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# Line-Earth Voltage in 3Phase unbalance loads6

## Line-Earth Voltage in 3Phase unbalance loads

(OP)
Hi all,

If we have a 3phase unbalance load (400V L-L, 230V L-N nominal voltages), which all loads are on 1phase and the other phases are unloaded, is it expected that L-E voltage in unloaded phases changes? (anything rather than 230V?)

I know that by unbalance loading, neutral point displaces and neutral voltage is something rather than 0. Therefore I expect L-N voltage changes on all phases. But my question is about line to earth voltage.
I ask this question because software simulation of such unbalanced load by DIgSILENT power factory shows such strange results!

### RE: Line-Earth Voltage in 3Phase unbalance loads

With an unbalanced load you will get a voltage drop on the loaded feeder conductor ans possibly the supply transformer. This may be significant.
With an unbalanced load you will also get a voltage drop on the neutral feeder. This may be significant. Additionally the neutral drop may have lessor ampacity than the line conductors.
Now, starting with an equal sided and equal angle star diagram and considering "A" phase to be the loaded phase,
The voltage drop on the neutral will be towards line "A" or "A" phase.
The voltage drop on the "A" phase feeder will be towards the neutral.
Now draw a triangle using the new position of "A".
The line to line angles are no longer 120 degrees.
Now using the new position of the neutral, draw a star diagram from the neutral to "A", "B", and "C".
The line to neutral angles are no longer displaced 120 degrees and while the voltage has dropped on "A"to neutra, you can see that it has raised slightly on "B"to neutral And "C" to neutral.
You don't want to add a grounded wye/delta transformer or a three phase motor to the mix.
It will get more interesting.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

Dear Mr. MAZ13
Q1. "...If we have a 3phase unbalance load (400V L-L, 230V L-N nominal voltages), which all loads are on 1phase and the other phases are unloaded, is it expected that L-E voltage in unloaded phases changes? (anything rather than 230V?). A. I am of the opinion that:
A1. with the N is solidly earthed:
A1.1, the loaded phase/line say A , V A-E will be lowered; due to the voltage drop in the transformer or the outgoing conductor,
A1.1 the loaded phase/line say A , V A-E will be

I know that by unbalance loading, neutral point displaces and neutral voltage is something rather than 0. Therefore I expect L-N voltage changes on all phases. But my question is about line to earth voltage.

### RE: Line-Earth Voltage in 3Phase unbalance loads

che12345
Dear Mr. MAZ13
Q1. "...If we have a 3phase unbalance load (400V L-L, 230V L-N nominal voltages), which all loads are on 1phase and the other phases are unloaded, is it expected that L-E voltage in unloaded phases changes? (anything rather than 230V?)...".
A. I am of the opinion that:
A1. if the N is solidly earthed:
A1.1, the loaded phase/line say A , V (A-E) will be lowered; due to the voltage-drop in the transformer and the outgoing conductor,
A1.2 the unloaded phases/lines say B&C , V (B-E) and V (C-E) will [remain the same 230V irrespective of whether line A is loaded or unloaded],
Q2. "...I know that by unbalance loading, neutral point displaces and neutral voltage is something
A2. if the N is not earthed, when say A is loaded; the N is not at 0 (the earth reference),
A2.1 the voltage of the loaded line A V (A-E) and unloaded lines V (B-E) & V (C-E) will [not be] 230V, as N is not at O (the earth reference).
Che Kuan Yau (Singapore)

### RE: Line-Earth Voltage in 3Phase unbalance loads

Dear Mr Che;
While your basic knowledge is very good, you obviously do not have a lot of North American experience.
You persist in assuming field conditions that don't exist in code compliant North American installations.
In North America the neutrals are earthed at the source.
Voltages measured at the load will be reduced by voltage drops in all current carrying conductors.
The neutral feeding a single phase line to neutral load will be one of the current carrying conductors and will experience a voltage drop.
It is a serious code violation in North America to ground a neutral at the load.
Even if there is an exception and the neutral is grounded at the load, there will be a voltage drop on the neutral path and this will be reflected as a voltage at the load that will be the source voltage minus the voltage drops on both the phase conductor and the voltage drop on the neutral current path.

