A 100 kva 2200/400 v transformer has R1=0.3 ohm,x1=1.1ohm,R2=0.01ohm,X...
Equivalent Impedance of Transformer
To calculate the equivalent impedance of the transformer, we need to combine the resistance and reactance of both primary and secondary windings. The formula to calculate the equivalent impedance is as follows:
Zeq = (R1 + R2) + j(X1 + X2)
Where,
R1 = Resistance of primary winding
R2 = Resistance of secondary winding
X1 = Reactance of primary winding
X2 = Reactance of secondary winding
Substituting the given values in the above formula, we get:
Zeq = (0.3 + 0.01) + j(1.1 + 0.035) = 0.31 + j1.135 ohm
Therefore, the equivalent impedance of the transformer is 0.31 + j1.135 ohm.
Total Copper Losses
Total copper losses are the sum of copper losses in both primary and secondary windings. Copper losses are the power lost due to the resistance of the windings. The formula to calculate copper losses is as follows:
Pc = I^2R
Where,
Pc = Copper losses
I = Current flowing through the winding
R = Resistance of the winding
To calculate the copper losses in the primary winding, we need to calculate the current flowing through it. The formula to calculate the current is as follows:
I1 = (KVA x 1000) / (V1 x √3)
Where,
I1 = Current flowing through primary winding
KVA = Rated power of the transformer
V1 = Voltage of the primary winding
Substituting the given values in the above formula, we get:
I1 = (100 x 1000) / (2200 x √3) = 27.15 A
Using the above formula, we can calculate the current flowing through the secondary winding as well.
I2 = (KVA x 1000) / (V2 x √3) = (100 x 1000) / (400 x √3) = 144.34 A
Now, we can calculate the copper losses in both primary and secondary windings using the above formulas.
Pc1 = I1^2R1 = 27.15^2 x 0.3 = 221.27 W
Pc2 = I2^2R2 = 144.34^2 x 0.01 = 208.98 W
Therefore, the total copper losses in the transformer are Pc = Pc1 + Pc2 = 430.25 W.