TRANSFORMER CIRCUIT MAGNETIZING REACTANCE

For an ideal transformer, the magnetizing current is assumed to be negligible. For a real transformer, some magnetizing current must flow when voltage is applied to the winding in order to establish a flux in the core.

The voltage induced in the winding by the flux restrains the magnetizing current. It was shown earlier that the magnetizing current is not really sinusoidal, but contains many odd harmonics in addition to the fundamental frequency.

If we neglect the harmonics and concentrate on the fundamental frequency, the magnetizing current in the winding lags the applied voltage by 90°. In a two-winding transformer, this is equivalent to placing a reactance Xm, called the magnetizing reactance, in parallel with the transformer terminals.

The peak value of the magnetizing current is determined from the B-H curve of the core, which we have seen is very nonlinear. Therefore, the magnetizing reactance is not a constant but is voltage dependent; however, if the peak flux density is kept well below the point of saturation, Xm can be approximated by a constant reactance in most engineering calculations.

It is generally desirable to maximize Xm in order to minimize the magnetizing current. We saw earlier that inductance is inversely proportional to the reluctance of the core along the flux path and the reluctance of an air gap is several thousand times the reluctance of the same distance through the steel.

Therefore, even tiny air gaps in the flux path can drastically increase the core’s reluctance and decrease Xm. A proper core design must therefore eliminate all air gaps in the flux path.

Since any flux that is diverted must flow between the laminations through their surfaces, it is vital that these surfaces lie perfectly flat against each other. All ripples or waves must be eliminated by compressing the core laminations together tightly.

This also points out why the oxide layers on the lamination surfaces must be extremely thin: since these layers have essentially the same permeability as air and since the flux that is diverted from the air gaps must then travel through these oxide layers, the core’s reluctance would greatly increase if these layers were not kept extremely thin.

CONNECTING THREE-PHASE BANKS USING SINGLE-PHASE TRANSFORMERS

There can be advantages to using single-phase transformers to make a three phase bank instead of building a three-phase unit. For instance, it may be impossible or impractical to fabricate or ship a three-phase transformer with an extremely large MVA capacity.

A bank of three single-phase transformers may then be the solution, although the total size, weight, and cost of three single-phase units will probably exceed the size, weight, and cost of one three phase unit.

An additional advantage of the bank arrangement is that a failure of one single-phase unit will usually be less costly to repair than a failure a larger three-phase unit. Furthermore, one spare single-phase transformer is usually all that is required to assure sufficient reliability for the entire bank.

With a three-phase transformer, an additional spare three-phase transformer would be required, so the total cost of the installation plus a spare transformer is twice the cost of the installation alone. The total cost of a bank of single phase transformers plus a spare is only 133% the cost of the bank alone.

Therefore, the total cost of a bank of single-phase transformers plus a spare is probably less than the cost of a three-phase transformer plus a spare.

Either Y or Δ connections are possible with single-phase transformers connected in banks. It is extremely important that the single-phase transformers are carefully matched when they are banked together, especially when the Δ connection is used.

Using mismatched transformers in the Δ connection will result in excessive circulating currents that will severely de-rate the bank or cause overheating.

One interesting configuration for a three-phase bank is the open Y-Δ connection used extensively in rural distribution systems. The open Y-Δ connection uses two single-phase transformers. An open Y-Δ connection requires only two phases plus the neutral on the primary side of the bank in order to develop a three-phase voltage at the secondary.

This is an obvious cost saving (in addition to the avoided cost of a third transformer) when the installation is far away from a three-phase primary circuit. If one of the transformers is center-tapped as then the bank provides a single-phase lighting leg in addition to a three-phase power circuit.