If the neutral is not earthed, the phase to ground voltages will be indeterminate and subject to possible change when major branch feeders are connected.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

Dear All,
Q. "...If we have a 3phase unbalance load (400V L-L, 230V L-N nominal voltages), which all loads are ..."
A. With the voltage (400V L-L, 230V L-N nominal voltages ...) it indicates to be in the IEC world. Therefore, the US practice does NOT come into the picture.
Che Kuan Yau (Singapore)

### RE: Line-Earth Voltage in 3Phase unbalance loads

I was not aware that IEC practice was to ground the neutral at each load. Thanks for the heads up.
Does that make this statement invalid?

#### Quote:

Even if there is an exception and the neutral is grounded at the load, there will be a voltage drop on the neutral path and this will be reflected as a voltage at the load that will be the source voltage minus the voltage drops on both the phase conductor and the voltage drop on the neutral current path.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

Dear Mr. waross

1. Your learned advice dated 28 Sep 20 02:41 is out of the scope to the question asked.
2. "...I was not aware that IEC practice was to ground the neutral at each load..." .
No, it is NOT the IEC practice " to ground the neutral at each load..."
3. Your statement "...Even if there is an exception and the neutral is grounded at the load, there will be..." is irrelevant. Reason see above 2.
4. I will answer to (Mr. MAZ13) in greater detail on a [three-phase system with neutral but the neutral is isolated from earth], in a separate mail to follow.
che Kuan Yau (Singapore)

### RE: Line-Earth Voltage in 3Phase unbalance loads

Dear Mr. MAZ13

This is an annexment to my earlier submission dated 27 Sep 20 23:38.
Q. "... a 3phase unbalance load (400V L-L, 230V L-N nominal voltages), which all loads are on 1phase and the other phases are unloaded, is it expected that L-E voltage in unloaded phases changes? (anything rather than 230V?)..."
A. On a [three-phase system with (neutral) but the [neutral is isolated from earth]
a) hypothetically, consider that the trafo is (suspending) in a [vacuum away from our earth], there is NO connection between the [neutral and our earth], then the voltage V (A-E), (B-E), (C-E) and (N-E) shall be 0 V. But, this is only [hypothetical]; in reality....,
b) when the trafo is placed on our planet [earth] and is surrounded by [air]; there unavoidably by [stray coupling capacitance] between line A, B, C and N to the earth. As the neutral is NOT connected to the earth, the voltage V (A-E), (B-E), (C-E) and (N-E) shall theoretically be 0 V. But in reality ....,
c) the [stray coupling capacitance] fooled our daily "careful" observation. The voltage reading V (A-E), (B-E), (C-E) and (N-E) are NOT 0 V; even readings are taken with a modern digital volt meter or a RMS reading meter!
d) theoretically, the voltage reading shall be 0V. But we read some reading on the high input impedance modern digital volt meter, due to the [stray coupling capacitance]. So, what is the voltage with respect to earth? It depends on many factors, even the scale value selected on the measuring meter affects the reading.....
Che Kuan Yau (Singapore)

### RE: Line-Earth Voltage in 3Phase unbalance loads

Let's say we have a 2500 kVA 3*400 V 6% short-circuit voltage grounded Y connected.
The copper losses 9000 W. Calculated Z=0.4^2/2.5*6%=3.8E-3 ohm[3.8mΩ]. In=2500/sqrt(3)/0.4=3.608E3 A [3.6084 kA]
R=9000/3/3608.4^2=2.3E-4 [0.23 mΩ]
X=SQRT(3.6084^2-0.23^2)=3.601 mΩ
A supply cable of 4*6 mm^2 copper XLPE insulated PVC jacketed of 100 m up to our main panel. x=0.144 ohm/km r=3 ohm/km Zcbl=sqrt(0.0144^2+0.3^2)=0.30035 ohm; Ycbl=Yo=1/0.30035=3.329
zcbl=0.3+j0.0144 ohm; Ycbl=3.326-j0.16 siemens[S]
Let's say we have a single phase [phase R and N] 400/√3=231V loaded with 10 kW and cos(ϕ)=0.85.
If the load is constant, we may calculate Zload=0.231^2/0.01177=4.5336 ohm YR=1/4.5336=0.220257 S
At main 3 phase terminals we have -almost-a unchangeable voltage of 400/sqrt(3)=231 V
Then we can neglect transformer impedance and cable impedance but we keep the neutral wire impedance in calculation.
From here we have a lot of way to continue calculation like Millman theorem, Kirchhoff and other. You may use absolute values or complex. Whatever the difference is less than 1%.
Using Millman theorem:
Vn[the voltage between the neutral at our main and the transformer neutral]
If YS=YT=0 then Vn=VR*YR/(YR+Yo)=14.35 V
Using complex numbers Vn=12.85-j6.63
Now Van=Va-Vn=231-14.35=216.65V
Using complex numbers Van=218.25V
Vbn=232 V
Vcn=243V
If we shall take Zo=∞ then Van=0.361431;Vbn=399.6;Vcn=399.8 V

