Percentage Impedance of Transformer & Its Calculation

What is the percentage impedance of a transformer?

Answer: The percentage impedance of a transformer is a measure of the transformer’s internal impedance (the combination of its resistance and reactance), expressed as a percentage of its rated voltage. It is an important parameter used in system design, fault analysis, and short-circuit calculations.

Where:

• Vtest​ is the voltage required to circulate full-load current through the transformer windings when the secondary is short-circuited.
• Vrated​ is the rated voltage of the transformer (usually the primary voltage).
• This test is called the short-circuit test.

Interpretation:

• If a transformer has 5% impedance, it means that applying 5% of the rated voltage to the primary side (with the secondary shorted) will produce full-load current.
• It also implies that under fault conditions, the maximum short-circuit current is limited by this impedance.

How it’s calculated:

The percentage impedance is typically determined through a short-circuit test. In this test:

1. The secondary winding of the transformer is short-circuited.
2. A reduced voltage (short-circuit voltage, V_SC​) is applied to the primary winding.
3. This voltage is gradually increased until the rated current (I_rated​) flows through the primary winding.
4. The percentage impedance is then calculated using the formula:

% Z of transformer =( V_sc/V_rated) X 100

Where:

1. • V_SC​ is the short-circuit voltage applied to the primary winding.
   • V_rated​ is the rated primary voltage of the transformer.

Significance and Importance:

The percentage impedance is highly significant in transformer applications for several reasons:

1. Fault Current Calculation: It is a critical factor in determining the maximum available short-circuit current in a power system. A lower percentage impedance means a higher potential short-circuit current, which requires more robust protective devices.
2. Voltage Regulation: It influences the voltage drop across the transformer under load conditions. Transformers with lower impedance generally have better voltage regulation (less voltage drop) but contribute to higher fault currents.
3. Parallel Operation: When operating transformers in parallel, it is essential that they have similar percentage impedances (within a certain tolerance, typically +/- 7.5% to 10%). This ensures proper load sharing between the transformers and prevents circulating currents that can lead to overheating and inefficient operation.
4. System Design and Coordination: Engineers use the percentage impedance to design and coordinate protection schemes within electrical systems, ensuring that protective devices (like circuit breakers and fuses) can safely interrupt fault currents.
5. Efficiency: While not a direct measure of efficiency, impedance does indirectly impact efficiency. Lower impedance can sometimes lead to lower losses, but a very low impedance can also lead to higher inrush currents during energization, which can be problematic.

Factors Influencing Percentage Impedance:

Several design factors influence the percentage impedance of a transformer:

• KVA Rating: Generally, as the kVA rating of a transformer increases, its percentage impedance tends to increase.
• Number of Turns: More turns in the windings typically lead to higher impedance.
• Core Material and Size: The type of core material, its size, and the core’s magnetic properties affect the impedance, particularly the reactance component.
• Winding Arrangement and Geometry: The physical arrangement of the primary and secondary windings, and the distance between them, significantly impact the leakage reactance, and thus the overall impedance.
• Insulation Thickness: Thicker insulation between windings can increase leakage reactance.

In summary, the percentage impedance is a fundamental characteristic of a transformer that provides valuable insights into its performance under various operating conditions, especially during fault situations and when paralleling with other transformers.

Mathematical Problems Solved:

1. A transformer of rating 132000/6600 volts transformer has a measured impedance drop of 600 volts. What is the percentage impedance of the transformer?

Solution:  

2.     Calculating Impedance Voltage

Given:          

• A 100 kVA, 11 kV/415 V transformer
• Full-load current on the HV side = ?
• Voltage required to circulate full-load current during short-circuit test = 550 V

Find: Percentage impedance

Solution:

Given:

• Transformer rating: 100 kVA
• Primary (HV) voltage: 11,000 V
• Secondary (LV) voltage: 415 V
• Voltage required to circulate full-load current during short-circuit test: 550 V
• This short-circuit voltage is measured on the HV side (since full-load current is being circulated from the HV side)

Solution:  

The percentage impedance of the transformer is 5%.

3. A 250 kVA, 11 kV / 400 V, 3-phase transformer has a percentage impedance of 4.5%. What voltage needs to be applied to the HV side during a short-circuit test to circulate full-load current?

Solution:

495 volts must be applied to the HV side to circulate full-load current during the short-circuit test.

4. A 500 kVA transformer has a percentage impedance of 6%. Calculate the full-load impedance of the transformer in ohms (referred to the HV side, if the HV voltage is 33 kV).

Solution :

Given:

The full-load impedance of the transformer (referred to the HV side) is 130.68 Ω.

5. Two transformers, A and B, are connected in parallel. Transformer A is 500 kVA with 5% impedance. Transformer B is 750 kVA with 5% impedance. If they supply a total load of 1000 kVA, how much load does each transformer supply?

Solution:

Given:

• Transformer A:
  • Rating S_A=500 kVA
  • Percentage impedance Z_A%=5%
• Transformer B:
  • Rating S_B=750 kVA
  • Percentage impedance Z_B%=5%
• Total load supplied by both transformers: S_total = 1000kVA

Since both transformers have the same percentage impedance (5%), we need to convert the impedances referred to a common base to calculate the current or load division.

Transformer A supplies 400 kVA and Transformer B supplies 600 kVA.

6. A 75 kVA, single-phase transformer has an impedance of 0.045 pu (per unit). Convert this per unit impedance to percentage impedance.

Solution:

The percentage impedance is 4.5%.

7. A transformer has a rated primary voltage of 13.2 kV and a percentage impedance of 5.5%. During a short-circuit test, the full-load current on the primary side is 20 A. What is the impedance of the transformer in ohms (referred to the primary side)?

Solution:

The impedance of the transformer (referred to the primary side) is 36.3 Ω.