three-phase circuits prof. siripong potisuk. faraday’s law “the emf induced in a circuit is...
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Three-Phase circuits
Prof. Siripong Potisuk
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Faraday’s Law
“The EMF induced in a circuit is directly proportional to the time rate of change of magnetic flux through the circuit.”
The EMF can be produced by changing B (inducedEMF) or by changing the area, e.g., by moving thewire (motional EMF).
It is the relative movement between the coil and the magnet that matters
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brush
Slip ring
MagneticFlux lines
Magnet
DC source
Conductorloop
Coil
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Start ¼ Cycle
½ Cycle ¾ Cycle
¼ C
ycle
½ C
ycle
¾ C
ycle
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¾ C
ycle
½ C
ycle
¼ C
ycle
Sta
rt
Phase 1
Phase 2
Phase 3
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Three-phase Voltage Sources
Y-connected Source -connected Source
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Balanced Y-connected Voltage Source
• Balanced phase voltages are equal in magnitude and are out of phase with one another by 120 degrees.
• Phase voltages sum up to zero.• Two possible combinations:
abc or (+) sequence acb or () sequence
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Balanced Y-connected Voltage Source
• Balanced line voltages are equal in magnitude and are out of phase with one another by 120 degrees.
• Line voltages sum up to zero.• The magnitude of line voltages is 1.732 times the magnitude of
the phase voltages• Line Voltages lead their corresponding phase voltages by 30
degrees
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Balanced Three-phase Load Configurations
Y-connected Load -connected Load
A balanced load is one in which the phase impedances are equalin magnitude and in phase.
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Balanced Y-Y Connection
ZY = ZS + Zl + ZL
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Example Calculate the line currents in the three-wire Y-Y system as shown.
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Balanced Y- Connection
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Example A balanced abc-sequence Y-connected source with V is connected to a -connected balanced load of 8+j4 per phase. Calculate the phase and the line currents.
10100anV
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Balanced - Connection
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Example A balanced -connected load having an impedance of 20-j15 is connected to a -connected, positive sequence generator having 0330abV V. Calculate the phase
currents of the load and the line currents.
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Balanced -Y Connection
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Example A balanced Y-connected load with a phase impedance of 40+j 25 is connected to a balanced, positive sequence -connected source with a line voltage of 210 V. Calculate the phase currents. Use Vab as reference.