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EEE3233

POWER SYSTEM

CHAPTER 3:CHAPTER 3:3-Phase System and Power3-Phase System and Power

ConceptConcept

Noorlina MohdNoorlina Mohd

ZainuddinZainuddin

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IntroductionIntroduction

q The generation, transmission anddistribution of electric power isaccomplished by means of

three-phase circuit.qAt the generating station, three

sinusoidal voltage have equal

magnitude and an equal 1200

-phase difference between anytwo phase.

q This is called a balanced source.

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qPositive phase sequence when thevoltages reaches their peak value in

the sequential ABCqNegative phase sequence when the

phase is order is ACB.

ECn

EBn

EAn

EAn

ECn

EBn

Positive or ABC phase

sequence

Negative or ACB phase

sequence

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Y-Connected Load Y-Connected Load

- -A Y connecter generator supplying a Y.connected load

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Y-Connected Load (cont.) Y-Connected Load (cont.)

§ Assume a positive sequence to find therelationship between the line voltage(line-to-line voltage) and phase voltage

(line-to-neutral voltage).§ Line –to-neutral voltage of the phase ischosen as a reference.

|Vp|= magnitude of phase voltage

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Y-Connected Load (cont.) Y-Connected Load (cont.)

§ The line voltages at the load terminals interms of the phase voltage are found by

application of Kirchhoff’s voltage law.

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§ - -C o m p a riso n o f th e se lin e to lin e vo lta g e s w ith th e

- -lin e to n e u tra l vo lta g e s o f le a d s to th e fo llo w in g

:co n clu sio n

- -In b a la n ced th re e p h a se Y con n e cte d

- , - -syste m w ith p o sitiv e se q u e n ce so u rce th e lin e to

√ - -lin e vo lta g e a re 3 tim e s th e lin e to n e u tra l

°. ;vo ltag e s an d le ad b y 30 Th a t is

V ab = √ 3V an + °30

Y-Connected Load (cont.) Y-Connected Load (cont.)

V bc = √ 3V bn + °30V ca = √ 3V cn + °30

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§ T h e re la tio n sh ip b e tw e e n th e lin e vo lta g e a n d p h a se vo lta g e :is sh o w n a s b e lo w

Y-Connected Load (cont.) Y-Connected Load (cont.)

Phasor diagram showing phase and linevoltages

Vab

Vbc

Vca

Van

Vbn

Vcn

Voltages Triangle

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§ RMS value of any of the line voltages is

denoted by VL, then one of the importantcharacteristic of the Y-connected tree-phaseload may be expressed as

Y-Connected Load (cont.) Y-Connected Load (cont.)

§ - -T h re e p h a se cu rre n t a lso p o ssess th re e p h a se sym m e try a n d a re g ive n b y

IL = IP

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§A balanced ∆-connected load (withequal phase impedances) is shown in

below:

∆ ∆-Connected Loads-Connected Loads

§ Lin e v o lta g e a re th e sa m e a s p h a se

.vo lta g e s

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§ The phase current Iab

is chosen as reference

∆ ∆-Connected Loads (cont.)-Connected Loads (cont.)

§ T h e re la tio n sh ip b e tw e e n p h a se a n d lin e

cu rre n ts ca n b e o b ta in e d b y a p p ly in g

’ .K irch h o ff s cu rre n t la w a t th e co rn e r o f ∆

I p = magnitude of

phase current

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§ The RMS of any of the line currents andphase is denoted by IL

∆ ∆-Connected Loads (cont.)-Connected Loads (cont.)

§ √ T h e m a g n itu d e o f lin e cu rre n t is 3 tim e s th e

,m a g n itu d e o f th e p h a se cu rre n t a n d th e lin e

°.cu rre n ts la g s o f p h a se cu rre n ts b y 3 0

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§ The relationship between the line currents and phase currents is showing

.in phase diagram

∆ ∆-Connected Loads (cont.)-Connected Loads (cont.)

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∆ -Y Transformation

§ ,Fo r a n a lyzin g n e tw o rk p ro b le m s it is-con ve n ie n t to re p la ce th e ∆ con n e cte d

-circu it w ith a n e q u iv a le n t Y co n n e cte d

.circu it

§ -C o n sid e r th e Y co n n e cte d circu it o f Z Y Ω /phase which isequivalent to a balanced

-co n n e cte d circu it o f Z ∆ Ω / .phase

∆ -connection -Y co n n e ctio n

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∆ - ( .)Y Transformation cont

§ -For ∆ co n n e cte d circu it

( )1

§ ,Fro m th e p h a sor d ia g ra m th e re la tio n sh ip

- -b e tw e e n b a la n ce d p h a se a n d lin e to lin e

;v o lta g e( )2

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∆ - ( .)Y Transformation cont

§ .( ) .( ),S u b stitu tin g eq 2 in to eq 1 w e g et

( )3

o r

( )4

§ - ,For Y co n n e cte d circu it w e h a ve

( )5

§ .( ) .( ),S u b stitu tin g e q 4 in to e q 5 w e fin d th a t

( )6