A (50/60 Hz) Transformer. Which one will give more Output? (When operates on 50 or 60 Hz frequency)...???

 A (50/60 Hz) Transformer. Which one will give more Output? 

A Transformer is designed to be operated on both 50 & 60 Hz frequency. For the Same rating, which one will give more out put; when,

1.  Operates on 50 Hz
2.   Operates on 60 Hz

Obviously! It will give more out put when we operate a transformer (of same rating) on 50 Hz instead of 60 Hz.

Because in previous posts, we proved that, in inductive circuit, when frequency increases, the circuit power factor decreases. Consequently, the transformer out put decreases.

Let’s consider the following example.

Suppose,

When Transformer operates on 50 Hz Frequency

Transformer = 100kVA, R=700Ω, L=1.2 H, f= 50 Hz.

X_L = 2πfL = 2 x 3.1415 x 50 x 1.2 = 377 Ω

Impedance Z = √ (R²+X_L²) = √ (700²+ 377²) = 795 Ω

Power factor Cos θ = R/Z = 700/795 =0.88

Transformer Output (Real Power)

kVA x Cos θ

100kVA x 0.88

88000 W = 88kW

Now,

When Transformer operates on 60 Hz Frequency

Transformer =100kVA, R=700Ω, L=1.2 H, f= 60 Hz.

X_L = 2πfL = 2 x 3.1415 x 60 x1.2 = 452.4 Ω

Impedance Z = √ (R²+X_L²) = √ (700²+ 452.4 ²) = 833.5 Ω

Power factor = Cos θ = R/Z = 700/833.5 =0.839

Transformer Output (Real Power)

kVA x Cos θ

100kVA x 0.839

=83900W = 83.9kW Output

Now see the difference (real power i.e., in Watts)

88kW- 83.9kW = 4100 W = 4.1kW

If we do the same (As above) for the power transformer i.e, for 500kVA Transformer, the result may be huge, as below.

(Suppose everything is same, without frequency)

Power Transformer Output (When operates on 50 Hz)

500kVA x 0.88 = 44000 = 440kW

Power Transformer Output (When operates on 60 Hz)

500kVA x 0.839 = 419500 = 419.5kW

Difference in Real power i.e. in Watts

440kW – 419.5kW = 20500 = 20kVA

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