Lesson 35 Per Phase Analysis

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Lesson 35Per Phase Analysis
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Learning Objectives

• Derive the relationship between line to line
  voltages and line to neutral voltages in a
  balanced Y-Y three phase circuit.
• For a balanced Y-Y three phase circuit convert
  the line to line voltage phasor to the line to
  neutral voltage phasor and vice versa.
• Plot the phasors of line to line voltages and
  line to neutral voltages for a Y-Y three phase
  circuit.
• Derive the relationship between line current and
  phase load current in a balanced Y- ? three phase
  circuit.
• For a balanced Y- ? three phase circuit convert
  the line current phasor to phase load current
  phasor and vice versa.
• Plot the phasors of line current and phase load
  current in a balanced Y- ? three phase circuit.

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Y-Y system
Review
Y Load
Generator
Lines
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PHASE/LINE VOLTAGES
 
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Line/Phase Voltages for a Wye Circuit

• Using the following relationship
• we can also convert back
• Therefore, given any voltage at a point in a
  balanced, 3-phase Y system, you can determine the
  remaining 5 voltages by inspection.

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Law of Sines

• The ratio of the length of a side to the sine of
  its corresponding opposite angle is constant
• Applying the law of sines to the vector EAB

EAN
EBN
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Nominal voltages

• If phase voltage Van 120 V then line voltages
  Vab 208 V.
• This is referred to as 120/208-V system.
• Two other common nominal voltages are 220/380-V
  and 347/600-V.

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Currents for a Wye Circuit

• For Y loads, line current and phase current are
  the same.

Line current
Phase current
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Wye-Wye Single Phase Equivalent
Original circuit
Single-phase equivalent
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Example Problem 1

• EAB 208?0? V .
• Find the phase voltages and line currents.

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? load definitions
Review
Y-Y
 
For ? loads, phase voltage and line voltage are
the same thing.
Line currents are the currents in the line
conductors. Phase currents are the currents
through phases .
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Line/Phase Currents for a Delta Circuit
Iab
Ica
Iab
Ibc
Line current
Phase current
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Line/Phase Currents for a Delta Circuit

• Relationship between line and phase currents
• For a balanced ? system, the magnitude of line
  current is 1.732 times the magnitude of the phase
  current and line current lags phase current by
  30?.
• Therefore, given any current at a point in a
  balanced, 3-phase ? system, you can determine the
  remaining 5 currents by inspection.

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Line/Phase Currents for a Delta Circuit
Phasor diagram
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Equivalent Ckt to solve Wye-Delta Problem

• This is just an equivalent circuit of the load
  side!
• What is missing from the equivalent circuit?
• Ia , Eab , Ean
• You can only use the equivalent circuit to solve
  for load side voltages and currents
• Vab, Iab
• Notice that this equivalent circuit uses LINE
  VOLTAGE
• 1 mistake with DELTA circuits is using the wrong
  kind of voltage!

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Example Problem 2

• Ia 41.6?6.9? A .
• Determine the phase currents in the load.
• Determine the supply line voltage EAB and the
  supply phase voltage EAN.

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Line Impedances in 3 Phase AC

• Impedances in transmission lines complicate three
  phase analysis
• Voltage drop in the transmission line must be
  accounted for EAN will not be the same as Van

VAa
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Wye-Wye Single Phase Equivalent
Original circuit
Single-phase equivalent

• Notice that the neutral line impedance drop is
  ignored on the single phase equivalent.
• No voltage drop occurs across this neutral line
  since in reality, no current flows through it.

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Wye-Wye Single Phase Equivalent
Original circuit
VAa -
Single-phase equivalent

• Use KVL on the single phase equivalent to find
  unknowns
• EAN VAa Van 0

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Example Problem 3

• EAB 208?0? V. Determine
• a. Line Currents
• b. Load phase voltages

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Delta To Wye (??Y) Conversion

• A Delta circuit with line impedances cannot be
  solved without first performing a ??Y conversion.
• The Delta load can be converted to an equivalent
  Wye load

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Equivalent Delta Ckt with LINE IMPEDANCES
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Example Problem 4

• EAB 208?0? V. Determine
• a. Find load phase voltage Vab
• b. Find the load phase current Iab .