FUNDAMENTALS OF ELECTRICAL ENGINEERING [ ENT 163 ] LECTURE #9 THREE – PHASE CIRCUITS HASIMAH ALI Programme of Mechatronics, School of Mechatronics Engineering, UniMAP. Email: hashimah@unimap.edu.my

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 A three-phase generator b c n Generator: 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.

The generated voltages are 120° apart from each other 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 Vbc Vab Vca 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, 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 abc sequence or positive sequence: Where, Vp is the effective or rms value of the phase

Balanced Three – Phase Voltages For negative sequence: 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, For balanced delta – connected load, Recall that,

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 Y-connected 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

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, Where they are out of phase with each other by 120°, and A single-phase equivalent circuit.

Balanced Wye – Wye Connection Example: 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: The line voltage The line currents 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: The line voltage The line currents

Balanced Wye – Delta Connection A balanced Y – ∆ system consists of a balanced Y-connected source feeding a balanced ∆ -connected load. ICA

The line voltages are equal to the voltages across the load impedances Balanced Wye – Delta Connection Assuming positive sequence, the phase voltage again: The line voltages are equal to the voltages across the load impedances From previous section, the line voltage are

Balanced Wye – Delta Connection These currents have same magnitude but out of phase with each other by 120° From these voltage, the phase current can be obtained by: The line currents can be obtain from phase currents by applying KCL at node A, B and C. Thus, Since,

Balanced Wye – Delta Connection Phase and line voltages/ currents for balanced Y-∆ system (assuming positive/ abc sequence) Phase voltages/currents Line voltages/ currents

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: 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 Line voltages/ currents

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

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).