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Class 4
Impedance & Three-phase System
Firmansyah Nur Budiman
Lab. Transmisi & Distribusi
Jurusan Teknik Elektro & Teknologi Informasi FT UGM
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Complex Number
B
A
B
ABABA
jBBB
jAAA
.
)sin(cos
)sin(cos
Polar form
Rectangular form
A
)sin(cos jA
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Complex Number
Example of Use:
Load 1:
TL light220 V, 40 W, pf = 0.4
Load 2:
Induction motor
220 V, 200 W, pf = 0.7
Find I, I1, I
2!
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Complex Number
VV 00220
01
1
0
4.6645.0
45.04.0220
40
4.664.0cos
I
AI
02
2
0
6.453.1
3.17.0220
200
6.457.0cos
I
AI
Load 1: Load 2:
0
21
9.5073.1)93.091.0()42.018.0(
jjI
III
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Complex Power
Complex power:
Apparent power:
where
Therefore, apparent power is the magnitude
of complex power, or
*VIjQPS
22QPS
sin
cos
IVQ
IVP
SS
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Impedance
Individual passive components:
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Impedance
Combination:
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Impedance
X
B
ZY
1
1
Y= admittance [Mho, Siemens]
X= reactance [Ohm]
B= suseptance [Mho, Siemens]
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Three-phase System
Single-phase electricity:
Three-phase electricity:
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Three-phase System
)240cos()(
)120cos()(
cos)(
0
0
tVtv
tVtv
tVtv
Mcn
Mbn
Man
)240cos()(
)120cos()(
)cos()(
0
0
tIti
tIti
tIti
Mc
Mb
Ma
Important properties:
Voltage & current:
0
0
CBA
CNBNAN
III
VVV
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Three-phase System
Advantages:
(1) Three-phase motors, generators, and
transformers are simpler, cheaper, and more
efficient.
(2) Three-phase transmission lines can deliver
more power for a given weight and cost.
(3) The voltage regulation of 3-phase
transmission lines is better.
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Three-phase System
Instantaneous power:
Note: this power is independent of time
cos2
3)( MMIV
tp
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Power in Single-phase System
0 90 180 270 360 450 540
-10
-5
0
5
10 va(t)
ia(t)
Angle (degree)
0 90 180 270 360 450 5400
10
20
30
40
50p
a(t)
Angle (degree)
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Power in Two-phase System
0 90 180 270 360 450 540
-10
-5
0
5
10 va(t)
ia(t)
Angle (degree)
0 90 180 270 360 450 540
-10
-5
0
5
10 vb(t)
ib(t)
Angle (degree)
0 90 180 270 360 450 5400
10
20
30
40
50
pa(t)
Angle (degree)
pb(t)
0 90 180 270 360 450 5400
10
20
30
40
50p
total(t)
Angle (degree)
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Power in Three-phase System
0 120 240 360 4800
10
20
30
40
50p
a(t)
Angle (degree)
pb(t) p
c(t)
0 120 240 360 480
0
25
50
75
100
ptotal
(t)
Angle (degree)
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Power in Three-phase System
Power in single-phase circuit:
Power in three-phase circuit:
IVS LN1
IVS LN31
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Example
The 3-phase generator shown is connected to
three 20load resistors. If the effective
voltage in each phase is 120V, calculate:
(a)Power dissipated in each resistor
(b)Power dissipated in 3-phase load
(c)Peak powerPmdissipated in eachresistor
(d)Total 3-phase power compared to Pm
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Wye Connection
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Wye Connection
Voltage relationship:
cabcabLL VVVV ,,
cnbnancabcab VVVVVV 333
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Examples
A 3-phase 60Hz generator, connected in wye,generates a line (line-to-line) voltage of 23900V.Calculate:
(a) Line-to-neutral voltage(b) Voltage induced in individual winding
(c) Time interval between positive peak voltage
of phase A and positive peak voltage ofphase B
(d) Peak value of line voltage
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Examples
A 3-phase generator generates a line voltage of
865V, and each load resistor has an impedance
of 50. Calculate:
(a)Voltage across each resistor
(b)Current in each resistor
(c)Total power output of generator
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Delta Connection
321 333 IIIIII cba
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Summary
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Examples
Three identical impedances are connected in
delta across a 3-phase 550V line. If the line
current is 10A, calculate:
(a) Current in each impedance
(b) Value of each impedance
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Examples
A manufacturing plant draws a total of 415kVA
from a 2400V(line-to-line) 3-phase line. If the
plant power factor is 87.5% lagging, calculate:
(a) Impedance of the plant, per phase
(b) Phase angle between line-to-neutral voltage
and line current
(c) Phasor diagram for the plant
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Homeworks
(1) A 3-phase motor connected to a 600V line drawsa line current of 25A. Calculate the apparentpower supplied to the motor!
(2) A 3-phase heater dissipates 15kW whenconnected to a 208V, 3-phase line.a) What is the line current if the resistors areconnected in wye?
b) What is the line current if the resistors areconnected in delta?
c) If the resistors are known to be connected inwye, calculate the resistance of each
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Homeworks
(3) Three 15resistors and three 8reactors areconnected as shown below.
If the line voltage is 530V, calculate:
a) Active, reactive, and apparent powersupplied to the 3-phase load
b) Voltage across each resistor