TOPIC 5 - 3 Phase System

DET20033-ELECTRICAL CIRCUITS
TOPIC 5:

THREE PHASE SYSTEM

Understand three phase system [CLO1]
Understand three phase system configurations [CLO1]

Reference : CHAPTER 20

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

COURSE LEARNING
OUTCOMES

• Understand three phase system
[CLO1]

• Understand three phase system
configurations [CLO1]

POWER SUPPLY SYSTEM

EMF waveform – Three

phase

A three-phase a.c. supply is carried by three conductors, called ‘lines’ which
are coloured red, yellow and blue. The currents in these conductors are
known as line currents (IL) and the p.d.’s between them are known as line
voltages (VL). A fourth conductor, called the neutral (coloured black, and
connected through protective devices to earth) is often used with a three-
phase supply.

If the three-phase windings shown in Fig. 20.2 are kept independent then six
wires are needed to connect a supply source (such as a generator) to a load
(such as motor). To reduce the number of wires it is usual to interconnect the
three phases. There are two ways in which this can be done, these being:

(a) a star connection, and (b) a delta, or mesh, connection. Sources of
three-phase supplies, i.e. alternators, are usually connected in star, whereas
three-phase transformer windings, motors and other loads may be connected
either in star or delta.

EMF waveform – single

phase
The voltage induced by a
single coil when rotated
in a uniform magnetic field
is shown in Fig. 20.1 and
is known as a single-
phase voltage

The standard voltage for a
singlephase
a.c. supply is 240V.

EMF waveform – Three phase

A three-phase supply is
generated when three coils are
placed 120◦ apart and the whole
rotated in a uniform magnetic field
as shown in Fig. 20.2(a). The result
is three independent supplies of
equal voltages which are each
displaced by 120◦ from each other
as shown in Fig. 20.2(b).

(i) The convention adopted to
identify each of the phase voltages
is: R-red,Y-yellow, and B-blue, as
shown in Fig. 20.2

The phase-sequence is given by the
sequence in which the conductors
pass the point initially taken by the
red conductor. The national
standard phase
sequence is R,Y, B.

EMF waveform – Three

phase

A three-phase a.c. supply is carried by three conductors, called ‘lines’ which
are coloured red, yellow and blue. The currents in these conductors are
known as line currents (IL) and the p.d.’s between them are known as line
voltages (VL). A fourth conductor, called the neutral (coloured black, and
connected through protective devices to earth) is often used with a three-
phase supply.

If the three-phase windings shown in Fig. 20.2 are kept independent then six
wires are needed to connect a supply source (such as a generator) to a load
(such as motor). To reduce the number of wires it is usual to interconnect the
three phases. There are two ways in which this can be done, these being:

(a) a star connection, and (b) a delta, or mesh, connection. Sources of
three-phase supplies, i.e. alternators, are usually connected in star, whereas
three-phase transformer windings, motors and other loads may be connected
either in star or delta.

VECTOR DIAGRAM

STAR connection

STAR connection

(i) A star-connected load is shown in Fig. 20.3 where the three line conductors
are each connected to a load and the outlets from the loads are joined together
at N to form what is termed the neutral point or the star point.

(ii) The voltages, VR, VY and VB are called phase voltages or line to neutral
voltages. Phase voltages are generally denoted by Vp.

(iii) The voltages, VRY, VYB and VBR are called line voltages.

(iv) From Fig. 20.3 it can be seen that the phase currents (generally denoted by Ip)
are equal to their respective line currents IR, IY and IB, i.e. for a star
connection:
IL = Ip

(v) For a balanced system:
IR = IY = IB, VR = VY = VB
VRY = VYB = VBR, ZR = ZY = ZB
and the current in the neutral conductor, IN =0 When a star-connected system is
balanced, then the neutral conductor is unnecessary and is often omitted.

DELTA connection

DELTA connection

From Fig. 20.10, it can be seen that the line voltages VRY, VYB and VBR
are the respective phase voltages, i.e. for a delta connection:
VL = Vp

(iii) Using Kirchhoff’s current law in Fig. 20.10, IR =IRY −IBR =IRY +(−IBR)
From the phasor diagram shown in Fig. 20.11, by trigonometry or by
measurement, IR =√3 IRY, i.e. for a delta connection:
IL = √3 Ip

FORMULA



EXERCISE

Problem 1.
Three loads, each of resistance 30,
are connected in star to a 415V, 3-phase
supply. Determine

(a) the system phase voltage (240v)
(b) the phase current (8A)
(c) the line current. (8A)

ANSWER PROBLEM 1

A ‘415V, 3-phase supply’ means that 415V is the line voltage, VL

(a)For a star connection, VL = √3 Vp. Hence phase voltage,
Vp =(VL/√3)
=(415/√3)

=239.6V

or 240V, correct to 3 significant figures.

