Part 2 - ENCON
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Transcript Part 2 - ENCON
Three-phase Circuits
Balanced 3-phase systems
Unbalanced 3-phase systems
SKEE 1043 Circuit Theory
Dr. Nik Rumzi Nik Idris
1
Balanced 3-phase systems
POWER CALCULATION
Instantaneous power
Phase voltage of Y connected
load with Z per phase:
Phase current, lagging by :
v AN(t) 2Vp cos(t)
ia (t) 2Ip cos(t )
vBN(t) 2Vp cos(t 120o )
ib (t) 2Ip cos(t 120o )
vCN(t) 2Vp cos(t 120o )
ic (t) 2Ip cos(t 120o )
Total instantaneous power: p = vANia + vBNib+ vCNic
p(t) 2VpIp [cos(t) cos(t ) cos(t) cos(t 120o ) cos(t) cos(t 120o )]
Which can be re-written as:
p(t) VpIp [3 cos cos(2t ) cos(2t 240o ) cos(2t 240o )]
p(t) 3VpIp cos
2
Balanced 3-phase systems
Instantaneous power
POWER CALCULATION
p(t) 3VpIp cos
• Instantaneous power is NON PULSATING
• Smoother energy conversion for electrical machine in 3phase system
• True for delta () connected load too
3
Balanced 3-phase systems
POWER CALCULATION
Complex, apparent, active, and reactive
Phase voltage Vp Vpv (rms)
Phase current
Ip Ipi
(rms)
The complex power per phase:
Sp VpIp* VpIp cos jVpIp sin
Pp jQp
Total complex power:
S 3VpIp* 3VpIp
For Y connection, Vp
VL
3
and Ip IL
S 3VLIL
Apparent power is as before, i.e.
S S
4
Balanced 3-phase systems
POWER CALCULATION
Power measurement using a wattmeter
wattmeter is an instrument used for measuring the average power.
The basic structure
Equivalent Circuit with load
If v(t) = Vmcos (t + v) and i(t) = Imcos (t + i)
then the wattmeter will measure the average power:
Reading on wattmeter P
VmIm
cos v i
2
5
Balanced 3-phase systems
POWER CALCULATION
Power measurement using a wattmeter
wattmeter is an instrument used for measuring the average power.
6
Balanced 3-phase systems
POWER CALCULATION
3-phase power measurement using wattmeters: two-wattmeter method
In order to measure average power in 3-phase system ONLY 2
wattmeters are needed
Vcb
Z Y Z Y
Vca
Ic
Vcn
Vab
30o
30o
Van
Vbn
Ia
30o
Vbc
Reading by wattmeter1,
P1 VabIa cos1 VLIL cos( 30o )
Reading by wattmeter2,
P2 VcbIc cos2 VLIL cos( 30o )
7
Balanced 3-phase systems
POWER CALCULATION
Reading by wattmeter1,
P1 VabIa cos1 VLIL cos( 30o )
Reading by wattmeter2,
P2 VcbIc cos2 VLIL cos( 30o )
IT CAN BE SHOWN :
P1 P2 3VLIL cos()
PTotal P1 P2
P2 P1 VLIL sin()
QTotal 3(P2 P1)
tan
QTotal
PTotal
• This is also true for a connected load as well
• This is also true if the load is unbalanced (ONLY for P1+P2)
• Two-wattmeter method CANNOT be used for a 3-phase, 4 wire system
UNLESS the neutral current = 0
• P1=P2 resistive load, P2 > P1 inductive load, P2 < P1 capacitive load
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