1. ELL100: INTRODUCTION TO ELECTRICAL ENGG.
Course Instructors:
J.-B. Seo, S. Srirangarajan, S.-D. Roy, and S. Janardhanan
Department of Electrical Engineering, IITD

2. AC power generation Magnetic flux
Magnetic flux density
Flux depends on orientation of surface with respect to B field.

3. AC power generation
Induced emf (electro-magnetic force) in a closed loop equals negative of time rate of change of magnetic flux through the loop
(Faraday’s Law)

4. AC power generation
Induced emf (electro-magnetic force) in a closed loop equals negative of time rate of change of magnetic flux through the loop
(Faraday’s Law)
Assume that N S
Water turning a turbine (hydroelectric)
Gasoline Motor turning a shaft (AC generator)
Note that
for

5. AC power generation
Induced emf (electro-magnetic force) in a closed loop equals negative of time rate of change of magnetic flux through the loop
(Faraday’s Law)
Assume that N S
Water turning a turbine (hydroelectric)
Gasoline Motor turning a shaft (AC generator)
Note that
for

6. AC power generation
Induced emf (electro-magnetic force) in a closed loop equals negative of time rate of change of magnetic flux through the loop
(Faraday’s Law)
Assume that N S
Water turning a turbine (hydroelectric)
Gasoline Motor turning a shaft (AC generator)
Note that
for

7. AC power generation N S

8. Generating three-phase voltage

9. Generating three-phase voltage
Single-phase voltage
 Three-phase voltage can be also generated with three single-phase voltage
Load
Load
Load

10. Generating three-phase voltage
Single-phase voltage
 Three-phase voltage can be also generated with three single-phase voltage
Load
– This can be combined as a single neutral line
Load
Load

11. Two methods of source connections
 voltages between the lines a,b,c and the neutral line n: phase voltages.
 voltages between the lines Vab, Vbc, Vca: phase voltages.

12. Two methods of source connections

13. Phase sequence
Balanced phase voltages are equal in magnitude and are out of phase with each other by 120.
There are two possible ways in which a source can be balanced
Positive or abc sequence
Negative or acb sequence

14. Phase sequence
Balanced phase voltages are equal in magnitude and are out of phase with each other by 120.
There are two possible ways in which a source can be balanced
Positive or abc sequence
Negative or acb sequence

15. Recalling the Y-Delta conversions (in Two port networks)

16. Balanced three phase load
Similar to the source, the load can also be Delta or Wye connected.
A balanced load: the phase impedances are equal in magnitude and in phase.

17. Connections with loads

18. Balanced Wye-Wye Connection – 1
Balanced load:
Line voltage (or line-to-line voltage)

19. Balanced Wye-Wye Connection – 1
Balanced load:
Line voltage (or line-to-line voltage)

20. Balanced Wye-Wye Connection – 1
Balanced load:
Line voltage (or line-to-line voltage)

21. Balanced Wye-Wye Connection – 2
By KVL, the current along the line (line current):
Voltage across neutral line is zero: it can be removed
Phase current is the current in each phase of the source of load.
In Y-Y system, the line current is the same as the phase current.

22. Balanced Wye-Wye Connection – 2
By KVL, the current along the line (line current):
Voltage across neutral line is zero: it can be removed
Phase current is the current in each phase of the source of load.
In Y-Y system, the line current is the same as the phase current.

23. Example of Y-Y system
Neutral line

24. Balanced Wye-Delta Connection – 1
Phase voltage
Line voltage is
Phase current can be
Alternatively,

25. Balanced Wye-Delta Connection – 1
Phase voltage
Line voltage is
Phase current can be
Alternatively,

26. Balanced Wye-Delta Connection – 2
Line currents are obtained by KCL
Magnitude of line currents:

27. Example
A balanced abc-sequence Y-connected source with is connected to
a Delta-connected balanced load per phase. Calculate the phase and line currents.
Using
and
we have
The phase current is
The line current

28. Balanced Delta-Delta Connection
Assuming a positive sequence, the phase voltages for a delta-connected source are
 The line voltages are the same as the phase voltage
The phase currents
The line currents are obtained from the phase currents by applying KCL at nodes A, B, and C

29. Balanced Delta-Delta Connection
Assuming a positive sequence, the phase voltages for a delta-connected source are
 The line voltages are the same as the phase voltage
The phase currents
The line currents are obtained from the phase currents by applying KCL at nodes A, B, and C

30. Example
A balanced -connected load having an impedance is connected to a -connected,
positive-sequence generator having Calculate the phase currents of the load
and the line currents.

31. Balanced Delta-Wye Connection
Assuming the abc sequence, the phase voltages of a delta-connected source are
These are also the line voltages as well as the phase voltages.
In order to get the line current, apply KVL to loop aANBba,

32. Balanced Delta-Wye Connection
In order to get the line current, apply KVL to loop aANBba,
Since we assume the abc sequence,
The phase currents are equal to the line currents.

33. Delta-Wye Transformation
Another possible way to analyze the Delta-Star connection.
Transform Delta connected source to Star connected source
Analyze the Y-Y connection.
Observing the phase voltage to line voltage relation in the Y-Y connection

34. Example
A balanced Y-connected load with a phase impedance of is supplied by a balanced, positive sequence -connected source with a line voltage of 210 V. Calculate the phase currents. Use as a reference

35. Power in a Balanced system
For a Y-connected load, the phase voltages are
the phase currents lag behind their corresponding phase voltages by
The total instantaneous power in the load is the sum of the instantaneous powers in the three phases

36. Power in a Balanced system
Applying the trigonometric identity,
Thus the total instantaneous power in a balanced three-phase system is constant—it does not change with time as the instantaneous power of each phase does.

37. Power in a Balanced system
The average power per phase for either the -connected load or the Y-connected load is p/3, or
The reactive power per phase
The apparent power per phase
The complex power per phase

38. Power in a Balanced system
The total average power is the sum of the average powers in the phases
The total reactive power
The total complex power

39. Advantage of three-phase circuit
Consider an amount of power PL being transmitted at the same line voltage VL using
Single phase supply
3-phase balanced supply
Power dissipation in transmission

40. Advantage of three-phase circuit
Power dissipation in transmission
If same amount of power loss is to be allowed
Ratio of material required for transmission wires
In other words, a 3-phase supply can deliver power, and follow power loss constraints using only 75% of the material as an equivalent single phase supply.