Derive the relationship between phase and line voltage in a star connected system
Answers
Consider a balanced star connected system as shown in figure below. Let VR , VY and VB represent the phase voltages (Vph) while line voltages (VL) are given by VRY , VYB and VBR .
Relationship between Line and Phase Voltages and Currents in Star Connection
Since it is a balanced system
but 120 ° (electrical) displaced from each other. Negative of a vector is obtained by just reversing it. The figure below shows vectorial addition of phase voltages.
Relationship between Line and Phase Voltages and Currents in Star Connection
It may be observed that when we say line voltage VRY , it means the voltage of terminal R with respect to terminal Y and can be represented in vector terms as
On the other hand, observation revealed that each line is in series with its individual phase winding. Hence in a star connection, the line current in each line is the same as the current in the phase winding to which the line is connected.
Let current in line R be IR , current in line Y be IY and current in line B be IB . Since IR = IY = IB= Iph ( balanced connection) , in a star connection it is generalined as
IL= Iph
i.e line currents = phase currents
To summarise, in star connection
1.The line voltages are 120 ° apart from each other.
2.The phase voltages are 120 ° apart from each other.
3.The line voltages lead their respective phase voltages by 30 °.
4.The line voltage magnitude is √3 times the phase voltage magnitude.
5.The line currents and phase currents are same.