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## Introduction

The International Elctrotechnical Commission (IEC) has established a method of recognizing the configurations of high voltage and low voltage windings of transformers, called the Vector Group. In the most simple sense, the vector group indicates the phase angle difference between the primary and secondary voltage of a transformer.

For example, the vector group Dy11, has it’s primary voltage (HV side) leading the secondary voltage (LV side) by 30 electrical degrees. The concept is to use the hour hand and minute hand of a clock to indicate the phase shift.

The high voltage winding is always taken as the reference vector and the rotation is counter-clockwise.

In the case of Dy11, Delta side (HV) is the reference and is represented by the hour hand of the clock. The Wye side (LV) is then represented by the minute hand of the clock. Since the rotation is counter-clockwise, therefore in the case of 11 o’clock, the hour hand (HV) is leading the minute hand (LV) by 30 degrees.

On the flip side, the vector connection for Dy1, has it’s Delta side (HV) lagging the Wye side (LV) by 30 degrees just how you would see the positions of hour hand and minute hand of a clock at a time of 1 o’clock.

For clarity: HV – High Voltage, LV – Low Voltage

## Importance of Vector Group

Now that we have established some basic concepts of the subject, it is important to understand why bother about this confusing discussion in the first place.

When paralleling transformers, one of the most important requirement is they must be of the same vector group to avoid circulating currents between the transformers. Failure to consider this will result to damaging your transformer and that is a very costly mistake.

## Mutual Inductance Between Two Coils

To properly understand vector groups, let’s go back to college days and take a look at our principles of electromagnetism subject.

Figure-1 illustrates the principle of a single phase transformer. When the coils are wound around in opposite direction as shown, the voltages on primary and secondary coils are in-phase. On the other hand, if the secondary coil is wound in the same direction as the primary coil then the voltages will be out of phase by 180 degrees.

The dots on the upper sides of the coils are called polarity markings. Current enters the first dot (primary winding) and comes out of the second dot (secondary winding), the dot where it enters and comes out from are both positive in polarity.

## Three-Phase Transformer Phase Shift

Now that we know how single phase transformer’s voltage shift works. Let’s look at the more complicated scenarios of 3-phase transformers.

Figure-2 above shows the derivation by manual calculations how the phase shifting from HV to LV side happens.

In the diagram, I showed how the windings are connected and the polarity markings are also shown to indicate the correct flow of current in the windings.

For simplicity, I used 1 per unit for delta side voltages. Remember that delta side is our start point since this is the high voltage.

Now it’s your turn, try to do the calculations for the rest of the vector group below: