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Transcript
THREE PHASE CIRCUIT Objectives • Explain the differences between singlephase, two-phase and three-phase. • Compute and define the Balanced ThreePhase voltages. • Determine the phase and line voltages/currents for Three-Phase systems. SINGLE PHASE TWO WIRE V p SINGLE PHASE SYSTEM • A generator connected through a pair of wire to a load – Single Phase Two Wire. • Vp is the magnitude of the source voltage, and is the phase. SINLGE PHASE THREE WIRE V p V p SINGLE PHASE SYSTEM • Most common in practice: two identical sources connected to two loads by two outer wires and the neutral: Single Phase Three Wire. • Terminal voltages have same magnitude and the same phase. POLYPHASE SYSTEM • Circuit or system in which AC sources operate at the same frequency but different phases are known as polyphase. TWO PHASE SYSTEM THREE WIRE V p V p 90 POLYPHASE SYSTEM • Two Phase System: – A generator consists of two coils placed perpendicular to each other – The voltage generated by one lags the other by 90. POLYPHASE SYSTEM • Three 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. THREE PHASE FOUR WIRE IMPORTANCE OF THREE PHASE SYSTEM • All electric power is generated and distributed in three phase. – One phase, two phase, or more than three phase input can be taken from three phase system rather than generated independently. – Melting purposes need 48 phases supply. IMPORTANCE OF THREE PHASE SYSTEM • Uniform power transmission and less vibration of three phase machines. – The instantaneous power in a 3 system can be constant (not pulsating). – High power motors prefer a steady torque especially one created by a rotating magnetic field. IMPORTANCE OF THREE PHASE SYSTEM • Three phase system is more economical than the single phase. – The amount of wire required for a three phase system is less than required for an equivalent single phase system. – Conductor: Copper, Aluminum, etc THREE PHASE GENERATION FARADAYS LAW • Three things must be present in order to produce electrical current: a) Magnetic field b) Conductor c) Relative motion • • Conductor cuts lines of magnetic flux, a voltage is induced in the conductor Direction and Speed are important GENERATING A SINGLE PHASE S N Motion is parallel to the flux. No voltage is induced. GENERATING A SINGLE PHASE S N Motion is 45 to flux. Induced voltage is 0.707 of maximum. GENERATING A SINGLE PHASE S x N Motion is perpendicular to flux. Induced voltage is maximum. GENERATING A SINGLE PHASE S N Motion is 45 to flux. Induced voltage is 0.707 of maximum. GENERATING A SINGLE PHASE S N Motion is parallel to flux. No voltage is induced. GENERATING A SINGLE PHASE S N Notice current in the conductor has reversed. Motion is 45 to flux. Induced voltage is 0.707 of maximum. GENERATING A SINGLE PHASE S N Motion is perpendicular to flux. Induced voltage is maximum. GENERATING A SINGLE PHASE S N Motion is 45 to flux. Induced voltage is 0.707 of maximum. GENERATING A SINGLE PHASE S N Motion is parallel to flux. No voltage is induced. Ready to produce another cycle. THREE PHASE GENERATOR GENERATOR WORK • The generator consists of a rotating magnet (rotor) surrounded by a stationary 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 three coils and induces voltages in the coils. • The induced voltage have equal magnitude but out of phase by 120. GENERATION OF THREE-PHASE AC S x x N THREE-PHASE WAVEFORM Phase 1 120 Phase 2 Phase 3 120 120 240 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. GENERATION OF 3 VOLTAGES Phase 1Phase 2 Phase 3 S x Phase 1 is ready to go positive. Phase 2 is going more negative. Phase 3 is going less positive. x N THREE PHASE QUANTITIES BALANCED 3 VOLTAGES • Balanced three phase voltages: – same magnitude (VM ) – 120 phase shift v an (t ) VM cos t vbn (t ) VM cos t 120 vcn (t ) VM cos t 240 VM cos t 120 BALANCED 3 CURRENTS • Balanced three phase currents: – same magnitude (IM ) – 120 phase shift ia (t ) I M cos t ib (t ) I M cos t 120 ic (t ) I M cos t 240 PHASE SEQUENCE van (t ) VM cos t vbn (t ) VM cost 120 vcn (t ) VM cost 120 Van VM 0 Van VM 0 Vbn VM 120 Vbn VM 120 Vcn VM 120 Vcn VM 120 POSITIVE SEQUENCE NEGATIVE SEQUENCE PHASE SEQUENCE EXAMPLE # 1 • Determine the phase sequence of the set voltages: van 200 cost 10 vbn 200 cost 230 vcn 200 cost 110 BALANCED VOLTAGE AND LOAD • Balanced Phase Voltage: all phase voltages are equal in magnitude and are out of phase with each other by 120. • Balanced Load: the phase impedances are equal in