Synchronous Generators
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Nov 19, 2022
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About This Presentation
This lecture note is about Synchronous machines specifically synchronous generators
Slide Content
Chapter Five
Chapter Five
Synchronous Machines
By Yimam A.
June 8, 2022
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous Machines
By Yimam A.
June 8, 2022
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Outline
1Introduction
2Synchronous Generator Construction
3The internal generated voltage of a synchronous generator
4The equivalent circuit of a synchronous generator
5Phasor diagram of a synchronous generator
6Power and torque in synchronous generators
7The synchronous generator operating alone
8Parallel operation of AC generators
By Yimam A. Chapter Five June 8, 2022
Outline
1Introduction
2Synchronous Generator Construction
3The internal generated voltage of a synchronous generator
4The equivalent circuit of a synchronous generator
5Phasor diagram of a synchronous generator
6Power and torque in synchronous generators
7The synchronous generator operating alone
8Parallel operation of AC generators
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Learning Objectives
At the end of this chapter the students should be able to:
Understand the working principle & the equivalent circuit of a synchronous generator.
Sketch phasor diagrams for a synchronous generator.
Know the equations for power and torque in a synchronous generator.
Understand the conditions required to parallel two or more synchronous generators.
Understand the operation of synchronous generators in parallel with a very large
power system (or infinite bus).
Understand the static stability limit of a synchronous generator
By Yimam A. Chapter Five June 8, 2022
Learning Objectives
At the end of this chapter the students should be able to:
Understand the working principle & the equivalent circuit of a synchronous generator.
Sketch phasor diagrams for a synchronous generator.
Know the equations for power and torque in a synchronous generator.
Understand the conditions required to parallel two or more synchronous generators.
Understand the operation of synchronous generators in parallel with a very large
power system (or infinite bus).
Understand the static stability limit of a synchronous generator
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Introduction
Introduction
Synchronous generators or alternators are used to convert mechanical power derived
from steam, gas, or hydraulic-turbine to ac electric power.
In synchronous machines, the armature winding either exports ac power (synchronous
generator) or imports ac power (synchronous motor) where as the field winding is
always energized from dc source
A three phase synchronous machine is doubly excited AC machines because its field
winding is energized from dc source and its armature winding is connected to ac
source.
A synchronous generator called an alternator and is universally employed for the
generator of three-phase power.
The generation of emf, in general depends on the relative motion between the field
flux and armature winding.
By Yimam A. Chapter Five June 8, 2022
Introduction
Introduction
Synchronous generators or alternators are used to convert mechanical power derived
from steam, gas, or hydraulic-turbine to ac electric power.
In synchronous machines, the armature winding either exports ac power (synchronous
generator) or imports ac power (synchronous motor) where as the field winding is
always energized from dc source
A three phase synchronous machine is doubly excited AC machines because its field
winding is energized from dc source and its armature winding is connected to ac
source.
A synchronous generator called an alternator and is universally employed for the
generator of three-phase power.
The generation of emf, in general depends on the relative motion between the field
flux and armature winding.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Introduction
Cont...
In view of this, an ac generator, alternator or synchronous generator may have either
rotating field poles and stationary armature or
rotating armature and stationary field pole.
But practically most of the alternators prefer rotating field type construction with
stationary armature due to certain advantages.
Synchronous machines are constructed with high power armature winding on the
stator and low power field winding on the rotor, though small synchronous machines
with the reverses arrangement may also be built.
By Yimam A. Chapter Five June 8, 2022
Introduction
Cont...
In view of this, an ac generator, alternator or synchronous generator may have either
rotating field poles and stationary armature or
rotating armature and stationary field pole.
But practically most of the alternators prefer rotating field type construction with
stationary armature due to certain advantages.
Synchronous machines are constructed with high power armature winding on the
stator and low power field winding on the rotor, though small synchronous machines
with the reverses arrangement may also be built.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Introduction
Cont...
The machines generating ac emf are called alternators or synchronous generators.
While the machine accepting input from AC supply to produce mechanical output are
called synchronous motors.
Both these machines work at a specific constant speed called synchronous speed and
hence in general called synchronous machines.
All the modern power stations consists of large capacity three phase alternators.
By Yimam A. Chapter Five June 8, 2022
Introduction
Cont...
The machines generating ac emf are called alternators or synchronous generators.
While the machine accepting input from AC supply to produce mechanical output are
called synchronous motors.
Both these machines work at a specific constant speed called synchronous speed and
hence in general called synchronous machines.
All the modern power stations consists of large capacity three phase alternators.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous Generator Construction
Construction of Synchronous Generator
For synchronous machines, the field windings are on the rotor, so the terms rotor
windings and field windings are used interchangeably.
Similarly, the terms stator windings and armature windings are used interchangeably.
Generally a synchronous generator must have at least 2 components:
1Stator Windings or Armature Windings
2Rotor Windings or Field Windings
a)Salient Pole
b)Non Salient Pole
By Yimam A. Chapter Five June 8, 2022
Synchronous Generator Construction
Construction of Synchronous Generator
For synchronous machines, the field windings are on the rotor, so the terms rotor
windings and field windings are used interchangeably.
Similarly, the terms stator windings and armature windings are used interchangeably.
Generally a synchronous generator must have at least 2 components:
1Stator Windings or Armature Windings
2Rotor Windings or Field Windings
a)Salient Pole
b)Non Salient Pole
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous Generator Construction
Salient Pole
Also called projected pole type as all the poles are projected out from the surface of
the rotor.
The field winding is provided on the pole shoe.
These rotors have large diameter and small axial length.
Mechanical strength of salient pole type is less, this is preferred for low speed
alternators ranging from 125 rpm to 500 rpm.
The prime movers used to drive such rotor are generally water turbines and I.C.
engines.
Number of salient poles is between 4 to 60.
Non salient pole rotors are normally used for rotors with 2 or 4 poles rotor, while
salient pole rotors are used for 4 or more poles rotor.
By Yimam A. Chapter Five June 8, 2022
Synchronous Generator Construction
Salient Pole
Also called projected pole type as all the poles are projected out from the surface of
the rotor.
The field winding is provided on the pole shoe.
These rotors have large diameter and small axial length.
