Neutral Shift

Just because a transformer has no wire connecting the neutral (return) to Earth doesn't mean that it is ungrounded. There is still an uncontrolled high resistance path to ground through the wiring insulation.

There is no neutral point in an ungrounded system.

If your ungrounded system is powered by a Y transformer winding [a grounded mid-point/common point of the Y would be called neutral] one must suppose you mean the voltage to ground of the centre of the star.

I think the Vo in the book is the physical voltage between the common star point of the winding and ground.

If you add the three VT voltages together, then the symmetrical positive and negative sequence voltages sum to zero, leaving the additive zero sequence voltages.

I have drawn a diagram below graphically summing the 3 VT voltages. In a real installation, the secondary windings of the VTs could be connected in "open delta" - VTs may have two secondary windings so both the "Y" voltages and the "open delta" voltages can be got simultaneously. For "open delta", "hot" of one VT secondary is connected to "ground" of the next, leaving one corner to be connected to meters or relays.

The symmetrical voltages to "star point" Vo are A-Vo, B-Vo, C-Vo.

A ground point Vg has been selected at random, with voltages to ground, the VT voltages VAg, VBg, VCg.

I have drawn in vectors VAg and VBg transposed to sum with VCg as the secondary winding voltages of VTs would sum. The open arrows > indicate their directions, please excuse the extension line of VAg, which I should have rubbed-out.

The sum of the 3 VT voltages is X-Vg. Note it is in phase with the Vo to ground vector and 3 times the length.

If the system were fed by a delta power winding or generator, the neutral point could be only theoretical but usefull as a concept to quantify unbalance.

Obviously, voltage from Vo to ground, results in a non-zero open delta voltage. If Vo were connected to ground by a resistor, such an offset could indicate an earth fault.

The "Anonymous post" question was about "How to measure the Neutral to Ground voltages in ungrounded system?". There is not any neutral point, the centre point of a star winding which would be earthed in a system with neutral is the nearest, but since the proposal is that "Vng = Vo", this requires answer.

I have added a point Vo' with star voltages A-Vo', B-vo', C-Vo', which still give a symmetrical Δ voltage ABC.

Note VAg, VBg, VCg are unchanged.

But Vo' to ground is not the same as Vo to ground.

So the VT voltages to ground can give you a zero sequence voltage Vo, a useful single number unbalance indicator, but they cannot tell the middle "neutral" voltage of the Y winding.

Conclusion is that Vng ≠ Vo if the system is not earthed by connecting the neutral to earth through a resistor.

Direct connection of neutral to earth in a real system is still a resistance because a single earth rod is only ~30 ohm in good conductive soil and even substation earthing is usually specified 0.5 ohm.

67model

Rixter,

Your first two paragraphs can only confuse the questioner!

The first suggests a totally isolated system - which does not exist.

The second suggests the other two phases/neutral do not have a voltage to ground until one phase is "earthed".

Questioner's reference to VTs makes it clear this is a realistic (high voltage) system and question is about how voltages to a "neutral" point can be measured, with knowledge that the zero sequence voltage is relevant.

The commendable diagrams you add go on to show that capacitance to ground (and inductance of VT primaries and leakage resistance[not drawn!]) do cause phases and "neutral" to have voltages to ground of uncertain value - due to "unbalance" of a practical system which has no designed resistive earthing.

67model

Maybe I am clever, but your explanation made perfect sense to me......and several others here too, thanks.

Not confusing at all.....

Is there another similar installation nearby that is available for study, perhaps?

The Neutral point is the line to line voltage divided by the square root of 3.

The neutral shift is implied by the 3 voltages measured to ground by your VTs.

The extreme neutral shift is when one of your VTs measures 0V, indicating a ground (fault) on one of the 3 phase legs.

You are correct with your understanding of the theory...which are based on Ideal conditions!

Which in real world applications will be limited due to imperfections! Inperfections in materials, manufacturing, processes, etc., that need considerations.

Leakage currents is an example I believe you failed to consider and include in your analyses!