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# Transformer %Z and X/R2

## Transformer %Z and X/R

(OP)
How a transformer %Z(so called percentage of impedance) and X/R (reactance versus resistance ratio)being controlled and determine during the manufacturing process?

Is there any standard tesing method which can be carried out to ensure the transformer that being sent to site are as per design?

### RE: Transformer %Z and X/R

I don't know %Z and X/R are controlled during design and manufacture of a transformer, but any good power system analysis text book will explain the open circuit and short circuit tests necessary to calculate both.

### RE: Transformer %Z and X/R

Transformer design is an Iterative process to achieve whatever is required by customer very cost effectively.

### RE: Transformer %Z and X/R

I do not know how to calculate X/R ratio for the technical specification sheet. Anyone can help me?
Thanks....

### RE: Transformer %Z and X/R

The X/R ratio can be determined if you know the impedance voltage and the losses.

Since the full-load losses include both the resistance losses and the iron losses, you subtract the no-load losses from the total losses.

The %resistance is 100 * (Full load loss -no load loss)/transformer rating.

Once you know the %R, you can use the %Z derived from the impedance voltage test to determine the %X and the X/R ratio.

### RE: Transformer %Z and X/R

Thank you dpc...
I want to ask some more. if you can answer or show the way to do I'll be glad. How can I calculate maximum continuous power rating of a transformer and duration of overload (for %25, %50 etc.)? I have the other parameters and specifications which may be needed. Thanks a lot...

### RE: Transformer %Z and X/R

For ANSI design transformers, see ANSI/IEEE C57.91 IEEE Guide for Loading Mineral-Oil-Immersed Transformers.

### RE: Transformer %Z and X/R

Transformer manufacturers during the years had been refined the transformer design process with sophisticated computer design tools that help to determine the impedance within narrow deviation from the user specified values. However, it is not possible to achieve 100% of accuracy calculating the impedance of a particular transformer design
do to the none linearity behavior of magnetic cores, hysteresis  , Eddy losses, tank magnetic coupling, leakage current and other random factors.

The major factor that affect the impedance are the core volume and  shape, the core material, the winding wire size, number of turns on the primary and secondary and the degree of magnetic coupling between the windings.

On the other hand, guides and standards such as ANSI/IEEE Std C57.12 & 12.1 applicable to liquid immersed and dry type transformers, help users to purchase units with impedance with reasonable degree of accuracy from specified values as follow:

DESCRIPTION    TOLERANCE
Two Windings:
Z < 2.5%        +/- 7.5%
Z > 2.5%        +/_ 10%
Three Windings        +/- 10%
Zigzag and
Autotransformers    +/-10%

For short circuit and other calculations an estimated guide may be found in the enclose material and other similar references.

http://cuky2000.250free.com/XFMR_XoverR.jpg

### RE: Transformer %Z and X/R

How to define these values most approximately? They are all about cooling of the transformers and dynamic capability, right? These values are approximate values but always there appears penalties defined in the tender techn. specs for out of standard values.

### RE: Transformer %Z and X/R

Impedance is composed of resistance and reactance. Resistance and reactance act at a phase angle of 90 degrees to each other. If the two transformers have the same impedance but different ratios of reactance to resistance the impedances will act at different angles and you will have circulating currents if the transformers are paralleled. The magnitude of the circulating currents may or may not be acceptable.
yours

### RE: Transformer %Z and X/R

A question for DPC...
I am trying to confirm a reactive loss in a load flow calculation for a GSU transformer. I multiplied the line current squared by the reactive ohms. I got the reactive ohms by multiplying the impedance base ohms by the %X. Zbase was found by dividing the phase-to-phase voltage squared by the three phase kVA of the transformer. All values all in three-phase. I'm being told that I then have to multiply my value by three to get the three-phase reactive losses. Why would I have to multiply by three if I am using three phase equivalent values?

### RE: Transformer %Z and X/R

Base impedance is

phase-to-phase kilovolts squared divided by the three phase MVA, or

phase-to-phase volts squared times 1000 divided by the three phase kVA.

For single phase values, use phase-to-neutral voltage and single phase kVA or MVA, same formula.

### RE: Transformer %Z and X/R

The impedance determines the voltage drop.
Use impedance and current to determine the voltage drop. The losses are caused by the resistance. Once you find voltage drop use V^2/R to find the losses. Impedance is per phase so multiply by 3. If you know the current you can use I^2R where R is the resistance. V in the above formula is voltage drop, not applied voltage.
jghrist I'm not familiar with your formula. Maybe I'm going to learn something. Can you work an example or two please?
respectfully.

### RE: Transformer %Z and X/R

Waross,

I should have noted that my post was in response to Snoopyfoot's question about base impedance, not the main topic of this thread.

Snoopyfoot was calculating reactive loss by as I²X, using a per unit value of X and then multiplying by the base impedance Zbase.  He will have to multiply by three to get the three phase reactive loss because as you say, the impedance is per phase.

For example, say you have a 100 MVA, 115 kV (Ø-Ø) transformer, with an impedance of 9%, an X/R ratio of 20, and a line current of 200A:

Zbase = 115²/100 = 132.25 ohms
R% = X%/20
Z%² = X%² + R%² = X%² + X%²/400 = X%²?(1+1/400)
X% = Z%/sqrt(1+1/400) = 8.989%
Xpu = 0.08989
Reactive loss = 3?I²?Xpu?Zbase = 3?200²?0.08989?132.25 = 1,426,554 W = 1,426.554 kW

Thanks jghrist
respectfully

### RE: Transformer %Z and X/R

I'm responding to enggan's original question. This maybe long winded so please bear with me. The answer is, both reactance (X) and resistance (R) are controlled in the manufacturing process of the transformer. These two values define two of the basic electrical characteristics of the transformer so the both are usually guaranteed by the supplier (within std tolerances) and specified by the user before manufacture.

In very simplistic terms, both parameters are determined by physical geometry so they are controllable. R is the winding resistance which is proportional to winding conductor resistivity, cross-sectional area and length.

X is inductance or leakage flux, which is determined by the the shape of the chunk of amp-turns (the winding), and the relative location of these amp-turn chunks to each other (i.e. HV to LV windings).

The transformer designer as you can imagine therefore has to specify the dimensions of the windings to the shop, and the shop has to build these windings to the exact dimensions (within tolerances). Manufacturers can normally hit guaranteed impedance and resistance within std tolerance nowadays (7.5% for IX and don't exceed the guaranteed losses for R).

The proof of the pudding is the final transformer test which includes winding resistance, and load loss and impedance tests (check out ANSI C57.12.90 for test descriptions). Failure to meet the guaranteed values in those tests normally indicates something has gone wrong along the way (may involve tear down of the transformer - ouch).

In the field, you're basically limited to resistance test only since the impedance test is normally done at full load current. You need a good size power supply with a bunch of capacitors for tuning since you'd be powering up an inductive load.

Hope this helps,
cheers

### RE: Transformer %Z and X/R

The impedance test is done at full load current, yes that is true, but it is not done at rated voltage.  Typically the low side of the transformer will be shorted and a reduced voltage applied to the high side such that rated load current flows in the secondary windings (or, in a minor variation, rated load current flows in the primary windings).  Power supply is typically a gen set with voltage control on manual.  As long as you stay well within the generator capability curve, there is no need for capacitors to correct the power factor; capacitors would only make the testing more difficult.

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