1. Power Triangle

2. Learning Objectives Define apparent power.
Calculate apparent power in AC series parallel networks.
Define the power triangle.
Using the power triangle determine relationships between real, reactive and apparent power.
Determine if AC series parallel networks are inductive, capacitive, or purely resistive.

3. Review
AC Power to a Resistive Load AC Power to a Inductive Load AC Power to a Capacitive Load

4. Review AC Power Summary P = VI (W) P = I2R =V2/R P = 0 (W) Q = 0 (VAR)
Real Power
P = VI (W)
P = I2R =V2/R
P = 0 (W)
Reactive Power
Q = 0 (VAR)
Q = VI (VARind)
Q = I2XL =V2/XL
Q = VI (VARcap)
= I2XC =V2/XC
Resistance Reactance R
XL = L
XC = 1/C

5. Apparent Power
For a load with voltage V and current I, the power that “appears to flow” to the load is VI where V and I are rms values.
S = VI (VA)
S is called the apparent power and has units of volt-amperes (VA).

6. Apparent Power
In terms of load impedance Z, apparent power can be expressed
S = I2Z = V2/Z (VA)
It is common to see apparent power give in kVA.

7. Example Problem 1
Determine the real, reactive, and apparent power.

8. Power Triangle
The power triangle graphically shows the relationship between real (P), reactive (Q) and apparent power (S).

9. Power Triangle
From the power triangle we can see that

10. Power Triangle
We can generalize the equations:

11. Real and Reactive Power
The power triangle also shows that we can find real (P) and reactive (Q) power.

12. Example Problem 2
Draw the power triangle for this circuit. Determine if this is an inductive, capacitive, or resistive circuit.

13. Example Problem 3
Determine the value of R and PT & QT. Draw the power triangle and determine S.