Per Unit System Confusion...

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Machiavelli999

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I am studying for the PE exam and I am constantly confused by the per unit system. Specifically, when it comes to using it to model 3-phase balanced loads.

I tried to break it down by trying to model the simplest 3-phase system I could think of. So, let me know where my thinking goes wrong:

You got a simple 480V balanced 3-phase system with one three phase balanced load on it that is 480VA.

The current is pretty easy to find: I = S / (sqrt(3) * V)

I = 480 / (sqrt(3) * 480) = 1 / sqrt(3) Amps

Now, I tried converting this system to per units. I picked the following obvious base values: Vbase = 480V, Sbase = 480VA

So, now my voltage source is 1 pu and my load is 1 pu.

And then I tried finding the current for this system in per units and that's where I ran into my problem.

I thought I could use the same equation as I did above: I = S / (sqrt(3) * V) with the per unit values. But that would give me I = 1/sqrt(3) pu.

The problem is when I convert that per unit value to amps I do not get the current value I found above: 1 / sqrt(3) Amps.

This is because Ibase = Vbase / (sqrt(3) * VAbase) = 1 / sqrt(3) A

And then to convert...

I = Ibase * Ipu = 1/sqrt(3) A * 1/sqrt(3) pu = 1/3 A!!!

So, that's obviously wrong. The only way it would work is I just find the current value by doing: I = S / V once I find the per unit values.

But that would mean that after I find a per unit model of my 3 phase balanced system, I treat it as if it is a single phase system. And I guess that's my big conclusion from doing all this. Am I correct?

Sorry, for the length. Hope someone could follow through all this.

Thanks!
 
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dkarst

Senior Member
Location
Minnesota
The per unit system can make life easier, but you sort of have to be "all in", i.e. you can't go back and forth in the middle of things. The other item is you can lose a sqrt3 if you aren't careful and you are doing some things per-phase and others in total three phase kvA for example. What reference are you using?

In the per unit system, first calculate your base current Ibase = (Base kvA-3p)/(sqrt3 * base voltage l-l) = 0.480/(sqrt3 *0.480) = 1/sqrt3 amps. Remember base current is in AMPS, not p.u. I think where you went wrong is in this case with 1pu volts into the base kva you have 1pu of current. Then to convert this back to actual current you have I actual = I base * I p.u. = 1/sqrt3 * 1 = 1/sqrt3 amps which equals your original solution.
 
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mull982

Senior Member
Machiavelli999 said:
I am studying for the PE exam and I am constantly confused by the per unit system. Specifically, when it comes to using it to model 3-phase balanced loads.

I tried to break it down by trying to model the simplest 3-phase system I could think of. So, let me know where my thinking goes wrong:

You got a simple 480V balanced 3-phase system with one three phase balanced load on it that is 480VA.

The current is pretty easy to find: I = S / (sqrt(3) * V)

I = 480 / (sqrt(3) * 480) = 1 / sqrt(3) Amps

Now, I tried converting this system to per units. I picked the following obvious base values: Vbase = 480V, Sbase = 480VA

So, now my voltage source is 1 pu and my load is 1 pu.

And then I tried finding the current for this system in per units and that's where I ran into my problem.

I thought I could use the same equation as I did above: I = S / (sqrt(3) * V) with the per unit values. But that would give me I = 1/sqrt(3) pu.

The problem is when I convert that per unit value to amps I do not get the current value I found above: 1 / sqrt(3) Amps.

This is because Ibase = Vbase / (sqrt(3) * VAbase) = 1 / sqrt(3) A

And then to convert...

I = Ibase * Ipu = 1/sqrt(3) A * 1/sqrt(3) pu = 1/3 A!!!

So, that's obviously wrong. The only way it would work is I just find the current value by doing: I = S / V once I find the per unit values.

But that would mean that after I find a per unit model of my 3 phase balanced system, I treat it as if it is a single phase system. And I guess that's my big conclusion from doing all this. Am I correct?

Sorry, for the length. Hope someone could follow through all this.

Thanks!
Click to expand...

I believe that your problem is you are trying to convert a base current into a per-unit current when in actuallaty these would be two different currents. You cannot have a p.u. current unless you have an base current to reference it against and since you are trying to use the base current as a per-unit current you are esentially referencing it to itself.

The equation I = S / (sqrt(3) * V) is indeed correct for finding the base current of a given system at a given base VA. Once you have this base current this will be the reference current for referencing all other system currents.

So for instance if you were given a problem that had you calculate the system fault current then you would convert all voltages, and impedances to their p.u. values, and then solve to find the p.u. current. Once you have the p.u. current you can find the actual current by multiplying the p.u. current times the base current.

Not sure if this helps but if you give a specific example or problem I can help you work through it.
 
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