ERT 105 ELECTRICAL
ENGINEERING
THREE PHASE SYSTEM
(week 8-9)
EXPECTED OUTCOME
Ability to :
•describe a single-phase supply
• describe a three-phase supply
• understand a star and a delta connection
• calculate power in three-phase systems
•compare star and delta connections
• appreciate the advantages of three-phase systems
BASIC UNDERSTANDING
ALTERNATING CURRENT
SINGLE PHASE
THREE PHASE
Motion of a current-carrying loop in a magnetic
field
F Rotation
I
N
brushes
L
R
S
F
Commutator
(rotates with
coil)
Vertical position of the loop:
Rotation
N
S
ONE PHASE SYSTEM
THREE PHASE SYSTEM
THREE PHASE SYSTEM
STAR CONNECTION OF THREE PHASE SYSTEM
The voltages, VR, VY and VB are called phase voltages or line to neutral voltages.
The voltages, VRY, VYB and VBR are called line voltages.
STAR CONNECTION : Voltage calculation
The standard electricity supply to consumers is 415/240 V, 50 Hz, 3-phase, 4-wire
alternating current
Problem example :
EXAMPLE 1.
Calculate the Line voltage for for a threephase star system if it is known that the
Phase voltage = 120 Volts
For the three phase star connection,
EXAMPLE 2.
Three loads, each of resistance 30 , are connected
in star to a 415 V, 3-phase supply.
Determine :
(a)the system phase voltage,
(a)the phase current
(c) the line current.
ANSWER :
A ‘415 V, 3-phase supply’ means that line voltage, VL = 415 V
(a) For a star connection,
VL= 239.6 V
--------------- Phase voltage =~~~ 240 V
(b) Phase current, = Phase voltage /30 -- Ip= 8 A
(c) For a star connection,
Line current = Phase current = 8 A
EXAMPLE 3.
Three loads, each of resistance 50 are connected in
delta to a 400 V, 3-phase supply. Determine
(a)the phase voltage,
(b)the phase current and
(c)the line current.
Line voltage VL = 400 V
Phase voltage = line voltage = 400 V
Phase current = V/R ------ = 400/50= 8 A
Line current = 1,7 x phase current = 13.4 A
EXAMPLE 4.
Three coils each having resistance 5 Ohm
are connected (i) in star and (ii) in delta to
a 415 V, 3-phase supply. Calculate for each
connection
(a) the line and phase voltages
(b) the phase and line currents.
The power dissipated in a three-phase load is given by the sum of
the power dissipated in each phase.
the total power P is given by:
Is a power factor
EXAMPLE 4.
Three 12 Ohm resistors are connected in
star to a 415 V, 3-phase supply.
Determine the total power dissipated by
the resistors.
ANSWER
(Since for a star connection)
Power
= 14 359 watt
Or = 14.4 kW
EXAMPLE 4.
The input power to a 3-phase a.c. motor is
measured as 5 kW. If the voltage and current to
the motor are 400 V and 8.6 A respectively,
determine the power factor of the system.
ANSWER