4 EDS Introduction to 3 Phase PDF

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Summary

Intro tutorial to 3 Phase questions...

Description

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4 Introduction+to+Three+Phase+Systems+ !

1 Introduction&to&Power&Systems

What!is!a!three!phase!system?! Why!do!we!use!one?!

2.1 Complex& Numbers

How!do!we!make!three!phase!connections?!

2.2 DC&Circuit& Theory

2.3 Sinusoidal& Waveforms

Are!there!any!benefits?! 3.1 AC&Circuit&Theory

! All!these!are!questions!we!hope!to!answer!when!we!give!you!a!quick!tour! of!three!phase!systems!and!connections!in!this!introduction.!At!the!end! we!hope!you!are!more!familiar!with!the!‘Star’!and!‘Delta’!terms!that!you! may!have!met!in!some!of!your!studies.!

3.2 AC&Power 4 Intro&to&3&Phase&Systems

You!are!Here!

!

5 Power&in&3&Phase&Systems

! Learning Objectives • •

To!understand!what!is!3-phase!transmission!and!why!it!is!used! To!be!familiar!with!delta!and!star!connections!and!to!be!able!to! complete!simple!analysis!involving!different!combinations!of! star/delta!connections.!

6 Introduction&to&Transformers 7 Transformers:&Circuit&Analysis 8 Safety&and&Earthing 9&&&10 Protective&Devices&and& Protective&Systems& 11&&&12 LV&Cable&Sizing

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!1! !

2.4 Electr magnet

4.1 What+is+3-Phase+Transmission?+ Three!Phase!transmission!is!the!transmission!of!3!AC!voltages!with!120o! phase!separation.!The!picture!shows!the!three!phase!lines.!Traditional! colours!in!the!UK!for!three!phase!were!red,!yellow,!blue!for!the!Line!1,2,3! and!black!for!the!neutral!line.!These!are!now!standardised!to!the!IEC! ruling!in!Europe!to!brown,!black,!grey!with!blue!neutral.!(You!will!see! many!three!phase!plots!with!red/yellow/blue!waveforms.)!Click!on!the! link!for!an!example!of!the!three!phase!voltage!waveforms.! Follow!the!link!to!a!page!which!shows!the!differing!colours!dependent!on! region/country.!! “Wiring!Color!Codes!Infographic”! https://www.allaboutcircuits.com/textbook/reference/chpt2/wiring-color-codes-infographic/! Question:!If!the!frequency!is!50!Hz,!what!time!interval!does!120o!phase! separation!correspond!to?! Answer:!A!frequency!of!50!Hz!corresponds!to!a!period!of!0.02!s.!120o! is!a!third!of!one!cycle!(360o)!so!the!phase!separation!is!equivalent!to! the!wave!forms!being!0.02/3!=!6.67!ms!apart.!! The!IEC!sets!standards!that!are!often!used!around!the!world.!The! following!link!is!to!a!document!that!mentions!the!low!voltage!standards! applied!in!many!worldwide!countries.!! !

International!Guide:!2006! http://www.legrand.com/files/fck/File/pdf/Guide-International.pdf!

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!2! !

4.2 Why+do+we+transmit+at+3-phase?+

The!three!inductor!coils!represent!the!three!phase!generator! which!is!producing!power!on!the!three!phase!lines.!The!three! phase!motor!is!connected!to!the!three!phases!(and!neutral)!and! the!household!supply!is!connected!to!a!single!phase!(plus! neutral).!

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For!the!same!amount!of!power,!a!three!phase!(three!wire)!circuit! used!less!conductor!material!(copper!or!aluminium)!that!a!single! phase!system.!Therefore!it!is!an!efficient!way!of!transmitting!high! power.! ! Industrial!Loads!are!usually!three!phase.! o !The!size!of!three!phase!motors!are!smaller!than!a!single! phase!motor!with!the!same!rating.!Three!phase!motors! are!‘self-starting’:!a!single!phase!motor!requires! additional!circuitry.! o Single!phase!motors!are!susceptible!to!vibration.!In!three! phase!motors!the!power!is!generally!uniform!and! vibrations!reduced.!!! o DC!rectification!has!less!ripple!with!a!three!phase!system:! the!diagram!shows!three!voltage!and!a!rectified!DC! waveform.! !

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!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!3! !