Mechanical strength of salient pole type is less, this is preferred for low speed
alternators ranging from 125 rpm to 500 rpm.
The prime movers used to drive such rotor are generally water turbines and I.C.
engines.
Number of salient poles is between 4 to 60.
Non salient pole rotors are normally used for rotors with 2 or 4 poles rotor, while
salient pole rotors are used for 4 or more poles rotor.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous Generator Construction
Cont...
Figure 1:Figure 2: By Yimam A. Chapter Five June 8, 2022
Synchronous Generator Construction
Cont...
Figure 1:Figure 2: By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous Generator Construction
Non-salient pole
This is also called smooth cylindrical type or non projected pole type or round rotor
construction.
The slots are covered at the top with the help of steel or manganese wedges.
The poles are not projecting out and the surface of the rotor is smooth which
maintains uniform air gap between stator and the rotor.
These rotors have small diameters and large axial lengths. This is to keep peripheral
speed within limits.
These are mechanically very strong and thus preferred for high speed alternators
ranging between 1500 to 3000 rpm.
Number of poles is usually 2 or 4.
The prime movers used to drive such type of rotors are generally steam turbines,
electric motors.
By Yimam A. Chapter Five June 8, 2022
Synchronous Generator Construction
Non-salient pole
This is also called smooth cylindrical type or non projected pole type or round rotor
construction.
The slots are covered at the top with the help of steel or manganese wedges.
The poles are not projecting out and the surface of the rotor is smooth which
maintains uniform air gap between stator and the rotor.
These rotors have small diameters and large axial lengths. This is to keep peripheral
speed within limits.
These are mechanically very strong and thus preferred for high speed alternators
ranging between 1500 to 3000 rpm.
Number of poles is usually 2 or 4.
The prime movers used to drive such type of rotors are generally steam turbines,
electric motors.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous Generator Construction
Cont...
By Yimam A. Chapter Five June 8, 2022
Synchronous Generator Construction
Cont...
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous Generator Construction
Cont...
A dc current must be supplied to the field circuit on the rotor.
There are two common approaches to supplying this dc power:
1Supply the dc power from an external dc source to the rotor by means of slip rings and
brushes.
2Supply the dc power from a special dc power source mounted directly on the shaft of the
synchronous generator
Synchronous generator stators are normally made of preformed stator coils in a
double layer winding.
The winding itself is distributed and chorded in order to reduce the harmonic content
of the output voltages and currents
By Yimam A. Chapter Five June 8, 2022
Synchronous Generator Construction
Cont...
A dc current must be supplied to the field circuit on the rotor.
There are two common approaches to supplying this dc power:
1Supply the dc power from an external dc source to the rotor by means of slip rings and
brushes.
2Supply the dc power from a special dc power source mounted directly on the shaft of the
synchronous generator
Synchronous generator stators are normally made of preformed stator coils in a
double layer winding.
The winding itself is distributed and chorded in order to reduce the harmonic content
of the output voltages and currents
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The speed of rotation of a synchronous generator
The speed of rotation of a synchronous generator
Synchronous generators are by definition synchronous, meaning that the electrical
frequency produced is locked in or synchronized with the mechanical rate of rotation
of the generator.
The rate of rotation of the magnetic fields in the machine is related to the stator
electrical frequency
nm=
120fe
p
Wherenm=rotation of synchronous machines magnetic field in rpm.
fe=electrical frequency in Hz
p=number of poles
By Yimam A. Chapter Five June 8, 2022
The speed of rotation of a synchronous generator
The speed of rotation of a synchronous generator
Synchronous generators are by definition synchronous, meaning that the electrical
frequency produced is locked in or synchronized with the mechanical rate of rotation
of the generator.
The rate of rotation of the magnetic fields in the machine is related to the stator
electrical frequency
nm=
120fe
p
Wherenm=rotation of synchronous machines magnetic field in rpm.
fe=electrical frequency in Hz
p=number of poles
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The internal generated voltage of a synchronous generator
The internal generated voltage of a synchronous generator
The magnitude of the voltage induced in a given stator
EA=Kϕω
Whereϕ=flux in the machine
ω=speed of rotation of the machine
k=constant representing the construction of the machine
The internal generated voltageEAis directly proportional to the flux and to the
speed, but the flux itself depends on the current flowing in the rotor field circuit.
SinceEAis directly proportional to the flux, the internal generated voltageEAis
related to the field current.
A plot of the exciting field current versus internal generated voltage of alternator is
known as
By Yimam A. Chapter Five June 8, 2022
The internal generated voltage of a synchronous generator
The internal generated voltage of a synchronous generator
The magnitude of the voltage induced in a given stator
EA=Kϕω
Whereϕ=flux in the machine
ω=speed of rotation of the machine
k=constant representing the construction of the machine
The internal generated voltageEAis directly proportional to the flux and to the
speed, but the flux itself depends on the current flowing in the rotor field circuit.
SinceEAis directly proportional to the flux, the internal generated voltageEAis
related to the field current.
A plot of the exciting field current versus internal generated voltage of alternator is
known as
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The internal generated voltage of a synchronous generator
Cont...
Figure 3:
By Yimam A. Chapter Five June 8, 2022
The internal generated voltage of a synchronous generator
Cont...
Figure 3:
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The equivalent circuit of a synchronous generator
The equivalent circuit of a synchronous generator
The voltageEAis the internal generated voltage produced in one phase of a
synchronous generator.
However, this voltageEAis not usually the voltage that appears at the terminals of
the generator.
In fact, the only time the internal voltageEAis the same as the output voltageVϕof
a phase is when there is no armature current flowing in the machine.
Why is the output voltageVϕfrom a phase not equal toEA?
By Yimam A. Chapter Five June 8, 2022
The equivalent circuit of a synchronous generator
The equivalent circuit of a synchronous generator
The voltageEAis the internal generated voltage produced in one phase of a
synchronous generator.
However, this voltageEAis not usually the voltage that appears at the terminals of
the generator.
In fact, the only time the internal voltageEAis the same as the output voltageVϕof
a phase is when there is no armature current flowing in the machine.
Why is the output voltageVϕfrom a phase not equal toEA?
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The equivalent circuit of a synchronous generator
Cont...
There are a number of factors that cause the difference betweenEAandVϕ
The distortion of the air-gap magnetic field by the current flowing in the stator,
called armature reaction.
