Single Phase Transformers ELE 2103 Electrical Machinery 1

Single Phase Transformers ELE 2103 Electrical Machinery 1

Practical Transformer - On Load X 1 R 1 V 1 I´ 2 Ic Rc Im. E 1 X m R 2 Ø N 1 N 2 Ideal R Load : RL Load : RC Load : X 2 E 2 I 2 V 2 LOAD

Why equivalent circuit ? R 2 X 1 R 1 X 2 Ø V 1 Ic Rc Im. E 1 X m N 1 N 2 E 2 V 2 LOAD Ideal • • 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 X 1 R 1 I 1 V 1 R 2 Io I'2 X 2 Ic Im Rc V 2 X m E 1 ZL E 2 N 1 N 2 Ideal Transformer • 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 R 1 X 1 I 1 V 1 R c Io Ic Im R 2 I'2 X 2 I 2 V 2 X m E 1 ZL E 2 N 1 N 2 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 copper loss Eq primary copper loss Equivalent secondary winding resistance as referred to primary 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 R 1 I 1 V 1 RC X'2 R'2 X 1 Io Ic Im I'2 X m E 1 = E'2 V'2 Z'L

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 X'2 R'2 X 1 R 1 I 1 V 1 Rc Io Ic Im I'2 Xm E 1 = E'2 V'2 Z'L

Approx equivalent circuit referred to primary I 1 V 1 Rc Io Ic Im I'2 Xm R 1 e X 1 e V'2 Equivalent winding resistance as referred to pry Equivalent winding reactance as referred to pry Equivalent winding impedance as referred to pry Z'L

Exercise [1] A 15 k. VA, 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. 63 o (b) 0. 008875 � , 0. 014 � , 0. 0166 � 57. 56 o (c) 165 W