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# Voltage Factor for Voltage Transformers

11/10/2017 2:05 AM

How the voltage factor for voltage transformers is calculated?

For example, for a VT connected between phase and neutral and with the system neutral effectively grounded/earthed, the rated voltage factor is 1.5. How this value of 1.5 is calculated?

Similarly, for a VT connected between phase and neutral and with the system neutral non-effectively grounded/earthed, the rated voltage factor is 1.9. How this value of 1.9 is calculated?

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#1

### Re: Voltage Factor for Voltage Transformers

11/10/2017 3:11 AM

..."The Rated Voltage Factor of Potential Transformers is the maximum limit of excess voltage up to which the voltage transformer can maintain its rated characteristics. It is mentioned in percentage of the nominal voltage.

For instance a Rated voltage factor of 1.2 would mean that the Potential Transformer can maintain its rated characteristics up to 120% of the nominal voltage. "...

These parameters are arrived at through testing the design....

http://electrical-engineering-portal.com/definitions-of-voltage-transformer-parameters

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#2
In reply to #1

### Re: Voltage Factor for Voltage Transformers

11/10/2017 5:02 AM

Do you think that I do not know this explanation?

I would like to know the calculation behind the values 1.5 & 1.9.

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#3
In reply to #2

### Re: Voltage Factor for Voltage Transformers

11/10/2017 8:23 AM

To my knowledge, 1.5 comes from the max overvoltage expected in unfaulted phases during single phase to ground faults in an effectively earthed system.

Similarly, 1.9 comes from that expected in case of unearthed system or ineffectively earthed system.

We can say that the voltage factors are related to earth fault factors (EFF) for a given system.

To add to this, the duration associated with voltage factor is dependent on whether automatic detection and removal of faulted feeder is available in the system or not.

Apologise if I have just repeated what already you know.

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#5
In reply to #3

### Re: Voltage Factor for Voltage Transformers

11/10/2017 9:16 AM

Sir, I am aware of EFF and duration, et al. How do you say that the max over voltage expected in unfaulted phases during single phase to ground faults in an effectively earthed system, is 1.5 and that expected in case of unearthed system or ineffectively earthed system is 1.9? Is there any scientific formula for arriving at these values?

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#7
In reply to #5

### Re: Voltage Factor for Voltage Transformers

11/10/2017 1:15 PM

I suppose if you already know all the answers then why are you posing a question?

If you want the rule here it is:

(1) hold your thumb up in front of your face

(2) hold up the rule near your thumb

(3) put these together and you have the rule of thumb

Try not phrasing your replies back to those attempting to help you in such a rude and inconsiderate way next time.

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#8
In reply to #7

### Re: Voltage Factor for Voltage Transformers

11/10/2017 4:31 PM

Ah, yes, another case of formulitis.

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#13
In reply to #7

### Re: Voltage Factor for Voltage Transformers

11/13/2017 5:19 AM

Mister,

I said I already know the values only but not how they are arrived at.

You van hold your thumb in your mouth & suck it, if you so like.

Thanks for your advice. If you feel I am rude, do not attempt to answer my queries.

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#11
In reply to #5

### Re: Voltage Factor for Voltage Transformers

11/12/2017 2:54 PM

You could contact the standards committee that wrote the specific standard and ask them where they got the figures from.

The original source material the standards are based on will likely be mentioned in some electrical theory book somewhere which became the basis for what we have now. Unfortunately I don't think any of us know WHERE that was first mentioned and hence are not able to supply the exact working out and original source, only what it has become.

However the actual formula are available I believe in the appropriate voltage transformer (or possibly HV cable installation) standards and potentially available off voltage transformer (or possibly HV cable) manufacturer website literature (for free), so you could try there.

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#12
In reply to #5

### Re: Voltage Factor for Voltage Transformers

11/12/2017 7:06 PM

If I was designing VTs for an unearthed 3 wire 3 phase system, I would expect the possible voltage to earth to be, allowing 10% tolerance above the nominal...

Nominal (V = Normal/Rated??) line voltage to earth X √3 x 1.1= V*1.732*1.1 = 1.905

Call it 1.9

Note that in the unearthed system, the earth current is usually negligible - a few amps - so line to line voltages and angles are unchanged by the earth & nominally symmetrical.

Even an earthed system does not have zero impedance on the faulted phase. The normal requirement for an earth system for a significant generating plant & substation is 0.5 ohm resistance, line impedance down to the fault adds to this. If there is a VT at the fault site and voltage at fault is zero, then the "earthed" star point at the source transfo is at a considerable voltage e.g. 10000 amp x 0.5 ohm = 5000 V. The vector addition of this to the line-star voltage of an unfaulted phase is not negligible e.g. 157% in 11 kV.

Of course, supposing the fault is at a sub-station away from the source, it too will have 0.5 ohm resistance to "earth" from its earth "mat", making total resistance 1 ohm.

In addition, an arc at the fault does not have zero voltage drop.

Most distribution end plant does not have the luxury of an 0.5 ohm earth, just a few rods at 30 ohm/rod in standard conductive soil, let alone a dry location with sandy soil.

So I can believe that a figure of 1.5 x phase-earth voltage would be a sensible standard. "standard" practices enable standard equipment to cover the majority of actual applications - each application requires its own system analysis.

