Single Phase Transformers ELE 2103 Electrical Machinery1

Practical Transformer - On Load Rc Xm Ø N1 N2 V2 V1 R1 X1 R2 X2 Ideal I1 E1 E2 Ic Im I´2 I2 R Load : RL Load : RC Load :

Why equivalent circuit ? LOAD Rc Xm Ø N1 N2 V2 V1 R1 X1 R2 X2 Ideal I1 E1 E2 Ic Im Transformer analysis can be carried out using phasor diagram approach More convenient to represent transformer by equivalent circuit Equivalent ckt is a circuit rep’n of equations that describe behavior Equivalent ckt enables application of simple circuit theory

Equivalent circuit representation Ideal Transformer E1 I1 R1 X1 Rc Xm Ic Im Io R2 X2 I2 ZL E2 V2 I'2 N1 N2 Transformer magnetization curve is assumed linear Ideal transformer is introduced to show transformation of voltage and current between primary and secondary windings

Eq. resistance, reactance & impedance V1 E1 I1 R1 X1 Rc Xm Ic Im Io R2 X2 I2 ZL E2 V2 I'2 N1 N2 Ideal Transformer Resistances & Reactances can be transferred to either side All quantities are referred to either primary side or secondary side Facilitates simplicity of calculations & result analysis

Equivalent circuit as referred to primary Primary winding impedance Secondary winding impedance Secondary copper loss Equivalent secondary winding resistance as referred to primary Eq primary copper loss Equivalent secondary winding reactance as referred to primary Equivalent sec winding impedance as referred to pry Equivalent load impedance as referred to pry

Exact equivalent circuit referred to primary E1 = E'2 I1 R1 X1 V1 RC Xm Ic Im Io R'2 X'2 Z'L V'2 I'2

Approximate equivalent circuit No load current Io is quite small as compared to rated primary current Voltage drops in primary due to Io is negligibly small Shunt branch circuit is shifted towards the supply side Enables ease of calculations, results obtained will only be approximate R'2 X'2 E1 = E'2 I1 V1 Rc Xm Ic Im Io Z'L V'2 I'2 R1 X1

Approx equivalent circuit referred to primary Xm Ic Im Io Z'L V'2 I'2 R1e X1e Equivalent winding resistance as referred to pry Equivalent winding reactance as referred to pry Equivalent winding impedance as referred to pry

Exercise [1] A 15 kVA, 2200 / 110 V, 50 Hz, 1 transformer has pry & sec winding resistances of 1.75  & 0.0045  and pry & sec winding reactances of 2.6  & 0.0075  respectively. Determine (a) equivalent resistance, reactance & impedance as referred to pry (b) equivalent resistance, reactance & impedance as referred to sec (c) total copper loss Ans: (a) 3.55 , 5.6 , 6.63 57.63o (b) 0.008875 , 0.014 , 0.0166 57.56o (c) 165 W