Complex Power

Complex power is the product of the complex effective voltage and the complex effective conjugate current. In our notation here, the conjugate is indicated by an asterisk (*).Complex power can also be computed using the peak values of the complex voltage and current, but then the result must be divided by 2. Note that complex power is applicable only to circuits with sinusoidal excitation because complex effective or peak values exist and are defined only for sinusoidal signals. The unit for complex power is VA.
 

S = Pav + jQ

S= 1/2 VI

S=VrmsIrms

Find:  S = Pav + jQ for the complex load.

Schematics, Diagrams, Circuits, and Given Data:  v(t) = 100 cos(ωt + 0.262) V;

i(t) = 2 cos(ωt − 0.262) A.

Assumptions:  Use rms values for all phasor quantities in the problem.

Analysis:  First, we convert the voltage and current to phasor quantities:

V˜ =

100

2

√

∠0.262 V

I˜ =

√

∠(−0.262) A

2

2

Next, we compute real and reactive power, using the definitions of equation 7.13:

Pav = |V˜

I˜| cos(θ) =

200

cos(0.524)

= 86.6 W

2

Q = |V˜

I˜| sin(θ) =

200

sin(0.524) = 50 VAR

2

Now we apply the definition of complex power (equation 7.28) to repeat the same calculation:

S

VI∗

100

0.262

2

(

0.262)

100

0.524

=

˜ ˜

= √

2

∠

× √

2

∠

−

−

=

∠

= 86.6 + j50 W

  

Therefore

P_av = 86.6 W        Q = 50 VAR

• voltage V = 4∠0o V, impedance Z = 2∠60o Ω, I = 2∠-60o A, ω = π/ 6 rad/s

• p(t) = 2 + 4 cos(π / 3 - 60°) W

• voltage V = 2.83∠0o Vrms, I = 2∠-60o Arms

• S = P + jQ = V I* = 2W + j 3.46VAr = 4 ∠60o VA

complex power is the product of the rms voltage phasor and the comples conjugate of the rms current phasor. as a complex quantity,

With Dennis James Matildo 

      2/20/16