11_Three Phase Circuits_2_2564

Polyphase Circuits 1 รศ. ดร. ศราวุธ ชัยมลู MetaRadiator

Key Concepts Electric Circuits KKU o Single-Phase and Poly-Phase Power Systems o Three-Phase Sources o Line Versus Phase Voltage and Line Versus Phase Current o Y-Connected and  -Connected Networks o Balanced Loads o Per-Phase Analysis o Power Measurement in Three-Phase Systems MetaRadiator 2

Single- and Two-phase systems Electric Circuits KKU Single-phase two-wire type Single-phase three-wire type MetaRadiator Two-phase three-wire system 3

Three-Phase Circuits Electric Circuits A three-phase circuit generates, distributes, and uses energy in the form of three voltages equal in KKU magnitude and symmetric in phase. (1)a three-phase source (2) a transmission line (3) a three-phase load Source Transmission line Load MetaRadiator a single-phase system a three-phase system 4

Double-Subscript Notation Electric Circuits KKU By definition, the voltage of point a with respect to point b is Vab. Vab Vad=Vab+Vbc +Vcd =Vab+Vcd =Vax+Vxd MetaRadiator 5

Balanced Three-phase Voltage Sources Electric Circuits (Two common methods) KKU a, b and c are called the line terminals. -connected source (3 wires) delta-connected Y-connected source (4 wires) wye-connected MetaRadiator สว่ นหยดุ นิง่ (stator) ส่วนนจี้ ะไมม่ ีการ ส่วนหมุน (rotor) ส่วนนีจ้ ะเคลอื่ นท่ี 6 เคล่ือนที่ และมักจะเปน็ ส่วนภายนอกของ ไดเ้ ป็นอิสระและมักจะอยูภ่ ายใน เคร่ืองจกั รกล เปน็ โครงสรา้ งแมเ่ หลก็ ที่มี เครอื่ งจักรกลที่มีขดลวดฝังอยใู่ นร่อง ขดลวดอยู่ภายใน ภายในโครงสรา้ ง

Y-connected source Electric Circuits KKU abc or positive sequence Balanced phase voltages are equal in magnitude and are out of phase with each other by 120° acb or negative sequence Phase Voltages Van, Vbn and Vcn 7 are respectively between lines a, b, and c, and the neutral line n. MetaRadiator

KKU Electric Circuits 8 abc or positive sequence acb or negative sequence MetaRadiator

abc or positive sequence Electric Circuits KKU Vab Van Vnb Van 220 0 Vrms Vbn 220 120 Vrms phasor diagram Vcn 220 240 Vrms 9 Vab Van Vnb Van Vbn 220 0 220 120 V =220-(-110-j190.5) V 281 30 V MetaRadiator

Balanced loads Electric Circuits KKU A balanced load is one in which the phase impedances are equal in magnitude and in phase. a balanced wye-connected load a balanced delta-connected load Z1 Z2 Z3 ZY Za Zb Zc Z ZY is the load impedance per phase in this case. Z is the load impedance per phase in this case. Z 3ZY or ZY 1 Z 3 MetaRadiator 10

4 Possible Source-Load Connections Electric Circuits KKU Y Y connection Y connection connection Y Y connection connection Y Y connection Y connection connection A balanced delta-connected load is more common than a balanced wye-connected load. This is due to the ease with which loads may be added or removed from each phase of a delta-connected load. This is very difficult with a wye connected load because the neutral may not be accessible. Transmission Line 11 MetaRadiator

Balance Y-Y Connection: Phase and Line Voltages ElectricCircuits Line Voltage Vab, Vbc and Vca KKU Phase Voltages Van, Vbn and Vcn are respectively between lines a, b, and c, and 12 the neutral line n. and MetaRadiator

Balance Y-Y Connection: Phase and Line Currents Electric Circuits KKU the line currents add up to zero, So that A balanced Y-Y system is to do so on a “per phase” basis Ia Ip 120 Ib Ia 120 Ic Ic A single-phase equivalent circuit. MetaRadiator 13

