Lec09 Three Phase

8/12/2019 Lec09 Three Phase

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THREE PHASE

CIRCUIT


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Objectives

Explain the differences between single-phase, two-phase and three-phase.

Compute and define the Balanced Three-

Phasevoltages. Determine the phase and line

voltages/currents for Three-Phase

systems.


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SINGLE PHASE TWO WIRE

pV


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SINGLE PHASE SYSTEM

A generator connected through a pairof wire to a loadSingle Phase TwoWire.

Vpis the magnitude of the sourcevoltage, and is the phase.


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SINLGE PHASE THREE WIRE

pV

pV


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SINGLE PHASE SYSTEM

Most common in practice: twoidentical sources connected to twoloads by two outer wires and the

neutral: Single Phase Three Wire. Terminal voltages have same

magnitude and the same phase.


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POLYPHASE SYSTEM

Circuit or system in which ACsources operate at the same

frequency but different phasesare known as polyphase.


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TWO PHASE SYSTEM THREE WIRE

pV

90pV


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POLYPHASE SYSTEM

Two Phase System:A generator consists of two coils placed

perpendicular to each other

The voltage generated by one lags theother by 90.


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POLYPHASE SYSTEM

Three Phase System:A generator consists of three coils placed

120apart.

The voltage generated are equal inmagnitude but, out of phase by 120.

Three phase is the most economical

polyphase system.


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IMPORTANCE OF THREE PHASE SYSTEM

All electric power is generated anddistributed in three phase.

One phase, two phase, or more than

three phase input can be taken fromthree phase system rather thangenerated independently.

Melting purposes need 48 phasessupply.


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Uniform power transmission and lessvibration of three phase machines.

The instantaneous power in a 3system

can be constant (not pulsating). High power motors prefer a steady

torque especially one created by a

rotating magnetic field.


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Three phase system is moreeconomical than the single phase.

The amount of wire required for a three

phase system is less than required for anequivalent single phase system.

Conductor: Copper, Aluminum, etc


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THREE PHASE GENERATION


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FARADAYS LAW

Three things must be present inorder to produce electrical current:a) Magnetic field

b) Conductorc) Relative motion

Conductor cuts lines of magnetic

flux, a voltage is induced in theconductor

Direction and Speed are important


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GENERATING A SINGLE PHASE

Motion is parallel to the flux.

No voltage is induced.

N

S


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N

S

Motion is 45to flux.

Induced voltage is 0.707 of maximum.



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x

N

S

Motion is perpendicular to flux.

Induced voltage is maximum.


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N

S



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N

S

Motion is parallel to flux.



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N

S

Notice current in the

conductor has reversed.

Inducedvoltage is

0.707 of maximum.



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N

S

Motion is perpendicular to flux.

Induced voltage is maximum.


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N

S




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Motion is parallel to flux.N

S


Ready to produce another cycle.


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THREE PHASE GENERATOR


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As the rotor rotates, its magnetic fieldcuts the flux from the three coils andinduces voltages in the coils.

The induced voltage have equalmagnitude but out of phase by 120.


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GENERATION OF THREE-PHASE AC

N

xx

S


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THREE-PHASE WAVEFORM

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

Phase 3lags phase 1by 240

Phase 1leads phase 3by 240

Phase 1 Phase 2 Phase 3

120 120 120

240

120 120 120

240

GENERATION OF 3 VOLTAGES


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Phase 1Phase 2Phase 3

GENERATION OF 3VOLTAGES

Phase 1is ready to go positive.

Phase 2is going more negative.

Phase 3is going less positive.

N

xx

S


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THREE PHASE QUANTITIES


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BALANCED 3VOLTAGES

120cos240cos)(

120cos)(

cos)(

tVtVtv

tVtv

tVtv

MMcn

Mbn

Man

Balanced three phase voltages: same magnitude (VM )

120phase shift


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BALANCED 3CURRENTS

Balanced three phase currents: same magnitude (IM )

120phase shift

240cos)(

120cos)(

cos)(

tIti

tIti

tIti

Mc

Mb

Ma


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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


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PHASE SEQUENCE


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EXAMPLE # 1

Determine the phase sequence ofthe set voltages:

110cos200

230cos200

10cos200

tv

tv

tv

cn

bn

an


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BALANCED VOLTAGE AND LOAD

Balanced Phase Voltage: all phasevoltages are equal in magnitude andare out of phase with each other by

120. Balanced Load: the phase

impedances are equal in magnitude

and in phase.


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THREE PH SE CIRCUIT

POWERThe instantaneous power is constant

)cos(3

cos2

3

)()()()(

rmsrms

MM

cba

IV

IVtptptptp


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THREE PH SE CIRCUIT

Three Phase Power,

SSSSS

3

CBAT


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THREE PHASE QUANTITIES

QUANTITY SYMBOL

Phase current I

Line current IL

Phase voltage V

Line voltage VL


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PHASE CURRENTS and LINE CURRENTS

Line current (IL) is the current ineach lineof the source or load.

Phase current (I) is the current ineach phaseof the source or load.


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THREE PHASE CONNECTION

SO C O CO C O


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SOURCE-LOAD CONNECTION

SOURCE LOAD CONNECTION

Wye Wye Y-Y

Wye Delta Y-

Delta Delta -

Delta Wye -Y

SOURCE LOAD CONNECTION


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SOURCE-LOAD CONNECTION

Common connection of source:WYEDelta connected sources: the

circulating current may result in the

delta mesh if the three phase voltagesare slightly unbalanced.

