# Thread: AC formulae and power analysis etc

1. Junior Member
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## AC formulae and power analysis etc

Hi

Is my categorization of complex power S into phasor form, polar form, and rectangular form correct? Did I miss any category? Thank you for your help.

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The first and the second line formulae are correct.
The third line result has to be: P=Vrms^2*R/(R^2+X^2) and Q=Vrms^2*X/(R^2+X^2) since: (R-jX)*(R+jX)=R^2+X^2

3. He did not need to use the conjugate for S = v^2/Z

4. Originally Posted by Ingenieur
He did not need to use the conjugate for S = v^2/Z
Quick question- what is "conjugate"?

5. Originally Posted by mbrooke
Quick question- what is "conjugate"?
If I = 100/60 deg = 50 + 86.6 j
I* = 100/-60 deg = 50 - 86.6 j
changing sign on complex portion

S = V I* iirc

6. Originally Posted by Ingenieur

If I = 100/60 deg = 50 + 86.6 j
I* = 100/-60 deg = 50 - 86.6 j
changing sign on complex portion

S = V I* iirc

(*) as in degrees?

7. Originally Posted by mbrooke
(*) as in degrees?
No it's the symbol for the conjugate of the qty
like '!' is the symbol for factorial

if you had phasor analysis you used conjugate

S = V (conjugate of I) = V I*

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[QUOTE=Ingenieur;1858884]He did not need to use the conjugate for S = v^2/Z[/QUOT
IEEE Std 1459-2010, IEEE Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions. 3.1.1.3 Reactive power (var)
“NOTE 1— If the load is inductive, then Q > 0. If the load is capacitive, then Q < 0. This means that when the current lags the voltage θ > 0 and vice versa.”
Using Z=R+jX instead of Z*=R-jX the resulted Q<0 [capacitive].Usually X is inductive.

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[QUOTE=Julius Right;1858996]
Originally Posted by Ingenieur
He did not need to use the conjugate for S = v^2/Z[/QUOT
IEEE Std 1459-2010, IEEE Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions. 3.1.1.3 Reactive power (var)
“NOTE 1— If the load is inductive, then Q > 0. If the load is capacitive, then Q < 0. This means that when the current lags the voltage θ > 0 and vice versa.”
Using Z=R+jX instead of Z*=R-jX the resulted Q<0 [capacitive].Usually X is inductive.
Yes he did!
Actually, the resulting Q2 is always positive, allowing Q to be either positive or negative.

If you do simple complex multiplication without the conjugate you get a negative value for
q2, which is impossible, and you get cross terms which still contain j, also unphysical for power.

10. Originally Posted by pg1995
Hi

Is my categorization of complex power S into phasor form, polar form, and rectangular form correct? Did I miss any category? Thank you for your help.

Nice cut and paste job (twice) but what point were you, the OP, endeavouring to make?

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