•Teknologi Elektrik

(BBT 3623)

Bab 1:Litar Elektrik

Teknologi Elektrik

(BBT 3623)

Bab 3:Sistem Tiga

Fasa

At the end of this chapter you should be able to:

• Describe a single-phase supply

• Describe a three-phase supply

• Understand a star connection, and recognise that IL =Ip and VL = √3Vp

• Draw a complete phasor diagram for a balanced, star connected load

• Understand a delta connection, and recognise that VL =Vp and IL =3Ip

• Draw a phasor diagram for a balanced, delta connected load

• Calculate power in three-phase systems using P=√3 VLIL cos Ø

• Appreciate how power is measured in a three-phase system, by the one two and three-wattmeter methods

• Compare star and delta connections

• Appreciate the advantages of three-phase systems

3.1 Introduction Generation, transmission and distribution of electricity via the National Grid system is accomplished by three phase alternating currents.

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

3.1 Introduction Most consumers are fed by means of a single-phase a.c. supply.

Two wires are used, one called the live conductor (usually coloured red) and the other is called the neutral conductor (usually coloured black).

The neutral is usually connected via protective gear to earth, the earth wire being coloured green.

The standard voltage for a single phase a.c. supply is 240V.

The majority of single-phase supplies are obtained by connection to a three-phase supply

3.2 Three-Phase SupplyA three-phase supply is generated when three coils are placed 120◦ apart and the whole rotated in a uniform magnetic field

3.2 Three-Phase Supply The convention adopted to identify each of the phase voltages

is: R-red,Y-yellow, and B-blue,. 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.

3.3 Three Phase Connection If the three-phase windings 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:

i. a star connection

ii. a delta connection

3.3 Three Phase Connection

Star connection (3 phase - 3 Wires)

R

Y

B

ZR

ZB ZY

3.3 Three Phase Connection

Star connection (3 phase - 4 Wires)

R

Y

B

N

ZR

ZB ZY

3.3 Three Phase ConnectionDelta connection

R

Y

B

ZRB ZRY

ZBY

3.4 Star Connection

VR, VY and VB are called phase voltages or line to neutral voltages. ( generally denoted by VP).

VRY, VYB and VBR are called line voltages

3.4 Star Connection

IR, IY and IB line current (denoted by IL)= Phase current denoted by IP

For a star connection IL=IP

3.4 Star ConnectionFor a balanced system

3.4 Star Connection

VRY =VR −VY

VRY =VR +(−VY))

By trigonometry, or by measurement,

3.4 Star ConnectionThe star connection of the three phases of a supply, together with a neutral conductor, allows the use of two voltages — the phase voltage and the line voltage.

A 4-wire system is also used when the load is not balanced. The standard electricity supply to consumers in Malaysia is 415/240V, 50 Hz, 3-phase, 4-wire alternating current

3.4 Star Connection

3.4 Star Connection

3.4 Star Connection

3.4 Star Connection

(i) Draw VR =VY =VB =240V and spaced 120◦ apart

(ii) Power factor= cos φ=0.966 lagging phase angle is given by cos−1(0.966)=15◦IR =IY =IB =5A, lagging VR, VY and VB respectively by 15◦.

(iii) VRY =VR −VY

VYB =VY −VB

VBR =VB −VR

VR=240V

VY=240VVB=240V

IR=5A

IY=5A

IB=5A

15˚

VRY=415V

30˚

VYB=415V

VBR=415V

3.4 Star Connection

3.4 Star Connection

3.5 Delta Connection

VRY, VYB and VBR phase voltages

For delta connection VP=VL

3.5 Delta Connection

IR =IRY −IBR =IRY +(−IBR)

3.5 Delta Connection

IR =IRY −IBR =IRY +(−IBR)

By trigonometri @ measurement

3.5 Delta Connection

3.5 Delta Connection

1

3.5 Delta Connection

3.5 Delta Connection

3.5 Delta Connection

Thus when the load is connected in delta,

three times the line current is taken from the supply than is taken if connected in star.

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

If a load is balanced then the total power P is given by:

P=3×power consumed by one phase.

The power consumed in one phase= or

VpIp cos Ø

(where Ø is the phase angle between Vp and Ip).

p2pRI

3.6 Power in three-phase systems

For a star connection,

3.6 Power in three-phase systems

For a delta connection,

3.6 Power in three-phase systemsHence for either a star or a delta balanced connectionthe total power P is given by:

Total volt-amperes

3.6 Power in three-phase systems

3.6 Power in three-phase systems

3.6 Power in three-phase systems

3.6 Power in three-phase systems

3.6 Power in three-phase systems

3.6 Power in three-phase systems

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

3.7 Measurement of power in three-phase systems

(i) One-wattmeter method for a balanced load

3.7 Measurement of power in three-phase systems

(ii) Two-wattmeter method for balanced or unbalanced loads

3.7 Measurement of power in three-phase systems

(iii) Three-wattmeter method for a three-phase, 4-wire system for balanced and unbalanced loads

SEKIANTERIMA KASIH