The self inductance of the armature coils.
The resistance of the armature coils.
The effect of salient-pole rotor shapes.
By Yimam A. Chapter Five June 8, 2022
The equivalent circuit of a synchronous generator
Cont...
There are a number of factors that cause the difference betweenEAandVϕ
The distortion of the air-gap magnetic field by the current flowing in the stator,
called armature reaction.
The self inductance of the armature coils.
The resistance of the armature coils.
The effect of salient-pole rotor shapes.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The equivalent circuit of a synchronous generator
Cont...
If a load is attached to the terminals of the generator, a current flows.
But a three-phase stator current flow will produce a magnetic field of its own in the
machine.
This stator magnetic field distorts the original rotor magnetic field, changing the
resulting phase voltage. This effect is called armature reaction because the armature
(stator) current affects the magnetic field which produced it in the first place.
With two voltages present in the stator windings, the total voltage in a phase is just
the sum of the internal generated voltageEAand the armature reaction voltageEstat
Vϕ=EA+Estat
IfXis a constant of proportionality,Estat=−jXIA
By Yimam A. Chapter Five June 8, 2022
The equivalent circuit of a synchronous generator
Cont...
If a load is attached to the terminals of the generator, a current flows.
But a three-phase stator current flow will produce a magnetic field of its own in the
machine.
This stator magnetic field distorts the original rotor magnetic field, changing the
resulting phase voltage. This effect is called armature reaction because the armature
(stator) current affects the magnetic field which produced it in the first place.
With two voltages present in the stator windings, the total voltage in a phase is just
the sum of the internal generated voltageEAand the armature reaction voltageEstat
Vϕ=EA+Estat
IfXis a constant of proportionality,Estat=−jXIA
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The equivalent circuit of a synchronous generator
Cont...
In addition to the effects of armature reaction, the stator coils have a self inductance
and a resistance.
If the stator self-inductance is calledLA(and its corresponding reactance is called
XA) while the stator resistance is calledRA, then the total difference betweenEA
andVϕis given by
Vϕ=EA−jXAIA−jXIA−RAIA
Vϕ=EA−j(XA+X)−RAIA
Vϕ=EA−jXsIA−RAIA
WhereXS- Synchronous reactance (X+XA)
By Yimam A. Chapter Five June 8, 2022
The equivalent circuit of a synchronous generator
Cont...
In addition to the effects of armature reaction, the stator coils have a self inductance
and a resistance.
If the stator self-inductance is calledLA(and its corresponding reactance is called
XA) while the stator resistance is calledRA, then the total difference betweenEA
andVϕis given by
Vϕ=EA−jXAIA−jXIA−RAIA
Vϕ=EA−j(XA+X)−RAIA
Vϕ=EA−jXsIA−RAIA
WhereXS- Synchronous reactance (X+XA)
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The equivalent circuit of a synchronous generator
Cont...
By Yimam A. Chapter Five June 8, 2022
The equivalent circuit of a synchronous generator
Cont...
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The equivalent circuit of a synchronous generator
Cont...
The internal field circuit resistance and the external variable resistance have been
combined into a single resistorRF.
EA< δ
◦
=Vϕ<0
◦
+IA<±θ
◦
(RA+jXS)
Figure 4:
By Yimam A. Chapter Five June 8, 2022
The equivalent circuit of a synchronous generator
Cont...
The internal field circuit resistance and the external variable resistance have been
combined into a single resistorRF.
EA< δ
◦
=Vϕ<0
◦
+IA<±θ
◦
(RA+jXS)
Figure 4:
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Phasor diagram of a synchronous generator
Phasor diagram of a synchronous generator
Because the voltages in a synchronous generator are AC voltages, they are usually
expressed as phasors.
Since phasors have both a magnitude and an angle, the relationship between them
must be expressed by a two dimensional plot.
When the voltages within a phase(Vϕ, EA, jXSIA,andRAIA)and the currentIAin
the phase are plotted in such a fashion as to show the relationships among them, the
resulting plot is called a
By Yimam A. Chapter Five June 8, 2022
Phasor diagram of a synchronous generator
Phasor diagram of a synchronous generator
Because the voltages in a synchronous generator are AC voltages, they are usually
expressed as phasors.
Since phasors have both a magnitude and an angle, the relationship between them
must be expressed by a two dimensional plot.
When the voltages within a phase(Vϕ, EA, jXSIA,andRAIA)and the currentIAin
the phase are plotted in such a fashion as to show the relationships among them, the
resulting plot is called a
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Phasor diagram of a synchronous generator
Cont...
(a)(b)(c)
By Yimam A. Chapter Five June 8, 2022
Phasor diagram of a synchronous generator
Cont...
(a)(b)(c)
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Phasor diagram of a synchronous generator
Cont...
For a given phase voltage and armature current, a larger internal generated voltage
EAis needed for lagging loads than for leading loads.
Therefore, a larger field current is needed with lagging loads to get the same terminal
voltage, becauseEA=kϕωandωmust be constant to keep a constant frequency.
For a given field current and magnitude of load current, the terminal voltage is lower
for lagging loads and higher for leading loads.
In real synchronous machines, the synchronous reactance is normally much larger
than the winding resistanceRA, soRAis often neglected in the qualitative study of
voltage variations.
By Yimam A. Chapter Five June 8, 2022
Phasor diagram of a synchronous generator
Cont...
For a given phase voltage and armature current, a larger internal generated voltage
EAis needed for lagging loads than for leading loads.
Therefore, a larger field current is needed with lagging loads to get the same terminal
voltage, becauseEA=kϕωandωmust be constant to keep a constant frequency.
For a given field current and magnitude of load current, the terminal voltage is lower
for lagging loads and higher for leading loads.
In real synchronous machines, the synchronous reactance is normally much larger
than the winding resistanceRA, soRAis often neglected in the qualitative study of
voltage variations.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
Power and torque in synchronous generators
Figure 6:
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
Power and torque in synchronous generators
Figure 6:
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
Cont...
Not all the mechanical power going into a synchronous generator becomes electrical
power out of the machine.
The difference between input power and output power represents the
machine.
