Balanced Wye-Delta Connection

Compared to balanced wye-wye connection, we will learn the most practical among the four configurations and it is the balanced wye-delta connection.

As its name implies, the balanced wye-delta connection is an electrical circuit where we have a balanced wye-connected source supplying a balanced delta-connected load.

This is the second configuration of four:

Balanced Wye-Delta Connection

Why do we need a balanced source and a balanced load?

Assume we have a balanced three phase voltage and a balanced three phase load, since there is no difference in magnitude, the electric current is also in harmony with the voltage. There is no difference in their sinusoidal waveforms in a balanced three phase system.

A balanced three phase system will have a balanced three phase power.

If a circuit has its voltage and current in harmony, the power factor will be close to unity. This means our circuit has good power transfer efficiency and makes our machine have a better lifetime.

What happens if we have an unbalanced three phase circuit? The most practical solution is a power factor correction but this needs an advanced understanding of AC circuits.

Remember that:

A balanced three phase wye-delta connection is a three phase source with a balanced wye-connected source and a balanced delta-connected load.

Let’s go straight to the circuit analysis and example.

Observe the balanced wye-delta wiring diagram below where we have a balanced three phase voltage source in wye configuration on the left and a balanced three phase load in delta configuration.

balanced wye-delta connection 1

From our discussion in the balanced wye-wye connection, we will remove:

  • ZS as the internal impedance of the phase winding of the generator as our source
  • Zl as the impedance of the line joining a phase of the source with a phase of the load, this is the impedance of our conductors
  • Zn is the impedance of the neutral line, connecting the neutral point from supply and load.

Because those three are negligible since their values are miniscule compared to load impedance.

We will use ZΔ as our equivalent impedances to represent the total impedance in  delta-connected loads.

Compared to a wye-wye connection where there is a neutral line between supply and load, there is no neutral line in a wye-delta connection diagram.

Assume that we have a positive sequence (abc-sequence), the phase voltages are

The line voltages are

Hence, it shows us that the voltage across the load impedances for this system is equal to the line voltages using this connection.

From these line voltages, we can obtain the phase current

These currents have the same magnitude but are out of phase with each other by 120°.

Another way to get these phase currents is to apply Kirchhoff’s Voltage Law. For example, we can apply KVL around loop aABbna

balanced wye-delta connection 2

And the phase current is

It is still the same with the previous phase current method. This one is easier to do since we can apply the basic KVL to the circuit.

The line currents are obtained from the phase currents by applying Kirchoff’s Current Law at nodes A, B, and C.

balanced wye-delta connection 3

Thus,

Since ICA = IAB∠−240°,

showing that the magnitude IL of the line current is √3 times the magnitude Ip of the phase current, or

Where

And

Also, the line currents lag the corresponding phase currents by 30°, assuming the positive sequence.

Below is a phasor diagram illustrating the relationship between the phase and line currents.

balanced wye-delta connection 4

An alternative way of analyzing the wye-delta circuit is to transform the delta-connected load to an equivalent wye-connected load.

Using the delta-wye transformation formula,

After this transformation, we now have a wye-wye system as in the balanced wye-wye connection.

We can redraw the three-phase wye-delta system in the illustration above to a single-phase equivalent circuit drawn below. This allows us to calculate only the line currents.

Why do we need to transform the delta load into wye load?

Because we can easily take a portion of wye-wye connection into a single phase circuit.

balanced wye-delta connection 5

The phase currents are obtained using the line current equation above and utilizing the fact that each of the phase currents leads the corresponding line current by 30°.

balanced wye-delta connection 6

Balanced Wye-Delta Connection Example

A balanced three phase AC circuit with balanced wye-delta configuration.

A balanced abc-sequence wye-connected source with Van = 100∠10° V is connected to a delta-connected balanced load (8 + j4) Ω per phase.

We need to calculate its phase and line currents.

Answer:

We can solve this problem in two ways.

Method 1

The load impedance is

If the phase voltage Van = 100∠10°, then the line voltage is

The phase currents are

The line currents are

Method 2

Alternatively, using single-phase analysis,

as above. Other line currents are obtained using the abc phase sequence.

Frequently Asked Questions

How do I know if my 3 phase is delta or wye?

The delta configuration has a three phase source or load connected in a shape of triangle where the head is connected to another tail and so on.

Is delta connection balanced?

Three phase delta connection has no neutral wire such as in a wye connection and the phase voltage is equal to the line voltage. The line current is root three (√3) times the phase current.

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