4.3 How+do+we+Generate+AC+electricity?!+ Watch!the!following!video!which!shows!how!we!can!produce!a!single! phase!AC!voltage.!Then!look!at!the!diagrams!which!show!three!phase! coils,!and!answer!the!questions.!

Simple* generator *–*1*turn!

“How!an!AC!generator!produces!Electricity”!~!4!mins.! https://www.youtube.com/watch?v=MW1YUy3Yqpc! * Single-coil*Generator*diagram:*

We*take*the* direction*of* induced*voltage* as*going*from*! Start*->*finish!

The!simple!generator!with!one!turn!is!shown!opposite.! Can!you!identify!the!following:! • •

•

The!Permanent!Magnets?!Where!would!the!flux!lines!be?! From!your!revision!of!electromagnetism,!at!what!angle!should!a! coil!be!to!get!! o No!induced!voltage! o Maximum!induced!voltage! Why!does!the!induced!voltage!alternate!in!sign?!

Click!on!the!link!for!the!Answer.!

Answer:* For!no!induced!voltage!the!coil!sides!would!have!to!be!parallel!to!the! field!flux!lines!(which!they!aren’t),!or!the!coil!sides!would!have!to!be! stationary!so!that!they!would!not!cut!any!field!flux!lines.!! For!maximum!induced!voltage,!the!coil!should!have!the!highest!rate! of!change!of!flux.!

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The!induced!voltage!changes!in!sign,!since!as!the!coil!rotates,!the! direction!of!current!reverses!each!time!the!coil!sides!are!in!line!with! the!axis!drawn.!

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! !Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!4!

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4.4 How+do+we+Generate+3-+Phase+AC+Electricity?!+ Three-Phase*Coils*Diagram.* Consider!the!simple!generator!shown!opposite.!It!has!a!permanent! magnet!and!three!coils!(red,!yellow,!blue).!The!coils!are!physically!fixed!at! 120o!with!respect!to!each!other.! • •

Find!the!flux!lines!on!the!diagram.! From!your!revision!of!electromagnetism,!at!what!angle!should! the!coil!be!to!get!! o No!induced!voltage! o Maximum!induced!voltage!

Click!on!the!link!for!the!Answer.! The!following!video!link!provides!an!example!of!a!3-phase!!generator.!It! notes!that,!as!in!the!previous!example,!we!can!create!an!emf!by! revolving!a!coil!in!a!magnetic!field,!we!can!also!revolve!a!magnetic!field! around!three!stationary!coils!to!provide!three!phase!AC!currents.!

Answer*

“How!does!an!Alternator!work?”! https://www.youtube.com/watch?v=tiKH48EMgKE!

Highest*rate*of* change*of*flux* (flux*lines*cut)* max*voltage* induced*

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No*rate*of*change*of* flux*–*no*voltage*in* coil*

Single!Phase!Generator!

4.5 Three-Phase+AC+Generation+Summary+ The!single!coil!generator!gave!us!the!principle!of!how!we!could!generate! electricity!in!one!coil.!!The!three!phase!discussion!showed!us!how!we! could!generate!electricity!in!the!three!coils.! The!waveforms!below!show!us!the!generated!voltage!in!the!red!(R!),! yellow!(Y)!and!blue!(B)!coils.!! o

o o

Can!you!see!where!the!blue!phase!line!(dotted)!crosses!0.!How!many! degrees!on!the!θ!axis!before!the!red!line!(solid)!crosses!0?!And,!from! there,!how!many!degrees!before!the!yellow!line!(dashed)!crosses!0?! Did!you!find!that!the!three!phases!are!120 o!apart?!If!not,!go!back!and! look!closely.! Voltage!distance!between!a!phase!and!the!‘0’,!or!neutral!is!call!the! phase!voltage,!Vph,!!or!LN!(Line-Neutral)!voltage,!VLN.! The!voltage!distance!between!each!phase!(shown!as!L-M!here)!is!the! ‘line-line’!voltage,!VLL.!!

Three-Phase!Generator!

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!6! !

4.6 3-Phase+Power+with+Single+Phases+ We!can!now!connect!the!generator!coils!to!our!three!loads!with!power! transmission!lines.! The!diagram!shows!each!phase!coil!connected!to!a!load.!! This!system!would!work!fine,!but!can*we*save*money!by!reducing!the! number!of!conductors?!! ! ! !

