Power system fundamentals - Wind Power Integration: Connection and System Operational Aspects - page 32

V = j wL I

f = 90°

I

Figure 2.8 Phasor diagram for inductance

I

f = -90°

V = -j(1 / wC ) I = (1 /j wC ) I

Figure 2.9 Phasor diagram for capacitance

We may obtain the power and reactive power in the inductance from (2.14):

P ¼ VI cos f ¼ 0
Q ¼ VI sin f ¼ VI ¼ XI 2

An inductive load absorbs positive reactive power.
Capacitance (C)
Capacitive current may be related to the voltage drop across it by consideration of
rate of change of charge:

q ¼ Cv

d q

d t ¼ C d v

i ¼

d t

1
w C I m cos ðw t p= 2 Þ
In this case the voltage phasor lags the current phasor by 90 ( p /2 rad). This corre-
sponds to a phase shift of j. The corresponding phasor diagram is shown in Figure 2.9.
The complex impedance of the capacitance is Z ¼ 1/j w C and the capacitive
reactance or impedance magnitude is given by X ¼ 1/ w C .
The power and reactive power taken by the capacitor are given by (2.14):

∴ v ¼

P ¼ VI cos f ¼ 0
Q ¼ VI sin f ¼ VI