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Synchronous Generators Workshop on Basic Electrical Engineering, held at VVCE, Mysuru, on 30-April-2016 R S Ananda Murthy Associate Professor Department of Electrical & Electronics Engineering, Sri Jayachamarajendra College of Engineering, Mysore 570 006
R S Ananda Murthy
Synchronous Generators
Learning Outcomes After completing this lecture the student should be able to – Describe the principle of operation of an alternator. Describe different types of construction of alternators. List the advantages of rotating field type of alternators. State the reasons for distributing armature conductors in slots. State the meaning of pitch factor, distribution factor, and winding factor in respect of armature winding of alternators. Find the frequency of the generated E.M.F. Calculate the generated E.M.F. in the alternator taking into account distribution factor and pitch factor.
R S Ananda Murthy
Synchronous Generators
Photographs of Practical Generators
Horizontal shaft type, typically driven by diesel engine.
R S Ananda Murthy
Synchronous Generators
Photographs of Practical Generators
Vertical shaft type, typically driven by water turbine. R S Ananda Murthy
Synchronous Generators
Photographs of Practical Generators
Horizontal shaft, turbo-alternator, driven by steam turbine. R S Ananda Murthy
Synchronous Generators
Principle of Operation of Synchronous Generator Stator
A1
B2
C2
Rotor
Rotating Field Coil
Stationary A1 Armature
N
C2 A2 B2
C1
B1
S
D.C. Supply
C1
A2
B1
When the poles on the rotor, driven by prime mover, move past the stator conductors, due to the relative motion of conductors with respect to the poles, the magnetic flux lines are cut by the conductors and voltage is induced in them.
R S Ananda Murthy
Synchronous Generators
Salient Pole and Cylindrical Rotor Types Cast Steel Frame . .
. .
. .
Armature Core
. .
N
S
. .
. .
. .
. .
N
S
N
S
Salient Pole Construction
Cylindrical Rotor Construction
If prime move speed is low as in case of water turbines, salient pole type is preferred. If the prime mover speed is high as in case of steam turbines, cylindrical rotor is preferred. R S Ananda Murthy
Synchronous Generators
Advantages of Rotating Field Construction
The coil connections can be made easily and securely on the stator than on the rotor. If the armature winding is placed on the rotor, then, three slip rings would be required where as if the poles are placed on the rotor, only two slip rings designed to carry low power for the field winding are required. Transferring large armature power through brush and slip ring causes them to wear out frequently which is prevented if the armature is stationary.
R S Ananda Murthy
Synchronous Generators
Advantages of Rotating Field Construction
As the generated voltage is 11 kV or above, armature winding requires thicker insulation which is difficult to design if the armature is on the rotor. Field winding is lighter than armature winding and therefore it is preferable to place it on the rotor. In very big synchronous generators, forced hydrogen cooling of armature winding is employed which can be conveniently implemented if the armature is stationary.
R S Ananda Murthy
Synchronous Generators
Reasons for Using Distributed Winding
Armature winding in practical generators is uniformly distributed in many slots for the following reasons — It is difficult to put all the conductors of a phase winding in one or two slots. Distributed winding reduces harmonics in the generated voltage and makes the waveform closer to sinusoidal shape. Distributed winding helps in more uniform heat distribution and cooling and thus helps in preventing insulation failure due to excessive heat in the winding.
R S Ananda Murthy
Synchronous Generators
Photograph of Stator Winding
Stator winding of a generator in a hydro-electric power plant. R S Ananda Murthy
Synchronous Generators
Armature Winding Coils Overhang Coil Span
A1
A2
A1
A2
Coil Side
P
Q
Full Pitched Coil
P
Q
Short Pitched Coil
In practical generators, short pitched coils are used to minimize the length of overhangs and also to reduce harmonics in the generated voltage. R S Ananda Murthy
Synchronous Generators
Pitch Factor (Kp ) of Armature Winding Due to short pitched coil, the magnitude of E.M.F. induced e will be slightly reduced when compared to a full pitched coil. For a short pitched coil, the pitch factor is defined as Kp =
Voltage generated in a short pitched coil Voltage generated in a full pitched coil
(1)
Formula for Kp is β (2) 2 where β is the angle in electrical degrees by which the coil is short pitched as shown in the previous slide. Typically Kp is about 0.9 in a practical generator. Kp = cos
R S Ananda Murthy
Synchronous Generators
Distribution Factor (Kd ) of Armature Winding For a distributed winding, the distribution factor, Kd is defined as Kd =
Voltage induced in a distributed winding Voltage induced in a concentrated winding
Kd is given by Kd =
sin(mα/2) m sin(α/2)
(3)
(4)
where α is known as slot angle and m are given by α=
180 S/P
and
m=
S 3P
where S is total number of slots, P is number of poles. Typically Kd is about 0.9 for a practical generator.
R S Ananda Murthy
Synchronous Generators
Frequency of Generated E.M.F.
