Per Unit Values

[Timm1]

I have to take the PE Electrical test on Friday; I’m having trouble solving problems involving per unit values. If the per unit values are not given and we are asked to solve the problem using per-unit, can we take per unit voltage and current as 1? Also, while taking the transformer voltage as base, sometimes we take the base as primary voltage and sometimes the secondary voltage. Can someone tell me how it works? Your cooperation is highly appreciated.

 

[JJHorak]

The topic you are asking requires a bit of working with example problems to figure out how the per unit system works, but here are a few hints:
You always find somewhere in the problem statement a V and a VA value that you use as your base. You usually calculate the A base from the V and VA. When you have a large system, a system base is given, but for a small network such as might be on a test, you frequently use the some large power limiting element in the system, such as a xfmr or generator. In the case of a xfmr, there will a Vbase on both sides of the xfmr, but after you convert the network to per unit, there is no xfmr in the network. The xfmr becomes a simple impedance and all voltages are in per unit. You always use the voltage ratio of the xfmr to determine voltage bases on each side, not some red herring voltage thrown at you. e.g. do not be led astray by "Given a 12.47kV/480V xfmr, and a 460V motor..." Your bases are 12.47kV and 480V. Not 460V. If motor impedance is given on a 460V base, you have to convert to 480V via the ratio of (480/460)^2.

 

[racobb]

Hate to say it, but if you only have 4 days and have not yet figured out per unit issues yet, you are probably going to have a difficult time with the exam.

Alan

Democracy is two wolves and a sheep deciding what to have for dinner. Liberty is a well armed sheep!
Ben Franklin

 

[Timm1]

Thanks Timesabroom for the information. I don't want to sound ignorant, but I have one more question. You say that there will be a V-Base on each side of the transformer that needs to be considered. But we know that there is only one impedance for the transformer. So how can we use both base voltages for one impedance? I am not saying that you are wrong, I just need explanation.

 

[dpc]

The base voltage used depends which side of the transformer you are interested in. The per unit voltage doesn't change.

Normally, you select a base voltage corresponding the system voltage you are working with, and a standard base MVA such as 100 MVA or maybe 10 MVA for an industrial system. For dealing with a single transformer, the transformer MVA is often used at the base MVA The base current is computed from the base voltage and base MVA.



"The more the universe seems comprehensible, the more it also seems pointless." -- Steven Weinberg

 

[pwrtran]

It is often you may have more than 2 voltage levels in your test, however, as long as you maintain the transformer voltage ratio for each level the pu impedance value will stay same. For actual current values you need to use Ibase for each voltage level to calculate. If the transformer rated voltage do not match your system nominal voltage, it might be little difficult for you having only few days.

 

[JJHorak]

Suppose you want to figure voltage drop when starting the 480V motor. You convert your system (12.47kV) impedance to a per unit impedance. Then the 480V cable impedance is converted to per unit. Then the xfmr impedance is put in between these two. You need to play with some typical xfmr impedances to see how it works, but if you reflect xfmr impedances to the LV side, and convert to PU at 480V, and then reflect xfmr impedance to the HV side and convert to PU, you get the same number. That is why xfmr impedances are almost always just listed as a single number, Z=5%. In a per unit representation, you have 3 impedances, and the xfmr is effectively a 1:1 xfmr and sort of is not a xfmr any longer. Then when you figure your voltage drops along the way, you convert from per unit back to real voltages on each side of the xfmr.

 

[marks1080]

Per unit is easier when you realize that YOU decide what the base is. Typical base to choose for MVA would be 100. If you are looking at a 230kV system, makes sense to choose your voltage base as 230kV.

You ALWAYS choose your own base.