Threephase Circuits Balanced 3 phase systems Unbalanced 3
Three-phase Circuits Balanced 3 -phase systems Unbalanced 3 -phase systems SKEE 1043 Circuit Theory Dr. Nik Rumzi Nik Idris 1
Balanced 3 -phase systems Single-phase two-wire system: • Single source connected to a load using two-wire system Single-phase three-wire system: • • Two sources connected to two loads using three-wire system Sources have EQUAL magnitude and are IN PHASE 2
Balanced 3 -phase systems Balanced Two-phase three-wire system: • • Two sources connected to two loads using three-wire system Sources have EQUAL frequency but DIFFFERENT phases Balanced Three-phase four-wire system: • • Three sources connected to 3 loads using four-wire system Sources have EQUAL frequency but DIFFFERENT phases 3
Balanced 3 -phase systems WHY THREE PHASE SYSTEM ? • ALL electric power system in the world used 3 -phase system to GENERATE, TRANSMIT and DISTRIBUTE • Instantaneous power is constant – thus smoother rotation of electrical machines • More economical than single phase – less wire for the same power transfer • To pass SKEE 1043 – to be able to graduate ! 4
Balanced 3 -phase systems Generation of 3 -phase voltage: Generator SEE VIDEO 5
Balanced 3 -phase systems Generation, Transmission and Distribution 6
Balanced 3 -phase systems Generation, Transmission and Distribution 7
Balanced 3 -phase systems Y and connections Balanced 3 -phase systems can be considered as 3 equal single phase voltage sources connected either as Y or Delta ( ) to 3 single three loads connected as either Y or SOURCE CONNECTIONS LOAD CONNECTIONS Y connected source Y connected load connected source connected load Y-Y Y- -Y - 8
Balanced 3 -phase systems SOURCE CONNECTIONS Source : Y connection a Van + + n Vcn + b Vbn RMS phasors ! c 240 o 120 o Van Vbn Vcn 9
Balanced 3 -phase systems SOURCE CONNECTIONS Source : Y connection a Van 120 o + + n Vcn + Vbn b 120 o c Phase sequence : Van leads Vbn by 120 o and Vbn leads Vcn by 120 o àThis is a known as abc sequence or positive sequence 10
Balanced 3 -phase systems SOURCE CONNECTIONS Source : Y connection a Van + + n Vcn + b Vbn RMS phasors ! c 120 o Van 240 o Vcn Vbn 11
Balanced 3 -phase systems SOURCE CONNECTIONS Source : Y connection a Van 120 o + + n Vcn + Vbn b 120 o c Phase sequence : Van leads Vcn by 120 o and Vcn leads Vbn by 120 o àThis is a known as acb sequence or negative sequence 12
Balanced 3 -phase systems SOURCE CONNECTIONS Source : connection Vab + Vca + b Vbc 120 o Vab RMS phasors ! c 240 o Vbc Vca 13
Balanced 3 -phase systems LOAD CONNECTIONS Y connection a a Z 1 n Z 2 b b Z 3 c c Zb Zc Za Balanced load: Z 1 = Z 2 = Z 3 = Z Y Za = Z b = Z c = Z Unbalanced load: each phase load may not be the same. 14
Balanced 3 -phase systems Ia Van c + + n Vbn N Ib b Ic Phase voltages ZY In Vcn A a + Balanced Y-Y Connection B line currents The wire connecting n and N can be removed ! ZY ZY C line-line voltages OR Line voltages 15
Balanced 3 -phase systems Balanced Y-Y Connection 16
Balanced 3 -phase systems Balanced Y-Y Connection 17
Balanced 3 -phase systems Balanced Y-Y Connection 18
Balanced 3 -phase systems Balanced Y-Y Connection 19
Balanced 3 -phase systems Balanced Y-Y Connection 20
Balanced 3 -phase systems where Balanced Y-Y Connection and Line voltage LEADS phase voltage by 30 o 21
Balanced 3 -phase systems Balanced Y-Y Connection For a balanced Y-Y connection, analysis can be performed using an equivalent per-phase circuit: e. g. for phase A: Van + A ZY In=0 + c a Vcn Ia Vbn N Ib b Ic B ZY ZY C 22
Balanced 3 -phase systems Balanced Y-Y Connection For a balanced Y-Y connection, analysis can be performed using an equivalent per-phase circuit: e. g. for phase A: Van a + n Ia A ZY N Based on the sequence, the other line currents can be obtained from: 23
Balanced 3 -phase systems Balanced Y- Connection Ia Van Z + n + c A + Vcn a Vbn Ib B Z Z C b Ic Using KCL, Phase currents 24
Balanced 3 -phase systems where Balanced Y- Connection and Phase current LEADS line current by 30 o 25
Balanced 3 -phase systems Balanced - Connection Ia a A + + + c Vca Vab Z Z Ib Vbc B Z b Ic C Using KCL, Phase currents line currents 26
Balanced 3 -phase systems Balanced - Connection Ia a A + + + c Vca Vab Z Z Ib Vbc b Ic B Z C Alternatively, by transforming the connections to the equivalent Y connections per phase equivalent circuit analysis can be performed. 27
Balanced 3 -phase systems Balanced -Y Connection Ia A a + + + c Vca Vab ZY Loop 1 N Ib Vbc b Ic B ZY ZY C How to find Ia ? Loop 1 Since circuit is balanced, Ib = Ia -120 o Therefore 28
Balanced 3 -phase systems Balanced -Y Connection Ia A a + + + c Vca ZY Vab N Ib Vbc b Ic B ZY ZY C How to find Ia ? (Alternative) Transform the delta source connection to an equivalent Y and then perform the per phase circuit analysis 29
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