The difference between the input power to the generator and the power converted in
the generator represents the
Pin=τappωm Pconv=τindωm= 3EAIAcosγ
Pout=
√
3VLILcosθ= 3VϕIAcosθ
Qout=
√
3VLILsinθ= 3VϕIAsinθ
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
Cont...
Not all the mechanical power going into a synchronous generator becomes electrical
power out of the machine.
The difference between input power and output power represents the
machine.
The difference between the input power to the generator and the power converted in
the generator represents the
Pin=τappωm Pconv=τindωm= 3EAIAcosγ
Pout=
√
3VLILcosθ= 3VϕIAcosθ
Qout=
√
3VLILsinθ= 3VϕIAsinθ
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
Cont...
If the armature resistanceRAis
ignored sinceXS≫RAand
Assuming that load connected to it is
lagging in nature.
WhenRAis assumed to be
zero,Pout=Pconv
SincePconv=τindωm, the induced
torque is:
τind=
3VϕEA
ωmXS
sinδ
Since the resistances are assumed to
be zero , there are no electrical losses
in this generator,
Power converted from mechanical form
to electrical formPconvin a
synchronous generator and the torque
inducedτindin the rotor of the
generator are dependent on the torque
angleδ.
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
Cont...
If the armature resistanceRAis
ignored sinceXS≫RAand
Assuming that load connected to it is
lagging in nature.
WhenRAis assumed to be
zero,Pout=Pconv
SincePconv=τindωm, the induced
torque is:
τind=
3VϕEA
ωmXS
sinδ
Since the resistances are assumed to
be zero , there are no electrical losses
in this generator,
Power converted from mechanical form
to electrical formPconvin a
synchronous generator and the torque
inducedτindin the rotor of the
generator are dependent on the torque
angleδ.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
Cont...
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
Cont...
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
Cont...
The power produced by a synchronous generator depends on the angle betweenVϕ
andEAwhich isδ.
δis known as the
IAcosθ=
EA
XS
sinδ P out= 3VϕIAcosθ
P=
3VϕEA
XS
sinδ
The maximum power that the generator can supply occurs whenδ= 90
◦
orsinδ= 1
which gives thestatic stability limit.
Pmax=
3VϕEA
XS
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
Cont...
The power produced by a synchronous generator depends on the angle betweenVϕ
andEAwhich isδ.
δis known as the
IAcosθ=
EA
XS
sinδ P out= 3VϕIAcosθ
P=
3VϕEA
XS
sinδ
The maximum power that the generator can supply occurs whenδ= 90
◦
orsinδ= 1
which gives thestatic stability limit.
Pmax=
3VϕEA
XS
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
Measuring Synchronous Generator Model Parameters
In order to completely describe the behavior of a real synchronous generator,the
equivalent circuit of a synchronous generator that has been derived contains three
quantities that must be determined
1The saturation characteristic: relationship betweenIFand flux (and therefore between
IFandEA)
2The synchronous reactance
3The armature resistance
The above three quantities could be determined by performing the following three
tests:
1Open circuit test
2Short circuit test
3DC test
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
Measuring Synchronous Generator Model Parameters
In order to completely describe the behavior of a real synchronous generator,the
equivalent circuit of a synchronous generator that has been derived contains three
quantities that must be determined
1The saturation characteristic: relationship betweenIFand flux (and therefore between
IFandEA)
2The synchronous reactance
3The armature resistance
The above three quantities could be determined by performing the following three
tests:
1Open circuit test
2Short circuit test
3DC test
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
1. Open circuit test
To perform this test:
The generator is rotated at the rated speed
The terminals are disconnected from all loads, and
The field current is set to zero and increased to maximum.
Record values of the terminal voltage and field current value
With the terminals open,IA= 0, soEAis equal toVϕ.
It is thus possible to construct a plot ofEAorVTversusIFfrom this information.
This plot is called
The linear portion of an OCC is called the air gap line of the characteristic.
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
1. Open circuit test
To perform this test:
The generator is rotated at the rated speed
The terminals are disconnected from all loads, and
The field current is set to zero and increased to maximum.
Record values of the terminal voltage and field current value
With the terminals open,IA= 0, soEAis equal toVϕ.
It is thus possible to construct a plot ofEAorVTversusIFfrom this information.
This plot is called
The linear portion of an OCC is called the air gap line of the characteristic.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
Cont...
Figure 7:Figure 8:
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
Cont...
Figure 7:Figure 8:
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
2. Short circuit test
To perform the short-circuit test:
Generator is rotated at rated speed
Adjust the field current to zero and
Short-circuit the terminals of the generator through a set of ammeters.
Then the armature currentIAor the line currentILis measured as the field current is
increased.
Such a plot is called a
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
2. Short circuit test
To perform the short-circuit test:
Generator is rotated at rated speed
Adjust the field current to zero and
Short-circuit the terminals of the generator through a set of ammeters.
Then the armature currentIAor the line currentILis measured as the field current is
increased.
Such a plot is called a
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
Cont...
The internal machine impedance is
given by
ZS=
q
R
2
A
+X
2
S
=
EA
IA
SinceXS≫RA, equation reduces to
XS≈
EA
IA
=
Eϕ,OC
IA
IfEAandIAare known for a given
situation, thenXScan be found.
Therefore, an approximate method for
determining the synchronous reactance
XSat a given field current is
1Get the internal generated voltage
EAfrom the OCC at that field
current.
2Get the short circuit current now
IA,SCat that field current from the
SCC.
3FindXSby applying the equation
above.
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
Cont...
The internal machine impedance is
given by
ZS=
q
R
2
A
+X
2
S
=
EA
IA
SinceXS≫RA, equation reduces to
XS≈
EA
IA
=
Eϕ,OC
IA
IfEAandIAare known for a given
situation, thenXScan be found.
Therefore, an approximate method for
determining the synchronous reactance
XSat a given field current is
1Get the internal generated voltage
EAfrom the OCC at that field
current.
2Get the short circuit current now
IA,SCat that field current from the
SCC.
3FindXSby applying the equation
above.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
3. DC test
The purpose of the DC test is to determineRA.
A variable DC voltage source is connected between two stator terminals.
The DC source is adjusted to provide approximately rated stator current, and the
resistance between the two stator leads is determined from the voltmeter and
ammeter readings.Then
RDC=
VDC
IDC
If the stator is Y connected,RDC=
RDC
2
If the stator is∆connected,RDC=
3
2
RDC
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
3. DC test
The purpose of the DC test is to determineRA.
