Electrical Engineering ⇒ Topic : Condition for Maximum Efficiency

Let us assume the iron losses = P_i

The total copper losses referred to the primary side = 

                        ...........(1)

In a given transformer, V₁ is approximately constant and hence for a given value of /₁ and cos Φ₁ the efficiency will be maximum when the denominator of Eq. (1) is minimum. Thus, differentiating both the sides with respect to /₁, we get

will be maximum when d/d/_i = O.

                        Copper loss = Iron loss                                   ............(2)

Hence, the efficiency of a transformer is maximum when the variable copper loss is equal to the constant iron loss. From Eq. (2), it follows that at maximum efficiency, the primary current

Similarly, at maximum efficiency, the load current

                                                                     ..........(3)

where R_e2 is the equivalent resistance of the transformer referred to the secondary side given by R_e2 = R₂ + (V₂/V₁)²R_i [Eq.)]. The efficiency versus load current curves are shown in Fig. (a) for different power factors

            FIGURE (a) Efficiency of a transformer as a function of the load current for different power factors

For a given transformer, the efficiency decreases with a decrease in power factor. Distribution transformers are generally designed to give maximum efficiency at 75% of full-load

CONDITION FOR MAXIMUM EFFICIENCY

                         ............ (1)

It may be noted that the output current corresponding to maximum efficiency is given by

                                                                              ............... (2)

                             Figure (a) Efficiency vs current.

The plot of efficiency vs current is shown in Figure (a).