1. FUNDAMENTALS OF ELECTRICAL ENGINEERING [ ENT 163 ]
LECTURE #9
THREE – PHASE CIRCUITS
HASIMAH ALI
Programme of Mechatronics,
School of Mechatronics Engineering, UniMAP.

2. Contents Introduction Balanced Three-Phase Voltages
Balanced Wye – Wye Connection
Balanced Wye – Delta Connection
Balanced Delta – Delta Connection

3. 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.

4. 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.

5. 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%)

6. 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.

7. 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

8. 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.

9. 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

10. Balanced Three – Phase Voltages
abc sequence or positive sequence:
Where,
Vp is the effective or rms value of the phase

11. 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.

12. Balanced Three – Phase Voltages
Two possible three-phase load configuration:
a) A Y-connected load, b) a- ∆ connected load

13. Balanced Three – Phase Voltages
For balanced wye – connected load,
For balanced delta – connected load,
Recall that,

14. 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

15. 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

16. Balanced Three – Phase Voltages
Phase and line voltages/ currents for balanced Y-Y system (assuming positive/ abc sequence):
Phase voltages/currents
Line voltages/ currents

17. Balanced Wye – Wye Connection
Phasor diagrams illustrating the relationship between line voltages and phase voltages

18. 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.

19. 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

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

21. 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

22. 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,

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

24. Balanced Wye – Delta Connection
Phasor diagram illustrating the relationship between phase and line currents.

25. 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.

26. Balanced Delta – Delta Connection
A balanced ∆- ∆ system is one which both the balanced source and balanced load are ∆-connected.
Vca c

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

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

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

30. Balanced Delta – Wye Connection
The single-phase equivalent circuit.

31. Further Reading
Fundamentals of electric circuit. (2th Edition), Alexander, Sadiku, McGrawHill. (chapter 12).
Electric circuits.8th edition, Nilsson &Riedel, Pearson. (chapter 11).