WIND ENERGY SYSTEMS - Cd3wd

Chapter 5—Electrical Network 5–9
The impedance is
Z = R + jX L − jX C =4+j8 − j11 = 4 − j3 =5/ − 36.87 o
Ω
Assuming V = |V |/0 o is the reference voltage, the current is
The complex power is
I = V Z = 100/0o
5/ − 36.87 o =20/36.87o A
S = |V ||I|̸ θ = (100)(20)/ − 36.87 o = 2000/ − 36.87 o
VA
The real power supplied to the circuit is just the real power absorbed by the resistor, since reactances
do not absorb real power.
It is also given by
P = I 2 R = (20) 2 (4) = 1600 W
The reactive power supplied to the inductor is
P = |V ||I| cos θ = 100(20) cos /36.87 o = 1600 W
The reactive power supplied to the capacitor is
Q L = I 2 X L = (20) 2 (8) = 3200 var
The net reactive power supplied to the circuit is
Q C = −I 2 X C = −(20) 2 (11) = −4400 var
It is also given by
Q = Q L + Q C = 3200 − 4400 = −1200 var
The power factor is
Q = |V ||I| sin θ = 100(20) sin(−36.87 o )=−1200 var
pf = cos θ =cos(−36.87 o )=0.8 lead
The word “lead” indicates that θ is negative, or that the current is leading the voltage.
We see that the real and reactive powers can be found either from the input voltage and
current or from the summation of the component real and reactive powers within the circuit.
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001