### Transcription

Introduction to Three-phase CircuitsBalanced 3-phase systemsUnbalanced 3-phase systems1

Introduction to 3-phase systemsSingle-phase two-wire system: Single source connected to aload using two-wire systemSingle-phase three-wire system: Two sources connected to twoloads using three-wire systemSources have EQUALmagnitude and are IN PHASE2

Circuit or system in which AC sources operate at the samefrequency but different phases are known as polyphase.Balanced Two-phase three-wire system: Two sources connected to two loadsusing three-wire systemSources have EQUAL frequency butDIFFFERENT phasesTwo Phase System: A generator consists of two coils placed perpendicular to each other The voltage generated by one lags the other by 90 .3

Balanced Three-phase four-wire system: Three sources connected to 3 loads usingfour-wire systemSources have EQUAL frequency butDIFFFERENT phasesThree 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.4

AC Generation Three things must be present in order to produceelectrical current:a) Magnetic fieldb) Conductorc) Relative motionConductor cuts lines of magnetic flux, a voltage isinduced in the conductorDirection and Speed are important

GENERATING A SINGLE PHASESNMotion is parallel to the flux.No voltage is induced.

GENERATING A SINGLE PHASESNMotion is 45 to flux.Induced voltage is 0.707 of maximum.

GENERATING A SINGLE PHASESxNMotion is perpendicular to flux.Induced voltage is maximum.

GENERATING A SINGLE PHASESNMotion is 45 to flux.Induced voltage is 0.707 of maximum.

GENERATING A SINGLE PHASESNMotion is parallel to flux.No voltage is induced.

GENERATING A SINGLE PHASESNNotice current in theconductor has reversed.Motion is 45 to flux.Induced voltage is0.707 of maximum.

GENERATING A SINGLE PHASESNMotion is perpendicular to flux.Induced voltage is maximum.

GENERATING A SINGLE PHASESNMotion is 45 to flux.Induced voltage is 0.707 of maximum.

GENERATING A SINGLE PHASESNMotion is parallel to flux.No voltage is induced.Ready to produce another cycle.

GENERATION OF THREE-PHASE ACSxx Three Voltages will be inducedacross the coils with 120 phasedifferenceN

Practical THREE PHASE GENERATOR The generator consists of a rotating magnet (rotor) surrounded by astationary 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 threecoils and induces voltages in the coils. The induced voltage have equal magnitude but out of phase by120 .

THREE-PHASE WAVEFORMPhase 1120 Phase 2Phase 3120 120 240 Phase 2 lags phase 1 by 120 .Phase 3 lags phase 1 by 240 .Phase 2 leads phase 3 by 120 .Phase 1 leads phase 3 by 240 .

WHY WE STUDY 3 PHASE SYSTEM ? ALL electric power system in the world used 3-phase system toGENERATE, TRANSMIT and DISTRIBUTE One phase, two phase, or three phase ican be taken from three phasesystem rather than generated independently. Instantaneous power is constant (not pulsating).– thus smootherrotation of electrical machines High power motors prefer a steady torque More economical than single phase – less wire for the same powertransfer The amount of wire required for a three phase system is less than requiredfor an equivalent single phase system.18

3-phase systemsGeneration, Transmission and Distribution19

3-phase systemsGeneration, Transmission and Distribution20

Y and connectionsBalanced 3-phase systems can be considered as 3 equal single phasevoltage sources connected either as Y or Delta ( ) to 3 single three loadsconnected as either Y or SOURCE CONNECTIONSLOAD CONNECTIONSY connected sourceY connected load connected source connected loadY-YY- -Y - 21

Balance Three-Phase Sources Two possible configurations:Three-phase voltage sources: (a) Y-connected ; (b) Δ-connected22

Balanced 3-phase systemsLOAD CONNECTIONS connectionY connectionaaZ1ZbZcnbZ2bZ3ZaccBalanced load:Z1 Z2 Z3 Z YZa Z b Zc Z ZY Z 3Unbalanced load: each phase load may not be the same.23

Phase SequenceThe phase sequence is the time order in which the voltages pass throughtheir respective maximum values.aVano Van Vp 0 o Vbn Vp 120vbn (t) 2Vp cos( t 120o )o Vcn Vp 120v cn (t) 2Vp cos( t 120o )nVcnbVbnv an (t) 2Vp cos( t)RMS phasors !c240o120oVanVbnVcn24

