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Lesson 34
3 PHASE Sources &
Loads
Learning Objectives

Review the induced AC voltage output for a three phase AC generator
as a function of time and as phasors.

Define a three-wire Y-Y three phase circuit and a four-wire Y-Y three
phase circuit.

Define the symbols for line to neutral voltages, line to line voltages, line
currents, and phase impedances that will be used in three phase
circuits.

Analyze Ohm’s law in a three-wire Y-Y three phase circuit and in a fourwire YY three phase circuit using a basic three phase generator that
produces three balanced voltages which are connected to balanced
loads.

Analyze Kirchhoff’s current law in a three-wire Y-Y three phase circuit
and in a four-wire Y-Y three phase circuit using a basic three phase
generator that produces three balanced voltages with a Y connected
balanced purely resistive loads.
Why three-phase?
http://www.youtube.com/watch?v=HqZtptHnC2I
1. Nearly all power generated and distributed is 3phase, 60 Hz (or 50 Hz outside the U.S.).
 When single phase is needed, it can simply be taken
from one of the three phases.
2. The instantaneous power in 3-phase system
can be constant (not pulsating).
 Results in less vibration in 3-phase machines.
3. Three phase systems are more economical
that single.
 Amount of wire needed is less than single phase.
THREE-PHASE GENERATOR
(a) Three-phase generator; (b) induced voltages of a three-phase generator.
THREE-PHASE GENERATOR
Phasor diagram for the
phase voltages of a
three-phase generator.
Demonstrating that
the vector sum of
the phase voltages
of a three-phase
generator is zero.
Y-CONNECTED GENERATOR
If the three terminals
denoted N in Fig. are
connected together, the
generator is referred to
as a Y-connected
three-phase
generator.
Y-connected generator.
Delta(), Wye(Y) Connections
Wye (Y)
Delta ()
Y-Y system
Y Load
Generator
Lines
4-wire Y-Y system
3-wire Y-Y system
The neutral voltage (VnN) in a balanced Y-Y system is zero.
Phase voltages
Phase voltages are the voltages across phases.
• For a Y load, phase voltage is measured from line to neutral (n)
• For the generator, EAN, EBN and ECN are the phase voltages.
Example Problem 1
EAN = 7620-18 V
What are the phase voltages EBN, and ECN?
E AN  E  0
E BN  E  120
ECN  E  120
Line voltages
Line voltages are the voltages between the lines A, B and C
PHASE/LINE VOLTAGES
Line and phase voltages of the
Y-connected three-phase
generator.
Determining a line voltage for
a three-phase generator.
Line/Phase Voltages for a Wye Circuit

Relationship between line and phase
voltages
Eab  Ean  Ebn
Eab  3Ean 30


For a balanced Y system, the
magnitude of line-to-line voltage is
1.732 times the magnitude of the
phase voltage.
Line to line voltage leads phase
voltage by 30.
Example Problem 2
EAN = 7620-18 V
What are the line voltages ?
E AN  E  0
E BN  E  120
ECN  E  120
Eab  Ean  Ebn
Eab  3Ean 30
CURRENTS
Line currents are the currents in the line conductors.
Phase currents are the currents through phases.
For Y loads, line current and phase current are the same.
Currents for a Wye Circuit

For Y loads, line current and phase current are the
same.
I a  Van / Z an
Line current
Phase current
Diagram of 3-phase system
I N = I A + I B + I C  10 A0  10 A  120  10 A  120  0 A
Example Problem 3
For the load depicted below, EAN = 277-30 V . Find the
phase voltages and line voltages and currents. Sketch
their phasor values.
-connected Load
For  loads, phase voltage and line voltage are the same
thing.
 load definitions
Y-Y
Line currents are the currents in the line conductors.
Phase currents are the currents through phases .
Line/Phase Currents for a Delta Circuit
Line current
Phase current