### RE: Line-Earth Voltage in 3Phase unbalance loads

Dear Mr. 7anoter4
Q. "... a 3phase unbalance load (400V L-L, 230V L-N nominal voltages), which all loads are on 1phase ..., is it expected that L-E voltage in unloaded phases changes? ... I know that by unbalance loading, neutral point displaces and neutral voltage is something rather and the than 0. Therefore ... But my question is about line to earth voltage...."

2. Mr. MAZ13 's question is " about line to earth voltage* "

3. Sorry, I am of the opinion that your learned advice is out of the scope, to the question* asked.
Che Kuan Yau (Singapore)

### RE: Line-Earth Voltage in 3Phase unbalance loads

If we measure the voltage at the terminal of the randomly charged transformer, another added unbalance load does not produce a significant voltage imbalance..
What I understood it is about of local voltage to local neutral point grounded. I admit now that it is not clear from the o.p.

### RE: Line-Earth Voltage in 3Phase unbalance loads

#### Quote (OP)

I ask this question because software simulation of such unbalanced load by DIgSILENT power factory shows such strange results!
7anoter4 and I have been attempting to address this statement.
Another poster wishes to focus on a narrow interpretation of the question and dismiss any additional information.
7anoter4 and I are trying to address this comment (strange results) and explain the answer.
A simple answer is simply that the line to ground voltage will drop by the amount of voltage drop in the hot conductor.
A explanation of the "strange results" requires consideration of the voltage across the load, the voltage drop on the neutral conductor, the neutral displacement and the effect of the neutral displacement on the voltage to ground of the unloaded phases taken at the location of the unbalanced load.
Scope is where you find it!
Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

In USA the neutral is grounded only at the source. In IEC World in order to detect a leakage to ground the local neutral has not to be grounded locally. Exception: only in TT earthing system the equipment is grounded through equipment grounding locally.

### RE: Line-Earth Voltage in 3Phase unbalance loads

Equipment grounding versus system grounding:
In the US equipment frames may be grounded locally to limit touch potentials.
System grounding refers to a connection between the system neutral and a ground source or electrode.
System grounding is done at only one location, at the source.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

2
LOL, there is no good answer without knowing the transformer and grounding configuration entered into the model.

How an installation is required to be wired in the NEC or the IEC worlds means jack squat when using a modelling program.

### RE: Line-Earth Voltage in 3Phase unbalance loads

Right on Lionel.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

Thank you LionelHutz
However,I don't think you took my exercise seriously. Because o.p. threw an idea I tried to give it some clothes. Besides, I agree with what you said. Like the statement that it is very difficult to get on a plane while flying.

### RE: Line-Earth Voltage in 3Phase unbalance loads

(OP)
Hi all,

First to make assumptions more clear: neutral point at load is not earthed. It is abviously clear that by an earthed neutral on load star point we would have a voltage drop on phase A (loaded phase) and nothing more (no change in neutral or other phases voltages).

The question is about phase to earth voltage of unloaded phases, when neutral is not earthed at load terminals and load is just on phase A.

In this case, I expect that a voltage drop occurs on phase A (Va<230), voltage on neautral point raises (Vn>0), phase to neutral voltage on phase A reduce (Van<230) and phase to neutral voltage on unloaded phases increase (Vbn>230 and Vcn>230 because of displacement in neutral voltage point). But I don't expect any change in Vb and Vc! (should be: Vb=Vc=230) However, DIgSILENT shows change in Vb and Vc! and important point: this is because of cable. It means when I use a 3core cable, the results are so that I expect, but when I use 5 core cable, these strage results come out.

I have read your answers carefully. But I think when Bill talks about drawing a triangle, he assumes Vb and Vc are on the same place (as I am) and when 7anoter4 calculates Vbn and Vcn, he also assumes Vb and Vc are 230V.

