Three-Phase circuits Prof. Siripong Potisuk

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 (induced EMF) or by changing the area, e.g., by moving the wire (motional EMF).  It is the relative movement between the coil and the magnet that matters

brush Slip ring Magnetic Flux lines Magnet DC source Conductor loop Coil

Start ¼ Cycle ½ Cycle ¾ Cycle ¼ Cycle ½ Cycle ¾ Cycle

½ Cycle ¼ Cycle Start Phase 1 Phase 2 Phase 3

Three-phase Voltage Sources Y-connected Source  -connected Source

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

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 times the magnitude of the phase voltages Line Voltages lead their corresponding phase voltages by 30 degrees

Balanced Three-phase Load Configurations Y-connected Load  -connected Load A balanced load is one in which the phase impedances are equal in magnitude and in phase.

Balanced Y-Y Connection Z Y = Z S + Z l + Z L

Example Calculate the line currents in the three-wire Y-Y system as shown.

Balanced Y-  Connection

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.

Balanced  -  Connection

Example A balanced  -connected load having an impedance of 20-j15  is connected to a  -connected, positive sequence generator having V. Calculate the phase currents of the load and the line currents.

Balanced  -Y Connection

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 V ab as reference.