The Delta-to-Delta Circuit

A balanced delta-to-delta system has a delta-connected source and load.

The delta-connected sources are assumed to be in positive sequence to express the phase voltages, which are identical to line voltages.

Assuming zero line impedances, phase voltages match the voltage across the impedances.

Phase currents equal the ratio of the phase voltage and load impedance per phase.

Line currents are derived from phase currents using Kirchhoff's Current Law at nodes of the delta-connected loads.

Each line current lags its corresponding phase current by 30 degrees, with its magnitude being the square root of three times the phase current.

Alternatively, the delta-to-delta circuit can be analyzed by converting the source and the load to their Y equivalents.

For the Y-connected source, the corresponding phase voltage equals each line voltage of the delta-connected source divided by a square root of three, and its phase is shifted by negative 30 degrees.

Y-connected load impedance equals delta-connected load impedance divided by three.

Now, the equivalent single-phase circuit can be used to determine the three line currents.