ERT 105 ELECTRICAL ENGINEERING

THREE PHASE SYSTEM(week 8-9)

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

EXPECTED OUTCOME

BASIC UNDERSTANDING

ALTERNATING CURRENT

SINGLE PHASE THREE PHASE

Motion of a current-carrying loop in a magnetic field

N SL R

I

F

F Rotation

Commutator (rotates with coil)

brushes

Vertical position of the loop:

N S

Rotation

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 three-phase 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,

(b)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

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.

EXAMPLE 3.

Line voltage VL = 400 VPhase voltage = line voltage = 400 V

Phase current = V/R ------ = 400/50= 8 A

Line current = 1,7 x phase current = 13.4 A

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.

EXAMPLE 4.

the total power P is given by:

The power dissipated in a three-phase load is given by the sum of the power dissipated in each phase.

Is a power factor

Three 12 Ohm resistors are connected in star to a 415 V, 3-phase supply.

Determine the total power dissipated by the resistors.

EXAMPLE 4.

(Since for a star connection)

Power

= 14 359 watt Or = 14.4 kW

ANSWER

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.

EXAMPLE 4.

ANSWER