Download Chapter 1_ 3PS : Power Calculation

POWER CALCULATION
 AVERAGE POWER IN BALANCED STAR
LOAD
 COMPLEX POWER IN BALANCED STAR
LOAD
 POWER CALCULATION IN BALANCED
DELTA LOAD
STAR-CONNECTED LOAD
IA
A
+
ZA
IB
VBN
B
+
ZB
-
N
ZC
IC
C
VAN
VBN
+
(1) STAR CONNECTED POWER
Average Power at Line A:
P A  VAN IA cosA  iA 
where, VA and iA is the phase
angle for VAN and IA.
By the same method, the average
power at line B and C can be also
accomplished:
P B  VBN IB cosB  iB 
PC  VCN IC cosC  iC 
AVERAGE POWER
P A  VAN IA cosA  iA 
P B  VBN IB cosB  iB 
PC  VCN IC cosC  iC 
In balanced star-connected three-phase system,
MAGNITUDE for each phase-line voltage and
phase current is EQUAL:
Phase-line Voltage
V  VAN  VBN  VCN
I  IA  IB  IC
Phase-line current
and
  A  iA  B  iB  C  iC
 We can concluded that the power
received by each phase which are PA,
PB, and PC is equal:
PA  PB  PC  P  V I  cos 
 P represents average power for each
phase. (i.e. average power per phase).
 By knowing TOTAL average power that been
received by load in balanced three-phase
system, we just total up the average power for
each phase:
PT  3P  3 V I  cos 
 PT represents the total average power that been
received by the load in star-connected threephase system.
If we have line voltage,VL and line current, IL
so the equation for total average power, PT
can be write as follows:
 VL 
PT  3
I L cos 
 3
 3 VL I L cos 
The angle difference
between phase
Voltage and phase
current
 VL=Line Voltage, and IL=Line Current.
REMEMBER!
VL  3 Vp
VL
 Vp 
3
•Phase Voltage normally can be represented
by Vp or V.
•Phase Voltage for star-connection are as
follows: VAN, VBN, and VCN.
TOTAL AVERAGE POWER,PT
PT  3P  3 V I  cos 
Total average power in phase voltage
and phase current.
PT  3 VL I L cos 
Total average power in line voltage and
line current.
REACTIVE POWER FOR STARCONNECTED LOAD
Reactive Power, Q and complex
power, S can be considered for starconnected load:
Q  V I sin 
 QT  3Q  3 VL I L sin 
COMPLEX POWER
 Complex Power can be calculated as
follows:

 
S  V I
VA 
 where, V and I represents voltage
and current for the specific phase. So,
generally:
ST  3 S  3 VL I L
VA 
(2) DELTA-CONNECTED POWER
 Average Power for each phase in
DELTA-connected are as follows:
PA  VAB I AB cosvAB  iAB 
PB  VBC I BC cosvBC  iBC 
PC  VCA ICA cosvCA  iCA 
For Balanced Delta load;
VAB  VBC  VCA  V
I AB  I BC  I CA  I 
 vAB  iAB   vBC  iBC   vCA  iCA  
So,
PA  PB  PC  P  V I  cos 
AVERAGE POWER
Total Average Power that been received by
delta-connected load is:
PT  3P

 3 V I  cos  

 IL 
 3VL 
 cos  
3


3 VL I L cos  
REACTIVE POWER
Reactive Power for each phase and
Total Reactive Power at the load can
be accomplished as follows:
Q  V I  sin 
 QT  3Q  3 V I  sin 
COMPLEX POWER
And, complex power for each phase
and total complex power is:

 
S  P  jQ   V I
 ST  3S  3VL I L 