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FUNDAMENTALS OF ELECTRICAL ENGINEERING [ ENT 163 ] LECTURE #9 THREE – PHASE CIRCUITS HASIMAH ALI Programme of Mechatronics, School of Mechatronics Engineering, UniMAP. Email: [email protected] Contents Introduction Balanced Three-Phase Voltages Balanced Wye – Wye Connection Balanced Wye – Delta Connection Balanced Delta – Delta Connection Introduction Single – phase ac power system consists of a generator connected through a pair of wires (transmission line ) to a load. a) b) Single-phase systems: a) two-wire type, b) three-wire type. Introduction Polyphase: circuits or systems in which the ac sources operate at the same frequency but different phases. Two-phase three-wire system. Three-phase four-wire system. Introduction Importance of three – phase system: Nearly all electric power is generated and distributed in three – phase. The instantaneous power in a three – phase system can be constant – results in uniform power transmission and less vibration (constant torque). More economical than the single – phase. The power delivery capacity tripled (increased by 200%) by increasing the number of conductors from 2 to 3 (increased by 50%) Balanced Three – Phase Voltages Often produced with a three – phase ac generator (alternator) A three-phase generator Generator: a b c n Consists of rotating magnet (rotor) surrounded by a stationary winding (stator) Three separate winding/ coils with terminal a-a’, b-b’ and c-c’ are physically placed 120° apart around the stator. As the rotor rotates, its magnitude field cuts the flux from the three coils and induces voltages in the coils. Balanced Three – Phase Voltages Because the coils are placed 120° apart, the induced voltages in the coils are equal magnitude but out of phase by 120 °. The generated voltages are 120° apart from each other Balanced Three – Phase Voltages Vca Vab Vbc Typical three – phase system: From the above figure, the voltages Van, Vbn, Vcn are respectively between the lines a, b, c and the neutral line n. These voltages are called phase voltage. If the voltage source have same amplitude and frequency ω and are out of phase with each other by 120°, the voltages are said to be balanced. Balanced Three – Phase Voltages This implies that, Van Vbn Vcn 0, Van Vbn Vcn Balanced phase voltages are equal in magnitude and are out of phase with each other by 120° Since the three–phase voltages are 120 ° out of phase with each other, there are two possible combinations. abc sequence or positive sequence acb sequence or negative sequence Balanced Three – Phase Voltages 1. abc sequence or positive sequence: Van V p 0 Vbn V p 120 Vcn V p 120 Vbn V p 240 Where, • Vp is the effective or rms value of the phase Balanced Three – Phase Voltages 1. For negative sequence: Van V p 0 Vcn V p 120 Vbn V p 120 Vbn V p 240 The phase sequence is the time order in which the voltage pass through their respective maximum values. A balanced load is one in which the phase impedances are equal in magnitude and in phase. Balanced Three – Phase Voltages Two possible three-phase load configuration: a) A Y-connected load, b) a- ∆ connected load Balanced Three – Phase Voltages For balanced wye – connected load, Z1 Z 2 Z3 ZY For balanced delta – connected load, Z a Zb Zc Z Recall that, Z 3Z Y 1 ZY Z 3 Balanced Three – Phase Voltages 4main elements in three – phase circuit: Phase Voltage (VØ): measured between the neutral and any line , i.e line to neutral voltage. Line Voltage (VL): measured between ant two of the three lines, i.e line to line voltage. Line current (IL): current in each line of the source or load. Phase current (IØ): current in each phase of the source or load. Four possibilities connections: Wye – wye (Y-Y) connection Wye – delta (Y-∆)connection Delta – delta (∆ - ∆) connection Delta – wye (∆ -Y) connection Balanced Wye – Wye Connection A balanced Y-Y system is a three-phase