1. Lesson 36 AC 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. 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 = I2XL =V2/XL
= I2XC =V2/XC
Resistance Reactance R
XL = L
XC = 1/C

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

5. Active Power 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. Example Problem 1a
EAN = 277-30 V . Compute PΦ, PT.

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

9. 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):

10. Example Problem 1b
EAN = 277-30 V . Compute QΦ, QT.

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

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

13. Example Problem 1c
EAN = 277-30 V . Compute SΦ, ST, and FP.

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

15. 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

16. 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:

17. Example Problem 2a EAN=120-30 V.
Determine per phase and total power (active, reactive, and apparent). Determine total powers (active, reactive, and apparent) by multiplying the per-phase powers by 3.

18. Example Problem 2b EAN=120-30 V.
Determine total powers (active, reactive, and apparent) by using these formulas:

19. 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 =? 19

20.  = cos-1(P / S)=cos-1(FP)
Review
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 the current or voltage.

21. Power Factor Correction
Review
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.

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

23. 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.

24. 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.