Phase SequenceVcn Vp 120oaVan 120onVcnVbnVan Vp 0o120o120obcVbn Vp 120oPhase sequence : Van leads Vbn by 120o and Vbn leads Vcn by 120o This is a known as abc sequence or positive sequence25

Phase SequenceVbn Vp 120oWhat if different phase sequence?o Van Vp 0van (t ) 2V p cos( t )120ov cn (t) 2Vp cos( t 120 ) Vcn Vp 120ooVan Vp 0o120ovbn (t) 2Vp cos( t 120o ) Vbn Vp 120o120oRMS phasors !Vcn Vp 120oPhase sequence : Van leads Vcn by 120o and Vcn leads Vbn by 120o This is a known as acb sequence or negative sequence120oVan240oVcnVbn26

ExampleDetermine the phase sequence of the set of voltages.van 200 cos( t 10 )vbn 200 cos( t 230 )vcn 200 cos( t 110 )Solution:The voltages can be expressed in phasor form asVan (200 / 2 ) 10 VVbn (200 / 2 ) 230 VVcn (200 / 2 ) 110 VWe notice that Van leads Vcn by 120 and Vcn in turn leads Vbn by 120 .Hence, we have an acb sequence.

Balanced 3-phase Y-YIaLine current phase currentAaVanVcn NnIbVbnIa Ib Ic ZYBb IcVp 0oZYPhasevoltagesVcn Vp 120oZYCmeasured between the neutraland any line(line to neutral voltage)Vab Va Vb Va Vb Vn Vn Van Vnb V p 0 o V p 60 oZYVp 120oVbn Vp 120oZYIncVan Vp 0olinecurrents 3V p 30 oVp 120oZY Ia Ib Ic In 0The wire connecting n and N can be removed !Vbc Vbn Vnc 3 Vp 90oVca Vcn Vna 3 Vp 150oline-linevoltagesORLinevoltages28

Balanced 3-phase systemsBalanced Y-Y ConnectionVab Van Vnb Vp 0o Vp 60o 3 Vp 30o29

Balanced 3-phase systemsVab Van Vnb Vp 0o Vp 60oBalanced Y-Y ConnectionVcnVan 3 Vp 30oVbn30

Balanced 3-phase systemsBalanced Y-Y ConnectionVab Van Vnb Vp 0o Vp 60o 3 Vp 30oVanVnb31

Balanced 3-phase systemsBalanced Y-Y ConnectionVab Van Vnb Vp 0o Vp 60o 3 Vp 30VanoVnbVbnVbc Vbn Vnc 3 Vp 90oVnc32

Balanced 3-phase systemsBalanced Y-Y ConnectionVnaVab Van VnbVcn Vp 0o Vp 60o 3 Vp 30VanoVnbVbnVbc Vbn Vnc 3 Vp 90oVncVca Vcn Vna 3 Vp 150o33

Balanced 3-phase systemsBalanced Y-Y ConnectionVcaVab Van Vnb Vp 0o Vp 60oVab30o Vcn30oVan 3 Vp 30oVbnVbc Vbn Vnc30o 3 Vp 90oVbcVca Vcn Vna 3 Vp 150oVL 3 VpwhereVL Vab Vbc Vcaand Vp Van Vbn VcnLine voltage LEADS phase voltage by 30o34

Balanced 3-phase systemsBalanced Y-Y ConnectionFor a balanced Y-Y connection, analysis can be performed using anequivalent per-phase circuit: e.g. for phase A:IaAaVanVcn ZYIn 0NnIbcVbnb IcZYBZYC35

Balanced 3-phase systemsBalanced Y-Y ConnectionFor a balanced Y-Y connection, analysis can be performed using anequivalent per-phase circuit: e.g. for phase A:IaAaVan ZYNnIa VanZYBased on the sequence, the other line currents can beobtained from:Ib Ia 120oIc Ia 120o36

Balanced 3-phase systemsBalanced Y- ConnectionIaaVanVcnA Z nIbcVbnVab 3 Vp 30oBV ABZ Vbn Vp 120oZ I AB Z IBCb IcIAB VABCICAUsing KCL,Vcn Vp 120oIa IAB ICA IAB (1 1 120o ) IAB 3 30oVbc 3 Vp 90oIBC VBCVca 3 Vp 150o VCAVan Vp 0oICA VBCZ VCAZ PhasecurrentsIb IBC IAB IBC (1 1 120o ) IBC 3 30oIc ICA 3 30o37

