Balanced 3 phase system

[electronicsLearner77]

I have few clarifications with the 3 phase balanced system.


Does a balanced 3 phased system mean that the impedance's Z1 = Z2 = Z3 is the only condition? because during that case the current through the Neutral is 0 else there is some current flowing through Neutral.
Few other questions on that is if z1 =z2=z3 does not satisfy then the RMS values of the 3 phase currents will be different as well or the peak values of the sine waves will differ, as Ia = Vrms/Z1, Ib = Vrms / Z2, Ic = Vrms / Z3. Am i correct?
If that is the case the 3 phase supply that is used to power the house holds how do you ensure z1=z2=z3?

 

[Harald Kapp]

Does a balanced 3 phased system mean that the impedance's Z1 = Z2 = Z3 is the only condition? because during that case the current through the Neutral is 0

That is what "balanced" means.

if z1 =z2=z3 does not satisfy then the RMS values of the 3 phase currents will be different as well or the peak values of the sine waves will differ

Of course. And the relation RMS = 1/sqrt(2)*Peak (for sinusoidal waveforms) still holds true.

how do you ensure z1=z2=z3?

You can't. Not exactly, at least. If all 3 phases are used, the armature connected usually is a high power motor or such and Z1=Z2=Z3 is ensured by design. If, however, one splits the 2 phase system to create 3 single phase systems (as customary for a typical household mains installation) or separate 2 phase systems (as is used afaik in the e.g. USA), one tries to distribute the different phases among different households to achieve a near equilibrium Z1 ~ Z2 ~ Z3. More reading e.g. here.

 

[Kabelsalat]

because during that case the current through the Neutral is 0

. . . . .
um, that got me thinking. Since the sum of currents in to a node is always zero, how can one state that current flows through it?

 

[Harald Kapp]

how can one state that current flows through it?

Because

the sum of currents in to a node is always zero

There some amount of charge flows into a node as flows out of the node (to avoid resurrecting the discussion about current not flowing because current is charge flowing...). So the charge flows effectively through the node. Voilá.

 

[electronicsLearner77]

. . . . .
um, that got me thinking. Since the sum of currents in to a node is always zero, how can one state that current flows through it?

I think the diagram i have drawn is not complete, the below diagram is what i feel complete

I am referring to the In the neutral current which is 0 for balanced loads.

That is what "balanced" means.

So i need not write z1,z2,z3 i can simply say z and it is true for all 3 phase circuits.

 

[Harald Kapp]

So i need not write z1,z2,z3 i can simply say z and it is true for all 3 phase circuits.

Only for those where z1=z2=z3. This is not necessarily the case. If it is, you can simply use z.

 

[Boure]

Three phase networks analysis
We can resolve a three phase network into a source configuration powering a particular load configuration,hence giving differing combinations for analysis, namely;

• star source powering a star load (neutral to neutral connection present; short circuit or loaded)
• star source powering a star load(no neutral to neutral connection present)
• star source powering a delta load
• delta source powering a star load
• delta source powering a delta load

To achieve a balanced network, we would have to have a three impedance equal and the line to line voltages equal.
As per the original question, there is no connection made from the neutral of the star connected load to the source side. Taking an arbitrary current value aN = Nc + Nb where;

1. aN = current flow from node a to node N
2. Nc = current flow from node N to node c
3. Nb = current flow from node N to node b

Final point to note is that for a balanced network, the magnitude of current flow through each arm is equal and can be a non zero value, however the currents are exactly 120 degrees out of phase with their corresponding 2 branch currents; as a result if any load or short is connected at the neutral and the neutral of the source(if any) will have no current flowing through it.