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
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Find: S = Pav + jQ for the complex load.
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Schematics,
Diagrams, Circuits, and Given Data: v(t) = 100 cos(ωt + 0.262) V;
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i(t)
= 2 cos(ωt
− 0.262) A.
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Assumptions: Use rms values for all phasor quantities in the
problem.
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Analysis: First, we convert the voltage and current to
phasor quantities:
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V˜ =
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100
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2
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√
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∠0.262 V
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I˜ =
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√
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∠(−0.262) A
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2
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2
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Next, we compute real and
reactive power, using the definitions of equation 7.13:
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Pav = |V˜
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I˜| cos(θ) =
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200
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cos(0.524)
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= 86.6 W
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2
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Q = |V˜
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I˜| sin(θ) =
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200
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sin(0.524) = 50 VAR
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2
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Now we
apply the definition of complex power (equation 7.28) to repeat the same
calculation:
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S
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VI∗
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100
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0.262
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2
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(
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0.262)
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100
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0.524
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=
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˜ ˜
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=
√
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2
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∠
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× √
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2
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∠
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−
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−
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=
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∠
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= 86.6 + j50 W
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Therefore
Pav = 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
