ThreePhase Systems

1
Lecture 13

• Three-Phase Systems

2
Single-Phase AC Voltage Generation
3
Three-Phase Voltage Generation

• Three-phase generators have three sets of
  windings and produce three ac voltages.
• The windings are placed 120 apart, so the
  voltages are three identical sinusoidal voltages
  120 apart.
• A set of voltages such as these are said to be
  balanced.
• If you know one of the voltages, then the other
  two are easily determined.

4
Four-Wire Systems

• All three loads have a common return wire called
  the neutral.
• If the load is balanced, the current in the
  neutral is zero and can be removed.
• In practice, this current may not be exactly
  zero, but is very small.
• Because this current is so small, this wire can
  be thinner than the others.

5
Three-Phase Relationships

• Line voltages are voltages between lines either
  at the generator (EAB) or at the load (VAB).
• Phase voltages are voltages across the phases.
  For a Y load, phases are from line to neutral
  for ? load, the phases are from line to line.
• Line currents are currents in the line
  conductors.
• Phase currents are currents through the phases.
  For a Y load the two currents are the same.

6
Voltages in a Wye Circuit

• For a balanced Y system, the magnitude of
  line-to-line voltage is times the magnitude
  of the phase voltage.
• Each line-to-line voltage leads its corresponding
  phase voltage by 30.
• The line-to-line voltages form a balanced set.

7
Currents for a Wye Circuit

• Line currents are the same as phase currents.
• In a balanced or 4-wire system Ia Van/Zan
• If the load is balanced line currents form a
  balanced set and if you know one current, you can
  determine the other five currents by inspection.

8
Currents for a Delta Load

• In a balanced delta, the magnitude of the line
  current is times the magnitude of the phase
  current.
• Each line current lags its corresponding phase
  current by 30.
• Given any current in a balanced, three-phase
  delta load, you can determine the remaining
  currents by inspection.

9
Power in a Balanced System

• To find total power in a balanced system,
  determine the power in one phase, then multiply
  by three.
• Use the ac power formulas previously developed.
• Since magnitudes are the same for all three
  phases, simplified notation may be used.

10
Active Power to a Balanced Wye Load

• P? V?I? cos ??
• PT 3P? 3V?I? cos ??
• PT VLIL cos ??
• P? I?2R?
• PT 3I?2R?

11
Reactive Power to a Balanced Wye Load

• Q? V?I? sin ??
• QT VLIL sin ??
• Q? I?2X?
• The unit is VAr.

12
Apparent Power to a Balanced Wye Load

• S? V?I?
• ST VLIL
• S? I?2Z?
• The unit is VA
• The power factor is
• pf cos ?? PT/ST P?/S?

13
Power to a Balanced Delta Load

• The power formulas for the ? load are identical
  to those for the Y load.
• In all these formulas, the angle ?? is the phase
  angle of the load impedance.
• You can also use the single-phase equivalent in
  power calculations. The power will be the power
  for just one phase.

14
Measuring Power in Three-Phase Circuits

• Measuring power to a 4-wire Y load requires three
  wattmeters (one meter per phase).
• Loads may be balanced or unbalanced.
• The total power is the sum of the individual
  powers.
• If the load could be guaranteed to be balanced,
  only one meter would be required, its value
  multiplied by 3.

15
Measuring Power in Three-Phase Circuits

• For a three-wire system, only two meters are
  needed.
• Loads may be Y or ?.
• Loads may be balanced or unbalanced.
• The total power is the algebraic sum of the meter
  readings.

16
Unbalanced Loads

• Unbalanced four-wire Y systems without line
  impedance, use Ohms law.
• Three-wire and four-wire systems with line and
  neutral impedance require the use of mesh
  equations.
• One of the problems with unbalanced loads is that
  you get different voltages across each phase of
  the load and a voltage between neutral points.

17
Power System Loads

• Residential and business customers require only
  single-phase power.
• Industrial customers may require single-phase and
  three-phase systems.
• Therefore, there is a need to connect both
  single-phase and three-phase loads to three-phase
  systems.

18
Power System Loads

• The utility tries to connect one-third of its
  single-phase loads to each phase.
• Three-phase loads generally are balanced.
• Real loads are seldom expressed in terms of
  resistance, capacitance, and inductance.
• Instead, real loads are described in terms of
  power, power factors, etc.