electrical technology (eet 103) pn haziah abdul hamid

ELECTRICAL TECHNOLOGY

(EET 103)PN HAZIAH ABDUL HAMID

SYLLABUS – PART II

SYLLABUS

•TOPIC 4: THREE PHASE CIRCUIT•TOPIC 5: TRANSFORMER•TOPIC 6: ELECTRICAL MACHINES

TOPIC 4: THREE PHASE CIRCUIT

SINGLE PHASE TWO WIRE

pV

SINGLE PHASE SYSTEM

• A generator connected through a pair of wire to a load – Single Phase Two Wire.

• Vp is the magnitude of the source voltage, and is the phase.

SINLGE PHASE THREE WIRE

pV

pV

SINGLE PHASE SYSTEM• Most common in practice: two

identical sources connected to two loads by two outer wires and the neutral: Single Phase Three Wire.

• Terminal voltages have same magnitude and the same phase.

POLYPHASE SYSTEM

•Circuit or system in which AC sources operate at the same frequency but different phases are known as polyphase.

TWO PHASE SYSTEM THREE WIRE

pV

90pV

POLYPHASE SYSTEM

• Two Phase System:– A generator consists of two coils

placed perpendicular to each other– The voltage generated by one lags

the other by 90.

POLYPHASE SYSTEM

• Three Phase System:– A generator consists of three coils

placed 120 apart.– The voltage generated are equal in

magnitude but, out of phase by 120.

• Three phase is the most economical polyphase system.

THREE PHASE FOUR WIRE

IMPORTANCE OF THREE PHASE SYSTEM

• All electric power is generated and distributed in three phase.– One phase, two phase, or more than

three phase input can be taken from three phase system rather than generated independently.

– Melting purposes need 48 phases supply.


• Uniform power transmission and less vibration of three phase machines.– The instantaneous power in a 3

system can be constant (not pulsating).

– High power motors prefer a steady torque especially one created by a rotating magnetic field.


• Three phase system is more economical than the single phase.– The amount of wire required for a

three phase system is less than required for an equivalent single phase system.

– Conductor: Copper, Aluminum, etc

THREE PHASE GENERATION

FARADAYS LAW• Three things must be present in

order to produce electrical current:a) Magnetic fieldb) Conductorc) Relative motion

• Conductor cuts lines of magnetic flux, a voltage is induced in the conductor

• Direction and Speed are important

GENERATING A SINGLE PHASE

Motion is parallel to the flux.

No voltage is induced.

N

S

x

N

S

Motion is 45 to flux. Induced voltage is 0.707 of maximum.



x

N

S

Motion is perpendicular to flux. Induced voltage is maximum.


Motion is 45 to flux.

x

N

S

Induced voltage is 0.707 of maximum.


N

S

Motion is parallel to flux. No voltage is induced.


x

N

S

Notice current in the conductor has reversed.




N

S

x

Motion is perpendicular to flux.

Induced voltage is maximum.


N

S

x




Motion is parallel to flux. N

S

No voltage is induced.Ready to produce another cycle.

THREE PHASE GENERATOR

GENERATOR WORK

• The generator consists of a rotating magnet (rotor) surrounded by a stationary winding (stator).

• Three separate windings or coils with terminals a-a’, b-b’, and c-c’ are physically placed 120 apart around the stator.

• As the rotor rotates, its magnetic field cuts the flux from the three coils and induces voltages in the coils.

• The induced voltage have equal magnitude but out of phase by 120.

GENERATION OF THREE-PHASE AC

N

xx

S

THREE-PHASE WAVEFORM

Phase 2 lags phase 1 by 120 Phase 2 leads phase 3 by 120Phase 3 lags phase 1 by 240 Phase 1 lags phase 3 by 120

Phase 1 Phase 2 Phase 3

120 120 120

240120 120 120

240

Phase 1 Phase 2 Phase 3

GENERATION OF 3 VOLTAGES

Phase 1 is ready to go positive.Phase 2 is going more negative.Phase 3 is going less positive.

Thealgebraicsum of theinstantaneousvoltages ofthe three phases equalszero.

