A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be_________ W (rounded off to 2 decimal places).
Concept:
Hysteresis losses: These are due to the reversal of magnetization in the transformer core whenever it is subjected to alternating nature of magnetizing force.
\({W_h} = \eta B_{max}^xfv\)
\({B_{max}} \propto \frac{V}{f}\)
Where
x is the Steinmetz constant
Bm = maximum flux density
f = frequency of magnetization or supply frequency
v = volume of the core
At a constant V/f ratio, hysteresis losses are directly proportional to the frequency.
Wh ∝ f
Eddy current losses: Eddy current loss in the transformer is I2R loss present in the core due to the production of eddy current.
\({W_e} = K{f^2}B_m^2{t^2}V\)
\({B_{max}} \propto \frac{V}{f}\)
Where,
K - coefficient of eddy current. Its value depends upon the nature of magnetic material
Bm - Maximum value of flux density in Wb/m2
t - Thickness of lamination in meters
f - Frequency of reversal of the magnetic field in Hz
V - Volume of magnetic material in m3
At a constant V/f ratio, eddy current losses are directly proportional to the square of the frequency.
We ∝ f2
Iron losses or core losses or constant losses are the sum of both hysteresis and eddy current losses.
Wi = Wh + We
At constant V/f ratio, Wi = Af + Bf2
Calculation:
The table below shows the given data.
Voltage (V) | Frequency (f) | V/f ratio | No load losses (W) | |
Case 1 | 200 V | 50 Hz | 4 | 450 |
Case 2 | 160 V | 40 Hz | 4 | 320 |
Case 3 | 100 V | 25 Hz | 4 | Required value |
The V/f ratio is constant in all the cases as shown in the above table.
Now, the equations for Case 1 and Case 2 are given below
Case 1: 450 = A (50) + B (50)2
Case 2: 320 = A (40) + B (40)2
By solving the above two equations,
A = 4, B = 0.1
Now, the required value for the Case 3 is
W3 = 4 (25) + 0.1 (25)2 = 162. 5 W
Important Questions from Transformer Core Losses
- What will be the eddy current loss if the supply frequency of a transformer becomes double?
- Which power loss is assessed by open-circuit test on transformer?
Eddy current loss in a transformer can be reduced by _________.
Stray load-losses in a motor vary according to square of the load current; are caused by the leakage flux induced by load currents in laminations and account for 4% to 5% of total losses. What is the way to reduce these losses?
For a single phase, two winding transformer, the supply frequency and voltage are both increased by 10%. The percentage changes in the hysteresis loss and eddy current loss, respectively, are