The Y-connected Generator Example : Y-Y Connection Electric Circuits KKU V▪ Pgehnaesreavtoorltawgiensdi(nVgs).are the voltage across the L 3V ▪ Line Voltages (VL) are the voltages across the lines (line to line). I ▪ Phase Currents (I) are the currents through the windings. IL ▪ LcoinneneCcutrinrgentthse(gILe)nearraetothrewciunrdrinengtsstion the lines the loads. MetaRadiator 14

Calculate the line voltage and currents in the three-wire Y-Y system Electric Circuits KKU กระแสไลน์ Ia, Ib และ Ic เน่ืองจากเป็นโหลดสมดุลขนาดของกระแสจะเทา่ กนั ตา่ งกันตาม เฟสของแรงดนั ดงั นั้น Ia Van 440 0 440 0 44 53 A ZY 6 j8 10 53 ดังนั้น Ib Ia 120 44 67 A Ic Ia 120 44 153 A แรงดันไลน์ Vab, Vbc และVca Vab 3(440) (0 30 ) 762.1 30 V Vbc 762.1 30 V Vca 762.1 120 762.1 120 V MetaRadiator 15

The -connected Generator Example : -  ConnectionElectric Circuits KKU ▪ Pgehnaesreavtoorltawgiensdi(nVgs).are the voltage across the VL V Vab Vp ▪ Line Voltages (VL) are the voltages across the lines Ia IAB 3 30 (line to line). Ib IBC 3 I▪ 3I Ic ICA 3 30 Ia 120 Phase Currents (I) are the currents through the L 30 Ia 120 windings. ▪ cLoinneneCcutrinrgentthse(gILe)nearraetothrewciunrdrinengtsstion the lines the loads. IAB Vab / Z , IBC Vbc / Z , ICA Vca / Z MetaRadiator 16

Balanced  -  Connection Electric Circuits KKU A balanced  -  system is one in which both the balanced source and balanced load are  -connected. The phase currents For a positive sequence The line currents The phase voltages The line voltages IL 3I Ia IAB 3 30 Ib IBC 3 VL V Ic ICA 3 30 Ia 120 30 Ia 120 MetaRadiator 17

Calculate the phase currents of the load and the line currents if ZL = 20-j15 . Electric Circuits KKU The line currents are Ia IAB 3 30 17.6 36.87 3 30 30.48 6.87 A Impedance in polar form ZL Z 20 j15 25 36.87 Ib Ia 120 30.48 113.13 A Since VAB = Vab, the phase currents are Ic Ia 120 30.48 126.87 A IAB VAB 440 0 17.6 36.87 Z 25 36.87 IBC IAB 120 17.6 83.13 ICA IAB 120 17.6 156.87 MetaRadiator 18

A balanced delta-connected load is supplied by a 60-Hz three-phase source with a line voltage of 240 V. Each load phase draws 6 kW Electric Circuits at a lagging power factor of 0.8. Find: KKU (a) the load impedance per phase (b) the line current (c) the value of capacitance needed to be connected in parallel with each load phase to minimize the current from the source MetaRadiator 19

Electric Circuits Summary of phase and line voltages/currents for balanced 3-phase systems. KKU [Positive or abc sequence is assumed.] The Y-connected Generator The -connected Generator MetaRadiator 20

3-Phase Power in a Balanced System Electric Circuits KKU S 3VpI p (VA) S 3VLIL (VA) P 3VLIL cos (W) P 3VpI p cos (W) Q 3VLIL sin (VAR) Q 3VpI p sin (VAR) S P jQ (VA) 3VLI L 3VLIL (cos j sin ) 3VpI p 3VpI p(cos j sin ) Power factor (PF) cos is the angle of the load impedance or the angle between the phase voltage and the phase current. MetaRadiator 21

KKU Electric Circuits 22 MetaRadiator

KKU Electric Circuits MetaRadiator 1 แรงมา้ (1 HP) = 746 W 23