A balanced delta-wye connection system is a system with delta-connected sources with wye-connected loads.
A balanced delta-wye system consists of a balanced ∆-connected source feeding a balanced Y-connected load.
Before you start, it wise for you to read what is three-phase circuits first.
Since both the three-phase source and the three-phase load can be either wye- or delta-connected, we have four possible connection :
- Balanced wye-wye connection (i.e., Y-connected source with a Y-connected load).
- Balanced wye-delta connection.
- Balanced delta-delta connection.
- Balanced delta-wye connection.
Balanced Delta-Wye Connection
Consider the ∆-Y circuit in Figure.(1).
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| Figure 1. A balanced ∆-Y connection |
Again, assuming the abc sequence, the phase voltages of a delta-connected source are
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| (1) |
These are also the line voltages as well as the phase voltages.
We can obtain the line currents in many ways. One way is to apply KVL to loop a AN B b a in Figure.(1), writing
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| (2) |
But Ib lags Ia by 120◦since we assumed the abc sequence; that is, Ib = Ia ∠− 120◦. Hence,
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| (3) |
Substituting Equation.(3) into (2) gives
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| (4) |
From this, we obtain the other line currents Ib and Ic using the positive phase sequence, i.e., Ib = Ia ∠− 120◦, Ic = Ia ∠+ 120◦. The phase currents are equal to the line currents.
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| Figure 2. Transforming a ∆-connected source to an equivalent Y-connected source. |
Another way to obtain the line currents is to replace the delta connected source with its equivalent wye-connected source, as shown in Figure.(2).
In balanced wye-wye connection, we found that the line-to-line voltages of a wye-connected source lead their corresponding phase voltages by 30◦.
Therefore, we obtain each phase voltage of the equivalent wye-connected source by dividing the corresponding line voltage of the delta-connected source by √3 and shifting its phase by −30◦.
Thus, the equivalent wye connected source has the phase voltages
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| (5) |
If the delta-connected source has source impedance ZS per phase, the equivalent wye-connected source will have a source impedance of ZS/3 per phase.
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| Figure 3. The single-phase equivalent circuit |
Once the source is transformed into the wye, the circuit becomes a wye-wye system.
Therefore, we can use the equivalent single-phase circuit is shown in Figure.(3), from which the line current for phase a is
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| (6) |
which is the same as Equation.(4)
Alternatively, we may transform the wye-connected load to an equivalent delta-connected load.
This results in a delta-delta system, which can be analyzed as in balanced delta-delta connection. Note that
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| (7) |
As stated earlier, the delta-connected load is more desirable than the wye-connected load.
It is easier to alter the loads in any one phase of the delta-connected loads, as the individual loads are connected directly across the lines.
However, the delta-connected source is hardly used in practice, because any slight imbalance in the phase voltages will result in unwanted circulating currents.
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Balanced Delta-Wye Connection Example
A balanced Y-connected load with a phase resistance of 40 Ω and a reactance of 25 Ω is supplied by a balanced, positive sequence ∆-connected source with a line voltage of 210 V.
Calculate the phase currents. Use Vab as reference.
Solution:
The load impedance is
and the source voltage is
When the ∆-connected source is transformed into a Y-connected source,
The line currents are
which are the same as the phase currents.