1. BASIC ELECTRICAL ENGINEERING
D. C. KULSHRESHTHA,
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2. Chapter 12 Three-Phase Circuits and Systems
D.C. Kulshreshtha
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3. Ch. 12 Three-Phasae Circuits and Systems
Thought of The DAY
The best way
out of a difficulty is
through it.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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4. Ch. 12 Three-Phasae Circuits and Systems
Topics to be Discussed
Three-Phase System.
Advantages.
Concept.
Generation.
Unbalanced Three-Phase System.
Voltages And Currents Relations.
(1) Star-Connected System.
(2) Delta-Connected System
Power In Three-phase System.
Power Measurement.
Two-Wattmeter Method.
Power Factor Measurement.
Important Points.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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5. Advantages of Three-Phase System
Transmission lines require much less conductor material.
A three-phase machine gives a higher output.
A three-phase motor develops a uniform (not a pulsating) torque.
The three-phase induction motors are self-starting.
Can be used to supply domestic as well as industrial (or commercial) power.
The voltage regulation is better.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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6. Concept of Three-phase Voltages
The phase order or phase sequence or phase rotation is abc.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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7. Ch. 12 Three-Phasae Circuits and Systems
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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8. Generation of Three-phase Voltages
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9. Ch. 12 Three-Phasae Circuits and Systems
Whether the coils rotate anti-clockwise or the magnet on the rotor rotates clockwise, the effect is the same.
But the latter is safer and easier to make external connections to stationary coils.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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10. Three windings connected to three loads using six line conductors
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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11. Ch. 12 Three-Phasae Circuits and Systems
Thus, the terminals on the periphery appear in the order : R, B’, Y, R’, B, Y’.
The three emfs generated eR, eY and eB connected to three respective loads L1, L2 and L3.
This necessitates the use of six line conductors.
Obviously, it is cumbersome and expensive.
Let us now consider how it may be simplified.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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12. Ch. 12 Three-Phasae Circuits and Systems
Three-phase Loads
There are two kinds of three-phase systems :
Star or wye (Y) connection, and
Delta (Δ) or mesh connection
If all the three impedances are equal, the load is said to be a balanced load.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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13. Star (Y) Connected Three-phase System
Thursday, November 22, 2018
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14. Ch. 12 Three-Phasae Circuits and Systems
Thursday, November 22, 2018
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15. Unbalanced Three-Phase System
The common point M is called local neutral point.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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16. Ch. 12 Three-Phasae Circuits and Systems
Practically, it may not be possible always to make this star-connected domestic load balanced.
However, as per KCL, the sum of the three line currents must still be zero.
Hence, the voltages across the three loads get adjusted, resulting in neutral shift or floating neutral.
This situation is definitely undesirable.
Therefore, we use Four-Wire Three-Phase Voltage System.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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17. Delta (Δ) Connected Three-phase System
Note that the ‘finish’ of one phase is connected to the ‘start’ of another phase.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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18. Ch. 12 Three-Phasae Circuits and Systems
Voltages And Currents Relations in 3-φ Systems (1) Star-Connected System
Thursday, November 22, 2018
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19. Ch. 12 Three-Phasae Circuits and Systems
In a three-phase system, there are two sets of voltages :
the set of phase voltages, and
the other is the set of line voltages.
VRN, VYN and VBN denote the set of three phase voltages.
The term ‘line voltage’ is used to denote the voltage between two lines.
VRY represents line voltage between the lines R and Y.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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20. Ch. 12 Three-Phasae Circuits and Systems
VBN
VRY
-VYN
30°
VRN
VRN cos 30°
VYN
Click
Thursday, November 22, 2018
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21. Star-connected System
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22. (2) Delta-Connected System
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23. Ch. 12 Three-Phasae Circuits and Systems
IB’B
IR’R cos 30°
IR’R
30°
IY’Y IR
-IB’B
Click
Thursday, November 22, 2018
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24. Delta-connected System
Thursday, November 22, 2018
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25. Important Points about Three-Phase Systems
It is normal practice to specify the values of the line voltages and line currents.
The current in any phase can be determined by dividing the phase voltage by its impedance.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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26. Ch. 12 Three-Phasae Circuits and Systems
Example 1
A 400-V, 3- supply is connected across a balanced load of three impedances each consisting of a 32-Ω resistance and 24-Ω inductive reactance. Determine the current drawn from the power mains, if the three impedances are
(a) Y-connected, and
(b) Δ-connected.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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27. Ch. 12 Three-Phasae Circuits and Systems
Click
Solution : Z = R + jX = (32 + j24) Ω.
Click
(a) Y-connection :
Click
(b) For Δ-connection :
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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28. Power In Three-phase System With A Balanced Load
Consider one phase only,
Click
Hence, the total power consumed,
For a star-connected system,
Click
For a delta-connected system,
Click
Click
Thus, for any balanced load,
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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29. Ch. 12 Three-Phasae Circuits and Systems
Thursday, November 22, 2018
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30. Ch. 12 Three-Phasae Circuits and Systems
In three-phase system with balanced load (such as a three-phase motor), there is no variation of power at all.