system with a balanced Yconnected source and a balance Y-connected load. A balanced Y-Y system Balanced Three – Phase Voltages • Phase and line voltages/ currents for balanced Y-Y system (assuming positive/ abc sequence): Phase voltages/currents Line voltages/ currents Van V p 0 Vab 3V p 30 Vbn V p 120 Vbc 3V p 90 Vab 120 Vcn V p 120 Vca 3V p 150 Vab 120 Van Ia ZY Van Ia ZY I b I a 120 I c I a 120 I b I a 120 I c I a 120 Balanced Wye – Wye Connection Phasor diagrams illustrating the relationship between line voltages and phase voltages Balanced Wye – Wye Connection • All phase and line voltages have the same magnitude, V p Van Vbn Vcn VL Vab Vbc Vca Where they are out of phase with each other by 120°, and VL 3 VP VL VP 30 A single-phase equivalent circuit. Balanced Wye – Wye Connection Example: 1. A Y-connected balanced three-phase generator with an impedance of 0.4+j0.3 Ω per phase is connected to a Y-connected balanced load with an impedance of 24+j19 Ω per phase. The line joining the generator and the load has an impedance of 0.6+j0.7 Ω per phase .Assuming a positive sequence for the source voltages and that Van=120 30° V. Find: a) The line voltage b) The line currents Balanced Wye – Delta Connection A balanced Y – ∆ system consists of a balanced Y-connected source feeding a balanced ∆ -connected load. ICA Balanced Wye – Delta Connection • Assuming positive sequence, the phase voltage again: Van V p 0 Vbn V p 120, Vbn V p 120 From previous section, the line voltage are Vab 3V p 30 VAB Vbc 3Vp 90 VBC Vca 3Vp 210 VCA The line voltages are equal to the voltages across the load impedances Balanced Wye – Delta Connection • From these voltage, the phase current can be obtained by: I AB • VBC VAB I BC Z Z I CA VCA Z The line currents can be obtain from phase currents by applying KCL at node A, B and C. Thus, These currents have same magnitude but out of phase with each other by 120° I a I AB I CA , I b I BC I AB , I c I CA I BC , Since, I CA I AB 240 I a I AB I CA I AB (1 1 240) I AB (1 0.5 j 0.866) 240) Balanced Wye – Delta Connection • Phase and line voltages/ currents for balanced Y-∆ system (assuming positive/ abc sequence) Phase voltages/currents Line voltages/ currents Van V p 0 Vab VAB 3V p 30 Vbn V p 120 Vcn V p 120 I AB V AB Z I BC V BC Z I CA VCA Z Vbc VBC Vab 120 Vca VCA Vab 120 I a I AB 3 30 I b I a 120 I c I a 120 Balanced Wye – Delta Connection Phasor diagram illustrating the relationship between phase and line currents. Balanced Wye – Delta Connection • Another alternative way of analyzing the Y-∆circuit is to transform the connected load to an equivalent Y-connected load, using: 1 ZY Z 3 • After this transformation, we now have a Y-Y system A single-phase equivalent circuit of a balanced Y- ∆ circuit. Balanced Delta – Delta Connection A balanced ∆- ∆ system is one which both the balanced source and balanced load are ∆-connected. Vca c Balanced Delta – Delta Connection • Phase and line voltages/ currents for balanced ∆ -∆ system (assuming positive/ abc sequence) Phase voltages/currents Vab V p 0 Vbc V p 120 Vca V p 120 I AB Vab Z I BC V bc Z I CA Vca Z Line voltages/ currents Vab V p 0 Vbc V p 120 Vca V p 120 I a I AB 3 30 I b I a 120 I c I a 120 Balanced Delta – Wye Connection A balanced ∆- Y system consists of balanced ∆-connected source feeding a balanced Y-connected load. Vca c Balanced Delta – Wye Connection • Phase and line voltages/ currents for balanced ∆ -Y system (assuming positive/ abc sequence) Phase voltages/currents Line voltages/ currents Vab V p 0 Vab V p 0 Vbc V p 120 Vbc V p 120 Vca V p 120 Vca V p 120 Ia V p 30 3Z Y Ia V p 30 3Z Y I b I a 120 I b I a 120 I c I a 120 I c I a 120 Balanced Delta – Wye Connection The single-phase equivalent circuit. Further Reading Fundamentals of electric circuit. (2th Edition), Alexander, Sadiku, McGrawHill. (chapter 12). Electric circuits.8th edition, Nilsson &Riedel, Pearson. (chapter 11).