(b) Phase current, Ip =(Vp/Rp)

=240/30

=8A

(c) For a star connection, Ip =IL hence the line current, IL =8A

EXERCISE

Problem 2.
A star-connected load consists of three
identical coils each of resistance 30Ω

and
inductance 127.3 mH. If the line current

is
5.08A, calculate the line voltage if the

supply
frequency is 50 Hz. (439.9v)

ANSWER PROBLEM 2

Inductive reactance
XL = 2πfL = 2π(50)(127.3 × 10−3) = 40Ω

EXERCISE

Problem 3. Fig. 1
A 415V, 3-phase, 4 wire, star-
connected system supplies
three resistive loads as
shown in Fig. 1
Determine
(a) the current in each line

(Ir=100A, Iy=75A,
Ib=50A)



EXERCISE

Problem 4.
Three identical coils each of resistance
30 and inductance 127.3mH are

connected
In delta to a 440V, 50 Hz, 3-phase

supply.
Determine

(a) The phase current (8.8A)
(b) The line current (15.2A)

ANSWER PROBLEM 4

EXERCISE

Problem 5.
Three identical capacitors are

connected in
delta to a 415V, 50 Hz, 3-phase supply.

If
the line current is 15A, determine the
capacitance of each of the capacitors.
(66.7µF)

ANSWER PROBLEM 5

Problem 6. EXERCISE

Three coils each having resistance 3Ω and
inductive reactance 4Ω are connected (i) in

star
and (ii) in delta to a 415V, 3-phase supply.
Calculate for each connection
(a) the line and phase voltages

(STAR : VL=415v, Vph=240v)
(DELTA : VL=Vph=415v)

(a) the phase and line currents.

(STAR : IL=Iph=48A)
(DELTA : IL=144A, Iph=83A)

Problem 6. EXERCISE

Three coils each having resistance 3Ω and
inductive reactance 4Ω are connected (i) in star

and (ii) in delta to a 415V, 3-phase supply.

Calculate for each connection

(a) the line and phase voltages

(b) the phase and line currents.





Problem 7. EXERCISE

Three identical coils, each of resistance 10Ω and

inductance 42mH are connected (a) in star and (b)

in delta to a 415V, 50 Hz, 3-phase supply.

Determine the total power dissipated in each case.

***Hence loads connected in delta dissipate three times the power than when connected in star, and
also take a line current three times greater.

Problem 7. EXERCISE

Three identical coils, each of resistance 10Ω and

inductance 42mH are connected (a) in star and (b)

in delta to a 415V, 50 Hz, 3-phase supply.

Determine the total power dissipated in each case.

(STAR : 6.3kW)

(DELTA : 18.87kW)

***Hence loads connected in delta dissipate three times the power than when connected in star, and
also take a line current three times greater.

EXERCISE





• Problem 8.
• Three 12 resistors are

connected in star to a 415V, 3-
phase supply. Determine the total
power dissipated by the resistors.



EXERCISE

Problem 8.
Based on the figure,
calculate :
a) Z (20Ω)
b) Iph (11.98A)
c) IL (11.98A)
d) Vph (239.6V)
e) P_single-phase (2.3kW)
f) P_three-phase (6.9kW)

ADVANTAGES OF 3 PHASE SYSTEM

Advantages of three-phase systems over single-
Phase supplies include:
(i) Saving of copper (or aluminium) and thus the

original installation costs are less.
(ii) Two voltages are available
(iii) Three-phase motors are very robust,

relatively cheap, generally smaller, have self-
starting properties, provide a steadier output
and require little maintenance compared with
single-phase motors.

Advantages of three-phase systems over single-phase supplies
include:

(i)For a given amount of power transmitted through a system, the three-
phase system requires conductors with a smaller cross-sectional area.
This means a saving of copper (or aluminium) and thus the original
installation costs are less.

(ii) Two voltages are available

(iii) Three-phase motors are very robust, relatively cheap, generally
smaller, have self-starting properties, provide a steadier output and
require little maintenance compared with single-phase motors.