A variable DC voltage source is connected between two stator terminals.
The DC source is adjusted to provide approximately rated stator current, and the
resistance between the two stator leads is determined from the voltmeter and
ammeter readings.Then
RDC=
VDC
IDC
If the stator is Y connected,RDC=
RDC
2
If the stator is∆connected,RDC=
3
2
RDC
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Power and torque in synchronous generators
Short Circuit Ratio(SCR)
The ratio of the field current required
for the rated voltage at open circuit to
the field current required for the rated
armature current at short circuit is
calledshort circuit ratioof a
generator.
SCR=
If,oc
If,sc
=
oa
od
=
ab
de
By Yimam A. Chapter Five June 8, 2022
Power and torque in synchronous generators
Short Circuit Ratio(SCR)
The ratio of the field current required
for the rated voltage at open circuit to
the field current required for the rated
armature current at short circuit is
calledshort circuit ratioof a
generator.
SCR=
If,oc
If,sc
=
oa
od
=
ab
de
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The synchronous generator operating alone
The synchronous generator operating alone
The behavior of a synchronous generator under load varies greatly depending on the
power factor of the load and on whether the generator is operating alone or in parallel
with other synchronous generator.
We shall disregardRAand rotor flux is assumed to be constant unless it is stated
that the field current is changed.
Also, the speed of the generator will be assumed constant, and all terminal
characteristics are drawn assuming constant speed.
By Yimam A. Chapter Five June 8, 2022
The synchronous generator operating alone
The synchronous generator operating alone
The behavior of a synchronous generator under load varies greatly depending on the
power factor of the load and on whether the generator is operating alone or in parallel
with other synchronous generator.
We shall disregardRAand rotor flux is assumed to be constant unless it is stated
that the field current is changed.
Also, the speed of the generator will be assumed constant, and all terminal
characteristics are drawn assuming constant speed.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The synchronous generator operating alone
The effect of load changes on a synchronous generator operating alone
Assumptions:
Field resistor has not been changed, field current is kept constant, hence flux is
constant.
Generator rotor speed is maintained constant.
ThereforeEAis constant.
Load increase:
An increase in the load is an increase in the real and/or reactive power drawn from
the generator.
Such a load increase increases the load current drawn from the generator.
Because the field resistor has not been changed, the field current is constant, and
therefore the fluxϕis constant.
Since the prime mover also keeps a constant speedω, the magnitude of the internal
generated voltageEA=Kϕωis constant.
By Yimam A. Chapter Five June 8, 2022
The synchronous generator operating alone
The effect of load changes on a synchronous generator operating alone
Assumptions:
Field resistor has not been changed, field current is kept constant, hence flux is
constant.
Generator rotor speed is maintained constant.
ThereforeEAis constant.
Load increase:
An increase in the load is an increase in the real and/or reactive power drawn from
the generator.
Such a load increase increases the load current drawn from the generator.
Because the field resistor has not been changed, the field current is constant, and
therefore the fluxϕis constant.
Since the prime mover also keeps a constant speedω, the magnitude of the internal
generated voltageEA=Kϕωis constant.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The synchronous generator operating alone
Initially Lagging pf
Load is increased with the lagging power factor maintained.
Magnitude ofIAwill increase but will maintain the same angle with reference toVϕ
(due to power factor is maintained lagging)
XSIAwill also increase and will maintain the same angle. Since
EA=Vϕ+jXSIA
jXSIAmust stretch betweenVϕat an angle of0
◦
andEA, which is constrained to be
of the same magnitude as before the load increase.
EAhas to remain constant.
Hence the only element which would change to compensate would beVϕ
By Yimam A. Chapter Five June 8, 2022
The synchronous generator operating alone
Initially Lagging pf
Load is increased with the lagging power factor maintained.
Magnitude ofIAwill increase but will maintain the same angle with reference toVϕ
(due to power factor is maintained lagging)
XSIAwill also increase and will maintain the same angle. Since
EA=Vϕ+jXSIA
jXSIAmust stretch betweenVϕat an angle of0
◦
andEA, which is constrained to be
of the same magnitude as before the load increase.
EAhas to remain constant.
Hence the only element which would change to compensate would beVϕ
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The synchronous generator operating alone
Cont...
Figure 9:
By Yimam A. Chapter Five June 8, 2022
The synchronous generator operating alone
Cont...
Figure 9:
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The synchronous generator operating alone
Initially Unity pf
Load is increased with the unity power factor maintained.
Magnitude ofIAwill increase but will maintain the same angle with reference toVϕ
(due to power factor is maintained unity)
XSIAwill also increase and will maintain the same angle. Since
EA=Vϕ+jXSIA
EAhas to remain constant
Hence the only element which would change to compensate would beVϕ.
Changes inVϕwould be decreasing but it would be less significant as compared to
when the load is lagging.
By Yimam A. Chapter Five June 8, 2022
The synchronous generator operating alone
Initially Unity pf
Load is increased with the unity power factor maintained.
Magnitude ofIAwill increase but will maintain the same angle with reference toVϕ
(due to power factor is maintained unity)
XSIAwill also increase and will maintain the same angle. Since
EA=Vϕ+jXSIA
EAhas to remain constant
Hence the only element which would change to compensate would beVϕ.
Changes inVϕwould be decreasing but it would be less significant as compared to
when the load is lagging.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The synchronous generator operating alone
Cont...
Figure 10:Figure 11:
By Yimam A. Chapter Five June 8, 2022
The synchronous generator operating alone
Cont...
Figure 10:Figure 11:
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The synchronous generator operating alone
Initially Leading pf
Load is increased with the leading power factor maintained.
Magnitude ofIAwill increase but will maintain the same angle with reference toVϕ
(due to power factor is maintained leading)
XSIAwill also increase and will maintain the same angle. Since
EA=Vϕ+jXSIA
EAhas to remain constant
Hence the only element which would change to compensate would beVϕ.
By Yimam A. Chapter Five June 8, 2022
The synchronous generator operating alone
Initially Leading pf
Load is increased with the leading power factor maintained.
