Question

A 100 kVA, 6600/400 V, 50 Hz single phase transformer has 80 turns on LV side. At 25 Hz its flux increases by 10%. The HV and kVA rating at 25 Hz will be respectively.
1. 3630 V, 55 kVA
2. 6600 V, 100 kVA
3. 7260 V, 100 kVA
4. 6600 V, 55 kVA

Answer 1

Correct Answer - Option 1 : 3630 V, 55 kVA

Number of turns on L.V side = 80

Flux increases by 10% at 25 Hz

We know that, V = √2 π f ϕ N

V ∝ f⋅ ϕ

\(\frac{{{V_{1H.V}}}}{{{V_{2V.H}}}} = \frac{{{f_1}}}{{{f_2}}} \cdot \frac{{{\phi _1}}}{{{\phi _2}}}\)

Here, V_1H.V = High voltage side voltage at 50 Hz

f₁ = 50 Hz

V_2.H.V = high voltage side voltage at 25 Hz

f₂ = 25 Hz

ϕ = flux at 50 Hz

ϕ₂ = flux at 25 Hz

ϕ₂ = 1.1 ϕ­₁ (Given)

\(\frac{{6600}}{{{V_{2.H.V}}}} = \frac{{50}}{{25}} \cdot \frac{{{\phi _1}}}{{1.1{\phi _1}}}\)

\(\Rightarrow {V_{2.H.V}} = \frac{{6600\; \times \;1.1}}{2}\)

⇒ V_2.H.V = 3630 V

We know that S = V.I

S ∝ V

\(\frac{{{S_1}}}{{{S_2}}} = \frac{{{V_{1.H.V}}}}{{{V_{2H.V}}}}\)

Here, S₁ and V_1H.V at 50 Hz

S₂ and V_2H.V at 25 Hz 

\(\frac{{100}}{{{S_2}}} = \frac{{6600}}{{3630}}\)

⇒ S₂ = 55 kVA