EQUIVALENT CIRCUIT OF A TRANSFORMER

•    Equivalent circuit of a transformer is an electric circuit, which gives the same performance as that of the transformer.

•    The core loss, copper loss, voltage drop and efficiency in the equivalent circuit should be equal to the transformer losses, voltage drop and efficiency.

•    If the resistance and inductive reactance of the primary and secondary windings are considered to be in series with those windings, we get the electrical circuits representing the primary and secondary sides of the transformer as shown in the figure:

Where V1 = Voltage applied to the primary winding.

I0 = No load primary current.

Im = Magnetizing component of no load primary current

Ic = Core loss component of no load primary current

I1 = Primary current on load

I2 = Secondary load current

V2 = Voltage across the secondary load terminals

I2 ‘= Primary equivalent of secondary load current

X0 =Inductive reactance of the magnetizing current path

R0 =Resistance representing the core loss

R1=Resistance of the primary winding

X1=Reactance of the primary winding

R2 =Resistance of the secondary winding

X2=Reactance of the secondary winding

E1 = E.M.F. induced in the primary winding

E2=E.M.F. induced in the secondary winding

•    The equivalent circuit consists of two circuits, one representing the primary winding and another is the secondary winding.

•    The transfer of power from one circuit to other takes place due to mutual induction.

•    To make the calculation simpler, transfer the voltage, current, resistance and reactance of one winding to the other side with their equivalents as shown in the following Figure

In that case we would have to work in one winding only which is more convenient. So the parameters of the secondary side can be represented as

Primary equivalent of the secondary induced voltage
    E2’ = E2/k = E2 N1 / N2 = E1

Primary equivalent of the secondary terminal voltage
    V2‘= V2/k = V2 N1 / N2 = V1

Primary equivalent of the secondary current
    I2‘= k I2 = (N1 / N2) I2

Primary equivalent of the secondary reactance
    X2‘= X2/k2 = X2 (N1 / N2)2

Primary equivalent of the secondary resistance
    R2‘= R2/k2 = R2 (N1 / N2)2

Primary equivalent of the secondary impedance
    Z2‘= Z2/k2 = Z2 (N1 / N2)2

Primary equivalent of the load impedance
    ZL‘= ZL/k2 = ZL (N1 / N2)2

Since the emf induced in the equivalent circuit representing the secondary side of the transformer is equal to the primary induced emf, the two circuits may be merged as shown in the following figure.