A balanced delta-wye system is an electrical circuit consisting of a balanced delta-connected source feeding a balanced wye-connected load.
Before you start, it is wise for you to read what a three-phase circuit is 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
- Balanced wye-delta connection
- Balanced delta-delta connection
- Balanced delta-wye connection
Balanced Delta-Wye Connection
Balanced delta-wye connection means this is an AC circuit with the power factor near unity. Its voltage sinusoidal waveform should be similar to its current sinusoidal waveform.
A balanced three phase voltage and balanced three phase current will generate a balanced three phase power.
We do not need any power factor correction to this balanced circuit.
Keep in mind that:
A balanced delta-wye connection system is a system with delta-connected sources with wye-connected loads.
Consider the delta-wye three phase circuit below.
Again, assuming the abc sequence, the phase voltages of a delta-connected source are
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 ANBba in the circuit above
We get
But Ib lags Ia by 120° since we assumed the abc sequence; that is, Ib = Ia ∠-120°. Hence,
Substituting between two previous equations gives
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.
Another way to obtain the line currents is to replace the delta connected source with its equivalent wye-connected source, as shown above.
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
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.
Once the source is transformed into the wye, the circuit becomes a wye-wye system.
Therefore, we can use the equivalent single-phase circuit shown above, from which the line current for phase a is
which is the same as the equation before.
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
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.
Balanced Delta-Wye Connection Example
A balanced wye-connected load with a phase resistance of 40 Ω and a reactance of 25 Ω is supplied by a balanced, positive sequence delta-connected source with a line voltage of 210 V.
Calculate the phase currents. Use Vab as reference.
Answer:
The load impedance is
and the source voltage is
When the delta-connected source is transformed into a wye-connected source,
The line currents are
which are the same as the phase currents.