IMPEDANCE MATCHING TRANSFORMER SELECTION BASIC AND TUTORIALS

Select a transformer with the correct turns ratio to match the 8- resistive load in Fig. 4.3 to the Thevenin equivalent circuit of the source.

Calculation Procedure
1. Determine the Turns Ratio
The impedance of the input circuit, Zi, is 5000 . This value represents the Thevenin impedance of the source. The load impedance, ZL , is 8 .

To achieve an impedance match, the required turns ratio is

Therefore, the impedance-matching transformer must have a turns ratio of 25:1.

Related Calculations. The maximum power transfer theorem (Sec. 1) states that maximum power is delivered by a source to a load when the impedance of the load is equal to the internal impedance of the source.

Because the load impedance does not always match the source impedance, transformers are used between source and load to ensure matching.

When the load and source impedances are not resistive, maximum power is delivered to the load when the load impedance is the complex conjugate of the source impedance.

POWER TRANSFORMER SERIES IMPEDANCE AND REGULATION BASIC AND TUTORIALS

The series impedance of a transformer consists of a resistance that accounts for the load losses and a reactance that represents the leakage reactance. This impedance has a very low power factor, consisting almost entirely of leakage reactance with only a small resistance.

As discussed earlier, the transformer design engineer can control the leakage reactance by varying the spacing between the windings. Increasing the spacing ‘‘decouples’’ the windings and allows more leakage flux to circulate between the windings, increasing the leakage reactance.

While leakage reactance can be considered a transformer loss because it consumes reactive power, some leakage reactance is necessary to limit fault currents. On the other hand, excessive leakage reactance can cause problems with regulation.

Regulation is often defined as the drop in secondary voltage when a load is applied, but regulation is more correctly defined as the increase in secondary output voltage when the load is removed. The reason that regulation is defined this way is that transformers are considered to be ‘‘fully loaded’’ when the secondary output voltage is at the rated secondary voltage.

This requires the primary voltage to be greater than the rated primary voltage at full load.

Let Ep equal the primary voltage and let Es equal the secondary voltage when the transformer is fully loaded. Using per-unit values instead of primary and secondary voltage values, the per-unit secondary voltage will equal Ep with the load removed. Therefore, the definition of regulation can be expressed by the following equations.


Regulation = (Ep - Es)/ Es


Since Es = 1 by definition,
Regulation Ep - 1 (3.8.2)
Regulation depends on the power factor of the load. For a near-unity power
factor, the regulation is much smaller than the regulation for an inductive load
with a small lagging power factor.

Example 3.4
A three-phase 1500 KVA 12470Y-208Y transformer has a 4.7% impedance. Calculate the three-phase fault current at the secondary output with the primary connected to a 12,470 V infinite bus. Calculate the regulation for a power factor of 90% at full load.

The three-phase fault is a balanced fault, so the positive-sequence equivalent circuit applies. The full-load secondary current is calculated as follows:

I 1.732 500,000 VA per phase/208 V 4167 A per phase
The per-unit fault current is the primary voltage divided by the series impedance:
1/0.047 = 21.27 per unit

The secondary fault current is equal to the per-unit fault current times the fullload current:
If 21.27 per unit 4167 A per phase 88,632 A per phase To calculate regulation, the secondary voltage is 1∠0° per unit by definition.

Applying a 1 per unit load at a 90% lagging power factor, I 1.0∠ 25.8°. Since the series impedance is mainly inductive, the primary voltage at full load Ep can be calculated as follows:

Ep 1∠0° + 1.0∠ 25.8° X 0.047∠90°
1.02 + j0.042 = 1.021 per unit
Regulation = Ep - 1 = 0.021 = 2.1%

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.

TRANSFORMER ZERO SEQUENCE IMPEDANCE BASICS AND TUTORIALS

ZERO SEQUENCE OF TRANSFORMERS BASIC INFORMATION
What Is The Zero Sequence of Transformers?


It is usual in performing system design calculations, particularly those involving unbalanced loadings and for system earth fault conditions, to use the principle of symmetrical components. This system is described and and ascribes positive, negative and zero-sequence impedance values to the components of the electrical system.

For a three-phase transformer, the positive and negative sequence impedance values are identical to that value described above, but the zero-sequence impedance varies considerably according to the construction of the transformer and the presence, or otherwise, of a delta winding.

The zero-sequence impedance of a star winding will be very high if no delta winding is present. The actual value will depend on whether there is a low reluctance return path for the third-harmonic flux.

For three-limb designs without a delta, where the return-flux path is through the air, the determining feature is usually the tank, and possibly the core support framework, where this flux creates a circulating current around the tank and/or core framework.

The impedance of such winding arrangements is likely to be in the order of 75 to 200% of the positive-sequence impedance between primary and secondary windings. For five-limb cores and three-phase banks of single-phase units, the zero-sequence impedance will be the magnetising impedance for the core configuration.

Should a delta winding exist, then the third harmonic flux will create a circulating current around the delta, and the zero-sequence impedance is determined by the leakage field between the star and the delta windings. Again the type of core will influence the magnitude of the impedance because of the effect it has on the leakage field between the windings.

Typical values for threelimb transformers having a winding configuration of core/tertiary/star LV/star HV are:

[Z0]LV approximately equal to 80 to 90% of positive-sequence impedance LV/tertiary

[Z0]HV approximately equal to 85 to 95% of positive-sequence impedance HV/tertiary

where Z0 = zero-sequence impedance.

Five-limb transformers have their zero-sequence impedances substantially equal to their positive-sequence impedance between the relative star and delta windings.