25-08-2017, 09:32 PM
Single & Three Phase Circuits
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• Single phase circuit components:
– Voltage or current sources
– Impedances (resistance,
inductance, and capacitance)
– The components are connected
in series or in parallel.
• The figure shows a simple circuit
where a voltage source (generator)
supplies a load (resistance and
inductance in series).
Complex Notation
• Engineering calculations need the amplitude (rms value) and
phase angle of voltage and current.
• The time function is used for transient analysis.
• The amplitude and phase angle can be calculated using complex
notation.
• The voltage, current, and impedance are expressed by complex
phasors.
Wye-Connected System
• Phasor diagram is used to visualize
the system voltages
• Wye system has two type of
voltages: Line-to-neutral, and
line-to-line.
• The line-to-neutral voltages are
shifted with 120o
• The line-to-line voltage leads the
line to neutral voltage with 30o
• The line-to-line voltage is times
the line-to-neutral voltage
Delta-Connected System
• The phasor diagram is used to
visualize the system currents
• The system has two type of
currents: line and phase currents.
• The delta system has only line-toline
voltages, that are shifted by
• The phase currents lead the line
currents by
• The line current is times the
phase current and shifted by 30
degree.
Power measurement
• In a four-wire system (3 phases
and a neutral) the real power is
measured using three single-phase
watt-meters.
• In a three-wire system (three
phases without neutral) the power
is measured using only two singlephase
watt-meters.
- The watt-meters are supplied by
the line current and the line-to-line
voltage.