BASIC ELECTRICAL TECHNOLOGY DET 211/3

1. BASIC ELECTRICAL TECHNOLOGY DET 211/3 Chapter - 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. Importance of Three-Phase systems • Nearly all electric power is generated and distributed in three-phase. • The instantaneous power in a three-phase system can be constant. • For the same amount of power, the three-phase system is more economical than the single-phase.

4. 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. The induce voltage in the coil equal in magnitude but out of phase by 120°.

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

6. Balanced phase voltage 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. These voltage are called phase voltage. This implies that: Balanced phase voltages are equal in magnitude and are out of phase with each other by 120°

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

8. The phasor diagram of the phase voltages Phase sequence ABC sequence or positive sequence

9. The phasor diagram of the phase voltages ACB sequence or negetive sequence

10. . By rearranging the phasors as shown in figure below, so

11. The sinusoidal expression for each of the phase voltages

12. Z Z Z Z Z Z 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.

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

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

15. Wye Connected Generator Phasor Diagram

16. VCN VAB VCA VAN Line-to-line voltages VBN Phase voltages VBC 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. Rearrange

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

18. IC ICA IAB IB IA Line-to-line currents IBC Phase currents 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.

19. 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

20. 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

21. 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

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

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

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

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

26. 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 VLLand 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

27. Assignment 1 Figure 2