relation between line voltage and phase voltage in delta connection
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Hii, your answer is here
Good question. This answer require 2 way approach, i.e.we should analyze star connected network and then withdraw relations between Line and Phase Voltages.
Similarly the same for Delta connected circuit by obtaining relevant equations of Line and Phase voltages.
Then after we should compare, i.e. as question contain statement voltage between star and delta, Such that we should now compare star connected network with delta, and capture the phase difference.
STAR NETWORK EQUATIONS :-
For simplicity in calculations let us consider the equations pertaining of 1 phase rather than 3 phases.
There is no doubt we can conclude that line currents are equal to phase currents in a phase in star network.
Coming to voltage relations, we know that each phase is displaced in space by 120° from each other.
Where VAN = voltage between line A to neutral.
The line voltage can be easily obtained by seeing the diagram, i.e
Line voltage between A and B phases will ve VAB=VAN-VBN.
Drawing same equation in phasor diagram format will be as;
I took reference voltage as VAN, and drawing respective other phasors from VAN displacing 120° each other we get above diagram.
We can conclude that LINE VOLTAGE LEADS PHASE VOLTAGE BY AN ANGLE_ 30° in a star connected network.
This can also be concluded by parallelogram analysis.
Equations for DELTA CONNECTED NETWORK;
Delta connected circuit will be as similar to a parallel connected network. Because, In delta connected there is no dividing point as in case of star(what i mean to say is in star there is neutral point wherein voltage divides equally wrt. that point, and current will be equal in individual phases if it is a balanced load).
But this is not the case in delta, and there is no star point in this circuit and windings resemble as parallel connected parts. Therefore Voltage will be equal with respect to individual phases. i.e. VOLTAGE IS EQUAL IN DELTA wrt PHASE AND LINE FOR ALL PHASES
VL=VPH In delta.
Now let us confine our topology to question asked;
This is the ciruit for question asked above;
We had concluded that from star ciruit analysis that Line Voltage leads phase voltage by 30°.
And also we conclude that in delta VL=VPH.
HENCE FOR A STAR AND DELTA CONNECTED NETWORK, PHASE DIFFERENCE BETWEEN LINE VOLTAGES WILL BE;
Equal in terms of Line voltage, i.e VL=VL for star and delta
As VL=Vph -30° ie. Line leads phase voltage in star, when we talk this same voltage wrt to delta we can also say that VL of delta Leads VPH of star by 30° .
Because the same phases AC of star is also connected to AC of delta it can be concluded that VL=VL for both circuits.
Hope you understand
...~~~Thanks~~~...
Good question. This answer require 2 way approach, i.e.we should analyze star connected network and then withdraw relations between Line and Phase Voltages.
Similarly the same for Delta connected circuit by obtaining relevant equations of Line and Phase voltages.
Then after we should compare, i.e. as question contain statement voltage between star and delta, Such that we should now compare star connected network with delta, and capture the phase difference.
STAR NETWORK EQUATIONS :-
For simplicity in calculations let us consider the equations pertaining of 1 phase rather than 3 phases.
There is no doubt we can conclude that line currents are equal to phase currents in a phase in star network.
Coming to voltage relations, we know that each phase is displaced in space by 120° from each other.
Where VAN = voltage between line A to neutral.
The line voltage can be easily obtained by seeing the diagram, i.e
Line voltage between A and B phases will ve VAB=VAN-VBN.
Drawing same equation in phasor diagram format will be as;
I took reference voltage as VAN, and drawing respective other phasors from VAN displacing 120° each other we get above diagram.
We can conclude that LINE VOLTAGE LEADS PHASE VOLTAGE BY AN ANGLE_ 30° in a star connected network.
This can also be concluded by parallelogram analysis.
Equations for DELTA CONNECTED NETWORK;
Delta connected circuit will be as similar to a parallel connected network. Because, In delta connected there is no dividing point as in case of star(what i mean to say is in star there is neutral point wherein voltage divides equally wrt. that point, and current will be equal in individual phases if it is a balanced load).
But this is not the case in delta, and there is no star point in this circuit and windings resemble as parallel connected parts. Therefore Voltage will be equal with respect to individual phases. i.e. VOLTAGE IS EQUAL IN DELTA wrt PHASE AND LINE FOR ALL PHASES
VL=VPH In delta.
Now let us confine our topology to question asked;
This is the ciruit for question asked above;
We had concluded that from star ciruit analysis that Line Voltage leads phase voltage by 30°.
And also we conclude that in delta VL=VPH.
HENCE FOR A STAR AND DELTA CONNECTED NETWORK, PHASE DIFFERENCE BETWEEN LINE VOLTAGES WILL BE;
Equal in terms of Line voltage, i.e VL=VL for star and delta
As VL=Vph -30° ie. Line leads phase voltage in star, when we talk this same voltage wrt to delta we can also say that VL of delta Leads VPH of star by 30° .
Because the same phases AC of star is also connected to AC of delta it can be concluded that VL=VL for both circuits.
Hope you understand
...~~~Thanks~~~...
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