The efficiency of a transformer can be calculated from
The total losses include the losses in the electric circuit, magnetic circuit, and the dielectric circuit. Stigant and Franklin [3, p. 97] state that a transformer has its highest efficiency at a load at which the iron loss and copper loss are equal. Therefore, the load at which the efficiency is the highest can be found from
Note that the iron losses (or core losses) include (1) hysteresis loss and (2) eddy-current loss. The hysteresis loss is due to the power requirement of maintaining the continuous reversals of the elementary magnets (or individual molecules) of which the iron is composed as a result of the flux alternations in a transformer core. The eddy-current loss is the loss due to circulating currents in the core iron, caused by the magnetic flux in the iron cutting the iron, which is a conductor.
The eddy-current loss is proportional to the square of the frequency and the square of the flux density. The core is built up of thin laminations insulated from each other by an insulating coating on the iron to reduce the eddy-current loss. Also, in order to reduce the hysteresis loss and the eddy-current loss, special grades of steel alloyed with silicon are used. The iron or core losses are practically independent of the load. On the other hand, the copper losses are due to the resistance of the primary and secondary windings.
In general, the distribution transformer costs can be classified as (1) the cost of investment, (2) the cost of lost energy due to the losses in the transformer, and (3) the cost of demand lost (i.e., the cost of lost capacity) due to the losses in the transformer. Of course, the cost of investment is the largest cost component, and it includes the cost of the transformer itself and the costs of material and labour involved in the transformer installation.
shows the annual cost per unit load vs. load level. At low-load levels, the relatively high costs result basically from the investment cost, whereas at high-load levels, they are due to the cost of additional loss of life of the transformer, the cost of lost energy, and the cost of demand loss in addition to the investment cost. Figure 3.15 indicates an operating range close to the bottom of the curve. Usually, it is economical to install a transformer at approximately 80% of its nameplate rating and to replace it later, at approximately 180%, by one with a larger capacity. However, presently, increasing costs of capital, plant and equipment, and energy tend to reduce these percentages.
Transformer efficiency chart applicable only to the unity PF condition. To obtain the efficiency at a given load, lay a straightedge across the iron and copper loss values and read the efficiency at the point where the straightedge cuts the required load ordinate. (From Stigant, S.A. and Franklin, A.C., The J&P Transformer Book, Butterworth, London, U.K., 1973.)