Three Phase Power, Magnetics

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ECE 333 (398RES)Renewable Energy Systems

• Lecture 4
• Three Phase Power, Magnetics
• Professor Tom Overbye
• Department of Electrical andComputer Engineering

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Announcements

• Be reading Chapter 1 and 2
• Homework 1 is 1.3, 1.4 (delayed to future HW),
  1.8, 1.11. Due date is January 29.
• Homework 2 is 2.2, 2.9, 2.10, SP1. Due date is
  Feb 5.

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SP1 (Special Problem 1)

• A delta connected load with each Z 8?30 ohms
  is supplied from a balanced three phase wye
  connected generator through lines having series
  impedance of 0.25 ? 30 ohms. The line-to-line
  voltage measured at the load is 208 volts (for
  the angle, please use load Vab as the reference,
  such that Vab 208 ? 0 volts).
• a. Calculate the three load phase currents
  (magnitude and angle).
• b. Calculate the magnitude of the line-to-line
  voltage at the generator.
• c. Calculate the power factor at the generator
  (be sure to indicate leading or lagging).

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Balanced 3 Phase (?) Systems

• A balanced 3 phase (?) system has
• three voltage sources with equal magnitude, but
  with an angle shift of 120?
• equal loads on each phase
• equal impedance on the lines connecting the
  generators to the loads
• Bulk power systems are almost exclusively 3?
• Single phase is used primarily only in low
  voltage, low power settings, such as residential
  and some commercial

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Balanced 3? -- No Neutral Current
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Advantages of 3? Power

• Can transmit more power for same amount of wire
  (twice as much as single phase)
• Torque produced by 3? machines is constrant
• Three phase machines use less material for same
  power rating
• Three phase machines start more easily than
  single phase machines

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Three Phase Transmission Line
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Three Phase - Wye Connection

• There are two ways to connect 3? systems
• Wye (Y)
• Delta (?)

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Wye Connection Line Voltages
-Vbn
(a 0 in this case)
Line to line voltages are also balanced
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Wye Connection, contd

• Define voltage/current across/through device to
  be phase voltage/current
• Define voltage/current across/through lines to be
  line voltage/current

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Delta Connection
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Three Phase Example

• Assume a ?-connected load is supplied from a 3?
  13.8 kV (L-L) source with Z 100?20?W

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Three Phase Example, contd
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Delta-Wye Transformation
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Delta-Wye Transformation Proof
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Delta-Wye Transformation, contd
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Per Phase Analysis

• Per phase analysis allows analysis of balanced 3?
  systems with the same effort as for a single
  phase system
• Balanced 3? Theorem For a balanced 3? system
  with
• All loads and sources Y connected
• No mutual Inductance between phases

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Per Phase Analysis, contd

• Then
• All neutrals are at the same potential
• All phases are COMPLETELY decoupled
• All system values are the same sequence as
  sources. The sequence order weve been using
  (phase b lags phase a and phase c lags phase a)
  is known as positive sequence later in the
  course well discuss negative and zero sequence
  systems.

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Per Phase Analysis Procedure

• To do per phase analysis
• Convert all ? load/sources to equivalent Ys
• Solve phase a independent of the other phases
• Total system power S 3 Va Ia
• If desired, phase b and c values can be
  determined by inspection (i.e., 120 degree
  phase shifts)
• If necessary, go back to original circuit to
  determine line-line values or internal ? values.
  

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Per Phase Example

• Assume a 3?, Y-connected generator with Van
  1?0? volts supplies a ?-connected load with Z?
  -j? through a transmission line with impedance of
  j0.1? per phase. The load is also connected to a
  ?-connected generator with Vab 1?0? through
  a second transmission line which also has an
  impedance of j0.1? per phase.
• Find
• 1. The load voltage Vab
• 2. The total power supplied by each generator,
  SY and S?

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Per Phase Example, contd
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Per Phase Example, contd
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Per Phase Example, contd
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Per Phase Example, contd