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!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!7! !

4.7 3-Phase+Power+Transmission+ To!save!money,!Line!2!and!3!can!be!joined,!as!can!line!4!and!5!and!1!and! 6.! Check!in!the!right!hand!diagram!that!you!can!see!the!connections!we! have!made.!! !!

Problem?*Will*this*give*a*short*circuit?* Let’s!apply!Kirchoff’s!Voltage!Law!and!find!out:!

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!8! !

Three-Phase!Transmission!Diagram!

4.8 Is+There+a+Short+Circuit+Problem?++ ! Problem?*Will*this*give*a*short*circuit?* ! We!could!demonstrate!this!using!Kirchoff’s!Voltage!Law:! ! Open!up!a!point!in!the!loop,!as!shown!in!the!Three-Phase! ! Transmission!Diagram,!and!calculate!the!potential!difference,!ΔV,! around!the!loop.! Δ!V!=!eR∠00!+!eY∠1200!+!eB∠2400!!

!

Δ!V!=!0! Due!to!the!phase!angles,!the!voltage!round!the!loop!at!any!given! instant!is!zero.!This!is!shown!in!the!phasor!diagram!below.! Since!there!is!no!Potential!difference,!there!will!be!no!circulating! current.!

eY ! 0

120 !

eY !

eB !

eR ! eB !

eR !

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!9! !

4.9 Delta+(Δ)+Connection+ The!previous!3-phase!connection!is!usually!drawn!as!shown.!! It!is!referred!to!as!a!DELTA*!connection,!from!the!Greek!capital!letter! Delta,!Δ.!It!is!also!known!as!a!mesh!connection.! ! Look!at!the!connections!in!the!top!and!lower!diagram.!Can!you!see!any! differences?.......! ! In!the!Δ!connection,!R!is!connected!to!Y1!instead!of!B1.!This!is!because!we! have!reversed!the!connections!of!this!phase!so!that!the!voltages!are! connected!so!that!they!point!round!the!loop.!Check!this!is!the!Δ!diagram.! ! ! ! ! ! !

!

Δ

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!10! !

Three!Single!Phase!Transmission!

*

Four!Wire!Star!Connection!

4.10 Alternative+3-phase+Connections+ ! Can!we!combine!the!lines!from!the!original!3!single!phase!transmission!is! another!way?! Yes,!Connect!lines!2,4!and!6,!to!a!single!neutral!conductor.!!This!will! reduce!the!transmission!lines!from!6!lines!to!4!lines.!! This!is!called!a!Four!Wire!start!connection.!!Find!the!following!in!the! diagram:! o o o o

The!neutral!line.!! Each!load!connected!to!a!phase!line!and!the!neutral!line.! The!emf!in!each!phase!has!the!same!polarity,!the!phase!currents! will!also!go!in!the!same!direction.! !The!return!path,!for!each!loop!is!through!the!neutral.!Therefore! ineutral!=!iR!+!iY!+!iB!

This!diagram!is!more!commonly!drawn!is!a!star!shape!as!shown!on! the!next!page.! ! !

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!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!11! !

4.11 Star+Connected+3-phase+Windings+ ! Comparison:!Click!on!the!link!to!show!the!diagram! from!the!previous!page:!Can!you!see!on!the!STAR! diagram!the!three!individual!phases!and!the!neutral! line?!Can!you!check!that!the!single!phase!loads!are! connected!in!both!cases!between!a!phase!line!and! the!neutral?!

N

R1 Industrial!3-phase!motors!would!be! connected here.

The!Star!Connection!is!also!known!as!a!‘Y’!,! pronounced!‘Wye’!connection,!since!by!rotating!the! star!shape!shown,!it!can!resemble!the!letter!Y.!

Four!Wire!Star!Connection!

Consumer,!single-phase!loads!would!be! connected!here:!lamps,!heaters,!etc.!!

Note! The!Star!Connection!is!also!known!as!a!‘Y’,! pronounced!‘Wye’,!connection,!since!by!rotating! the!star!shape!shown,!the!three!phases!can!be! drawn!to!resemble!the!letter!Y.! !Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!12! !

4-wire!Star!Connected!System!!

