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Lesson 35 Per Phase Analysis

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Per Phase Analysis Learning Objectives Derive the relationship between line to line voltages and line to neutral voltages in a balanced Y-Y three phase circuit. – PowerPoint PPT presentation

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Title: Lesson 35 Per Phase Analysis


1
Lesson 35Per Phase Analysis
2
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.

3
Y-Y system
Review
Y Load
Generator
Lines
4
PHASE/LINE VOLTAGES
 
5
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.

6
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
7
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.

8
Currents for a Wye Circuit
  • For Y loads, line current and phase current are
    the same.

Line current
Phase current
9
Wye-Wye Single Phase Equivalent
Original circuit
Single-phase equivalent
10
Example Problem 1
  • EAB 208?0? V .
  • Find the phase voltages and line currents.

11
? 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 .
12
Line/Phase Currents for a Delta Circuit
Iab
Ica
Iab
Ibc
Line current
Phase current
13
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.

14
Line/Phase Currents for a Delta Circuit
Phasor diagram
15
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!

16
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.

17
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
18
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.

19
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

20
Example Problem 3
  • EAB 208?0? V. Determine
  • a. Line Currents
  • b. Load phase voltages

21
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

22
Equivalent Delta Ckt with LINE IMPEDANCES
23
Example Problem 4
  • EAB 208?0? V. Determine
  • a. Find load phase voltage Vab
  • b. Find the load phase current Iab .
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