1. Lesson 33: Three Phase Power

2. Learning Objectives
Compute the real, reactive and apparent power in three phase systems.
Calculate currents and voltages in more challenging three phase circuit arrangements.
Apply the principles of Power Factor Correction to a three phase load.

3. 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 = I2XL =V2/XL
Q= I2XC =V2/XC
Resistance Reactance
R [Ω]
XL = L
XC = 1/C

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

5. Active Power (P) to Wye (Y) Load
Single phase of Y-load

6. Active Power (P) to Wye (Y) Load
Because we are considering a balanced system, the power per phase (P) is identical and the total active power (PT) is simply PT = 3 P.
Using line voltage ( ) and line current (IL=I):

7. Reactive Power (Q) to Wye (Y) Load
The reactive power per phase (Q) is given by:
Q = V I sin  P S 

8. Reactive Power (Q) to Wye (Y) Load
Because we are considering a balanced system, the power per phase (Q) is identical and the total reactive power (QT) is simply QT = 3 Q.
Using line voltage (VL ) and line current (IL):

9. Apparent Power (S) to Wye (Y) Load
The apparent power per phase (S) is given by:
S = V I Q  P

10. Power Factor (FP)
The power factor (FP) is given by: S Q  P

11. Example Problem 1 For the Y-Y system shown, EAN = 277-30 V .
Find PΦ, PT, QΦ, QT, SΦ, ST, and FP.
10Ω
277-30 V
15Ω
system is capacitive (-VAR)

12. Example Problem 1 cont. For the Y-Y system shown, EAN = 277-30 V .
Find PΦ, PT, QΦ, QT, SΦ, ST, and FP.
10Ω
277-30 V
15Ω
Remember that current is our indicator here and since the system is capacitive (-VAR) we can say it’s leading.

13. Power to a Delta () Load
Single phase of -load

14. Active Power (P) to Delta () Load
Total active power (PT) is simply PT = 3 P:
Using line voltage (VL=V) and line current ( ):
Which was the EXACT same equation as for Y loads.

15. Reactive and Apparent Power
to Delta (Δ) Load
The equations for calculating total reactive and apparent power are also identical to the Wye load versions:

16. Example Problem 2 EAN=120-30 V.
a) Determine per phase and total power (active, reactive, and apparent).
2080 V
12Ω
Iab 6Ω
system is inductive (+VAR) b B

17. Power in Advanced 3 Phase
You must pay attention to the problem statement!
Does it ask for total or per-phase power?
What kind of power? S, P, or Q?
Where is the power?
Generator
Line Impedances
Load
Pline=?
Qline =?
Sgen =?
Pgen =?
Qgen =?
Sload =? Pload =?
Qload =? 17

18.  = cos-1(P / S)=cos-1(FP)
Power Factor
Power factor (FP) tells us what portion of the apparent power (S) is actually real power (P).
FP = P / S = cos 
Power factor angle
 = cos-1(P / S)=cos-1(FP)
For a pure resistance:  = 0º
For a pure inductance:  = 90º
For a pure capacitance:  = -90º
NOTE:  is the phase angle of ZT, not current or voltage.

19. Power Factor Correction
In order to cancel the reactive component of power, we must add reactance of the opposite type.
This is called power factor correction.

20. Three Phase Power Correction
Capacitors will be connected in parallel with each load phase.

21. Power Factor Correction Solution Steps
Calculate the reactive power (Q) of ONE PHASE of the load.
Insert a component in parallel of the load that will cancel out that reactive power. e.g. If the load has QΦ = 512 VAR, insert a capacitor with QΦ = -512 VAR.
Calculate the reactance (X) that will give this value of Q Normally the Q = V2/X formula will work.
Calculate the component value (F or H) required to provide that reactance.
Note the (-) sign here! Always use the opposite value of calculated Qφ

22. Example Problem 3 EAB=4800 V. Frequency 60 Hz.
Determine value of capacitor which must be placed across each phase of the motor to correct to a unity power factor.
The Qφ is what will be used for Qc in determining the value of the capacitor to used
149𝜇𝐹

23. QUESTIONS?