4.12 Star+Connected+Balanced+Load+ What!if!the!loads!on!the!original!4!wire!system!are! balanced?!That!is,!L1!=!L2!=!L3?!

N!

!

R1!

Currents!in!Balanced!System! !

iY ! 0

120 ! iR ! iB !

iY !

iB !

! ! !

iR !

! !

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3-wire!Star!Connected!System!with!Balanced!Load! !

Therefore,!we!can!remove!the!neutral!line,!and!have!only!3! transmission!lines!(A!3-wire!star!connected!system.)!

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!13! !

Diagram!2!

Diagram!1! R!

4.13 Star-Connected+System:+Voltages+ ! !

What is the relationship between line and

ENR!

Line voltage

phase voltage? (Star connected System)!

! ! Diagram*1!shows!the!phase!voltages!as!the!voltage!across!each! phase!winding!(from!the!Neutral!point).! ! The!line!voltage!is!the!voltage!between!the!lines.!! ! Diagram*2*shows!a!phasor!diagram!of!the!three!phase!voltages! ! with!voltage!ENR!leading!ENY!by!120o!and!ENB!lagging!by!a!further! 120o.!!The!phase!voltages!represent!the!voltages!from!Neutral! across!the!phase!winding.!! The!phasor!in!purple!shows!the!line!voltage!across!the!two! lines!Y!and!R,!E YNR.!! !

EBNY!=!-!EBN!+!ENY!

N! 120

Phase voltage

o!

ENY! 120

o!

30

ENB!

B! R! Diagram!3! ENR!

Since!the!magnitudes!of!the!phase!voltages!are!equal!,!the! triangle!BNY!is!an!isosceles!triangle!and!therefore!the!angle! NYB!is!30o.!!

N!

Diagram*3*shows!that!we!have!formed!two!right!angled! triangles!from!triangle!BNY.!

120o!

60o!

30o!

ENY! Y! 30o! EBNY!

The!length!of!EBNY!will!be!twice!the!length!of!the!dashed!line.!By! trigonometry! !

EBNY!=!2*!ENY!*!cos!(30 o)!=!2*!ENY!*!(√!3/2)!=!√!3!*!ENY!

THEREFORE,!FOR!A!STAR-!CONNECTED!SYSTEM: ! !

ENB! B!

VLL!=!√!3!*!VPh! !Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!14!

!

o!

Y! EBNY!

4.14 Star-Connected+System:+Currents+

+ Diagram!1!

What is the relationship between line and phase current? (Star connected System)!

Diagram*1!shows!that!for!a!star!connected!system,!the!phase! and!line!currents!are!the!same.! !

!

!

THEREFORE,!FOR!A!STAR-!CONNECTED!SYSTEM: ! !

Iph IL Phase current = Line current

IL!=!Iph!

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!15! !

4.15 Delta-Connected+System:+Voltages+

+

What is the relationship between line and phase Voltage? (Delta connected System)!

V ,V LL

ph

Diagram*1!shows!that!for!a!delta!connected!system,!the!phase! and!line!voltages!are!the!same.!The!voltage!across!each!phase! winding!is!the!line-line!voltage.!! !

!

!

V ,V LL

V ,V LL

ph

ph

THEREFORE,!FOR!A!Δ!-!CONNECTED!SYSTEM: ! !

VLL!=!Vph!

!

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!16! !

4.16 Delta-Connected+Systems:+Currents+

Diagram!1!

! !

Diagram!2! What is the relationship between line and

IR!

phase current? (Delta connected System)!

! -I3! ! Diagram*1!shows!the!line!currents!and!phase!currents.!They! are!not!the!same.!At!any!instant!in!time,!the!RMS!currents!are! ! assumed!to!flow!round!the!loop!in!the!indicated!direction.! ! Line!currents!flow!from!the!generator!to!the!balanced!load.!! !

I2 !

I1 ! N! 120

30

o!

IY!

o!

By!Kirchoff’s!Laws,!the!current!in!phase!R!is!given!as: !

120o!

!

I3 !

IR!=!I1!–!I3!

EBNY!

However,!we!need!to!add!them!as!phasors.!! Diagram*2!shows!the!phasor!diagram!with!the!line!and!phase! currents!indicated.!We!have!noted!that!IR!is!the!summation!of! I1!+!(-I3).!!The!triangle!formed!by!the!sides,!IR,!I1!and!–I3!form!an! isosceles!triangle.!