Magnitude ofIAwill increase but will maintain the same angle with reference toVϕ
(due to power factor is maintained leading)
XSIAwill also increase and will maintain the same angle. Since
EA=Vϕ+jXSIA
EAhas to remain constant
Hence the only element which would change to compensate would beVϕ.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The synchronous generator operating alone
Cont...
Note
However, in practical it is best to keep the output voltage of a generator to be
constant, henceEAhas to be controlled which can be done by controlling the field
currentIF. VaryingIFwill vary the flux in the core which then will varyEA
accordingly.
Generally
1If lagging loads (+Q or inductive reactive power loads) are added to a generator,Vϕ, and
the terminal voltageVTdecrease significantly.
2If unity power factor loads (no reactive power) are added to a generator, there is a slight
decrease inVϕand the terminal voltage.
3If leading loads (-Q or capacitive reactive power loads) are added to a generator,Vϕand
the terminal voltage will rise.
By Yimam A. Chapter Five June 8, 2022
The synchronous generator operating alone
Cont...
Note
However, in practical it is best to keep the output voltage of a generator to be
constant, henceEAhas to be controlled which can be done by controlling the field
currentIF. VaryingIFwill vary the flux in the core which then will varyEA
accordingly.
Generally
1If lagging loads (+Q or inductive reactive power loads) are added to a generator,Vϕ, and
the terminal voltageVTdecrease significantly.
2If unity power factor loads (no reactive power) are added to a generator, there is a slight
decrease inVϕand the terminal voltage.
3If leading loads (-Q or capacitive reactive power loads) are added to a generator,Vϕand
the terminal voltage will rise.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The synchronous generator operating alone
Voltage regulation and efficiency of synchronous generator
The voltage regulation (VR) of a generator is
V R=
Vnl−Vf l
Vf l
×100%
WhereVnlis the no load voltage of the generator
Vf lis the full load voltage of the generator
A convenient way to compare the voltage behavior of two generators is by their
voltage regulation.
For lagging loads, VR would be very positive
For leading loads, VR would be very negative.
For unity loads, VR would be positive
By Yimam A. Chapter Five June 8, 2022
The synchronous generator operating alone
Voltage regulation and efficiency of synchronous generator
The voltage regulation (VR) of a generator is
V R=
Vnl−Vf l
Vf l
×100%
WhereVnlis the no load voltage of the generator
Vf lis the full load voltage of the generator
A convenient way to compare the voltage behavior of two generators is by their
voltage regulation.
For lagging loads, VR would be very positive
For leading loads, VR would be very negative.
For unity loads, VR would be positive
By Yimam A. Chapter Five June 8, 2022
Chapter Five
The synchronous generator operating alone
Cont...
In practical it is best to keep the output voltage of a generator to be constant, hence
EAhas to be controlled which can be done by controlling the field currentIF.
VaryingIFwill vary the flux in the core which then will varyEAaccordingly.
Efficiency of synchronous generator
η=
Pout
Pin
×100%
=
Pout
Pout+losses
×100%
@Examples
By Yimam A. Chapter Five June 8, 2022
The synchronous generator operating alone
Cont...
In practical it is best to keep the output voltage of a generator to be constant, hence
EAhas to be controlled which can be done by controlling the field currentIF.
VaryingIFwill vary the flux in the core which then will varyEAaccordingly.
Efficiency of synchronous generator
η=
Pout
Pin
×100%
=
Pout
Pout+losses
×100%
@Examples
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Parallel operation of AC generators
For all usual generator applications, there is more than one generator operating in
parallel to supply the power demanded by the loads.
Why synchronous generators are operated in parallel?
1Handling larger loads-Several generators can supply a bigger load than one machine by
itself.
2Maintenance can be done without power disruption-Having many generators operating
in parallel allows one or more of them to be removed for shutdown and preventive
maintenance.
3Increasing system reliability-The failure of anyone of them does not cause a total power
loss to the load.
4Increased efficiency-If only one generator is used and it is not operating at near full load,
then it will be relatively inefficient.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Parallel operation of AC generators
For all usual generator applications, there is more than one generator operating in
parallel to supply the power demanded by the loads.
Why synchronous generators are operated in parallel?
1Handling larger loads-Several generators can supply a bigger load than one machine by
itself.
2Maintenance can be done without power disruption-Having many generators operating
in parallel allows one or more of them to be removed for shutdown and preventive
maintenance.
3Increasing system reliability-The failure of anyone of them does not cause a total power
loss to the load.
4Increased efficiency-If only one generator is used and it is not operating at near full load,
then it will be relatively inefficient.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
The conditions required for paralleling
Paralleling two or more generators must be done carefully as to avoid generator or
other system component damage.
Before connecting a generator in parallel with another generator, it must be
synchronized.
A generator is said to be synchronized when it meets all the following conditions
1The rms line voltages of the two generators must be equal.
2The two generators must have the same phase sequence.
3The phase angles of the two phases must be equal.
4The oncoming generator (the new generator) must have a slightly higher operating
frequency as compared to the frequency of the running system.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
The conditions required for paralleling
Paralleling two or more generators must be done carefully as to avoid generator or
other system component damage.
Before connecting a generator in parallel with another generator, it must be
synchronized.
A generator is said to be synchronized when it meets all the following conditions
1The rms line voltages of the two generators must be equal.
2The two generators must have the same phase sequence.
3The phase angles of the two phases must be equal.
4The oncoming generator (the new generator) must have a slightly higher operating
frequency as compared to the frequency of the running system.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Frequency-power and voltage-reactive power characteristics of SG
All generators are driven by a prime mover, which is the generator’s source of
mechanical power.
All prime movers tend to behave in a similar fashion as the power drawn from them
increases, the speed at which they turn decreases.
The decrease in speed is in general non linear, but some form of governor mechanism
is usually included to make the decrease in speed linear with an increase in power
demand
Whatever governor mechanism is present on a prime mover, it will always be adjusted
to provide a slight drooping characteristic with increasing load.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Frequency-power and voltage-reactive power characteristics of SG
All generators are driven by a prime mover, which is the generator’s source of
mechanical power.
All prime movers tend to behave in a similar fashion as the power drawn from them
increases, the speed at which they turn decreases.