N

xx

S

THREE PHASE QUANTITIES

BALANCED 3 VOLTAGES

120cos240cos)(

120cos)(

cos)(

tVtVtv

tVtv

tVtv

MMcn

Mbn

Man

• Balanced three phase voltages:– same magnitude (VM )

– 120 phase shift

BALANCED 3 CURRENTS• Balanced three phase currents:

– same magnitude (IM )

– 120 phase shift

240cos)(

120cos)(

cos)(

tIti

tIti

tIti

Mc

Mb

Ma

PHASE SEQUENCE

120cos)(

120cos)(

cos)(

tVtv

tVtv

tVtv

Mcn

Mbn

Man

120

120

0

Mcn

Mbn

Man

VV

VV

VV

120

120

0

Mcn

Mbn

Man

VV

VV

VV

POSITIVESEQUENCE

NEGATIVESEQUENCE

PHASE SEQUENCE

EXAMPLE• Determine the phase sequence

of the set voltages:

110cos200

230cos200

10cos200

tv

tv

tv

cn

bn

an

Ans: Negative Sequence

BALANCED VOLTAGE AND LOAD

• Balanced Phase Voltage: all phase voltages are equal in magnitude and are out of phase with each other by 120.

• Balanced Load: the phase impedances are equal in magnitude and in phase.

THREE PHASE CIRCUIT

• POWER– The instantaneous power is constant

)cos(3

cos2

3

)()()()(

rmsrms

MM

cba

IV

IV

tptptptp

THREE PHASE CIRCUIT

• Three Phase Power,

SSSSS 3 CBAT

THREE PHASE QUANTITIES

QUANTITY SYMBOL

Phase current I

Line current IL

Phase voltage V

Line voltage VL

PHASE VOLTAGES and LINE VOLTAGES

•Phase voltage is measured between the neutral and any line: line to neutral voltage

•Line voltage is measured between any two of the three lines: line to line voltage.

PHASE CURRENTS and LINE CURRENTS

• Line current (IL) is the current in each line of the source or load.

• Phase current (I) is the current in each phase of the source or load.

THREE PHASE CONNECTION

SOURCE-LOAD CONNECTION

SOURCE LOAD CONNECTION

Wye Wye Y-Y

Wye Delta Y-

Delta Delta -

Delta Wye -Y

SOURCE-LOAD CONNECTION

• Common connection of source: WYE– Delta connected sources: the

circulating current may result in the delta mesh if the three phase voltages are slightly unbalanced.

• Common connection of load: DELTA– Wye connected load: neutral line may

not be accessible, load can not be added or removed easily.

WYE CONNECTION

WYE CONNECTED GENERATOR

n

a

b

c

Vab

Vbc

Vca

Vbn

Vcn

Van

Ia

Ib

Ic

WYE CONNECTED LOAD

ZY

ZY

ZY

a

c

b

nLoad

ZY

a

b

c

Load

n

OR

BALANCED Y-Y CONNECTION

PHASE CURRENTS AND LINE CURRENTS

• In Y-Y system:

φL II

PHASE VOLTAGES, V

• Phase voltage is measured between the neutral and any line: line to neutral voltage

n

a

b

c

Vab

Vbc

Vca

Vbn

Vcn

Van

Ia

Ib

Ic

Van

Vbn

Vcn

PHASE VOLTAGES, V

an M

bn M

cn M

V V 0 volt

V V 120 volt

V V 120 volt

LINE VOLTAGES, VL

• Line voltage is measured between any two of the three lines: line to line voltage.

n

a

b

c

Vab

Vbc

Vca

Vbn

Vcn

Van

Ia

Ib

Ic

Vab

Vbc

Vca

LINE VOLTAGES, VL

ancaca

cnbnbc

bnanab

VVV

VVV

VVV

150V3V

90V3V

30V3V

Mca

Mbc

Mab

ab M

bc M

ca M

V 3 V 30 volt

V 3 V 90 volt

V 3 V 150 volt

an M

bn M

cn M

V V 0 volt

V V 120 volt

V V 120 volt

PHASE VOLTAGE (V)

LINE VOLTAGE

(VL)

PHASE DIAGRAM OF VL

AND V

30°

120°

Vca Vab

Vbc

Vbn

Van

Vcn

-Vbn

PROPERTIES OF PHASE VOLTAGE

• All phase voltages have the same magnitude,

• Out of phase with each other by 120

an bn cnV V V V

PROPERTIES OF LINE VOLTAGE

• All line voltages have the same magnitude,


ab bc caV V V VL

RELATIONSHIP BETWEEN V and VL

1. Magnitude

2. Phase

- VL LEAD their corresponding V by 30

LV 3 V

30VVL

EXAMPLE • Calculate the line currents

Single Phase Equivalent Circuit

• Phase ‘a’ equivalent circuit

5-j2

810 j

21.86.8121.816.155

0110I

Z

VI

a

Y

ana

A2.986.811.8266.81

024II

A141.86.81

120II

ac

ab

DELTA CONNECTION

DELTA CONNECTED SOURCES

DELTA CONNECTED LOAD

OR

BALANCED - CONNECTION

PHASE VOLTAGE AND LINE VOLTAGE

• In - system, line voltages equal to phase voltages:

φL VV

PHASE CURRENTS, I• Line voltages are equal to the

voltages across the load impedances.

