8.6:
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.
8.6:
The Delta-to-Delta Circuit
In a delta-delta configuration, the source and the load are connected in a delta manner, forming a closed loop that divides the network into three distinct phases. This configuration makes the phase voltages identical to line voltages. Assuming the sources are in positive sequence, the phase voltages can be expressed directly without having a neutral wire.
The phase currents in a delta-connected load are calculated by dividing the phase voltage by the load impedance per phase:
In this configuration, Kirchhoff's Current Law (KCL) gives each line current as the vector sum of currents of the remaining two phases, leading to the general principle that each line current is the square root of three times the magnitude of the phase current. It lags the phase current by 30 degrees due to the phase differences created by the delta connection.
The analyses of such systems involve converting the source and load into their wye-equivalents. This conversion simplifies the three-phase system into a single-phase equivalent circuit. The conversion involves adjusting both the magnitude and phase of the delta-connected source's line voltages:
Furthermore, the impedance of each wye-connected load is one-third of the impedance of the delta-connected load.
Balanced delta-to-delta configurations are used in industrial applications for high-power machinery, transformers, and motor control centers. They enable efficient power transmission over long distances, reduce harmonic distortion, and facilitate the smooth operation of three-phase motors by maintaining consistent voltage levels without needing a neutral connection.