In a three-phase star (or wye) connected system, the relationships between line voltage and phase voltage, as well as line current and phase current, are fundamental for understanding how power is distributed in such systems. Let’s break these relationships down:
### 1. Line Voltage vs. Phase Voltage
- **Phase Voltage (\( V_{ph} \))**: This is the voltage measured across each individual phase of the system. It is the voltage between one phase and the neutral point (the center of the star connection).
- **Line Voltage (\( V_{L} \))**: This is the voltage measured between any two of the three lines or phases in the system.
For a star-connected system, the relationship between the line voltage (\( V_{L} \)) and phase voltage (\( V_{ph} \)) is given by:
\[ V_{L} = \sqrt{3} \times V_{ph} \]
This comes from the geometry of the system where the line voltage is the vector sum of the phase voltages, which are separated by 120 degrees.
### 2. Line Current vs. Phase Current
- **Phase Current (\( I_{ph} \))**: This is the current flowing through each individual phase of the system.
- **Line Current (\( I_{L} \))**: This is the current flowing through each of the lines connecting to the phases.
In a star-connected system, the line current (\( I_{L} \)) is equal to the phase current (\( I_{ph} \)):
\[ I_{L} = I_{ph} \]
This is because each line carries the current from one phase of the load to the neutral point.
### Summary of Relationships
- **Voltage Relationships**:
\[ V_{L} = \sqrt{3} \times V_{ph} \]
- **Current Relationships**:
\[ I_{L} = I_{ph} \]
### Practical Implications
Understanding these relationships is crucial for designing and analyzing three-phase systems. For instance:
- **Voltage Regulation**: In a star-connected system, the phase voltage is often lower than the line voltage, which can influence insulation requirements for equipment.
- **Current Handling**: The fact that line current equals phase current means that each conductor in a star connection must handle the same current as the individual phase currents, simplifying design and protection schemes.
These relationships ensure the balanced operation of three-phase systems and are key to correctly sizing transformers, cables, and other components in electrical installations.