Calculating Transformer Percent Impedance 7

[jimgineer]

I know I’m missing something fundamental when understanding transformer impedances.

How is %Z calculated? It seems to me that if you looked at one winding of a transformer secondary (on a typical 480delta to 208wye transformer) you would find less turns, but more conductor. I am wondering if percent impedance is literally the ratio of impedance of the secondary (low) side as a percent of the impedance of the high side. Is it just this simple? I feel like I am missing something fundamental.

Also,
This information I understand to typically vary based on the transformer size/voltage and specs, which would make sense because this would impact the impedance on both the high and low side of a transformer. It sounds like this is always something that should be verified from the manufacturer, but I’ve noticed that within SKM there is a calculator present to pop out values.

So the follow up is, for an isolation transformer, that is 480 high and also 480 low, lets say as an example, is the %Z then = 100%?

Please fill in the gaps. I need to master this stuff.

 

[jimgineer]

Also please explain how X, R, fit in with the original question.

Thanks!

 

[davidbeach]

A good Power System Analysis text would provide lots of answers. Several are mentioned in faq238-1287.

 

[DanDel]

Another way to understand what the %Z represents is that it is also the % of the primary voltage applied which would cause the FLA to flow through a shorted secondary winding.

 

[pwrengrds]

%Z is also the % of secondary voltage drop from no load to full load on the transformer.

 

[jghrist]

%Z is also the % of secondary voltage drop from no load to full load on the transformer.

This is regulation, not impedance. They are related, but not the same thing.

 

[dpc]

The transformer impedance is primarily the leakage reactance of the transformer and the winding resistance. The leakage reactance is the reactance related to flux that does not fully link both windings. If 100% of the flux in the core linked both windings, the transformer impedance would be only the winding resistance (and very low). But real transformers do not have perfect flux linkage and there is always some leakage reactance. This can be controlled to some degree to allow the impedance to be increased or decreased (within some range) by design changes in the coils and core of the transformer.

 

[slavag]

Hi.
Dandel's explanation is classical answer.
Shortly and fully.
Best Regards.
Slava

 

[magoo2]

%Z is calculated by a simple test.

Take a single-phase transformer and short out the secondary terminals.

Connect a variac to the primary and adjust the voltage until you measure rated current on the secondary. Express that voltage as a % of rated primary voltage and the result is % impedance.

As an example, take a 7200 V 240 V tranformer. Say you measure 144 V on the primary to give you rated secondary current. 144/7200 is 2% IZ where I is 1 per unit, so 2% is your Z.

You can put a wattmeter in the circuit to see how much of the impedance is resistive, and then work out %R and %X.

So it's not the %Z on one side of the transformer compared to the other.

Even an isolation tranformer will have some %Z and I wouldn't expect it to be as high as 100%.

 

[waross]

I once sent a group of students to the shop to verify the % impedance of some small dry type transformers. They had significant errors compared to the nameplate value. The answer was that % imp is based on a transformer at operating temperature. If you try to verify it on a room temperature transformer you will get a low figure. (Higher current)

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

 

[jimgineer]

OK, this makes a bit more sense, I guess after reading these explanations.

Let me start with dpc’s:
The way that I am reading that is that essentially the high and low side of the transformer are not perfectly coupled, or that not all of the magnetic field is induced in the transformer’s core (and the that conductor is not wrapped ‘perfectly’ perpendicular to the core). This does make sense, however in a practical sense when calculating the short circuit current (for infinite bus), you use the formula FLA (based on XFMR size only) / %Z. My only complaint in this is that it would seem that if there truly was an infinite supply, it would seem like the amount of energy lost due to this effect would (although not nessacarily a linear relationship), would keep increasing as your available fault current of your supply increased.

DanDel’s:
This does help quite a bit, and jives with Magoo2’s explanation of what to do experimentally to get the %Z of a transformer (this process I have encountered on these boards before). I guess I’m trying to go a little deeper though into ‘what’ exactly this quantity/variable is. I have no problem, for example of doing a linear regression and then coefficients pop out, and they don’t really ‘mean’ anything. They are just a part of a method for approximating fitting something to a linear model. Maybe that’s just what this %Z is, in that it doesn’t really ‘mean’ anything.

I also want to put a couple things I’ve noticed, expounding on your explanations thus far:

The ‘X’ and the ‘R’ quantities, which dpc is referring to as reactance and resistance of the transformer, respectively, form a ratio of X/R, which appears to be VERY CLOSE but not quite spot on the %Z of the transformer. I’m wondering where this difference comes from, and how/why (if at all) the X and R variables are related to %Z. Also, I am wondering how to experimentally verify (test) the values for X and R. (We’ve already established how to test for %Z). It sounds like in terms of power system studies, the %Z is the more important quantity because it allows for you to quickly get the short circuit current levels.

Thanks much guys as always.

 

[jimgineer]

Bill did you do that to teach a lesson, or did you accidentally teach yourself a lesson in the process?

If there is such a substantial deviation based on operating temperature, does IEEE methods for calculating this stuff take that into account? (In other words I’m wondering if my software is taking that into account)..

