8.3.1. Three-phase transformation with single-phase transformers

For economical reasons the transmission of electric power these days is not undertaken by single-phase systems but by three-phase systems. Thereby, three-phase alternating voltage has to be transformed into another, like frequency and number of phases. The transformation is possible by means of three identical single-phase transformers.

The resultant voltages must not only possess the same value but shall also evidence a mutual phase displacement of 120 degrees.

Consequently, the mains connection of the single-phase transformers must ensure a delta or star circuit despite the spatially separate installation of electric primary and secondary winding connections.

Figure 136 - Transformation through three single-phase transformers

In view of their size, big transformers of this kind come as so-called three-phase (transformer) bank. They are generally added by a fourth single-phase transformer. This latter unit constitutes the reserve and can be switched on if another transformer fails.

Material and space requirements are usually too great for medium and small power units for this kind of transformation. The constructional fusion into a unit leads to substantial material economies.

8.3.2. Three-phase transformers

Core transformers are most frequently constructed.

An input and an output coil each have been positioned on the common limb. Following three-phase mains connection the three input coils along with three-phase consumers, can be linked up into a star (Y) or delta (D) connection.

Figure 137 - Three-phase transformer in Y_y circuitry

1 Upper voltage winding
2 Under voltage winding

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:

Yy	Yd
Dy	Dd

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

Example:

Yy0	Y star connection of the uppervoltage winding OS
	y star connection of the undervoltage winding US
0 30 degrees =	0 degrees phase displacement
Dy5	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
Dy5
Yd5
Yz5
Yy0

8.3.4. Application of three-phase transformers in power supply

Figure 145 - Utilisation of transformer vector groups in power supplies

1 Power station generator, 2 Machine transformer, 3 Network transformer, 4 Distribution transformer, 5 Substation transformer

Block and machine transformers

- Block transformers along with a generator make up one unit. They establish the connection between the generator and the high-voltage side.

- Machine transformers operate in the same manner as block transformers whereby, initially, several generators work together on a bus bar.

- Preferred vector group for both transformers is Yd5.

Mains transformers

- Mains transformers function as a link between transmission networks of differing voltage planes, e.g. between the 380 kV and 220 kV mains.

- Network transformers are preferred in the Yy0 vector group.

Distribution and urban network transformers

- Distribution transformers link the transmission network to the consumer system.

- Urban network transformers are transformers whose undervoltage is less than 1 kV. Particular significance accrues to supplying the asymmetrically loaded urban network.

- The vector group Dy5 is suitable for urban network and distribution transformers.

8.3.5. Parallel operation of transformers

Basic information on parallel operation

The extension of existing electrotechnical installations makes it necessary to parallel connect further transformers to the existing ones.

Excessive transmission ratings may also necessitate multiple operation of several transformers.

Parallel operation signifies the upper and undervoltage inter-switching of several transformers.

Conditions for parallel operation

In order to prevent the transformers being preloaded or subject to unequal load distribution amongst themselves because of compensating currents, the following conditions must prevail:

- the vector group must have the same index figure

- same transformation ratio

- same short circuit voltages U. They shall not deviate by more than 10 per cent from one another

- rated power ratios should not be greater than 3 : 1.

8.3.6. Technical data of customary transformers

The surveys 22 and 23 feature the index figures of several mains and distribution transformers.

Survey 22 - Characteristic values of distribution transformers (three-phase oil transformer)

Rated power	kVa	100	160	250	400	630	1000	1600
Rated uppervoltage	kV	(6; 10; 15; 20)		(6; 10; 15; 20; 30)			(6; 10; 15; 20; 30)
Adjustment range	%	± 4		± 5			± 5
Rated undervoltage	kV	(0.231; 0.4; 0.525)		(0.4; 0.525)			(0.4; 0.525; 6.3)
Idling losses	W	380	550	700 (740)	1000 (1050)	1450 (1550)	2200 (2400)	3200 (3400)
Short circuit losses	W	2200 (2300)	2900 (3200)	4400	5900	7800	11000	16000
Short circuit voltage	%	3.8 (4)		6	6	6	6	6
Dimensions length a 1	mm	1110	1260	1810 (1870)	1980 (2040)	2110 (2170)	2300 (2350)	2650 (2800)
width b	mm	640	800	800 (880)	1100	1100	1000	1000
height h1	mm	1420	1590	1870 (1900)	1950 (2000)	2215 (2255)	2490 (2600)	2700 (2775)
Oil filling	kg	215	300	470 (570)	620 (700)	755 (860)	1150 (1250)	1550 (1750)
total weight	kg	790 (800)	1070 (1080)	1520 (1680)	2020 (2200)	2620 (2850)	4000 (4250)	5750 (5950)
Vector group	-	(Yy0; Yz5)		(Yy0; Dy5)			(Yy0; Dy5)

Survey 23 - Characteristic values of dry-type transformers

Rated power	kVa	63	100	160	250	400	630	1000
Rated upper-voltage	kV	(2; 3; 5; 6; 10; )				(2; 3; 5; 6; 10; )
rated under-voltage	kV	(0,231; 0,4; 0,525)				(0,4; 0,525)
Rated frequency	Hz	(50)				(50)
Idling losses	W	580	750	900	1200	1750	2500	2900
Short-circuit losses	W	1330	1700 (1780)	2570 (2750)	3200	5250	6500	10400
Short-circuit voltage	%	(3, 8(4))				(6)

Figure 146 serves as an example of the dimensional size of a three-phase oil transformer.

Figure 146 - Oil transformer for the 250 - 16000 kVA range

1 Oil level, 2 Thermo-pockets, 3 Oil removal device, 4 Converter, 5 Eye bolt, 6 Earthing screw, 7, 8 Oil opening, 9 Buchholz relay, 10 Stop valves (from 1000 kVA onwards), 11 Shoulder hooks, 12 Hoisting points, 13 Variable dimensions

Questions for revision and control

1. Describe the basic construction and range of a transformer.
2. How can iron and winding losses be determined in a transformer?
3. How can short-circuit voltage be determined?
4. Which factors cause a voltage drop in a transformer?
5. What is the significance of the index figure in vector group data? Which index figures are cited?
6. Which are the most common vector groups and for which purposes are they used?
7. Name the parallel switching conditions.