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A transformer is connected to 2200 V, 40 Hz supply. The core loss is 800 Watts out of which 600 Watts are due to hysteresis and remaining eddy current losses. What is the core loss if the supply voltage and frequency are 3300 V and 60 Hz respectively?

A transformer is connected to 2200 V, 40 Hz supply. The core loss is 800 Watts out of which 600 Watts are due to hysteresis and remaining eddy current losses. What is the core loss if the supply voltage and frequency are 3300 V and 60 Hz respectively? Correct Answer 1350 Watts

Concept:

Iron losses (Pi) = Hysteresis loss(Ph) + Eddy current loss(Pe)

Hysteresis loss ∝ Bn f ∝  f

Bn is flux density

with flux density being kept constant → Hysteresis loss ∝ k1 f

Eddy current loss ∝ B2 f2 ∝ f2

 with flux density being kept constant → Eddy current loss ∝ K2 f2 

Where, K1 and K2 are constant for a particular transformer.

Hence total iron losses

Pi = k1f + k2f2

Calculation:

Given:

For 40 Hz frequency 

Core (iron) loss (Pi) = 800 watts

Ph = 600 = k1f 

⇒ k1 = 600/40 = 15

Pe = (800 - 600) = 200 = k2f2

⇒ k2 = √(200/ 402) =0.125

For 60 Hz frequency

Pi = (15 × 60) + (0.125)(602)= 1350 watts

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