 

[jimgineer]

Also magoo it looks like you gave details on how to get X and R of a transformer too, experimentally. Makes sense, thanks

 

[waross]

A word on the use of % impedance values.
The % Imp is on the nameplate of most transformers. This describes the steady state short circuit current.
The actual transient fault current may be much higher. It depends on the X/R ratio and the point on the sine wave that the fault occurred. Protection experts calculate the actual value based on the worst possible case of point on the wave.
The value of current based on % Imp is used to select equipment with adequate clearing ability. A switch, breaker \ or fuse rated for an available short circuit current of 10kA will safely interrupt the maximum instantaneous current available from a transformer with an available short circuit current of 10 kA or less.
Anyone who can divide the % Imp into the rated current of a transformer secondary winding can easily and confidently determine the steady state short circuit current even though the actual fault transient may be much higher.
The utilization equipment may then be selected based on this value. Equipment rated for the available short circuit current (also called the symmetrical current component) will have an adequate safety margin built in to safely handle the fault current or asymmetrical current.
The available short circuit convention and practice makes an important equipment selection very easy and simple.
By the way, this is not the only use for % Imp values, but it may be the most often used application by far.



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

 

[Bronzeado]

Hi folks,

Philosophycally, the %Z is something like the percentage of "loss of voltage transformation" in a transformer when it is full loaded.

In a ideal transformer with two concentric windings, the leakage reactance is proportional to the volume of the space between the windings. Note that, in this case, this space will be the same does not matter if it is seen from the primary or the secondary side.

Best regards,

H. Bronzeado

 

[dpc]

jimgineer,

I guess I don't understand your "complaint" regarding the system impedance versus the transformer impedance.

The %Z stamped on the nameplate IS the impedance voltage, determined by actual test after the transformer is built. This will be temperature sensitive, due to the resistive component.

 

[PHovnanian]

A word on temperature sensitivity of the impedance value. It all depends on what you are trying to calculate. For voltage drop under normal operating conditions, use the max operating temperature Z (highest). For available fault current, use the Z at the minimum expected ambient temperature (lowest).

 

[jimgineer]

dpc let me rephrase my mis-understanding:

I don't see why/how an infinite source would ever be able to provide a finite short circuit current when put through an impedance of any sort. There is something else going on in a transformer, no?

This would hold true in a circuit (although boring) that just consists of real impedence components. (ie infinite source generates infinite available current in a fault) I know there's not really such thing as an 'infinite' source, but what I'm not understanding, maybe, is the wording of calling something infinite if it isn't. And if it is in the calculation, then why can't it supply infinite fault current?

I know AC gets a bit more interesting when you introduce your C or L in an RC circuit... that's where you have to look at your frequency response to really get a feel for what your output waveform magnitude (and phase shift) all come from.

From my experience, power engineers are often very far removed from these kinds of mathematical exactations and the understanding of the real underlying theory and math that goes into some of this stuff. I'm not saying that's where you guys are here, only that I am trying to avoid falling into that trap myself.

 

[davidbeach]

An infinite bus has a source impedance of 0 (zero). So, infinite bus on primary of transformer, fault on secondary, the only impedance to limit the fault current is the transformer impedance.

 

[prc]

Let me add little more-

Percentage impedance of a transformer is the percentage of voltage to be applied on primary to get rated current in the shorted secondary.It is also 1/Z times of full load current that will pass in secondary in the event of a shorting on secondary terminals with rated voltage on the primary.

It is the square root of X2 + R2,where X is the leakage reactance between primary and secondary winding, R is the total resistance of both windings (or copper loss /rating in pu).X depends on the geometrical dimensions of the windings and number of turns( varies as square of turns) and when expressed as %pu on MVA of trf.When we say leakage flux please dont think it as a flux leaking out of core.It is the flux developed between two concentric windings( remember the current carrying solenoid with flux lines)It is zero at no-load and rated %Z at full load ie %Z varies linearly with load ( approx) .For small trfs R is significant compared to X and hence temperature sensitive.But for large trfs R is insignificant compared to X and hence Z is almost same as X and independent of temperature. % Z as per standards is always to reference ambient temp of 75 C ( IEC) or 85 C (ANSI)

Coming to the physical explanation of it-it is the price ( in terms of voltage ie voltage regulation) that we pay to shift current from primary to secondary winding.This was said by that great Transformer engineer who lived in the first half of last centuary,L F Blume of GE.Voltage regulation ie secondary voltage dip with load is happening because of %Z.

For each kVA rating of a transformer,based on geometric dimensions there is an optimum % Z value.If you move from this value up or down, cost increases.When % Z goes up, we call it a copper machine as copper quantity goes up( load loss goes up) and core iron quantity comes down ( no-load loss comes down)When % Z comes down,it is called a iron machine and reverse is the truth.Many times the system operational requirements decide the %z rather than the optimum cost.

For parallel operation,the %z of transformers shall be same to the respective kVA of transformers to avoid circulating currents between transfornmers.