The decrease in speed is in general non linear, but some form of governor mechanism
is usually included to make the decrease in speed linear with an increase in power
demand
Whatever governor mechanism is present on a prime mover, it will always be adjusted
to provide a slight drooping characteristic with increasing load.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
The speed droop (SD) of a prime mover is defined as:
SD=
nnl−nf l
nf l
×100%
Wherennlis the no-load prime mover speed
nf lis the full-load prime mover speed.
Typical values of SD are 2% – 4%.
Most governors have some type of set point adjustment to allow the no-load speed of
the turbine to be varied.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
The speed droop (SD) of a prime mover is defined as:
SD=
nnl−nf l
nf l
×100%
Wherennlis the no-load prime mover speed
nf lis the full-load prime mover speed.
Typical values of SD are 2% – 4%.
Most governors have some type of set point adjustment to allow the no-load speed of
the turbine to be varied.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
Since mechanical speed is related to the electrical frequency and electrical frequency
is related with the output power, hence we will obtain the following equation:
P=sp(fnl−fsys)
Where P= output power
fnl=no load frequency of the generator
fsys=operating frequency of system
sp=slope of curve in kW/Hz or MW/Hz
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
Since mechanical speed is related to the electrical frequency and electrical frequency
is related with the output power, hence we will obtain the following equation:
P=sp(fnl−fsys)
Where P= output power
fnl=no load frequency of the generator
fsys=operating frequency of system
sp=slope of curve in kW/Hz or MW/Hz
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
Figure 12:
mover
Figure 13:
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
Figure 12:
mover
Figure 13:
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
When a lagging load is added to a
synchronous generator, its terminal
voltage drops.
When a leading load is added to a
synchronous generator, its terminal
voltage increases.
It is possible to make a plot of
terminal voltage versus reactive power.
Figure 14: VTvsQcurve of SG
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
When a lagging load is added to a
synchronous generator, its terminal
voltage drops.
When a leading load is added to a
synchronous generator, its terminal
voltage increases.
It is possible to make a plot of
terminal voltage versus reactive power.
Figure 14: VTvsQcurve of SG
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
When a single generator is operating alone, then
For any given real power, the governor set points control the generator operating
frequency (fe) of the power system.
For any given reactive power, the field current controls the generator’s terminal
voltage (VT) of the power system.
Real and reactive power supplied will be the amount demanded by the load attached
to the generator-the P and Q supplied cannot be controlled by the generator’s
controls.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
When a single generator is operating alone, then
For any given real power, the governor set points control the generator operating
frequency (fe) of the power system.
For any given reactive power, the field current controls the generator’s terminal
voltage (VT) of the power system.
Real and reactive power supplied will be the amount demanded by the load attached
to the generator-the P and Q supplied cannot be controlled by the generator’s
controls.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Operation of generators in parallel with large power systems
Changes in one generator in large power systems may not have any effect on the
system.
A large power system may be represented as an infinite bus system.
An infinite bus is a power system so large that its voltage and frequency do not vary
regardless of how much real and reactive power is drawn from or supplied to it.
The power frequency characteristic and the reactive power-voltage characteristic are
shown below.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Operation of generators in parallel with large power systems
Changes in one generator in large power systems may not have any effect on the
system.
A large power system may be represented as an infinite bus system.
An infinite bus is a power system so large that its voltage and frequency do not vary
regardless of how much real and reactive power is drawn from or supplied to it.
The power frequency characteristic and the reactive power-voltage characteristic are
shown below.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
Figure 15: fvsPFigure 16: VTvsQ
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
Figure 15: fvsPFigure 16: VTvsQ
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
Consider adding a generator to an infinite bus supplying a load.
The frequency and terminal voltage of all machines must be the same.
Therefore, their power-frequency and reactive power voltage characteristics can be
plotted with a common vertical axis.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
Consider adding a generator to an infinite bus supplying a load.
The frequency and terminal voltage of all machines must be the same.
Therefore, their power-frequency and reactive power voltage characteristics can be
plotted with a common vertical axis.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
Figure 17:
infinite bus
Figure 18:
(house diagram) for a SG in parallel with an
infinite bus.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
Figure 17:
infinite bus
Figure 18:
(house diagram) for a SG in parallel with an
infinite bus.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
The effect of increasing the governor’s set points
If an attempt is made to increase the speed of the generator after it is connected to
the infinite bus, the system frequency cannot change and the power supplied by the
generator increases.
EAsinδhas increased, while the magnitude ofEAremains constant, since both the
field currentIFand the speed of rotation is unchanged.
As the governor set points are further increased the no-load frequency increases and
the power supplied by the generator increases.
As the power output increases,EAremains at constant magnitude whileEAsinδis
further increased.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
The effect of increasing the governor’s set points
If an attempt is made to increase the speed of the generator after it is connected to
the infinite bus, the system frequency cannot change and the power supplied by the
generator increases.
EAsinδhas increased, while the magnitude ofEAremains constant, since both the
field currentIFand the speed of rotation is unchanged.
As the governor set points are further increased the no-load frequency increases and
the power supplied by the generator increases.
As the power output increases,EAremains at constant magnitude whileEAsinδis
further increased.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
Figure 19:Figure 20:
governor’s set point on the phasor diagram
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
Figure 19:Figure 20:
governor’s set point on the phasor diagram
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Field current control effects
Increasing the governor set point will increase power but will cause the generator to
absorb some reactive power.
By adjusting the field current of the machine, it is possible to make it to make the
generator supply or consume reactive power Q.
If the power supplied is constant as the field current is changed, then the distances
proportional to the power in the phasor diagram(IAcosθ&EAsinδ)cannot change.
When the field current is increased, the fluxϕincreases, and therefore(EA=kϕω)
increases.
IfEAincreases, butEAsinδmust remain constant, then the phasorEAmust “slide”
along the line of constant power.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Field current control effects
Increasing the governor set point will increase power but will cause the generator to
absorb some reactive power.
By adjusting the field current of the machine, it is possible to make it to make the
generator supply or consume reactive power Q.
If the power supplied is constant as the field current is changed, then the distances
proportional to the power in the phasor diagram(IAcosθ&EAsinδ)cannot change.
When the field current is increased, the fluxϕincreases, and therefore(EA=kϕω)
increases.
IfEAincreases, butEAsinδmust remain constant, then the phasorEAmust “slide”
along the line of constant power.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont..
