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 = 2 

4. Phase Shift f = 624 Hz T = 1 / 624 Hz = 1.60 ms voltage leads current by 0.22 ms (  v -  i ) / 360° = 0.22 ms / 1.60 ms  v -  i = 50° (lagging) For an impedance with v(t) and i(t), θz = θv - θi = 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 (VAR’s or volts amps reactive

6. Apparent Power units: volt-amperes, VA Ideal pf = 1 lagging if ( θv – θi) > 0º leading if (θv – θi) < 0º

7. Inductive Load Neglecting Rs Delivered to R 1 and R 2 Delivered to L

8. Compensated Load To increase power factor to 1, add compensating capacitor: [ ] (same as before) Which is zero if pf = 1. Again neglecting Rs

9. Current or

10. Power Triangle