Transformer Percentage impedance; Importance of Transformer impedance; Calculating Transformer Impedance

Percentage Impedance of a Transformer (Z%)

The percentage impedance (Z%) of a transformer is one of the most important parameters marked on its nameplate. It influences voltage regulation, fault levels, and load sharing when transformers are connected in parallel.

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Definition

The percentage impedance of a transformer is:

• The voltage drop at full load caused by the resistance and leakage reactance of the windings, expressed as a percentage of the rated voltage.

• Alternatively, it can be defined as the percentage of rated terminal voltage required to circulate full-load current under short-circuit conditions.

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Measurement of Transformer Impedance

Transformer impedance is measured by performing a short-circuit test:

1. One winding of the transformer is short-circuited.

2. A reduced voltage (at rated frequency) is applied to the other winding.

3. The voltage is gradually increased until the rated full-load current flows through the windings.

The percentage impedance is then calculated as:

$$Z\% = \frac{V_{SC}}{V_{Rated}} \times 100$$

Where:

• $V_{SC}$ = Short-circuit voltage (the applied voltage required to circulate full-load current)

• $V_{Rated}$ = Rated voltage of the transformer

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Design Factors Affecting Impedance

The natural impedance of a transformer depends on leakage flux, which is influenced by:

• Winding ampere-turns

• Leakage flux path length and area

• Geometric arrangement of windings

• Volts per turn

By altering these design parameters, manufacturers can increase or decrease the impedance as per system requirements.

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Effect of Transformer Impedance on Fault Levels

The impedance value directly influences the fault current during system short circuits.

Example:
For a 5 MVA transformer with 5% impedance, the maximum fault MVA is:

$$Fault \, MVA = \frac{MVA \times 100}{Z\%} = \frac{5 \times 100}{5} = 100 \, MVA$$

From this, the primary and secondary fault currents can be calculated.

• Higher impedance → Lower fault current (safer for system protection)

• Lower impedance → Higher fault current (increases fault level stresses)

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Importance of Transformer Impedance

1. Determines Fault Level

   • A low impedance transformer results in higher fault levels, while high impedance limits fault currents.

2. Voltage Regulation

   • The percentage impedance indicates the voltage drop under load conditions, affecting system voltage stability.

3. Parallel Operation

   • For load sharing between multiple transformers, similar impedance values are necessary. Significant mismatch can cause unequal load distribution.

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Sequence Impedance (Z₁, Z₂, Z₀)

For balanced 3-phase faults, only the positive sequence impedance (Z₁) is relevant. However, unbalanced faults (e.g., phase-to-earth, phase-to-phase) require symmetrical component analysis.

• Positive Sequence Impedance (Z₁): Same as negative sequence impedance in transformers.

• Negative Sequence Impedance (Z₂): Equal to Z₁ in practice.

• Zero Sequence Impedance (Z₀): Depends on transformer winding connections and earthing.

Key Notes on Zero Sequence Impedance:

• Zero sequence currents flow only when a path is available (e.g., delta winding or grounded star).

• Any impedance in the earth return path increases Z₀, thereby limiting earth fault currents.

• This property is often used in distribution systems to control earth fault levels.

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Quick Summary

• Z% = (Short-circuit test voltage ÷ Rated voltage) × 100

• High Z% → Low fault current, higher voltage drop, less parallel compatibility

• Low Z% → High fault current, lower voltage drop, better regulation

• Critical for fault level calculation, voltage regulation, and transformer parallel operation

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⚡ Practical Tip: When designing or selecting a transformer, always check its impedance value on the nameplate, as it directly impacts system protection and load sharing performance.

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