Percentage Impedance

September 9, 2023
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Author: Engr. Jahangir Amir

The impedance of a transformer is marked on most nameplates –  but what is it and what does the Z% figure mean?

The percentage impedance of a transformer is the volt drop on full load due to the winding resistance and leakage reactance expressed as a percentage of the rated voltage.

It is also the percentage of the normal terminal voltage required to circulate full-load current under short circuit conditions 

Measuring Impedance
The impedance is measured by means of a short circuit test.  With one winding shorted, a voltage at the rated frequency is applied to the other winding sufficient to circulate full load current – see below:

The percentage impedance can then be calculated as follows:

Z%  =  Impedance Voltage   x  100
Rated Voltage

 Changing the Impedance Value
The most economical arrangement of core and windings leads to a ‘natural’ value of impedance determined by the leakage flux.  The leakage flux is a function of winding ampere turns and the area and length of the leakage flux path.  These can be varied at the design stage by changing the volts per turn and the geometric relationship of the windings.

The Effect of Higher and Lower Impedances
The impedance of a transformer has a major effect on system fault levels.  It determines the maximum value of current that will flow under fault conditions.

It is easy to calculate the maximum current that a transformer can deliver under symmetrical fault conditions.  By way of example, consider a 2 MVA transformer with an impedance of 5%.  The maximum fault level available on the secondary side is:

                    2 MVA x 100/5 = 40 MVA

and from this figure the equivalent primary and secondary fault currents can be calculated.

A transformer with a lower impedance will lead to a higher fault level (and vice versa)

The figure calculated above is a maximum.  In practice, the actual fault level will be reduced by the source impedance, the impedance of cables and overhead lines between the transformer and the fault, and the fault impedance itself.

As well as fault level considerations, the impedance value also:

bulletdetermines the volt drop that occurs under load – known as ‘regulation’
bulletaffects load sharing when two or more transformers operate in parallel

Sequence Impedance (ZZ2  Z0)
The calculation above deals with a balanced 3-phase fault.  Non-symmetrical faults (phase-earth, phase-phase etc) lead to more complex calculations requiring the application symmetrical component theory.  This in turn involves the use of positive, negative and zero sequence impedances (Z1,Z2 and  Z0 respectively).

As with all passive plant, the positive and negative sequence impedances (Z1 andZ2) of a transformer are identical.

However, the zero sequence impedance is dependent upon the path available for the flow of zero sequence current and the balancing ampere turns available within the transformer.  Generally, zero sequence current requires a delta winding, or a star connection with the star point earthed.  Any impedance in the connection between the star point and earth increases the overall zero sequence impedance.  This has the effect of reducing the zero sequence current and is a feature that is frequently put to practical use in a distribution network to control the magnitude of current that will flow under earth fault conditions.

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