-
1
Juliusz B. GajewskiProfessor of Electrical Engineering
1
-
2222
FACULTY OF MECHANICAL AND ELECTRIC POWER ENGINEERING
Process Engineering and Equipment, Electrostaticsand Tribology
Research Group
Wybrzeże S. Wyspiańskiego 2750-370 Wrocław, POLAND
Building A4 „Stara kotłownia”, Room 359Tel.: +48 71 320 3201;
Fax: +48 71 328 3218
E-mail: [email protected]:
www.itcmp.pwr.wroc.pl/elektra
-
33
Contents
1. Terms. Fundamental Definitions and Units.2. Electrostatics.
Electrostatic and Electric Fields.3. Electrodynamics. DC Current.4.
Electromagnetism. Magnetic Field of DC Current.5. Electric Circuit
Elements.6. Sinusoidal AC Voltage.7. Complex Frequency Concept.8.
Electric Filters.9. Electrical Measurements.
10. Three-Phase Circuits.11. Electrical Signals.12. Electric
Switches.
-
4
Three-Phase Circuits
-
5
Three-Phase Voltage and Current
Three-Phase Circuits
-
6
Three-Phase Voltage and Current
Three-Phase Circuits
-
7
Three-Phase Voltage and Current
Three-Phase Circuits
-
8
Three-Phase Voltage and Current
Three-Phase Circuits
-
9
Three-Phase Circuits
2sin4sin2sin
sin
mm3
m2
m1
tUtUutUu
tUu
L
L
L
0321 LLL uuu
2m
321UUUU LLL
0321 LLL UUU
Three-Phase Voltage and Current
-
10
Three-Phase Circuits
t
u
2/30
uL1 uL2 uL3
4/3 2
Three-Phase Voltage and Current
-
11
-
12
Three-Phase Circuits
Three-Phase Voltage and Current
120°
120°
120°
UL3
UL1
UL2
UL3
UL1
UL2
-
13
Three-Phase Circuits
4sin3/2sin
sin
m3
m2
m1
tIitIitIi
L
L
L
π
ZL1 ZL2 ZL3UL1 UL2 UL3 IL1 IL2 IL3
Three-Phase Voltage and CurrentAssumption
-
14
Three-Phase Circuits
Three-Phase Voltage and Current
120° 120°
120°
UL3
UL1
UL2
IL1
IL3
IL2
-
15
Three-Phase Circuits
Three-Phase Star (Y) Configuration
U
X Y Z
W V
L1
L2L3N 1331
3223
2112
LL
LL
LL
UUUUUUUUU
0321 LLL UUU
-
16
Three-Phase Circuits
Three-Phase Star (Y) Configuration
ppp 323230cos2 UUUU
UUUU 312312
60°
L1
L2 L3
30° U12 U31
U23
UL1
UL3UL2
U12
UL1
UL2
-
17
Three-Phase Circuits
Three-Phase Star (Y) Configuration
L1 L2 L3 N
M 3~
M 1~
-
18
Three-Phase Circuits
Three-Phase Star (Y) Configuration
Balanced Load (Network)
0321 LLL III
0NI
Unbalanced Load (Network)
0321 LLLN IIII
-
19
Three-Phase Circuits
Three-Phase Star (Y) Configuration
L3
0 0
IL1
I L3
I L2
UL1
UL3 UL2
L1 L2 0
I L1 I L2
I L3I N
Unbalanced Load (Network)
-
20
Three-Phase Circuits
Three-Phase Delta () Configuration
U
X
Y
Z
W
V
L1
L2
L3
UL1
UL2
UL3
331
223
112
L
L
L
UUUUUU
pp 3and IIUU
0321 LLL UUU
-
21
Three-Phase Circuits
Power in Star Configuration of Load cos33cos pppppp IUPPIUP
L1
L2
L3
UpZp
I Ip
U 3 Up
star
-
22
Three-Phase Circuits
Power in Delta Configuration of Load cos33cos pppppp IUPPIUP
L1
L2
L3
I 3 Ip
U UpIp
Zp
delta
-
23
Three-Phase Circuits
Power of Symmetric Three-Phase System
IIUU pp ,3 3, pp
IIUU
]VA[3
]var[sin3
]W[cos3
UIS
UIQ
UIP
star delta
cos33cos pppppp IUPPIUP
-
24
-
25
Three-Phase Circuits
Measurement of Power and Energyin Three-Phase System
L1
L2
L3
N
W
W
W
P1
P3
ZL1
P2
ZL2
ZL3
321 PPPP pp321 3PPPPPP Unbalanced Load Balanced Load
-
26
Three-Phase Circuits
Measurement of Power and Energyin Three-Phase System
L1
L2
L3
W
W
LoadOdb.
P
P
IL1
IL3
U12
U32
Aron’s Circuit — Two Wattmeter Circuit
Power is measured with only two wattmetersin a 3-phase system
without neutral.
-
27
Three-Phase Circuits
Measurement of Power and Energyin Three-Phase System
Aron’s Circuit — Two Wattmeter Circuit
30cos30cos
UIPUIP
cos330cos30cos UIUIPPP
coscos 112332 LL IUIUPPP Unbalanced Load — General Case
Balanced Load
-
28
Three-Phase Circuits
Measurement of Power and Energyin Three-Phase System
[°]
-50
50
150
-100
0
100
200
P [%
]
0
P
P
P
90 60 30 30 60 90
capacitive character
inductive character
Aron’s Circuit — Two Wattmeter Circuit
-
29
Three-Phase Circuits
Measurement of Power and Energyin Three-Phase System
Aron’s Circuit — Two Wattmeter Circuit
UIUIPP2330cos
When 0 cos 1
When 60° cos 0,5
UIPPP 3
UIPPP23;0
-
30
Three-Phase Circuits
Measurement of Power and Energyin Three-Phase System
L1
L2
L3
W IL1
U23
ZL1
ZL2
ZL3
Wattmeter or watt-hour meter
Power and Reactive Energy in Symmetric System
-
31
Three-Phase Circuits
Measurement of Power and Energyin Three-Phase System
Power and Reactive Energy in Symmetric System
90° 0
IL1
U23
UL1
UL3 UL2
sin111 LLL IUQ
sin90cos 123123 LL IUIUP Reactive power by definition
Active power measured
-
32
Three-Phase Circuits
Measurement of Power and Energyin Three-Phase System
Power and Reactive Energy in Symmetric System
123 3 LUU
PQQPQ LL 333 11
QtAb Reactive energy
Reactive power
-
33
Thank you for your attention!
© 2010 Juliusz B. Gajewski
