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BASIC ELECTRICAL ENGINEERING ELE 290

3.0 THREE PHASE SYSTEM

Three phase colour codes

Wiring connection or a three phase s!ste"

The trans"ission and distri#ution o electric po$er to residences% co""ercialesta#lish"ents and industrial are "ost acco"plished "ostl! #! "eans o threephase net$or&ing consisting o trans or"ers% trans"ission and distri#ution lines%and associated protecti'e s!ste"s% such as rela!s% circuit #rea&ers% uses% etc( In

act% "ost o the #alanced three phases s!ste" uni'ersall! use three phases!ste"s( In a #alanced three phase s!ste"% there are three sinusoidal 'oltagesources o e)ual a"plitude and e)ual re)uenc! o 'ariation #ut out o phase$ith each other #! *20+ or ,- electrical(

Three phase po$er s!ste" are "ore e icient and ro#ust and possess operationalad'antages o'er single phase s!ste"s( This chapter $ill discuss a#out./

* T$o "ethods o three phase connection(

2 Relationship #et$een phase and line currents and 'oltages(

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BASIC ELECTRICAL ENGINEERING ELE 290

3 The "ethods o connection or "easuring the po$er in three phases!ste"(

Three phase s!ste" connection can #e di'ided into 2/groups $hich are./*( Star4$!e connection

2( 5elta46 connection

Both o the connection stated a#o'e can #e in #alanced or un#alancedconnection(

3.0.1 THE PHASE SEQUENCE

The phase se)uence is de ined as the se)uence or the order in $hich the phase'oltages attain their "a7i"u" 'alues( The phase se)uence is re erred to as RE5/

8ELL W/BL:E or positi'e se)uence $hen the 'oltage RE5 leads that o phase 8ELL W and the 'oltage 8ELL W leads the 'oltage o phase BL:E( In this topic%onl! positi'e or RE5/8ELL W/BL:E se)uence is co'ered(

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BASIC ELECTRICAL ENGINEERING ELE 290

3.0.2 STAR/WYE connection (Balance !

Sche"atic diagra" or W8E/connection ;hase 'oltagephasor diagra"

It can #e seen that ro" the phasor diagra" or phase 'oltage that./

a

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BASIC ELECTRICAL ENGINEERING ELE 290

c

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3.0.3 "elta/# connection (Balance !

Sche"atic diagra" or 6/connection

=ro" the sche"atic diagra" or delta connected% it can #e seen that the line'oltage and phase 'oltage is e)ual.

* 8ello$ ? neutral

2

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3.1 P$WER %N THREE PHASE SYSTEM

The calculation or po$er in three phase s!ste" can #e used or 8 > connectionand or 6 / connection( In other $ords% it is the sa"e e)uation that can #e used

or #oth connections(

i Real po$er W

The real po$er deli'ered to each phase is.

Where is the phase angle #et$een I ; ASE and < ; ASE

The total three phase po$er to the #alanced load is.

ii Reacti'e po$er

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Tutorials

1. The three-phase balanced system as shown in the Figure (1) has per-phase load ofZY = (4+j1 ! " and the supply line #olta$e is %& = 41' )*% (rms! and the phasese uence is a-b-c. ,etermine the followin$ -

i! hase #olta$es (%an/ %bn/ %cn!

ii! &ine current (0 a/ 02b/ 03c!

iii! Total three phase acti#e power/ reacti#e power and apparent power.

i#! ,raw the phasor dia$ram showin$ the relationship between currents and#olta$es.

Figure (1)

. The three-phase -connected $enerator represented in Figure Q2 is dri#in$ abalanced load such that each phase current is 1) in ma$nitude. 5hen 0 6a =1) 7) o / determine the followin$

i! The polar e8pression for the other phase currentsii! The polar e8pression for each of the line currents

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Figure Q2

7. Three similar coils/ each which has impedance ) + j' are connected in three-phasesystem 41' %/ ')9: supply. ,raw the circuit dia$ram and calculate the followin$

when connected in star.

i! 0mpedance in each phase

ii! ower factor of the coil

iii! hase current

i#! &ine current

#! Total power absorbed by the coil.

4. balanced three phase system as shown in Figure Q4 / maintained at constant#olta$e and fre uency is to supply a three- phase load/ with three sin$le-phaseimpedance. 0f Vab = 44) 7)* %/ find

i! The load phase currents I AB / IBC / and ICA .ii! The real power/ reacti#e power/ apparent power and the power factor of the

load.

Figure Q4

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'. ,raw the followin$ connection in three phase balanced system with all parametersbein$ labelled

i! 5ye-,eltaii! 5ye-5ye

;. +j4! per phase.

i! 3alculate the phase and line currents.ii! 3alculate the total real/ reacti#e/ comple8 and apparent power at the source side.

>. 7 phase/ wye connected balanced load with a impedance of 7 + j;" per phase isconnected to a wye connected source ha#in$ a line #olta$e of 44)%. ,raw theconnection between the source and the load. 3alculate -

i! %olta$e phases for each phase

ii! ?a$nitude of line current

iii! hase current for each phase

i#! @eal power/ reacti#e power and the apparent power for the 7 phase system

,raw the phasor dia$ram for the phase components (%olta$e phase and current phase!

A. 7 phase source is connected in parallel with a 7 phase loads consistin$ of -

7 phase motor with ratin$ of 7)B% at ).>'p.f. la$$in$

7 phase weldin$ machine with ratin$ of )B5 at ).A)p.f. leadin$

7 phase chiller unit with ratin$ of 1)B%ars at ).A'p.f. leadin$

,raw the dia$ram representin$ the source and load connection. ,etermine -

i! The real power/ reacti#e power and apparent power for each load

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ii! The total apparent power for the o#erall load.

1).

Figure Q11

Cor the three phase system in Figure Q11 abo#e/ find

i! The phase #olta$e for each phase.ii! The ma$nitude of line currents.iii! The total real and reacti#e power of the system.