Download Three phase transformers and more Lecture notes Power Plant Engineering in PDF only on Docsity!
Three-Phase Transformers
Introduction
Transformer power levels range from low-power applications, such as consumer electronics power supplies to very high power applications, such as power distribution systems. For higher- power applications, three-phase transforms are commonly used. The typical construction of a three-phase transformer is shown in Figure 1. The detailed analysis of this circuit is not straightforward since there are numerous combinations of flux paths linking various windings. For this reason, the three-phase transformer will be modeled as three independent single-phase transformers herein.
For practical calculations, it is reasonable to model the three-phase transformer as three ideal transformers as shown in Figure 2. Since these transformers are ideal, the secondary voltages are related to the primary voltages by the turns ratio according to
a (^) N V a
N
V 1
1
2 ˆ 2 = ˆ (1)
b (^) N V b
N
V 1
1
2 ˆ 2 = ˆ (2)
c (^) N V c
N
V 1
1
2 ˆ 2 = ˆ (3)
The delta-to-wye connection is shown in Figure 5. From the ideal transformer equations, it can be determined that
ab^ (^ a b )^ ( V^ BC VAB )
N
N
V V
N
N
V ˆ ˆ ˆ ˆ ˆ
1
2 1 1 1
In this analysis A-B-C sequence is assumed. If a source does not have this sequence the input lines can be relabeled so that it does. With this sequence, (5) is equivalent to
o 1
ab (^) N VAB
N
V (6)
As can be seen, the secondary line-to-line voltage leads the primary by 30 o. A factor of 3 is also inserted in the magnitude calculation as well.
The wye-to-delta connection is shown in Figure 6. With this arrangement, it can be shown that
o 1
ab =^ VAB ∠− N
N
V (7)
In this case, the turns ratio is divided by 3 and the secondary phase lags by 30o.
In early power systems, two-phase transmission was used as well as three-phase. To supply a two-phase system from a three-phase source, two transformers were connected in the Scott-T connection shown in Figure 7. In this case, the primary windings must have tap locations at 1/
and 3 /2. As it turns out, many 240-V laboratory transformers have tap settings at 120-V and at
208-V (which is nearly 3 /2). Considering the connection diagram of Figure 7 and the ideal transformer relationships,
a =^ VAB + VBC N
N
V ˆ
ˆ^1
ˆ^2
1
b (^) N V BC
N
V ˆ ˆ
1
In terms of the primary voltage V ˆ AB^ , the secondary voltages are
o 1
a VAB N
N
V (10)
o 1
b VAB N
N
V (11)
As can be seen, there is a 90o^ phase relationship between the two secondary voltages which is necessary in a two-phase system.
Laboratory Transformers
Figure 9 shows the laboratory transformer and a corresponding electrical connection diagram. The transformer has multiple primary and secondary windings which may be connected in series or parallel for different voltage ratings. Internally, the primary windings have been connected in series and the secondary has been connected in parallel yielding the ratings show in the table below.
Laboratory transformer ratings. V ˆ 1 (^) = 240 V V ˆ 2 = 120 V
I ˆ 1 (^) = 4. 17 A I ˆ 2 = 8. 33 A
From the voltage ratings, it can be seen that the turns ratio is 2 2
N
N
. The connection diagram
also shows the primary taps which are accessible through the connectors.
As can be seen, primary taps at 120-V and 208-V are available using terminals H2-H3 and H respectively. In commercial applications, 120-V is a common voltage level. This is typically obtained by splitting a 240-V winding. Alternatively, 120-V can be obtained from the line-to- neutral voltage of a 208-V three-phase system. For these reasons, 120-V and 208-V tap settings are commonly available on many 240-V transformers.
Laboratory Work
Connect the transformers in the delta-to-delta connection as shown in Figure 10. The load box should be set to use two resistors in series in each phase by setting the switches as shown in Figure 11. Note: it will be simpler to connect the source and load cables to the transformer first and place the interconnecting wires on top since these wires will be changed to make the other types of connections. Switch on the load box fans. Energize the circuit and increase the primary voltage to 100% (approximately 208-V line-to-line). Note the voltage ratio corresponds to the turns ratio according to (4). Select Delta-Delta as a Connection Type and add the data to the log. Reduce the voltage to zero and switch off the source power switch.
Re-configure the transformer to the delta-to-wye configuration as shown in Figure 12. Note that this is very similar to the delta-to-delta configuration and only the interconnecting wires between the transformers need be changed. Repeat the above test with this configuration. Be sure to change the Connection Type to Delta-Wye and log the data.
Repeat the above test for the wye-to-wye and then the wye-to-delta configurations as shown in Figures 13 and 14 respectively. Log the data for each case; labeling appropriate connection type.
Connect the transformers in the Scott-T connection as shown in Figure 15. Before energizing the circuit, change the Connection Type to Scott-T so that the waveforms display properly. Switch on the source circuit breaker and increase the voltage to 100%. Notice the 90 o^ phase relationship between the secondary voltages as predicted by (10-11) verifying two-phase output. Print the waveforms on the screen, lower the source voltage to zero and switch off the source circuit breaker.