When a conductor moves past a pair of poles, one cycle of sinusoidal voltage is completed. If P = total number of poles in the machine, then, Number of cycles per revolution =
P 2
(5)
If N = R.P.M. of the motor, then, the rotor makes N/60 R.P.S. Hence, the frequency of the induced E.M.F. is given by f=
PN P N × = Hz 2 60 120
R S Ananda Murthy
Synchronous Generators
(6)
Equation for Induced E.M.F. in an Alternator If P = number of poles in the machine, and Φ = flux per pole, magnetic flux cut by a conductor in one revolution of the rotor = PΦ. If N is the R.P.M., then, time taken by the rotor to make one revolution = 60/N seconds. Therefore, Flux cut per second by a conductor =
PΦ 60/N
But average induced E.M.F. in a conductor = flux cut per second. Therefore Average induced E.M.F. in a conductor =
R S Ananda Murthy
Synchronous Generators
PΦN 60
Equation for Induced E.M.F. in an Alternator If T = total number of turns connected in series per phase, and since each turn will have two conductors, we have Z = Total number of conductors in series per phase = 2T . So, Average E.M.F. induced per phase = |Eav | =
PΦN · 2T 60
The air gap flux in the generator will have more or less sinusoidal distribution. Then, the induced E.M.F. in each phase will also be sinusoidal. For a sinusoidal waveform we have Form Factor =
|Eph | = 1.11 |Eav |
where Eph = R.M.S. value of the induced voltage per phase.
R S Ananda Murthy
Synchronous Generators
Equation for Induced E.M.F. in an Alternator Therefore, the R.M.S. voltage induced per phase is |Eph | = 1.11 ×
PΦN 2.22PΦNT × 2T = 60 60
But the frequency of the induced E.M.F. is given by f=
PN 120
2f =
=⇒
PN 60
Substituting this in Eq. (7) we get |Eph | = 4.44ΦfT
R S Ananda Murthy
Volts
Synchronous Generators
(7)
Equation for Induced E.M.F. in an Alternator In a practical machine the armature winding is evenly distributed in the slots and short pitched coils are used. Due to this, the induced E.M.F. is slightly reduced by a factor Kw where Kw = Kp Kd is known as the winding factor. So, the induced E.M.F. in an actual machine is given by |Eph | = 4.44ΦfTKw
Volts
(8)
Since the three coils in the armature winding of a practical generator are always star connected, the line voltage at the terminals of the synchronous generator is given by √ (9) |E| = 3 × |Eph |
R S Ananda Murthy
Synchronous Generators
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
R S Ananda Murthy
Synchronous Generators
R S Ananda Murthy
Synchronous Generators
Learning Outcomes After completing this lecture the student should be able to – Describe the principle of operation of an alternator. Describe different types of construction of alternators. List the advantages of rotating field type of alternators. State the reasons for distributing armature conductors in slots. State the meaning of pitch factor, distribution factor, and winding factor in respect of armature winding of alternators. Find the frequency of the generated E.M.F. Calculate the generated E.M.F. in the alternator taking into account distribution factor and pitch factor.
R S Ananda Murthy
Synchronous Generators
Photographs of Practical Generators
Horizontal shaft type, typically driven by diesel engine.
R S Ananda Murthy
Synchronous Generators
Photographs of Practical Generators
Vertical shaft type, typically driven by water turbine. R S Ananda Murthy
Synchronous Generators
Photographs of Practical Generators
Horizontal shaft, turbo-alternator, driven by steam turbine. R S Ananda Murthy
Synchronous Generators
Principle of Operation of Synchronous Generator Stator
A1
B2
C2
Rotor
Rotating Field Coil
Stationary A1 Armature
N
C2 A2 B2
C1
B1
S
D.C. Supply
C1
A2
B1
When the poles on the rotor, driven by prime mover, move past the stator conductors, due to the relative motion of conductors with respect to the poles, the magnetic flux lines are cut by the conductors and voltage is induced in them.
R S Ananda Murthy
Synchronous Generators
Salient Pole and Cylindrical Rotor Types Cast Steel Frame . .
. .
. .
Armature Core
. .
N
S
. .
. .
. .
. .
N
S
N
S
Salient Pole Construction
Cylindrical Rotor Construction
If prime move speed is low as in case of water turbines, salient pole type is preferred. If the prime mover speed is high as in case of steam turbines, cylindrical rotor is preferred. R S Ananda Murthy
Synchronous Generators
Advantages of Rotating Field Construction
The coil connections can be made easily and securely on the stator than on the rotor. If the armature winding is placed on the rotor, then, three slip rings would be required where as if the poles are placed on the rotor, only two slip rings designed to carry low power for the field winding are required. Transferring large armature power through brush and slip ring causes them to wear out frequently which is prevented if the armature is stationary.