Balanced 3-phase systemsBalanced Y- ConnectionIcICA30o30oIBCIbIL 3IpIABIa IAB ICA30o IAB (1 1 120o ) IAB 3 30oIaIb IBC IAB IBC (1 1 120o ) IBC 3 30oand Ip IAB IBC ICA owhere IL Ia Ib IcIc ICA 3 3038Phase current LEADS line current by 30o

Balanced 3-phase - Line-line voltage is thesame as phase voltage in - Vab Vp 0oIaaAVcaVabIb cVbcVab VABZ BZ I AB Z IBCb IcIABV ABZ Vbc Vp 120oUsing KCL,CICAVcn Vp 120oIa IAB ICA IAB (1 1 120o ) IAB 3 30oVbc VBCVca VCAIBC ICA VBCZ VCAZ PhasecurrentsIb IBC IABlinecurrents IBC (1 1 120o ) IBC 3 30oIc ICA 3 30o39

Balanced 3-phase systemsBalanced - ConnectionIaaVab Vp 0oAVcaZ Ib cVabVbcb IcBVbc Vp 120oZ I AB Z IBCCICAVcn Vp 120oAlternatively, by transforming the connections to the equivalent Yconnections per phase equivalent circuit analysis can be performed.40

Balanced -Y ConnectionBalanced 3-phase systemsIaAaVcaNIbVbcZY Ia Ib VabZYBb IcLoop1 - Vab Z YIa Z YIb 0Since circuit is balanced, Ib Ia -120oIa VpZY3Vca Vp 120oZYHow to find Ia ?ThereforeVbc Vp 120oZYLoop1 cVabVab Vp 0oC Ia Ib Ia (1 1 ( 120o )) Ia 3 30o 30o41

Balanced -Y ConnectionBalanced 3-phase systemsIaAaVcaNIbVbcVbc Vp 120oZYVab cVab Vp 0ob IcZYBVca Vp 120oZYCHow to find Ia ? (Alternative)Transform the delta source connection to an equivalent Y and thenperform the per phase circuit analysis42

A balanced Y-Y system, showing the source, line and load impedances.Line ImpedanceSource ImpedanceLoad ImpedanceEquivalent Circuit43

Three-phase CircuitsUnbalanced 3-phase systemsPower in 3-phase system44

UNBALANCED DELTA-CONNECTED LOADThe line currents will not be equal nor will they have a 120 phasedifference as was the case with balanced loads.45

UNBALANCED FOUR-WIRE, WYE-CONNECTED LOAD On a four-wire system the neutral conductor will carry a current when the loadis unbalanced The voltage across each of the load impedances remains fixed with the samemagnitude as the line to neutral voltage. The line currents are unequal and do not have a 120 phase difference.46

UNBALANCED THREE-WIRE, WYE-CONNECTED LOAD The common point of the three load impedances is not at thepotential of the neutral and is marked "O" instead of N. The voltages across the three impedances can vary considerablyfrom line to neutral magnitude, as shown by the voltage trianglewhich relates all of the voltages in the circuit. Draw the circuit diagram and select mesh currents as shown in Fig. Write the corresponding matrix equations (Crammer Rule)47

UNBALANCED THREE-WIRE, WYE-CONNECTED LOADNow the voltages across the three impedances are given by the productsof the line currents and the corresponding impedances.48

POWER IN BALANCED THREE-PHASE LOADS Since the phase impedances of balanced wye or delta loads containequal currents, the phase power is one-third of the total power. The voltage across is line voltage The current is phase current. The angle between V & I is the angleon the impedance. The voltage across is phase voltage The current is line current. The angle between V & I is the angleon the impedance.Phase powerPhase powerTotal powerTotal powerFor a balanced Δ-connected loads:For a balanced Y-connected loads:49

POWER IN BALANCED THREE-PHASE LOADS50

INSTANTANEOUS THREE-PHASE POWER Remember:The instantaneous Single-phase power51

INSTANTANEOUS THREE-PHASE POWERThe instantaneous 3-phase powerp 𝑡 𝑉𝐴𝑁 𝐼𝑎 𝑉𝐵𝑁 𝐼𝑏 𝑉𝐶𝑁 𝐼𝐶52

𝑉3𝑝𝑉1𝑝55 3 (𝑙 𝑆3𝑝)2 (𝑙 𝑆1𝑝) 3 (𝑆1𝑝/2)2 (𝑆1𝑝) 34

ALL electric power system in the world used 3-phase system to GENERATE, TRANSMIT and DISTRIBUTE One phase, two phase, or three phase ican be taken from three phase system rather than generated independently. WHY WE STUDY 3 PHASE SYSTEM ? Instantaneous power is constant (not