magnitude and in phase. THREE PHASE CIRCUIT • POWER – The instantaneous power is constant p(t ) pa (t ) pb (t ) pc (t ) VM I M 3 cos 2 3Vrms I rms cos( ) THREE PHASE CIRCUIT • Three Phase Power, S T S A S B S C 3 S THREE PHASE QUANTITIES QUANTITY SYMBOL Phase current I Line current IL Phase voltage V Line voltage VL PHASE VOLTAGES and LINE VOLTAGES • Phase voltage is measured between the neutral and any line: line to neutral voltage • Line voltage is measured between any two of the three lines: line to line voltage. PHASE CURRENTS and LINE CURRENTS • Line current (IL) is the current in each line of the source or load. • Phase current (I) is the current in each phase of the source or load. THREE PHASE CONNECTION SOURCE-LOAD CONNECTION SOURCE LOAD CONNECTION Wye Wye Y-Y Wye Delta Y- Delta Delta - Delta Wye -Y SOURCE-LOAD CONNECTION • Common connection of source: WYE – Delta connected sources: the circulating current may result in the delta mesh if the three phase voltages are slightly unbalanced. • Common connection of load: DELTA – Wye connected load: neutral line may not be accessible, load can not be added or removed easily. WYE CONNECTION WYE CONNECTED GENERATOR Ia a Van Vab n Vbn Ib Vca b Vcn Vbc Ic c WYE CONNECTED LOAD a a Y Z ZY b OR b Load ZY c n c n ZY ZY ZY Load BALANCED Y-Y CONNECTION PHASE CURRENTS AND LINE CURRENTS • In Y-Y system: IL Iφ PHASE VOLTAGES, V • Phase voltage is measured between the neutral and any line: line to neutral voltage Ia a VVanan n VVbnbn Vab Ib Vca b VVcn cn Vbc Ic c PHASE VOLTAGES, V Van VM 0 volt Vbn VM 120 volt Vcn VM 120 volt LINE VOLTAGES, VL Ia • Line voltage is measured between any two of the three lines: line to line voltage. a Van Vab ab n Vbn Ib b Vcn V V bc bc Ic c VVcaca LINE VOLTAGES, VL Vab Van Vbn Vbc Vbn Vcn Vca Vcn Van Vab 3VM 30 Vbc 3VM 90 Vca 3VM 150 Van VM 0 volt Vbn VM 120 volt Vcn VM 120 volt LINE VOLTAGE (VL) PHASE VOLTAGE (V) Vab 3 VM 30 volt Vbc 3 VM 90 volt Vca 3 VM 150 volt PHASE DIAGRAM OF VL AND V Vca Vcn Vab 30° 120° Vbn Vbc -Vbn Van PROPERTIES OF PHASE VOLTAGE • All phase voltages have the same magnitude, = V = V Van bn Vcn • Out of phase with each other by 120 PROPERTIES OF LINE VOLTAGE • All line voltages have the same magnitude, = V = VL Vab bc Vca • Out of phase with each other by 120 RELATIONSHIP BETWEEN V and VL 1. Magnitude VL 3 V 2. Phase - VL LEAD their corresponding V by 30 VL V 30 EXAMPLE 1 • Calculate the line currents DELTA CONNECTION DELTA CONNECTED SOURCES DELTA CONNECTED LOAD OR BALANCED - CONNECTION PHASE VOLTAGE AND LINE VOLTAGE • In - system, line voltages equal to phase voltages: VL Vφ PHASE VOLTAGE, V • Phase voltages are equal to the voltages across the load impedances. PHASE CURRENTS, I • The phase currents are obtained: VBC VCA VAB I AB , I BC , I CA ZΔ ZΔ ZΔ LINE CURRENTS, IL • The line currents are obtained from the phase currents by applying KCL at nodes A,B, and C. LINE CURRENTS, IL I a I AB I CA I b I BC I AB I c I CA I BC I a 3 I AB 30 I b I a 120 I c I a 120 PHASE CURRENTS (I) I AB I BC I CA VAB ZΔ VBC ZΔ VCA ZΔ LINE CURRENTS (IL) I a 3 I AB 30 I b I a 120 I c I a 120 PHASE DIAGRAM OF IL AND I PROPERTIES OF PHASE CURRENT • All phase currents have the same magnitude, Iφ I AB I BC ICA Vφ ZΔ • Out of phase with each other by 120 PROPERTIES OF LINE CURRENT • All line currents have the same magnitude, I L Ia I b Ic • Out of phase with each other by 120 RELATIONSHIP BETWEEN I and IL 1. Magnitude I L 3 I 2. Phase - IL LAG their corresponding I by 30 I L I 30 EXAMPLE A balanced delta connected load having an impedance 20-j15 is connected to a delta connected, positive sequence generator having Vab = 3300 V. Calculate the phase currents of the load and the line currents. Given Quantities ZΔ 20 j15 25 36.87 Vab 3300 Phase Currents VAB 3300 I AB 13.236.87A ZΔ 25 36.87 I BC I AB 120 13.2 - 83.13A I CA I AB 120 13.2156.87A Line Currents I a I AB 3 30 13.236.87 3 30 A 22.866.87 I b I a 120 22.86 - 113.13A I c I a 120 22.86126.87A BALANCED WYE-DELTASYSTEM EXAMPLE 2 A balanced positive sequence Yconnected source with Van=10010 V is connected to a -connected balanced load (8+j4) per phase. Calculate the phase and line currents. THREE PHASE POWER MEASUREMENT EXAMPLE 3 Determine the total power (P), reactive power (Q), and complex power (S) at the source and at the load EXAMPLE #4 A three phase motor can be regarded as a balanced Y-load. A three phase motor draws 5.6 kW when the line voltage is 220 V and the line current is 18.2 A. Determine the power factor of the motor