R S Ananda Murthy
Synchronous Generators
Advantages of Rotating Field Construction
As the generated voltage is 11 kV or above, armature winding requires thicker insulation which is difficult to design if the armature is on the rotor. Field winding is lighter than armature winding and therefore it is preferable to place it on the rotor. In very big synchronous generators, forced hydrogen cooling of armature winding is employed which can be conveniently implemented if the armature is stationary.
R S Ananda Murthy
Synchronous Generators
Reasons for Using Distributed Winding
Armature winding in practical generators is uniformly distributed in many slots for the following reasons — It is difficult to put all the conductors of a phase winding in one or two slots. Distributed winding reduces harmonics in the generated voltage and makes the waveform closer to sinusoidal shape. Distributed winding helps in more uniform heat distribution and cooling and thus helps in preventing insulation failure due to excessive heat in the winding.
R S Ananda Murthy
Synchronous Generators
Photograph of Stator Winding
Stator winding of a generator in a hydro-electric power plant. R S Ananda Murthy
Synchronous Generators
Armature Winding Coils Overhang Coil Span
A1
A2
A1
A2
Coil Side
P
Q
Full Pitched Coil
P
Q
Short Pitched Coil
In practical generators, short pitched coils are used to minimize the length of overhangs and also to reduce harmonics in the generated voltage. R S Ananda Murthy
Synchronous Generators
Pitch Factor (Kp ) of Armature Winding Due to short pitched coil, the magnitude of E.M.F. induced e will be slightly reduced when compared to a full pitched coil. For a short pitched coil, the pitch factor is defined as Kp =
Voltage generated in a short pitched coil Voltage generated in a full pitched coil
(1)
Formula for Kp is β (2) 2 where β is the angle in electrical degrees by which the coil is short pitched as shown in the previous slide. Typically Kp is about 0.9 in a practical generator. Kp = cos
R S Ananda Murthy
Synchronous Generators
Distribution Factor (Kd ) of Armature Winding For a distributed winding, the distribution factor, Kd is defined as Kd =
Voltage induced in a distributed winding Voltage induced in a concentrated winding
Kd is given by Kd =
sin(mα/2) m sin(α/2)
(3)
(4)
where α is known as slot angle and m are given by α=
180 S/P
and
m=
S 3P
where S is total number of slots, P is number of poles. Typically Kd is about 0.9 for a practical generator.
R S Ananda Murthy
Synchronous Generators
Frequency of Generated E.M.F.
When a conductor moves past a pair of poles, one cycle of sinusoidal voltage is completed. If P = total number of poles in the machine, then, Number of cycles per revolution =
P 2
(5)
If N = R.P.M. of the motor, then, the rotor makes N/60 R.P.S. Hence, the frequency of the induced E.M.F. is given by f=
PN P N × = Hz 2 60 120
R S Ananda Murthy
Synchronous Generators
(6)
Equation for Induced E.M.F. in an Alternator If P = number of poles in the machine, and Φ = flux per pole, magnetic flux cut by a conductor in one revolution of the rotor = PΦ. If N is the R.P.M., then, time taken by the rotor to make one revolution = 60/N seconds. Therefore, Flux cut per second by a conductor =
PΦ 60/N
But average induced E.M.F. in a conductor = flux cut per second. Therefore Average induced E.M.F. in a conductor =
R S Ananda Murthy
Synchronous Generators
PΦN 60
Equation for Induced E.M.F. in an Alternator If T = total number of turns connected in series per phase, and since each turn will have two conductors, we have Z = Total number of conductors in series per phase = 2T . So, Average E.M.F. induced per phase = |Eav | =
PΦN · 2T 60
The air gap flux in the generator will have more or less sinusoidal distribution. Then, the induced E.M.F. in each phase will also be sinusoidal. For a sinusoidal waveform we have Form Factor =
|Eph | = 1.11 |Eav |
where Eph = R.M.S. value of the induced voltage per phase.
R S Ananda Murthy
Synchronous Generators
Equation for Induced E.M.F. in an Alternator Therefore, the R.M.S. voltage induced per phase is |Eph | = 1.11 ×
PΦN 2.22PΦNT × 2T = 60 60
But the frequency of the induced E.M.F. is given by f=
PN 120
2f =
=⇒
PN 60
Substituting this in Eq. (7) we get |Eph | = 4.44ΦfT
R S Ananda Murthy
Volts
Synchronous Generators
(7)
Equation for Induced E.M.F. in an Alternator In a practical machine the armature winding is evenly distributed in the slots and short pitched coils are used. Due to this, the induced E.M.F. is slightly reduced by a factor Kw where Kw = Kp Kd is known as the winding factor. So, the induced E.M.F. in an actual machine is given by |Eph | = 4.44ΦfTKw
Volts
(8)
Since the three coils in the armature winding of a practical generator are always star connected, the line voltage at the terminals of the synchronous generator is given by √ (9) |E| = 3 × |Eph |
R S Ananda Murthy
Synchronous Generators
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
R S Ananda Murthy
Synchronous Generators
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