If you specify the actual standard which gives the 1.5 & 1.9 numbers, maybe someone will know better the reasoning or statistics behind the standard.

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#14
In reply to #12

### Re: Voltage Factor for Voltage Transformers

11/13/2017 5:24 AM

Oh! Thank you.

That clears 1.9 for a non-effectively earthed system.

But, 1.5 for effectively earthed system is still not very clear.

My reference to these values are from IEC 60044-2

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#17
In reply to #14

### Re: Voltage Factor for Voltage Transformers

11/14/2017 6:17 AM

By definition, overvoltage in effectively earthed system is limited to 0.8xVL.

This corresponds to ~1.4Vph.

That's the basis for Voltage factor of 1.5, I guess.

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#18
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### Re: Voltage Factor for Voltage Transformers

11/14/2017 11:48 AM

Ok, I thought further & looked about for reference to IEC60064-2. It is a spec for inductive voltage transformers & a look at a VT makers website shows transfos from 63V primary - so it is wide-ranging in voltage. Classes 3P1.2, 3P1.5 & 3P1.9 are offered. I guess 3P1.5 applies for 3 ph earthed systems, 3P1.2 for single phase. Sorry, I do not have standard to look at: unless you have an employer or institutional access to a standards service, however I would be surprised if it explained why it has 1.2, 1.5, 1.9.
A look at UK national standard BS7671 (which applies up to 1000 VAC line-line) shows in 1981 it began a process of harmonizing with IEC 364 "Electrical Installations of Buildings". It specifies that the minimum cross-section of earth conductors should be 1/2 of that for the phase conductors for phase conductors >= 35 square mm [if it is of the same material - e.g. copper] - IF the user decides not to do any specific calculations!!. That is unchanged in current edition.
Assuming a final circuit fed from source of zero impedance, for a short down the circuit at a VT location, 2/3 of the voltage drop is in the earth conductor when it has half the cross-section of the phase.
So the possible voltage across a VT connected to the earth conductor at the fault or beyond is given by the vector sum of an unfaulted normal phase voltage at 120 degrees to the 2/3 phase voltage across the earth conductor (in phase with the faulted phase voltage for resistive circuit).
I just drew myself that phasor diagram with a ruler & protractor & found that for a sum of 1.5 x rated phase voltage the voltage across the earth conductor is 0.73 x phase voltage, compared to 0.667 expected from the resistance ratio 2/3.
But 0.73/0.666 = 1.096, which looks like a 10% margin.
In fact, according to BS7671, for cables <35 sq.mm, earth core resistance may be 2.667 x phase resistance, even for cables above 35 sq.mm using armour as earth return, earth core resistance may exceed 5x phase.
If a better calculation is used, taking into account the source impedance which is significantly inductive at circuit rated currents high relative to feeder transfo rating, the VT voltage may exceed 1.5 rated, even with earth core resistance 2 x phase core resistance, so you have to do calculations.

Example :- For a circuit with source voltage U & impedance Z + R, the impedance is 2xR if Z is resistive and = R - but if Z is inductive & same impedance then the load impedance is √(R2 + Z2) - which is 1.4142 x short circuit current compared to resistive source. So voltage across earth core is greater and because current lags faulted phase voltage, so does resistance volt drop & consequently vector sum with unfaulted phase has increased magnitude.

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#4
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### Re: Voltage Factor for Voltage Transformers

11/10/2017 8:56 AM

SE did say that those values are determined by testing the design . . . . .

Based on my limited knowledge of transformer design, I don't believe there are any specific calculations to churn out a number. However, if a program like ANSYS were to be used to design a transformer, I would imagine that given models for the lamination materials, windings and all, one could empirically derive the voltage factor for a particular design using the simulation software.

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#6
In reply to #4

### Re: Voltage Factor for Voltage Transformers

11/10/2017 10:45 AM

...but it would still need to be tested for verification....The manufacturing method, equipment used and material quality vary, as do other extenuating circumstances...

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#15
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### Re: Voltage Factor for Voltage Transformers

11/13/2017 5:25 AM

I am afraid it has nothing to do with transformer design It is a system parameter, to which VTs are designed to withstand to.

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#9

### Re: Voltage Factor for Voltage Transformers

11/11/2017 11:59 AM

The voltage ratios of a V transformer is equal to the turns ratio. 100 turns on primary and 150 on secondary yields a V gain of 1.5.

The manual for the transformer should have these values.

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#16
In reply to #9

### Re: Voltage Factor for Voltage Transformers

11/13/2017 5:26 AM

I am discussing a step down voltage transformer here, wherein the secondary turns are far less than primary turns.

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#10

### Re: Voltage Factor for Voltage Transformers

11/11/2017 8:03 PM

Nowadays most engineers use regulations, which are rules stated by a group of scientist generated as a summary from experimental data. Most of them are in France and Switzerland, as far as I know.

Normally, we buy the a document which tells us what rules we should follow, such as the values that can be used for the voltage factor. However, they do not tell you how they came to that conclusion.

If you really need to know what kind of experiments and data analysis they made for this particular topic, you probably could call them, even though I do not know how likely it is for them to answer you.

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