### RE: Line-Earth Voltage in 3Phase unbalance loads

From what I can understand, OP is asking a very teorethical question and che12345 is correct with his answer (but without any context, all the answers here are valid at some point):

#### Quote (MAZ13)

If we have a 3phase unbalance load (400V L-L, 230V L-N nominal voltages), which all loads are on 1phase and the other phases are unloaded, is it expected that L-E voltage in unloaded phases changes? (anything rather than 230V?)
I know that by unbalance loading, neutral point displaces and neutral voltage is something rather than 0. Therefore I expect L-N voltage changes on all phases. But my question is about line to earth voltage.

I think he is referring to the fact that in an ungrounded star system with an unbalanced 3 phase load, the neutral voltage (N in figure below) shifts from the theoretical earth potencial (E). This usually obtained with the symmetrical components method for solving unbalanced 3 phase systems.

For the case mentioned by OP: all loads on 1 single phase, and the other 2 unloaded, there is no such phenomenon (in the symmetrical components kind of way) and the only neutral voltage displacement would be the one produced by the voltage drop on the neutral conductor as waross mentioned and 7anoter4 showed by example. This could be more or less noticeable depending on the neutral ground connection (far from the load-> more noticeable / close to the load -> less noticeable).

And to answer OP specific question: There will be no change of voltage on the unloaded phases with respect to earth E as che12345 already said, but it will with respect to neutral N as waross and 7anoter4 said.

Now, what is OP thinking or trying to simulate to bring up such questions?.. it beats me.

EDIT: Oops.. I was still typing when OP made the last reply and didn't read it untill I posted, but the core of my answer stands so I will not change it.

### RE: Line-Earth Voltage in 3Phase unbalance loads

#### Quote (MAZ13)

...However, DIgSILENT shows change in Vb and Vc! and important point: this is because of cable. It means when I use a 3core cable, the results are so that I expect, but when I use 5 core cable, these strage results come out.

The best way to give you a proper answer regarding this last issue would be if you post the circuit you are simulating and where are you measuring the voltages to ground on DigSilent, at least a handmade rough diagram with both cases: 3 core cable and 5 core cable.

Or we will continue to guess what's going on.

### RE: Line-Earth Voltage in 3Phase unbalance loads

argotier:
For the neutral grounded at the source;
In your diagram, the neutral displacement will be along the line A-E, from E towards A.
Yes, the voltages to ground on the unloaded phases will be unchanged but the voltages on the unloaded phases from line to neutral, taken at the point of the load will change.
If you modify your sketch so that the neutral displacement is on the line E-A, then the voltages and the voltage changes from line to neutral compared to line to ground (E) will be clearly shown.
MAZ13;
Three phases and a neutral requires four wires.
I am wondering about the connections of the 3 core cable and the 5 core cable.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

Is the neutral earthed anywhere?

### RE: Line-Earth Voltage in 3Phase unbalance loads

(OP)
Hi all,

I have simulated 2 cases: on the left side is a single phase load 15,7A, supplied from phase L1.
On the right side is a 3phase unbalanced load, which all load (15,7A) is on phase L1.

Supply cable cross section is same 2.5mm2 in both cases.

I expect no difference between these 2 cases. It means: I expect same L1-E voltage, same neutral voltage (as it is) and same L1-N voltage. Also I expect L2-E and L3-E stay 230V (nominal voltage) because they are unloaded (while L2-N and L3-N could be different because of neutral displacement).

I don't know why the results on 3phase load do not follow my expectations! Do you have any Idea?

### RE: Line-Earth Voltage in 3Phase unbalance loads

That attachment was rather useless. Post the system, not results....

### RE: Line-Earth Voltage in 3Phase unbalance loads

Try running a simulation with a unity power factor load.
It is the skewed neutral offset that is cauaing the unequal phase voltages.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

Source: it could be a transformer and one need to know Srated , uk% and load losses in order to calculate Zxfr and the actually voltage drop.
Whatever the busbar potential has to be 225 V [390 V between phases].
3*2.5 mm^2 side:
It seems you have a neutral conductor still, other way I1=Io=0 since no other return way.
5*2.5 mm^2 side:
It seems to me that it is correct [ and 60oC conductor temperature it is o.k.]

### RE: Line-Earth Voltage in 3Phase unbalance loads

(OP)
Dear Waross

This is the case with unity power factor. There is not too much differenece:

### RE: Line-Earth Voltage in 3Phase unbalance loads

(OP)
Dear 7anoter4

What are you talking about? The network is as simple as is indicated. There is no transformeres and for voltage drop calculations you don't need to know what equipment is on upstream! Voltage on main busbar is 400V-3ph-N.