PHASE CURRENTS, I• The phase currents are obtained:

Δ

CACA

Δ

BCBC

Δ

ABAB Z

VI,

Z

VI,

Z

VI

LINE CURRENTS, IL• The line currents are obtained from

the phase currents by applying KCL at nodes A,B, and C.

LINE CURRENTS, IL

BCCAc

ABBCb

CAABa

III

III

III

120I I

120I I

30I 3I

ac

ab

ABa

PHASE CURRENTS (I)

LINE CURRENTS (IL)

Δ

CACA

Δ

BCBC

Δ

ABAB

Z

VI

Z

VI

Z

VI

120I I

120I I

30I 3I

ac

ab

ABa

PHASE DIAGRAM OF IL

AND I

PROPERTIES OF PHASE CURRENT

• All phase currents have the same magnitude,


Δ

φCABCABφ Z

VIIII

PROPERTIES OF LINE CURRENT

• All line currents have the same magnitude,


cbaL IIII

1. Magnitude

2. Phase

- VL LAG their corresponding V by 30

FL II 3

RELATIONSHIP BETWEEN I and IL

30II FL

EXAMPLE

A balanced delta connected load having an impedance 20-j15 is connected to a delta connected, positive sequence generator having Vab = 3300 V. Calculate the phase currents of the load and the line currents.

Given Quantities

0330V

87.3625 j1520Z

ab

Δ

Phase Currents

A87.15613.2120II

A13.83-13.2120II

A36.8713.238.8725

0330

Z

VI

ABCA

ABBC

Δ

ABAB

A87.12686.22120II

A13.311-86.22120II

87.686.22

A30336.8713.2

303II

ac

ab

ABa

Line Currents

BALANCED DELTA-WYE SYSTEM

EXAMPLE

A balanced positive sequence Y-connected source with Van=10010 V is connected to a -connected balanced load (8+j4) per phase. Calculate the phase and line currents.

Given Quantities

•Balanced WYE source–Van= 10010 V

•Balanced DELTA load–Z= 8+j4

Phase Currents

43.1336.19j48

40173.2I

V 402.731V

30V 3V

Z

VI

AB

AB

anAB

Δ

ABAB

VAB= voltage across Z = Vab= source line voltage

Phase Currents

A

A

43.13336.19I

12043.1336.19I

57.10636.19I

12043.13II

43.1336.19I

CA

CA

BC

ABBC

AB

Line Currents

A

A

A

43.103 53.33120 II

57.136 53.33120 II

57.16 53.33I

3043.13 (19.36) 3

30 I 3I

ac

ab

a

ABa

DELTA TO WYE CONVERSION

3

Z

Z

THREE PHASE POWER MEASUREMENT

FOUR WIRE SYSTEM• Each phase measured separately:

A

A

V

W

W

Phase A

Phase B

Phase C

VAN

IA

IC

V

A

V

W

IB

VBN

VCN

Neutral (N)

PA

PB

PC

THREE PHASE THREE WIRE SYSTEM

A

A

V

V

W

W

Phase A

Phase B

Phase C

VAB = VA - VB

VCB = VC - VB

IA

IC

PAB

PCBCBABT PPP

The three phase power is the sum of the two watt-meters reading

EXAMPLE Determine the total power (P), reactive power (Q), and complex power (S) at the source and at the load

Single Phase Equivalent Circuit

• Phase ‘a’ equivalent circuit

5-j2

810 j

Known Quantities

•V =Van = 1100 V

•ZY = 10+j8

•Zline =5-j2

Line/Phase Currents

21.86.8121.816.155

0110I

ZZ

VI

a

Yline

ana

Source & Load Power

Var 834.6Q W,2087P

j834.6)VA(2087

I3VS

ss

φφsource

Var 1113Q W,1392P

j1113)VA(1392

ZI3S

LL

2

φLoad

EXAMPLE

A three phase motor can be regarded as a balanced Y-load. A three phase motor draws 5.6 kW when the line voltage is 220 V and the line current is 18.2 A. Determine the power factor of the motor

Known Quantities

• PLoad =5600 W

• VL = 220 V

• IL = 18.2 A

Power factor

• Power factor = cos

VA 6935.13

IV 3I3VS LLφφ

0.86935.13

5600

S

Pθ cos

θ cosSP

|S|Q

P

electrical technology (eet 103) pn haziah abdul hamid

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