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close this bookElectrical Machines - Basic vocational knowledge (Institut für Berufliche Entwicklung, 144 p.)
close this folder8. Transformer
close this folder8.3. Three-phase transformer
View the document8.3.1. Three-phase transformation with single-phase transformers
View the document8.3.2. Three-phase transformers
View the document8.3.3. Vector groups
View the document8.3.4. Application of three-phase transformers in power supply
View the document8.3.5. Parallel operation of transformers
View the document8.3.6. Technical data of customary transformers

8.3.3. Vector groups

Circuitry of windings

- The primary and secondary circuits of the three-phase transformer each consist of three strands. These three strands can form a delta connection if the terminals x, y and z are connected to v, w and u.

Figure 138 - Delta connection

In the delta connection the conductor voltage U equals the phase voltage U. Strand current is made up thus:

- Where the terminals x, y and z are interconnected we obtain a star circuit.

Figure 139 - Star connection

As opposed to the delta circuit, phase voltage is phase and conductor current values are identical.

- A special kind of star connection is the zigzag connection which, however, is only very rarely employed.

Phase position of upper and undervoltages

- The delta and star connection of the upper and under voltages yields the following combinations:





The designation Yy indicates that the upper and undervoltage windings have been star-connected. Yd denotes uppervoltage winding as star and undervoltage winding as delta.

Figure 140 indicates that these designations are not final.

Figure 140 - Connection options of a star-star circuit

(1) Upper voltage windings, (2) Undervoltage windings

Circuits 1 and 2 and 3 and 4 are identical; however, both groups differ as regards the phase position of under to upper voltage. The upper and undervoltage windings of circuits 1 and 2 feature opposing winding senses. As a result, in line with the transformer principle, there is no phase displacement between upper and lower voltage.

Figure 141 - Voltage indicator for the voltages 1 and 2 of Figure 140

The windings of circuits 3 and 4 possess the same winding sense. For this reason there is a phase displacement of 180 degrees between upper and undervoltage, that is to say the voltages are counter-directed to each other.

Figure 142 - Voltage indicator for circuits 3 and 4 of Figure 40

Consequently any comprehensive vector group designation must not only indicate winding circuits but also data pertaining to the phase position of the voltages.

The example of the star delta connection shows how to determine the phase position from the circuit diagram.

Figure 143 - Star-delta connection

The circuit diagram is added by the phase voltages (I, II, III, 1, 2, 3) whose indicators are always directed towards the terminals. The uppervoltage indicators (I, II, III) are inserted into a twelve-segment circle which serves as construction aid (Figure 144). The position of the indicator can be varied ad lib; however, amongst themselves they should heed a mutual phase displacement of 120 degrees and the winding circuit (star). The position of the under voltage indicator is determined by the uppervoltage indicator. The circuit diagram shows that the undervoltage indicators are counter-directed to the uppervoltage indicators (indicator 1 counter to indicator 1 etc.). Where the indicators 1, 2 and 3 are inscribed into the twelve-segment circle heeding the (delta) undervoltage winding circuit, the position of the undervoltage terminals u, v and w are stipulated. The phase position of like-named conductor voltages, for example between the upper-voltage terminals U, V and the undervoltage terminals u and v can now be derived from the indicator figure. In our example the undervoltage lags behind the upper voltage by 150 degrees.

Figure 144 - Indicator of a star-delta connection

A phase displacement of the undervoltage against the upper voltage of 30 degrees in each case, from zero; 30; 60 etc. up to 360 (0) degrees can be attained through varying linkage of the delta and star connections. However, in practice, one sticks to those connections where the displacement is 0; 150; 180 and 330 degrees. Thereby angle indication does not ensue directly but by means of a so-called index. This is derived from the division of the phase angle by 30 degrees.

Vector group designation

Vector group = circuit + index



Y star connection of the uppervoltage winding OS

y star connection of the undervoltage winding US

0 30 degrees =

0 degrees phase displacement


D delta connection OS

y star connection US

5 30 degrees =

150 degrees phase displacement

The index indicates by how many times of 30 degrees the undervoltage lags behind the upper voltage

Standardized vector groups

Survey 21 focuses attention on the most common of the 12 vector groups.

Survey 21 - Standardized vector groups of three-phase transformers

Vector group circuit

Circuit diagram

Indicator image

Transformation ratio