Balanced Delta-Delta Connection

Balanced delta-delta connection is basically a balanced three phase system with a balanced delta source supplying a balanced delta connected load.

This is the third of four configuration we will learn completely, they are:

• Balanced wye-wye connection
• Balanced wye-delta connection
• Balanced delta-delta connection
• Balanced delta-wye connection

Balanced Delta-Delta Connection

Balanced three phase electric circuit has a power factor near unity since its sinusoidal waveforms of voltage and current have the same shape. From this balanced three phase voltage will produce a balanced three phase power if the load is also balanced.

Since we have a three phase AC circuit that is balanced, we do not need to do power factor correction to make our circuit deliver better power transfer efficiency and makes our machine has longer lifetime.

We remember that:

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

Let us go straight to the circuit.

Consider the 3 phase balanced delta connected system drawn below, where a delta-connected source is connected to a delta-connected load. Of course, since it has no neutral point, it does not have the neutral wire.

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

• Z_S as the internal impedance of the phase winding of the generator as our source
• Z_l 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
• Z_n 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.

Our task here like another configuration is to find the value of:

• Phase current
• Line current

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

Assume the sequence is positive (abc-sequence), the phase voltages are

Since each voltage source is connected to its corresponding load with a single wire forming a single phase circuit, the line voltage is equal to its phase voltage. Observe the delta connection diagram below where each of phase can be taken out to be a single phase AC circuit.

Opposite of that, in a 3 phase delta connection diagram, each electric current flowing from one wire to a node connected to another two wire, the line current will be the vector sum of the two joining phase currents.

Since the line impedances are negligible, the phase voltages are equal to the voltages across the impedances, thus

The phase currents are

Since the load is delta-connected just as in the balanced wye-delta connection, some of the formulas derived there apply here.

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

as we did in the previous section

Also, as shown in the last section, each line current lags the corresponding phase current by 30°; the magnitude I_L of the line current is √3 times the magnitude I_p of the phase current,

An alternative way of analyzing the delta-delta circuit is to convert both the source and the load to their wye equivalents.

We already know that Z_Y = Z_∆/3. To convert a delta-connected source to a wye-connected source, see the example below.

Balanced Delta-Delta Connection Example

A balanced delta-connected load having an impedance 20 − j15 Ω is connected to a delta-connected, positive-sequence generator having V_ab = 330∠0° V.

Calculate the phase currents of the load and the line currents.

Answer:

The load impedance per phase is

The phase currents are

For a delta load, the line current always lags the corresponding phase current by 30° and has a magnitude √3 times that of the phase current.

Hence, the line currents are

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