This is the reason why for driving heavy mechanical loads we prefer a three-phase motor rather than a single-phase motor.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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31. Ch. 12 Three-Phasae Circuits and Systems
Example 2
A 400-V, 3- supply is connected to a balanced network of three impedances each consisting of a 20-Ω resistance and a 15-Ω inductive reactance.
If the three impedances are (a) star-connected, and (b) delta-connected, in each case determine
(i) the line current,
(ii) the power factor, and
(iii) the total power in kW.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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32. Ch. 12 Three-Phasae Circuits and Systems
(a) For star-connected load :
Click
Click
(i)
Click
(ii)
Click
(iii)
Thursday, November 22, 2018
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33. Ch. 12 Three-Phasae Circuits and Systems
(b) For delta-connected load :
Click
(i)
Click
(ii) The power factor is same as above,
pf = 0.8 (lagging)
Click
(iii)
Click
Note that power consumed has become 3 times.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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34. Star-Connected System Delta-Connected System
No.
Star-Connected System
Delta-Connected System 1. 2. 3. 4. 5. 6.
Similar ends are joined together.
Neutral wire available.
4-wire, 3- system possible.
Both domestic and industrial loads can be handled.
By earthing the neutral wire, relays and protective devices can be provided in alternators for safety.
Dissimilar ends are joined.
Neutral wire not available.
4-wire, 3- system not possible.
Only industrial loads can be handled.
Due to absence of neutral wire, it is not possible.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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35. Ch. 12 Three-Phasae Circuits and Systems
Measurement of Power
Three-Wattmeter Method : This is simplest and straight forward method.
Two-Wattmeter Method : This can be used for any balanced or unbalanced load, star- or delta-connected.
One-Wattmeter Method : This can be used only for a star-connected balanced load.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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36. Ch. 12 Three-Phasae Circuits and Systems
Thursday, November 22, 2018
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37. Ch. 12 Three-Phasae Circuits and Systems
Two-Wattmeter Method
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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38. Ch. 12 Three-Phasae Circuits and Systems
The sum of the wattmeter readings gives the average value of the total power absorbed by the three phases
Proof :
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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39. Ch. 12 Three-Phasae Circuits and Systems
Since we did not assume a balanced load or a sinusoidal waveform, it follows that the sum of the two wattmeter readings gives the total power under all conditions.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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40. Power Factor Measurement by Two-Wattmeter Method
Concept of ‘power factor’ is meaningful only if the load is balanced.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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41. Ch. 12 Three-Phasae Circuits and Systems
Since the load is balanced,
Since VRB = VRN  VBN, and VYB = VYN  VBN, we can determine the line voltages VRB and VYB by phasor method,
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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42. Ch. 12 Three-Phasae Circuits and SystemsIB
VBN Φ
VRN Φ IR Φ
VYN IY
VRB
-VBN
VYB
Thursday, November 22, 2018
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43. Ch. 12 Three-Phasae Circuits and Systems
It is seen that the line voltage VRB lags the phase voltage VRN by 30° and VYB leads VYN by 30°.
Thus, the phase angle between VRB and IR is (30°  ).
Similarly, the phase angle between VYB and IY is (30° + ).
Therefore, the readings of the two wattmeters are
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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44. Ch. 12 Three-Phasae Circuits and Systems
Click
Click
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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45. Ch. 12 Three-Phasae Circuits and Systems
By applying componendo and dividendo,
Click
Click
Calculate the phase angle , and then determine the power factor.
Thursday, November 22, 2018
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46. Ch. 12 Three-Phasae Circuits and Systems
Important Points :
If Ф = 0°, P1 = P2.
If Ф < 60°, both P1 and P2 are positive; and
P = P1 + P2
If Ф = 60°, P2 is zero.
If Ф > 60°, (i.e., if pf < 0.5), P2 is negative.
In such case, the connection of either the current coil or the potential coil has to be reversed to make positive deflection.
The value P2 should then be taken as negative while calculating the power factor or the total power.
Thursday, November 22, 2018
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47. Ch. 12 Three-Phasae Circuits and Systems
Example 3
Two-wattmeter method was used to determine the input power to a three-phase motor. The readings were 5.2 kW and -1.7 kW, and the line voltage was 415 V. Calculate
(a) the total power,
(b) the power factor, and
(c) the line current.
Thursday, November 22, 2018
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48. Ch. 12 Three-Phasae Circuits and Systems
Solution :
(a) The total power,
Click
Click
(b)
Click
(c)
Thursday, November 22, 2018
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49. Ch. 12 Three-Phasae Circuits and Systems
Review
Three-Phase System.
Advantages.
Concept.
Generation.
Unbalanced Three-Phase System.
Voltages And Currents Relations.
(1) Star-Connected System.
(2) Delta-Connected System
Power In Three-phase System.
Power Measurement.
Two-Wattmeter Method.
Power Factor Measurement.
Important Points.
Thursday, November 22, 2018
Ch. 12 Three-Phasae Circuits and Systems
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