Lab 13

1
Lab 13 Complex Power

• EE 188L

2
Instantaneous Power
Time domain
3
Instantaneous Power
constant with time P (real or average power)
time varying frequency 2w
4
Phase Shift
f 624 Hz T 1 / 624 Hz 1.60 ms voltage
leads current by 0.22 ms (qv - qi) / 360
0.22 ms / 1.60 ms qv - qi 50
(lagging) For an impedance with v(t) and i(t),
?z ?v - ?i 50 (resistive and inductive)
5
Complex Power
Frequency domain using phasors
P j?Q
where
S is the complex power (VA) P is the average
power (watts) Q is the reactive power (VARs or
volts amps reactive
where
6
Apparent Power
units volt-amperes, VA
Ideal pf 1 lagging if (?v ?i) gt 0º
leading if (?v ?i) lt 0º
7
Inductive Load
Neglecting Rs
Delivered to R1 and R2
Delivered to L
8
Compensated Load
To increase power factor to 1, add compensating
capacitor
Again neglecting Rs
(same as before)

Which is zero if pf 1.
9
Current
or
10
Power Triangle