ee301 lesson 36 three phase power
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Lesson 36 AC Three Phase Power
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.
AC Power SummaryReview
Real Power P = VI (W)
P = I2R =V2/R
P = 0 (W) P = 0 (W)
Reactive Power
Q = 0 (VAR) Q = I2XL =V2/XL = I2XC =V2/XC
Resistance Reactance
R XL = L XC = 1/C
Power Triangle
The power triangle graphically shows the relationship between real (P), reactive (Q) and apparent power (S).
P
QL
S
S
P
QC
Review
cos cos
sin sin
P VI S
Q VI S
(W)
(VAR)
Y-load
Active Power to Wye (Y) Load
Single phase of Y-load
22cos R
Z R X j
VP V I I R
R
Z phase impedance
= = phase power
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):
3T an bn cnP P P P P
Active Power (P) to Wye (Y) Load
3 3 cos 3 cos3
3 cos
LT L
L L
VP P V I I
V I
(W)
3LV V
Example Problem 1a
EAN = 277-30 V . Compute PΦ, PT.
The reactive power per phase (Q) is given
Reactive Power (Q) to Wye (Y) Load
22
sin
X
Q V I
VI X
X
(VAR)
(VAR)
Q = V I sin
P
S
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):
3T an bn cnQ Q Q Q Q
Reactive Power (Q) to Wye (Y) Load
3 sinT L LQ V I (VAR)
Example Problem 1b
EAN = 277-30 V . Compute QΦ, QT.
The apparent power per phase (S) is given
Apparent Power (S) to Wye (Y) Load
22
3T L L
S V I
VI Z
Z
S V I
(VA)
(VA)
(VA)
Q
P
S = V I
The power factor (FP) is given
Power Factor (FP)
cosTP
T
PPF
S S
Q
P
S
Example Problem 1c
EAN = 277-30 V . Compute SΦ, ST, and FP.
3T ab bc caP P P P P
-load Single phase of -load
cos
phase impedance
phase power
Z
P V I
Z
Power to a 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
3T ab bc caP P P P P
Active Power (P) to Delta () Load
3 3 cos 3 cos3
3 cos
LT L
L L
IP P V I V
V I
(W)
3LI I
The equations for calculating total reactive and apparent power are also identical to the Wye load versions:
Reactive and apparent power to Delta (Δ) Load
3 sinT L LQ V I (VAR)
3T L LS V I (VA)
Example Problem 2aEAN=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.
Example Problem 2bEAN=120-30 V.
Determine total powers (active, reactive, and apparent) by using these formulas: 3
cos
sin
T L L
T T
T T
S V I
P S
Q S
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 =?
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
P
QS
NOTE: is the phase angle of ZT, not the current or voltage.
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.
Review
Three Phase Power Correction Capacitors will be connected in parallel with
each load phase
Power Factor Correction Solution Steps
1. Calculate the reactive power (Q) of ONE PHASE of the load
2. 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.
3. Calculate the reactance (X) that will give this value of Q Normally the Q=V2/X formula will work
4. Calculate the component value (F or H) required to provide that reactance.
Example Problem 3EAB=4800 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.