Equivalent circuit of Transformer

1. Equivalent circuit of Transformer

       The term equivalent circuit of a machine means the combination of fixed and variable resistances and reactances, which exactly simulates performance and working of the machine.
       For a transformer, no load primary current has two components,
                   Im = Io sinΦo = Magnetizing component 
                   Ic = IcosΦo = Active component 
       Im produces the flux and is assumed to flow through reactance Xo called no load reractance while Ic is active component representing core losses hence is assumed to flow through the reactance Ro. Hence equivalent circuit on no load can be shown as in the Fig. 1. This circuit consisting of Ro and Xo in parallel is called exciting circuit. From the equivalent circuit we can write,
Ro = V1/Ic
and  Xo= V1/Im
Fig. 1 No load equivalent circuit

       When the is connected to the transformer then secondary current I2 flows. This causes voltage drop across R2 and R2. Due to I2, primary draws an additional current
       I2' = I2/ K. Now I1 is the phasor addition of Io and I2'. This I1 causes the voltage drop across primary resistance R1 and reactance X1.
       Hence the equivalent circuit can be shown as in the Fig. 2.
Fig. 2
       But in the equivalent circuit, windings are not shown and it is further simplified by transferring all the values to the primary or secondary. This makes the transformer calculation much easy.
       So transferring secondary parameters to primary we get,
                          R2'= R2/K2 ,      X2' = X2/K2'  ,       Z2' = Z2/K2
While                  E2' = E2/K'               I2' = K I2
Where                 K = N2 /N1
      While transferring the values remember the rule that
                  Low voltage winding High current Low impedance 
                  High voltage winding Low current High impedance
        Thus the exact equivalent circuit referred to primary can be shown as in the Fig. 3.
Fig.  3   Exact equivalent circuit referred to primary

       Similarly all the primary value can be referred to secondary and we can obtain the equivalent circuit referred to secondary.
                     R1' = K2 R1 ,        X1' = K2 X1,       Z1' = K2 Z1
                      E1'= K E1,             Io' = I1 /K'    Io' = Io /K
       Similarly the exciting circuit parameters also gets transferred to secondary as Ro'and Xo '. The circuit is shown in the Fig.4.
Fig. 4  Exact equivalent circuit referred to secondary

       Now as long as no load branch i.e. exciting branch is in between Z1 and Z2', the impedances can not be combined. So further simplification of the circuit can be done. Such circuit is called approximate equivalent circuit.
1.1 Approximate Equivalent Circuit
       To get approximate equivalent circuit, shift the no load branch containing Ro and Xo to the left of R1 and X1. By doing this we are creating an error that the drop across R1 and X1due to Io is neglected. Hence such an equivalent circuit is called approximate equivalent circuit.
       So approximate equivalent circuit referred to primary can be as shown in the Fig. 5.
Fig. 5 Approximate equivalent circuit referred to primary

       In this circuit now R1 and R2' can be combined to get equivalent resistance referred to primary R1e as discussed earlier. Similarly X1and X1' can be combined to get X1e. And equivalent circuit can be simplified as shown in the Fig. 6.
Fig. 6

       We know that,  R1e = R1 + R2'= R1 + R2/K2
                               X1e = X1 + X2' = X1 + X2/K2
                                Z1e = R1e + j X1e
                                 Ro = V1 /Iand   Xo = V1 /Im
                                I= IcosΦo and   Im = IsinΦo
       In the similar fashion, the approximate equivalent circuit referred to secondary also can be obtained.

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