thu, in term of the total loe, P loe, the above equation may be exreed a; P P η P \ loe P P + P loe P P + P coer + P The winding or coer lo i load deendent, wherea the core lo i contant and almot indeendent of the load on the tranformer. core The efficiency can alo be obtained by uing the er-unit ytem. Examle 3: Tranformer oltage Regulation. 8
Examle 3..0 Oen Circuit and Short Circuit. Oen Circuit Tet. The oen circuit tet i conducted by alying rated voltage at rated frequency to one of the winding, with the other winding oen circuited. The inut ower and current are meaured. For reaon of afety and convenience, the meaurement are made on the low-voltage (L) ide of the tranformer. Equivalent Circuit of the Oen-Circuit Tet. Figure above i the equivalent circuit for the oen-circuit tet. The high voltage (H) ide i oen, the inut current i equal to the no load current or exciting current ( 0 ), and i quite mall. The voltage dro in the rimary leakage reactance and winding reitance may be neglected. The inut ower i almot equal to the core lo at rated voltage and frequency. θ oc i the angle by which o_l lag oc. The core lo current, c i in hae with oc while m lag oc by 90. Then; The core-lo current, c, may be found from above equation, then Rc_L may be calculated by the equation below, The magnetization current m i given by the above equation or may be found from oc and c uing Short Circuit Tet. The hort-circuit tet i ued to determine the equivalent erie reitance and reactance. One winding i horted at it terminal, and the other winding i connected through roer meter to a variable, low-voltage, high-current ource of rated frequency. The ource voltage i increaed until the current into the tranformer reache rated value. To avoid unneceary high current, the hort-circuit meaurement are made on the high-voltage ide of the tranformer. The tet circuit with the effective equivalent circuit i hown in Figure below. Equivalent Circuit of the Short-Circuit Tet. eglecting 0, the inut ower during thi tet i conumed in the equivalent reitance referred to the rimary or highvoltage ide, Req_H. Then 9
0