Approximate Voltage Drop in Transformer

 Approximate Voltage Drop in Transformer

      Consider the equivalent circuit referred to secondary as shown in the Fig. 1.

Fig. 1 

       From the Fig. 1 we can write,

       As primary parameters are referred to secondary, there are no voltage drops in primary.

       When there is no load, I₂ = 0 and we get no load terminal voltage V₂₀ as E₂.

.^..                   V₂₀ = E₂ = No load terminal voltage

while              V₂ = Terminal voltage on load

       Consider the phasor diagram for lagging p.f. load. The current I₂ lags V₂ by angle Φ₂. Take V₂ as reference phasor. I₂ R_2e is in phase with I₂ while I₂ X_2e leads I₂ by 90^o. The phasor diagram is shown in the Fig.2.

Fig. 2

       To derive the expression for approximate voltage drop, draw the circle with O as centre and OC as redius, cutting extended OA at M. As OA = V₂ and now OM = E₂, the total voltage drop is AM = I₂ Z_2e.

       But approximating this voltage drop is equal to AN instead of AM where N is intersection of perpendicular drawn from C on AM. This is because angle is practically very very small and in practice M and N are very close to each other.

       Approximate voltage drop = AN

       Draw perpendicular from B on AM intersecting it at D and draw parallel to DN from B to the point L shown in the Fig. 2.

.^..                      AD = AB cos Φ₂= I₂ R_2e cos Φ₂

and                    DN = BL = BC sin Φ₂ = I₂ X_2e sin Φ₂

.^..                       AN = AD + DN = I₂ R_2e cos Φ₂ + I₂ X_2e sin Φ₂

Assuming            Φ₂=  Φ₁= Φ

.^..  Approximate voltage drop = I₂ R_2e cos Φ + I₂ X_2e sin Φ

       If all the parameters are referred to primary then we get,

       Approximate voltage drop = I₁ R_1e cos Φ +  I₁ X_1e sin Φ

       If the load has leading p.f. then we get the phasor diagram as shown in the Fig. 3. The I₂ leads V₂ by angle Φ₂ .

Fig. 3

       In this case, the expression for approximate voltage drop remains same but the sign of I₂ X_2e sin Φ reverses.
Approximate voltage drop  = I₂ R_2e cos Φ - I₂ X_2e sin Φ    ....... Using referred to secondary values
                                           = I₁ R_1e cos Φ - I₁ X_1e sin Φ   ...........Using referred to primary values

       It can be noticed that for leading power factor E₂ < V₂.

       For the unity power factor, the phasor diagram is simple and is shown in the Fig. 4. For this case, as cos Φ  = 1 and sin Φ   = 0, the approximate voltage drop is I₂ R_2e or I₁R_1e.

Fig. 4

       Thus the general expression for the total approximate voltage drop is,
       Approximate voltage drop = E₂ - V₂
                                         = I_2e R_2e  cosΦ  I_2e X_2e sin Φ     ........Using referred to secondary values
                                         = I_1e R_1e  cos Φ   I_1e X_1e sin Φ     ........Using referred to primary values

       + sing for lagging power factor while - sign for leading power factor loads.

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