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How do I calculate |In|, magnitude of neutral current, given Ia, Ib, Ic?

Posted 11 years ago

I've been trying to get Mathematica to provide me the magnitude of the neutral current, In; from the sum of the 3, 3-phase current vectors: Ia, Ib, and Ic.

Before I enter the following expression, I tell Mathematica that q, my variable for the angle, has the value 0. I then put the following expression (or a variation of it) on the Mathematica input line:

Abs[Ia Exp[I (q)] + Ib Exp[I (q + 2 [Pi]/3)] +  Ic Exp[I (q + 4 [Pi]/3)]] 

By doing that, I am, I hope, asking Mathematica to sum 3 vectors, with magnitudes Ia, Ib, and Ic; with angles 0 deg, 240 deg, and 120 deg, respectively; and compute the magnitude of the resulting sum, using the Mathematica "Abs" function.

The correct answer, which I computed using paper and pencil, is

Sqrt[Ia^2 + Ib^2 + Ic^2 - IaIb - IbIc -IaIc]

But Mathematica gives me this on the output line:

Abs[Ia + E^((2 I [Pi])/3) Ib + E^(-((2 I [Pi])/3)) Ic]

After I tell Mathematica to "Simplify" the above expression, I get this:

Abs[Ia + (-1)^(2/3) Ib - (-1)^(1/3) Ic]

After I tell Mathematica to "FullSimplify" the above expression, I get this:

Abs[Ia + (-1)^(2/3) Ib - (-1)^(1/3) Ic]

(The same result as above.)

Would someone please tell me why I can't get Mathematica to actually perform the "Abs" function on the above argument.

POSTED BY: Mark Bennett
3 Replies
Posted 11 years ago
POSTED BY: David Keith
ComplexExpand[Abs[Ia + E^((2 I*Pi)/3) Ib + E^(-((2 I*Pi)/3)) Ic]]

Also you will want to use appropriate Mathematica syntax. Square brackets are not used for collecting terms; only parens are used for that. Square brackets have a very different meaning in Mathematica.

POSTED BY: Daniel Lichtblau
Posted 11 years ago

That was the key issue: I see that I need to use the "ComplexExpand" function after I use the "Abs" function.

I don't understand yet why that's necessary, but I'll read about the ComplexExpand function very soon.

BTW, in my original post, the square brackets that are not associated with a Mathematica function (for example: [Pi]) were put there by this webpage when I pasted the text from Mathematica.

Thank you.

POSTED BY: Mark Bennett
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