chapter 8: three-phase circuits - oakland...
TRANSCRIPT
![Page 1: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/1.jpg)
2/3/00 Electromechanical Dynamics 1
Chapter 8: Three-Phase Circuits
![Page 2: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/2.jpg)
2/3/00 Electromechanical Dynamics 2
Three-phase circuits
• A 3-phase generator has three identical windings on the stator, placed at 120º to each other– at constant speed, the voltages
induced in the windings have the same effective value
– the voltage peaks occur at different times
-120
-80
-40
0
40
80
120
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
![Page 3: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/3.jpg)
2/3/00 Electromechanical Dynamics 3
Three-Phase Generation
• The generation of three-phase ac power can be viewed as three separate power sources, each with a 120º degree angular shift in time of the sinusoidal waveform with respect to the other sources.
( )( )( )ππ
πππ
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mc
mb
ma
a
bcn
va(t)vc(t)
vb(t)
![Page 4: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/4.jpg)
2/3/00 Electromechanical Dynamics 4
Three-Phase Waveforms
-120
-80
-40
0
40
80
120
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
va
vb
vc
n
![Page 5: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/5.jpg)
2/3/00 Electromechanical Dynamics 5
Wye connected circuits
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va(t)vc(t)
vb(t)
a
R
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a
clineccalineacca
blinebbclinecbbc
alineaablinebaab
iivvvv
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iivvvv
−−
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==−===−===−=
![Page 6: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/6.jpg)
2/3/00 Electromechanical Dynamics 6
Delta connected circuits
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va(t)vc(t)
vb(t)
a
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iiiivv
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−−
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R
R R
![Page 7: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/7.jpg)
2/3/00 Electromechanical Dynamics 7
Three-Phase Circuits
• Example– the 3-phase generator shown below is connected to three 20
ohm load resistors. The generator supplies a voltage of 120 V rms
– calculate• the power dissipated in each resistor and in the 3-phase load
• the peak power Pm and the ratio of Pm to the total load
![Page 8: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/8.jpg)
2/3/00 Electromechanical Dynamics 8
Three-Phase Circuits
• Example– a 3-phase, 60 Hz, wye connected generator has a line voltage
of 23900 V
– calculate• the line-to-neutral voltage
• voltage induced in the individual windings
• the time interval between the positive peak voltage of phases A and B
• the peak value of the line voltage
![Page 9: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/9.jpg)
2/3/00 Electromechanical Dynamics 9
Three-Phase Circuits
• Example– three identical impedances are connected in delta across a
550 V line. The current drawn is 10 A
– calculate• the current in each impedance
• the impedance values
![Page 10: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/10.jpg)
2/3/00 Electromechanical Dynamics 10
Phase Sequence
• 3-phase systems have a property called phase sequence– it determines the direction of
rotation of 3-phase motors
– it means the order in which the three line voltages become successively positive
– two sequences: ABC & ACB
• positive sequence: ABC
• negative sequence: ACB
• Phase sequence is determined by a simple circuit– one lamp always burns brighter
– the sequence order is bright lamp, dim lamp, capacitor
![Page 11: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/11.jpg)
2/3/00 Electromechanical Dynamics 11
Power Measurements
• Wattmeters measure active power– single-phase wattmeters have two pairs
of terminals: voltage & current
– each terminal pair has polarity markings
– polarity markings determine the direction of power flow
• 3-phase, 3-wire circuits– power is measured by two single-phase
wattmeters
– total power is the sum of the two meters
• 3-phase, 4-wire circuits– power is measured by three single-phase
wattmeters
– total power is the sum of the three meters
![Page 12: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/12.jpg)
2/3/00 Electromechanical Dynamics 12
Power Measurements
• Example– a full-load test on a 10 hp, 3-phs motor yields the following:
• at VLine = 600 V, P1 = +5950 W; P2 = + 2380 W; ILine = 10A
– calculate the power factor of the motor
• Example– the same motor runs at no-load
• ILine drops to 3.6 A and P1 = +1295 W; P2 = - 845 W
– calculate the no-load losses and the power factor
![Page 13: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/13.jpg)
2/3/00 Electromechanical Dynamics 13
Power Measurements
• Example– three identical resistors connected as a wye, dissipate a total
power of 3000 W when energized by a 550 V line
– calculate• the current in each line
• the resistor values
![Page 14: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/14.jpg)
2/3/00 Electromechanical Dynamics 14
Power Measurements
• Example– A 3-phase, 550 V, 60 Hz line is connected to three identical
capacitors in a delta configuration which draws 22 A
– calculate the capacitance in each capacitor
![Page 15: Chapter 8: Three-Phase Circuits - Oakland Universitysecs.oakland.edu/~frick/EE4220-EM_Dynamics/lecture10.pdf– A 3-phase, 550 V, 60 Hz line is connected to three identical capacitors](https://reader031.vdocuments.mx/reader031/viewer/2022021504/5aae68a97f8b9a190d8c20ac/html5/thumbnails/15.jpg)
2/3/00 Electromechanical Dynamics 15
Homework
• Homework Problems: 7.8, 7-12, 7-18, 7-22, 8-4, 8-12, 8-16, and 8-26