Calculating Transformer X/R from kW Losses

[ish1284]

I have a transformer test report where the %Z is given along with the load losses broken down into I2R losses and then stray losses, and then it totals them together in a third column as total load losses.

I need to use this information to calculate the X/R ratio of the transformer. Is the correct way to determine the "R" component of X/R to consider the I2R losses only or both the I2R plus the stray losses?

Note that there is a separate column for no-load losses which I know not to include. In the example provided, the I2R losses are 159.68kW, stray losses 15.93kW, and total load losses as 175.6kW.

 

[D. Castor]

Assuming you are using this to calculate short circuit current, equipment duty, arc-flash, etc, I would use only the I2R losses since you have the data available. The no-load losses include core losses that, while they can be represented as resistance, are not really winding resistance that goes into to determining that transformer's response to faults and its voltage drop. If you are trying to track losses, you can model the no-load losses as a constant load on the primary side of the transformer since they don't change much load.

 

[ish1284]

Assuming you are using this to calculate short circuit current, equipment duty, arc-flash, etc, I would use only the I2R losses since you have the data available. The no-load losses include core losses that, while they can be represented as resistance, are not really winding resistance that goes into to determining that transformer's response to faults and its voltage drop. If you are trying to track losses, you can model the no-load losses as a constant load on the primary side of the transformer since they don't change much load.

This is to calculate short circuit current/arc flash/etc. I thought to only use I2R as well as those would be the copper losses, but what throws me off is that the "stray" losses column is considered as a load loss per the report...159.68 (I2R)+15.93 (stray) = 175.6 (total load loss, see "Load" column). There is a separate column (second to last column) that reports the no-load losses.

 

[jim dungar]

Losses and %Z are not directly related. I have never tried to go from one to the other.

I would think you should use 100% of the losses, as %Z is the amount of primary voltage needed to drive 100% of rated current into a bolted short circuit on the secondary.

 

[jim dungar]

This is to calculate short circuit current/arc flash/etc.

How big are these transformers? For transformer smaller than 500kVA I usually used typical X/R ratios unless i was given specific values from a manufacturer. For larger transformers test results were usually provided showing the X/R.

 

[ish1284]

Losses and %Z are not directly related. I have never tried to go from one to the other.

I would think you should use 100% of the losses, as %Z is the amount of primary voltage needed to drive 100% of rated current into a bolted short circuit on the secondary.

Calculating the "r" component from kW losses is a common practice. So much so that a calculator is built into SKM software. If you know both the Z component and r component, then it's easy to calculate the x component and thus the x/r ratio. The SKM guide makes it clear to use the kW loss at rated current. What isn't clear is would this include stray losses as reported in my original attached screenshot, or just copper I2R losses?

 

[ish1284]

How big are these transformers? For transformer smaller than 500kVA I usually used typical X/R ratios unless i was given specific values from a manufacturer. For larger transformers test results were usually provided showing the X/R.

These are big 72MVA transformers. The x/r is not explicitly stated in the mfg's test report. Just %Z and measured load losses. Here's the full page of what I have to work with

 

[jim dungar]

Calculating the "r" component from kW losses is a common practice. So much so that a calculator is built into SKM software. If you know both the Z component and r component, then it's easy to calculate the x component and thus the x/r ratio. The SKM guide makes it clear to use the kW loss at rated current. What isn't clear is would this include stray losses as reported in my original attached screenshot, or just copper I2R losses?

I understand the relationship between %Z and %R (impedance triangle). Based on the data you provided I think you should be using 100% of the measured kW losses. But you can make a point for using just the I²R losses also.

Why not see how the two values actually change your short circuit current and if the difference is significant.

 

[D. Castor]

Calculating X/R ratio from loss data is an accepted practice. Which loss figure you use is probably not going to make that much difference for short circuit calculations. For larger transformer, the winding resistance is probably provided directly. For equipment duty calculations, you need a reasonable value for transformer X/R to get a reasonable value for the peak asymmetrical current.