Impedance for replacement transformers at off-nominal taps

[siberhusky]

Hi...

We initially specified a 69/13.8 kV transformer with an impedance of .1942 p.u. (56 MVA, 69 kV).

Then it was decided to specify the transformer with a high-side voltage of 67.275 kV instead.

The goal was to come up with an equivalent impedance at the new highside voltage... so that we would obtain the same fault level on the 13.8kV bus as we had at the originally specified nominal voltage (69 kV).

Performing an impedance conversion using the following formula...

Znewbase = Zoldbase x [(Old kV)^2/(New kV)^2]

... we obtained a new impedance value of .2043 p.u. (56 MVA, 67.275 kV)


However, comparative fault levels obtained when modeling these transformers clearly indicates that these are not equivalent transformers. (The situation worsens as the difference between the two specified voltages increases.)

My understanding is that this method is not accurate, despite the per-unit conversion, because it does not take into consideration the change in the transformer winding ratio when one changes from a nominal voltage of 69 kV to a nominal voltage of 67.275 kV. I'm not sure I get this, because what use is the per-unit system if you can't obtain equivalent impedances at different voltages?

How does one go about correctly determining the proper revised impedance?

 

[rcw retired EE]

Per unit impedance is based on the transformer base MVA, not the voltage. The per unit impedance will not change for different primary voltages. The actual ohms impedance will be different at the various voltages, as will the full load amps, but the per unit impedance is the same.

The maximum let through MVA of the transformer is = MVA / (Z p.u.)
You want to keep this let through MVA the same. Voltage does not appear in this equation so there is no change in per unit impedance for a change in voltage.

That is the advantage of the per unit system!

 

[davidbeach]

Sorry rcwilson, but per unit impedances are associated with both a V-base and and S-base. Converting the transformer impedance from its machine base, to a system base will require using an equation with voltage included.

siberhusky, your formula appears to be correct, as far as it goes, for an S-base of 56MVA. When you parallel these transformers in your calculation, you also need to include a 0.975:1 (or 1:1.0256) transformer in the equations to account for the off nominal voltage ratio.

 

[rcw retired EE]

David - I assumed a constant short circuit MVA for the 69 kV system.

I was thinking that since transformer impedance is specified on the transformer's rated MVA, not on an arbitrary base MVA, we should specify the same per unit impedance to obtain the same effective impedance. The base impedance does not change, it is still the equipment rating.

My EZ Power program gives a difference in current between the two designs of about 0.1% with a 100,000 MVA system fault level (on 69 kV) and 1.8% with a 500 MVA fault level. That is close enough for me. [Both xfmrs 56 MVA, Z= 19.42%, one 69-13.8 kV, other 67.275-13.8kV.]

But I still would like to find an equation to make it match exactly.

You are right about needing to consider the voltage when doing any paralleling, load flow or other evaluations.

 

[siberhusky]

Thank you both for your replies...

Ok, but can you be more specific when you say I need to "include a 0.975:1 (or 1:1.0256) transformer in the equations" when I parallel these transformers in my calculation? Let's say, for example, I have 4 transformers of this specification feeding a 13.8 kV Bus.

- john

 

[davidbeach]

siberhusky, I think you're going to need a good power system analysis text. In the per unit system, the price for being able to remove all the transformers is that every time you cross a transformer the ratio of the voltage bases has to equal the voltage ratio of the transformer. If you have voltage bases of 69kV and 13.8kV, your first transformer meets this condition and only its impedance shows up in the calculations. The second transformer has a voltage ration of 67.275:13.8 rather than 69:13.8. To allow that transformer to be used in a per unit analysis between voltage bases of 69kV and 13.8kV, there needs to be a correction transformer included in the calculation to account for the voltage ration error.

 

[siberhusky]

Ok, thanks for your help...

- john