AY - Δ transformer bank cannot be paralleled with either a Y-Y or a Δ - Δ transformer bank because the phasor voltage difference between the two systems would be:

Why AY-Δ Transformer Bank Cannot Be Paralleled with Y-Y or Δ-Δ Banks:

Understanding the Issue:

In electrical power systems, transformer banks are often used to step up or step down voltages. When multiple transformer banks are connected in parallel, their voltages must be synchronized in both magnitude and phase to ensure proper operation. Any mismatch between the phase angles or voltage magnitudes can lead to circulating currents, inefficiencies, or even damage to the transformers.

In the case of an AY-Δ (Auto-Y-Delta) transformer bank, the winding configuration introduces a specific phase shift between the primary (Y-side) and secondary (Δ-side) voltages. This phase shift causes a difference in the relative positioning of the voltage phasors when compared to the voltages of other transformer banks, such as Y-Y or Δ-Δ configurations. This makes direct paralleling impossible without severe operational issues.

Phase Shift in AY-Δ Transformers:

• The AY-Δ transformer bank introduces a 30-degree phase shift between the primary and secondary windings. This phase shift arises because of the difference in how the windings of the star (Y) and delta (Δ) configurations interact with the magnetic flux in the transformer core.
• In contrast, Y-Y and Δ-Δ transformer banks typically maintain a 0-degree phase shift between their primary and secondary voltages.

Impact of Phase Difference:

• When attempting to parallel an AY-Δ transformer bank with a Y-Y or Δ-Δ transformer bank, the 30-degree phase shift creates a significant phasor voltage difference between the two systems.
• This voltage difference causes large circulating currents to flow between the transformer banks, which leads to overheating, increased losses, and potential damage to the transformers.

Calculating the Voltage Difference:

The phasor voltage difference between the AY-Δ and Y-Y or Δ-Δ transformer banks can be calculated as a fraction of the secondary voltage. Let’s determine this value step by step:

1. The phase shift between the two systems is 30 degrees.
2. The voltage difference due to this phase shift is proportional to the sine of the angle between the voltage phasors. Mathematically, this can be expressed as:
   Voltage Difference = V × sin(30°), where V is the secondary voltage.
3. The sine of 30 degrees is 0.5. Therefore, the voltage difference becomes:
   Voltage Difference = 0.5 × V.
4. This means the phasor voltage difference is 0.5 times the secondary voltage.

Conclusion:

Because of the 30-degree phase shift, the phasor voltage difference between the AY-Δ transformer bank and a Y-Y or Δ-Δ transformer bank is equal to 0.5 times the secondary voltage. For this reason, the two systems cannot be paralleled without causing operational issues. Thus, the correct answer is:

Option 4: 0.5 times the secondary voltages.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 0.75 times the secondary voltages

This option is incorrect because the phase shift between the AY-Δ and Y-Y or Δ-Δ systems is 30 degrees. The sine of 30 degrees is 0.5, not 0.75. Therefore, the voltage difference is 0.5 times the secondary voltage, not 0.75 times.

Option 2: Equal to the secondary voltages

This option is incorrect because the voltage difference arises due to the phase shift of 30 degrees. The voltage difference is a fraction of the secondary voltage (0.5 × V), not equal to the entire secondary voltage.

Option 3: 0.25 times the secondary voltages

This option is also incorrect because the sine of 30 degrees is 0.5, not 0.25. The voltage difference is 0.5 times the secondary voltage, not 0.25 times.