AC formulae and power analysis etc

[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.

 

[Julius Right]

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

 

[Ingenieur]

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

 

[mbrooke]

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

Quick question- what is "conjugate"? :dunce:

 

[Ingenieur]

Quick question- what is "conjugate"? :dunce:

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

 

[mbrooke]

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?

 

[Ingenieur]

(*) 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*

 

[Julius Right]

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.

 

[GoldDigger]

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.

 

[Besoeker]

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?

 

[GoldDigger]

Nice cut and paste job (twice)....

It was only pasted once. The Forum software chooses to do the double display for some image types and sizes.

 

[Besoeker]

It was only pasted once. The Forum software chooses to do the double display for some image types and sizes.

Whatever. It was a cut and paste with no other input that I can see from the OP. My question remains........

 

[mbrooke]

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*

Makes sense now, thank you for clearing up my misunderstanding

 

[Ingenieur]

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.

incorrect
Xc = -j
Xl = j
the sign convention for reactance takes care of that

 

[mbrooke]

incorrect
Xc = -j
Xl = j
the sign convention for reactance takes care of that

This applies to all forms or just vector?

 

[Ingenieur]

This applies to all forms or just vector?

polar (vector/phasor) or rectangular (complex form Re + Img j)

 

[mbrooke]

polar (vector/phasor) or rectangular (complex form Re + Img j)