1. BASIC ELECTRICAL TECHNOLOGY Chapter 3 - Three Phase System
DET 211/3
Chapter 3 - Three Phase System

2. INTRODUCTION TO THREE PHASE SYSTEM
In general, three phase systems are preferred over single phase systems for the transmission of the power system for many reasons, including the following:
Thinner conductors can be used to transmit the same kVA at the same voltage, which reduces the amount of copper required (typically about 25% less) and turn reduces construction and maintenance costs.
The lighter lines are easier to install, and the supporting structures can be less massive and farther apart.
In general, most larger motors are three phase because they are essentially self starting and do not require a special design or additional starting circuitry.

3. Three phase voltages
A 3-phase generator basically consists of a rotating magnet (called the rotor) surrounded by a stationary winding (called the stator). Three separate windings or coils with terminals a-a’, b-b’ and c-c’ are physically placed 120o apart around the stator.

4. Generated Voltages
The three phase generator can supply power to both single phase and three phase loads

5. The sinusoidal expression for each of the phase voltages

6. The phasor diagram of the phase voltages
The effective value of each is determined by

7. If the voltage sources have the same amplitude and frequency ω and are out of the phase with each other by 120o, the voltages are said to be balanced. By rearranging the phasors as shown in figure below, so
Where

8. Generator and Load Connections
Each generator in a 3-phase system maybe either Y- or D-connected and loads may be mixed on a power system. Z Z

9. Wye Connected Generator
Applying KVL around the indicated loop in figure above, we obtain

10. Wye Connected Generator
For line-to-line voltage VAB is given by:

11. Wye Connected Generator
Phasor Diagram

12. Wye Connected Generator
The relationship between the magnitude of the line-to-line and line-to-neutral (phase) voltage is:
The line voltages are shifted 300 with respect to the phase voltages. Phasor diagram of the line and phase voltage for the Y connection is shown below.
VAB
VAN
VBC
VBN
VCA
VCN
Line-to-line voltages
Phase voltages
Rearrange

13. Delta Connected Generator
For line-to-line voltage VAB is given by:

14. Delta Connected Generator
The relationship between the magnitude of the line and phase current is:
The line currents are shifted 300 relative to the corresponding phase current. Phasor diagram of the line and phase current for the Y connection is shown below. IA
IAB
IBC IB
ICA
Line-to-line currents
Phase currents IC

15. Phase sequence
The phase sequence is the order in which the voltages in the individual phases peak. VA VB VC VA VC VB
abc phase sequence
acb phase sequence

16. Power relationship-phase quantities
The power equations applied to Y-or D- load in a balanced 3-phase system are:
Real power
Unit=Watts(W)
Reactive power
Unit=Volt-Amps-Reactive (VAR)
Apparent power
Unit=Volt-Amps (VA)
q - angle between voltage and current in any phase of the load

17. Power relationship-Line quantities
The power equations applied to Y-or D- load in a balanced 3-phase system are:
Real power
Reactive power
Apparent power
q - angle between phase voltage and phase current in any phase of the load

18. Y-Y connections (i.e: Y-connected source with a Y-connected load).
Since both the three-phase source and the three-phase load can be either Y- or - connected, we have 4 possible connections:
Y-Y connections (i.e: Y-connected source with a Y-connected load).
Y- connection.
- connection
-Y connection

19. (i) Y connected generator/source with Y connected load

20. D- must consists of three equal impedances
(ii) Y-D Connection
A balanced Y- system consists of a balanced Y-connected source feeding a balanced -connected load
Z/3 Z
D- must consists of three equal impedances

21. (iii) ∆-∆ Connection
A balanced ∆- system consists of a balanced ∆-connected source feeding a balanced -connected load Z Z

22. (iv) D-Y Connection
A balanced -Y system consists of a balanced -connected source feeding a balanced Y-connected load
Z/3 Z

23. Example 1
A 208V three-phase power system is shown in Figure 1. It consists of an ideal 208V Y-connected three-phase generator connected to a three-phase transmission line to a Y-connected load. The transmission line has an impedance of 0.06+j0.12W per phase, and the load has an impedance of 12+j9W per phase. For this simple system, find
The magnitude of the line current IL
The magnitude of the load’s line and phase voltages VLL and VfL
The real, reactive and apparent powers consumed by the load
The power factor of the load
The real, reactive and apparent powers consumed by the transmission line
The real, reactive and apparent powers supplied by the generator
The generator’s power factor

24. Example 1 Figure 1 0.06 i0.12 V Vcn=120-2400 Van=12000 208VZ
Z=12+ i9 - +
0.06 _
i0.12 V
Van=12000
Vbn=120-1200
Vcn=120-2400
208V
Figure 1

25. The magnitude of the line current IL
Solution Example 1
The magnitude of the line current IL
So, the magnitude of the line current is thus 7.94 A

26. and the magnitude of the load’s line voltage is
Solution Example 1
(b) The magnitude of the load’s line and phase voltages VLL and VfL
The phase voltage on the load is the voltage across one phase of the load. This voltage is the product of the phase impedance and the phase current of the load:
Therefore, the magnitude of the load’s phase voltage is
and the magnitude of the load’s line voltage is

27. Solution Example 1 (c) The real power consumed by the load is
The reactive power consumed by the load is
The apparent power consumed by the load is

28. (d) The load power factor is
Solution Example 1
(d) The load power factor is
(e) The current in the transmission line is
and the impedance of the line is or
per phase. Therefore, the real, reactive and apparent powers consumed in the line are:

29. Solution Example 1
(f) The real and reactive powers supplied by the generator are the sum of the powers consumed by the line and the load:
The apparent power of the generator is the square root of the sum of the squares of the real and reactive powers:

30. Solution Example 1
(g) From the power triangle, the power factor angle  is
Therefore, the generator’s power factor is

31. Assignment 2
A 208V three-phase power system is shown in Figure 2. It consists of an ideal 208V Y-connected three-phase generator connected to a three-phase transmission line to a -connected load. The transmission line has an impedance of 0.06+j0.12W per phase, and the load has an impedance of 12+j9W per phase. For this simple system, find
The magnitude of the line current IL
The magnitude of the load’s line and phase voltages VLL and VfL
The real, reactive and apparent powers consumed by the load
The power factor of the load
The real, reactive and apparent powers consumed by the transmission line
The real, reactive and apparent powers supplied by the generator
The generator’s power factor

32. Assignment 2
Figure 2