FREQUENCY EFFECT ON TRANSFORMER OUTPUT (50/60 Hz)

When the Transformer operates on 50 Hz Frequency

we will solve this using suppose values :

Let

Transformer =100kVA, R=800, L=1.2 H, f= 50 Hz

We know = XL = √(2πfL)

XL = √ ( 2 ✕ 3.145 ✕ 50 ✕ 1.2 )= 377Ω

We know Impedance Z:√ (R^2+XL ^2 )

Z= √ (800^2 + 377^2)=884.380Ω

Power Factor Cos θ = R/Z

                                Power Factor Cos θ = 800/884.380 = 0.904588

We know the Output of the Transformer is Real Power =KVA

KVA  ✕ Cos θ= 100 ✕  0.904588 = 90.45 KW

When the Transformer operates on 60 Hz Frequency

                                    Let

Transformer =100kVA, R=800, L=1.2 H, f= 60 Hz

We know = XL = √(2πfL) 

XL = √ ( 2 ✕ 3.145 ✕ 60 ✕ 1.2 )= 452.88Ω

We know Impedance Z:√ (R^2+XL ^2 )

Z= √ (800^2 + 452.88^2)=919.2933Ω

Power Factor Cos θ = R/Z 

                                Power Factor Cos θ = 800/919.2933 = 0.8702

We know the Output of the Transformer is Real Power =KVA

KVA  ✕ Cos θ= 100 ✕  0.8702 = 87.02 KW

The difference came out: 90.45 - 87.02 = 3.42KW