Lecture 11 Transformer Equivalent Circuit 1 Transformer Equivalent

Lecture # 11 Transformer Equivalent Circuit 1

Transformer Equivalent Circuit • Using the previous relationships, we can derive an equivalent circuit model for the real transformer. • For regulation analysis, parallel branches RC , Lm and stray capacitance have negligible effect and can be neglected. 2

Transformer Simplified Equivalent Circuit • This yields the simplified circuit as shown below. 3

Transformer Simplified Equivalent Circuit • Even greater simplification is achieved by reflecting secondary impedances into the primary. • The reflected load voltage is a V 2 and the reflected load current is I 2/a. • Regulation calculations are performed using this simplified circuit. Re q RP a 2 Rs X eq X 4 p a 2 X s

Transformer Voltage Regulation EXAMPLE: A 10: 1 transformer has primary and secondary resistance and reactance of (4 + j 4) and (0. 04+ j 0. 04) respectively as shown in the Figure. a. Determine its equivalent circuit. b. If VL= 120 V∠ 0° and IL= 20 A∠ 30°, what is the supply voltage, Eg? c. Determine the regulation. 5

Transformer Voltage Regulation 6

Transformer Voltage Regulation c) Now consider the no-load condition. Let VNL be the no-load voltage. As indicated, a. VNL = 1222 V. Thus, VNL = 1222/a =1222/10 = 122. 2 V and 7

Transformer Efficiency • Efficiency is the ratio of output power to input power. • But Pin=Pout+Ploss. For a transformer, losses are due to I 2 R losses in the windings (called copper losses) and losses in the core (called core losses). Thus, • Large power transformers are exceptionally efficient, (98% to 99 %). • The efficiencies of smaller transformers are around 95% or better. 8