8.7:
The Delta-to-Y Circuit
A balanced delta-to-Y system features a balanced delta-connected source powering a balanced Y-connected load.
In this delta-Y circuit, a positive abc sequence is assumed to express the phase voltages, which also serve as the line voltages of the delta-connected source.
Kirchhoff's voltage law can be applied to a loop in the circuit to derive a relationship between two of the line currents.
Since a positive sequence is assumed, these line currents have a phase difference of 120 degrees, which is used to determine one of them.
The other two line currents are obtained using the positive phase sequence.
The phase currents of the delta-Y circuit are approximately equal to the line currents.
Alternatively, the delta-connected source can be replaced with its equivalent Y-connected source.
The obtained Y-Y circuit is analyzed by considering an equivalent single-phase circuit and determining the three-line currents.
This circuit can also be transformed into a delta-delta system for analysis purposes as delta-connected load is often preferred due to the ease of altering individual loads.
8.7:
The Delta-to-Y Circuit
In the delta-wye circuit, the source is delta-connected, while the load is in a wye configuration. This means that the phase voltage of the delta-connected source is equal to the line voltage of the wye-connected load. The connection between two-line currents originates from the delta-connected source. The phase difference in the balanced system allows for calculating one line current given the other, utilizing the positive sequence of phases. In the delta-wye system, the phase currents in the wye-connected load are directly equal to the line currents from the delta source, due to the load's wye configuration simplifying the flow from the delta source. The relationship between the line and phase currents in a wye configuration shows that the phase current in the wye-connected load equals the line current of the delta-connected source.
Another way to obtain the line currents is to replace the delta-connected source with its equivalent wye-connected source. The line-to-line voltages of a wye-connected source lead their corresponding phase voltages by 30 degrees. This means that each phase voltage of the equivalent wye-connected source is obtained by dividing the corresponding line voltage of the delta-connected source by the square root of three and shifting its phase by -30 degrees. As a result, the equivalent wye-connected source has phase voltages shifted by 120 degrees accordingly.
By converting a delta configuration to a star configuration, the system can achieve better voltage regulation and allow for the use of a neutral wire. This neutral wire enables the system's grounding, enhancing safety and stability.
The balanced delta-to-delta configuration is used to transmit electricity over long distances, where high voltage levels need to be stepped down to usable levels for industrial, commercial, and residential use.