8.4:
The Y-to-Y Circuit
Balanced four-wire Y-to-Y systems consist of three balanced Y-connected sinusoidal voltage sources and loads with the neutral wire connecting both the neutral nodes of the source with the load.
The load impedance for each phase equals the sum of the source, line, and load impedances. The source and line impedances are neglected to simplify the system.
Considering the positive phase sequence, phase voltages determine the three-line voltages
Kirchhoff's Voltage Law is applied to each phase, and the line currents are determined to have equal magnitudes and 120-degree phase differences.
Their sum equals zero, implying zero current in the neutral wire.
In a balanced Y system, the total power delivered to the three-phase load is three times the power delivered in each phase.
For an unbalanced Y-to-Y system with an unbalanced load, the line currents are unbalanced, resulting in a non-zero neutral current.
Another method of analyzing a balanced Y-to-Y system is considering one phase and analyzing its single-phase equivalent circuit to determine its line current. The phase sequence then yields the other two line currents.
8.4:
The Y-to-Y Circuit
In a balanced four-wire wye-to-wye system, the arrangement involves wye-connected sinusoidal voltage sources and loads, connected through a neutral wire that links the neutral nodes of the source and load. The load impedance is connected across each phase of the load. The wye-connected source can be connected to the wye-connected load in four-wire and three-wire arrangements. A three-phase system is considered balanced when the load on each phase is equal, leading to uniform current flow and phase angle across all stages. On the other hand, in an unbalanced system, variations in load impedance or source voltages result in unequal line currents.
Analysis of the four-wire wye-wye circuit configuration is relatively straightforward. In this setup, each impedance of the three-phase load is connected directly across its respective phase voltage from the three-phase source. Assuming a positive phase sequence and balanced conditions, the phase voltages are instrumental in analyzing the system. These phase voltages directly influence the voltages across each load impedance.
The current in the wire connecting the neutral node of the source to the neutral node of the load is:
Kirchhoff's Voltage Law, when applied to each phase of a balanced three-phase circuit, confirms that the sum of the voltages around any closed loop is zero. This leads to line currents of equal magnitude but with 120-degree phase shifts between them. These currents effectively sum to zero at any point, which justifies why the neutral wire carries no current under balanced conditions.
In an unbalanced wye-to-wye system, variations in load impedance or source voltages result in unequal line currents. Each phase in the system is treated as a single-phase circuit to calculate its line current. However, the currents for the remaining phases require individual analysis rather than deduction solely based on the sequence of phases, as each phase may be influenced uniquely by its specific electrical conditions.