Common connection of load:DELTA

Wye connected load: neutral line maynot be accessible, load can not beadded or removed easily.


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WYE CONNECTION

WYE CONNECTED GENERATOR


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WYE CONNECTED GENERATOR

n

a

b

c

Vab

Vbc

Vca

Vbn

Vcn

Van

Ia

Ib

Ic


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WYE CONNECTED LO D

ZY

ZY

ZY

a

c

b

nLoad

ZY

ZYZ Y

a

b

c

Load

n

OR

BALANCED Y Y CONNECTION


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BALANCED Y-Y CONNECTION

PHASE CURRENTS AND LINE CURRENTS


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PHASE CURRENTS AND LINE CURRENTS

In Y-Y system:

L II

PHASE VOLTAGES V


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PHASE VOLTAGES, V

Phase voltage ismeasured betweenthe neutral and anyline: line to neutralvoltage

n

a

b

c

Vab

Vbc

Vca

Vbn

Vcn

Van

Ia

Ib

Ic

Van

Vbn

Vcn

PHASE VOLTAGES V


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PHASE VOLTAGES, V

an M

bn M

cn M

V V 0 volt

V V 120 volt

V V 120 volt

LINE VOLTAGES V


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LINE VOLTAGES, VL

Line voltage ismeasured between

any two of the threelines: line to linevoltage.

n

a

b

c

Vab

Vbc

Vca

Vbn

Vcn

Van

Ia

Ib

Ic

Vab

Vbc

Vca

LINE VOLTAGES V


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LINE VOLTAGES, VL

ancnca

cnbnbc

bnanab

VVV

VVV

VVV

150V3V

90V3V

30V3V

Mca

Mbc

Mab


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PROPERTIES OF PHASE VOLTAGE


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PROPERTIES OF PHASE VOLTAGE

All phase voltages have the samemagnitude,

Out of phase with each other by 120

an bn cnV V V V = =

PROPERTIES OF LINE VOLTAGE


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PROPERTIES OF LINE VOLTAGE

All line voltages have the samemagnitude,


ab bc caV V V VL = =

RELATIONSHIP BETWEEN V and V


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RELATIONSHIP BETWEEN Vand VL

1. Magnitude

2. Phase

-VLLEADtheir corresponding Vby 30

LV 3 V

30VVL

EXAMPLE 1


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EXAMPLE 1

Calculate the line currents


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DELTA CONNECTION

DELTA CONNECTED SOURCES


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DELTA CONNECTED SOURCES


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DELT CONNECTED LO D

OR

BALANCED CONNECTION


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BALANCED-CONNECTION


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PHASE VOLTAGE V


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PHASE VOLTAGE, V Phase voltages are equal to the

voltages across the load impedances.

PHASE CURRENTS I


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PHASE CURRENTS, I

The phase currents are obtained:

CA

CA

BC

BC

AB

AB Z

V

I,Z

V

I,Z

V

I

LINE CURRENTS I


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LINE CURRENTS, IL

The line currents are obtained from thephase currents by applying KCL atnodes A,B, and C.

LINE CURRENTS I


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LINE CURRENTS, IL

BCCAc

ABBCb

CAABa

III

III

III

120II

120II

30I3I

ac

ab

ABa

PHASE


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PHASE

CURRENTS (I

)

LINE CURRENTS (IL)

CACA

BCBC

ABAB

Z

VI

Z

VI

Z

VI

120II

120II

30I3I

ac

ab

ABa


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PH SE DI GR M OF I

L

ND I

PROPERTIES OF PHASE CURRENT


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PROPERTIES OF PHASE CURRENT

All phase currents have the samemagnitude,


CABCABZVIIII


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RELATIONSHIP BETWEEN I and I


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1. Magnitude

2. Phase

- ILLAGtheir corresponding Iby 30

IIL 3

RELATIONSHIP BETWEEN Iand IL

30IIL

EXAMPLE


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EXAMPLE

A balanced delta connected load havingan impedance 20-j15 is connected toa delta connected, positive sequence

generator havingVab= 3300V.Calculate the phase currents of the loadand the line currents.

Given Quantities


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Given Quantities

0330V

87.3625j1520Z

ab

Phase Currents


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Phase Currents

A87.15613.2120II

A13.83-13.2120II

A36.8713.236.8725

0330ZVI

ABCA

ABBC

ABAB

Line Currents


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A87.12686.22120II

A13.311-86.22120II

87.686.22

A30336.8713.2

303II

ac

ab

ABa

Line Currents

BALANCED WYE-DELTASYSTEM


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BALANCED WYE-DELTASYSTEM

EXAMPLE 2


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EXAMPLE 2

A balanced positive sequence Y-connected source withVan=10010Vis connected to a -connected

balanced load (8+j4)per phase.Calculate the phase and line currents.


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THREE PH SE POWER

ME SUREMENT

EXAMPLE 3


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EXAMPLE 3

Determine the total power (P), reactive

power (Q), and complex power (S) at thesource and at the load

EXAMPLE #4


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EXAMPLE #4

A three phase motor can beregarded as a balanced Y-load. Athree phase motor draws 5.6 kW

when the line voltage is 220 Vandthe line current is 18.2 A. Determinethe power factor of the motor

Documents

Lec09 Three Phase