Question

Problem 3 A 50-Hz transformer is operated from a 60 Hz supply. Assume that the load does not change. Discuss the corresponding effects on its flux, reactive power requirements, losses, and efficiency. а- [5 Points] A 50-kVA, 2400/240 V, 60-Hz, single-phase distribution transformer has the following equivalent circuit parameters referred to the high-voltage side Xea 3.0 Req= 0.5 Xm 4,500 S2 Use the equivalent Cantilever model circuit shown in Figure (1). Assume that the load on the secondary of the transformer is 40 kVA at 0.8 p.f. lagging with the receiving end voltage maintained at 240 V b- Determine the following voltage at the primary side, current at the primary side, i- active power input at the primary side, iv- reactive power input at the primary side, V power factor at the primary side, and vi- efficiency of the transformer at this loading Re 30,000 2 i- [15 Points] Хая ண 2 V/2 Figure () Equivalent Circuit of Transformer for Problem 3 000

Answer 1

Transformer is a constant flu a device so, whether load is fixed (8) Variable it won't have any effect on flax since load is constant, reactive powes requirement is also constant. - and - iron loss (constant losses independant of load] L L copper loss ( load de pers dant] since load is constant, coppes losses are also constant and hence to dal losses and constant. Efficiency also load defens dacant. As loadis constant, efficiency also constant. y

0.0- 3/- Limmagini ई २५- २५ 240 240 ५०००० .. 66-666 prims any voltage Jo= 240200 + 166-666 ( 1-36-800 (0-5+53) __- 240 + 5०-५१५ ८1१.५५१ - 777११ +5 168.79 , 737.६५ 113-२२१° v . primary current + t: 737.5५/ 13-२२७° 30. + ९०.) 0.1667 1-63-२५६° A 0.657 1- 68.२ ५६ + (66 - 666 1-36 - १४° 133.५५५ -J100. 13०५ - 166 - १० ) 30-36• १११° A

Gú ) Active power input = output + losses - 40000 x0.8+(166.666 J xo.5 +637.56) = 45906-909 w 30000 (1) Reactive power input : 737-54 x 166-8073 x sin ( 36-1890) = 73849.043 VAR (iv) primary power factor = cos ( 36-8890) -0.79 v efficiency= 40000xo.8 Xloo 45906.909 = 69.77