IB!

Line currents

Phase currents Diagram!3!

Diagram*3*!indicates!that!the!triangle!formed!in!Diagram!2!can! be!divided!into!two!right-angled!triangles!and!that!the!! magnitude!of!IR!can!be!calculated!as!twice!the!length!of!one! side!of!the!right-angled!triangle.!This!is!similar!to!how!we! calculated!a!length!for!start!connected!voltages.!! By!trigonometry! !

IR! -I3!

N!

IR!=!2*!I1!*!cos!(30 o)!=!2*!I1!*!(√!3/2)!=!√!3!*!I1!

120

THEREFORE,!FOR!A!DELTA-!CONNECTED!SYSTEM:! !

IL!=!√!3!*!IPh!

I2 !

I1 ! 30

o!

IY!

o!

120o!

EBNY!

I3 ! !Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!17!

! IB!

4.17 Summary:+Delta+and+Star+Connections+ !

!

Delta-connected!system!

VLL = Vph IL = √3 x IPh

Star-connected!system!

VLL = √3 x Vph IL = Iph

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!18! !

4.18 What+are+the+requirements+for+a+balanced+system?+ For!a!3-phase!system!to!be!balanced:! • • •

All!3!sources!(in!this!case!the!three!phase!generators)!are! represented!by!a!set!of!balanced!3-phase!variables! All!three!loads,!L,!!are!3-phase!with!equal!impedances! All!three!line!impedances,!Zline,!!are!equal.!

The!advantage!of!having!a!balanced!circuit!is!that!we!can!simplify!the! circuit!analysis.!We!can!find!the!voltages!currents!for!one!phase!and!use! simple!equations!to!solve!for!the!remaining!phases.!For!example,!we!will! find!that!the!power!dissipated!in!all!the!balanced!loads!will!be!three!times! the!power!dissipated!in!one!load.!!!

ZLine!

ZLine!

If!the!circuit!is!not!balanced,!all!three!phases!should!be!considered! separately.!

+

+

ZLine!

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!19! !

4.20 Example:+Unbalanced+Load+#1+ Worked Example In!a!3-phase!Star!connected!4!wire!system,!the!line!voltage!is! 400V,!!and!3!resistive!loads!are!connected!between!the!line! conductors!and!the!neutral.!!! (a) Calculate!the!magnitude!of!currents!on!each!line!! (b) Sketch!a!phasor!diagram!for!the!line!currents.! (c) What!should!the!total!current!in!the!neutral!be!for!a! balanced!load?!Calculate!the!total!current!in!the!neutral! and!comment!on!your!result.! ! !

Solution Is!the!system!balanced?!---!NO.!If!the!system!were!balanced!the! three!loads!would!have!the!same!impedance!and!produce!the! same!power.!!Therefore!the!current!in!each!line!may!be! different.!The!three!loads!are!connected!between!each!line!(R,Y! or!B)!and!Neutral.!

E.g. houses

(a) Magnitude*of*Line*Currents:*I*=*P/V* What*is*the*phase*voltage?*Since!this!is!a!star-connected! system,!Vph!=!VL!/!√!3! Vph!=!400/√!3!=!230!V.! Calculate!the!magnitude!of!each!line!current:! IR!=!PR!/!VRN!=!10!000/!230!=!43.5!A!! IY!=!PY!/!VYN!=!!8!000/!230!=!34.8!A ! IB!=!PB!/!VBN!=!5!000/!230!=!21.7!A! !

!Electrical!Distribution!Systems:!Intro!to!Three!Phase!Systems!page!20!

4.21 Example:+Unbalanced+Load+#2+ Worked Example In!a!3-phase!Star!connected!4!wire!system,!the!line!voltage!is! 400V,!!and!3!resistive!loads!are!connected!between!the!line! conductors!and!the!neutral.!!! (b) Sketch!a!phasor!diagram!for!the!line!currents.! ! ! Solution The!currents!are!phasors!and!set!120o!apart.!We!can!take!any! point!as!reference!and!form!the!resultant!phasors.!

IB!=!21.7!∠!120o!

Resulting!Phasor!Diagram!

o

30 !

For!example,!we!could!take!IR!=!43.5!∠!0o.!!Then!! IY!=!34.8!∠!-120o!

IR!=!43.5...