Transformer efficiency

The efficiency of the transformer is determined by the ratio of the power P2 delivered by the transformer to the load to the power P1 consumed by the network:

η = P2 / P1

Efficiency characterizes the efficiency of voltage conversion in a transformer.

In practical calculations, the efficiency of the transformer is calculated by the formula

η = 1 — (∑P — (P2 + ∑P),

where ∑P = Pmail + Pmg — total losses in the transformer.

This formula is less sensitive to errors in the determination of P1 and P2 and therefore allows a more accurate efficiency value to be obtained.

The net power delivered by the transformer to the network is calculated by the formula

P2 = m NS U2n NS I2n NS kng NS Cosφ2 = kng NS Сn NS Cosφ2,

where kng = I2 / I2n — load factor of the transformer.

The electrical losses in the windings are determined by the short circuit experience of the transformer.

Pmail = kng2 NS PYes,

where Pk = rk x I21n — short-circuit losses at nominal current.

Losses in steel Rmg are determined by the idle test rmg = Ro

They are assumed constant for all modes of operation of the transformer, since when u1 = const EMF E1 in the modes of operation changes insignificantly.

Based on the above, the efficiency of the transformer can be determined by the following formula:

η = (Po + kng2 NS PSe) / (kng NS Сn NS Cosφ2 + Po + kng2 NS PSe),

Analysis of this expression shows that the efficiency of the transformer has a maximum value at the load when the losses in the windings are equal to those in the steel.

Rice. 1. Determination of the optimal value of the load factor of the transformer

From this we get the optimal value of the load factor of the transformer:

kngopt = √Po / PTo be

In modern power transformers, the loss coefficient Po/ P1 = (0.25 — 0.4); therefore, the maximum of η occurs at kng = 0.5 — 0.6 (Fig. 1).

From the η (kng) curve, it can be seen that the transformer has almost constant efficiency over a wide range of load variation from 0.5 to 1.0. At low loads, the η of the transformer drops sharply.

Transformer substation