Left side is a single phase load (L1-N) which is supplied from 3x2.5mm2 cable.
On the right side is a 3phase load (Y-N) supplied from 5x2.5mm2, that just phase1 is in service. It means that actually a single phase is in service and there should be no difference between the results on right and left side. At least I think so!

### RE: Line-Earth Voltage in 3Phase unbalance loads

With a unity PF load, the L2 and L3 voltages should become equal, removing some of the strange effects originally shown.
The hand calculation of both the single phase line to ground voltage and the single phase line to neutral voltages becomes more straightforward.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

I don't like a program made by others for sale because you don't know exactly what kind of data the robot wants to be given and how to interpret exactly the data that the robot provides you.
In this case, which is extremely simple - a simple calculation with a single-phase voltage - it has become enormously complicated with a three-phase network and a lot of unnecessary data.
I think that using a three-conductor cable in a three-phase network, the robot considered three phases. So, I consider that you only have a two-conductor cable to employ.

### RE: Line-Earth Voltage in 3Phase unbalance loads

(OP)
Could anyone simulate this example in any other software and share the results? So we may compare the results and get to a conclusion.

### RE: Line-Earth Voltage in 3Phase unbalance loads

I'm kind of old school.
Rather than play musical software, we dinosaurs would hand calculate the answer.
I had a hard day today and am too tired to take that on just now.
Maybe someone else will.
I don't think that the software properly understands the question and I don't think that we properly understand what the software is trying to tell us.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

From the attached diagram that was made by the computer, it is difficult to understand what each digit represents.
For example, the diagram shows an External Network and next to it a current and three-phase active and reactive power values. It is not understood whether they represent nominal values or a certain load.
Also for the 5 * 2.5 cable, 2 currents are noted, one in three-phase and another in single-phase.
In order to calculate the voltages towards the neutral and towards the earth, a real scheme is needed.
I think there are actually two different overlapping problems, one three-phase and one single-phase.

### RE: Line-Earth Voltage in 3Phase unbalance loads

Do you have a model that we can look at or can't you be bothered providing that kind of info? I'm completely dumbfounded that others here are trying hard to figure this out without even seeing a model of the system you are posting about.

### RE: Line-Earth Voltage in 3Phase unbalance loads

What values did you originally enter into the software?

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: Line-Earth Voltage in 3Phase unbalance loads

I think the solution is as per attached sketch[calculated in simlpy excel using complex functions]

### RE: Line-Earth Voltage in 3Phase unbalance loads

(OP)
Hi all,

I'm surprised what special data are you looking for?
The short circuit capacity of "External Network" , as an input data for example, has no role on voltage drop calculation! Main busbar should be considered as "PV" and External network produces as much power as required to maintain 1pu voltage on main busbar (there is no other meaningful option! How else could one simulate this?)

There is no cable between "External Network" and main busbar. Therefore there could be no more this question, if the Neutral is earthed on External Network or on main busbar!

My input data about cable is cross section (2.5 mm2) and length (76 m). Load current is 15.7A with 0,92 capacitive power factor.
Any other parametere should be calculated.

Please clear it up, what parameter or model data are you looking for.

### RE: Line-Earth Voltage in 3Phase unbalance loads

(OP)
Dear 7anoter4

you made it well. Thank you.

Now the question is about "VL1E" , "VL2E" and "VL3E" in your 3phase load. Could you indicate it on the diagram?

By me, "V1LE" , "V2LE" and "V3LE" are far away from my expectations and it made me to raise this thread.

### RE: Line-Earth Voltage in 3Phase unbalance loads

For the 5-conductor cable side VL1E it is the bus voltage Va minus one-time VN and VL1N it is Va minus two times VN.
VL2E=VL2N and VL3E=VL3N
However, the accurate calculation it has to be done in complex.

### RE: Line-Earth Voltage in 3Phase unbalance loads

(OP)
Why do you think VL2E=VL2N and VL3E=VL3N ?
VN is not 0!
As you mentioned, we have: VN=8.871

### RE: Line-Earth Voltage in 3Phase unbalance loads

I'm sorry, my mistake! According to my definition V2E = VR-0 [ground], so V2E ≠ V2N [same as V3E]. This means that V2E and V3E are nonsense. Also, basically, V2N and V3N are not usable.

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