Figure 21:
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont..
Figure 21:
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
For a generator operating in parallel with an infinite bus:
1Frequency and terminal voltage of generator is controlled by the connected system.
2Changes in governor set points will control real power to be supplied.
3Changes in field current will control the amount of reactive power to be supplied.
Note that
These effects are only applicable for generators in a large system only.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
For a generator operating in parallel with an infinite bus:
1Frequency and terminal voltage of generator is controlled by the connected system.
2Changes in governor set points will control real power to be supplied.
3Changes in field current will control the amount of reactive power to be supplied.
Note that
These effects are only applicable for generators in a large system only.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Generators in parallel with other generators of the same size
In this system, the basic constraint is that the sum of the real and reactive powers
supplied by the two generators must equal the P and Q demanded by the load.
The system frequency is not constrained to be constant, and neither is the power of a
given generator constrained to be constant.
Ptot=Pload=PG1+PG2
Qtot=Qload=QG1+QG2
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Generators in parallel with other generators of the same size
In this system, the basic constraint is that the sum of the real and reactive powers
supplied by the two generators must equal the P and Q demanded by the load.
The system frequency is not constrained to be constant, and neither is the power of a
given generator constrained to be constant.
Ptot=Pload=PG1+PG2
Qtot=Qload=QG1+QG2
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
Figure 22:
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
Figure 22:
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
Unlike the case of an infinite bus, the
slope of the frequency-power curve of
G1is of the same order of magnitude
as that ofG2.
The power frequency diagram right
afterG2is connected to the system is
shown to the right.
In order forG2to come in as a
generator, its frequency should be
slightly higher than that ofG1.
Figure 23:
generator 2 is paralleled with the system.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
Unlike the case of an infinite bus, the
slope of the frequency-power curve of
G1is of the same order of magnitude
as that ofG2.
The power frequency diagram right
afterG2is connected to the system is
shown to the right.
In order forG2to come in as a
generator, its frequency should be
slightly higher than that ofG1.
Figure 23:
generator 2 is paralleled with the system.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
When 2 generators are operating
together in parallel, an increase in
governor set points on one of them
1Increases the system frequency.
2Increases the power supplied by that
generator, while reducing the power
supplied by the other one.
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
When 2 generators are operating
together in parallel, an increase in
governor set points on one of them
1Increases the system frequency.
2Increases the power supplied by that
generator, while reducing the power
supplied by the other one.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Parallel operation of AC generators
Cont...
When 2 generators are operating
together in parallel and the field
current ofG2is increased,
1The system terminal voltage is
increased.
2The reactive power Q supplied by
that generator is increased, while the
reactive power supplied by the other
generator is decreased.
3To bring the voltage down, the field
current ofG1must be reduced.
@Examples
By Yimam A. Chapter Five June 8, 2022
Parallel operation of AC generators
Cont...
When 2 generators are operating
together in parallel and the field
current ofG2is increased,
1The system terminal voltage is
increased.
2The reactive power Q supplied by
that generator is increased, while the
reactive power supplied by the other
generator is decreased.
3To bring the voltage down, the field
current ofG1must be reduced.
@Examples
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous generator capability curve
Synchronous generator capability curve
The operation of the synchronous generator is restricted by the following factors
Heating limit of the armature winding
Heating limit of the field winding
Maximum Power limit
The capability curve is a graphic representation of the limit of the operating
condition.
The curve is plotted in a complex power plane(S=P+jQ). The curve is derived
from the phasor diagram (withRa= 0)
The stator and rotor heat limits, together with any external limits on a synchronous
generator, can be expressed in graphical form by a generator capability diagram.
Assume that a voltage phasor as shown, operating at lagging power factor and its
rated value.
By Yimam A. Chapter Five June 8, 2022
Synchronous generator capability curve
Synchronous generator capability curve
The operation of the synchronous generator is restricted by the following factors
Heating limit of the armature winding
Heating limit of the field winding
Maximum Power limit
The capability curve is a graphic representation of the limit of the operating
condition.
The curve is plotted in a complex power plane(S=P+jQ). The curve is derived
from the phasor diagram (withRa= 0)
The stator and rotor heat limits, together with any external limits on a synchronous
generator, can be expressed in graphical form by a generator capability diagram.
Assume that a voltage phasor as shown, operating at lagging power factor and its
rated value.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous generator capability curve
Cont...
?The capability curve of the synchronous
generator represent power limits of the
generator, hence there is a need to convert
the voltage phasor into power phasor.
Horizontal component(Voltage)
OA=IaXscos (90
◦
−θ) =IaXssinθ
Vertical component(Voltage)
AB=IaXssin (90
◦
−θ) =IaXscosθ
Figure 24: Ra= 0
By Yimam A. Chapter Five June 8, 2022
Synchronous generator capability curve
Cont...
?The capability curve of the synchronous
generator represent power limits of the
generator, hence there is a need to convert
the voltage phasor into power phasor.
Horizontal component(Voltage)
OA=IaXscos (90
◦
−θ) =IaXssinθ
Vertical component(Voltage)
AB=IaXssin (90
◦
−θ) =IaXscosθ
Figure 24: Ra= 0
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous generator capability curve
Cont...
The conversion factor needed to
change the scale of the axes from volts
to volt amperes (power units) is
3Vϕ
XS
:
P=
3Vϕ
XS
(XSIAcosθ) = 3VϕIAcosθ
Q=
3Vϕ
XS
(XSIAsinθ) = 3VϕIAsinθ
S=
3Vϕ
XS
(XSIA) = 3VϕIA
Figure 25:
By Yimam A. Chapter Five June 8, 2022
Synchronous generator capability curve
Cont...
The conversion factor needed to
change the scale of the axes from volts
to volt amperes (power units) is
3Vϕ
XS
:
P=
3Vϕ
XS
(XSIAcosθ) = 3VϕIAcosθ
Q=
3Vϕ
XS
(XSIAsinθ) = 3VϕIAsinθ
S=
3Vϕ
XS
(XSIA) = 3VϕIA
Figure 25:
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous generator capability curve
Cont...
On the voltage axes, the origin of the
phasor diagram is atVϕon the
horizontal axis, so the origin on the
power diagram is at
Q=
3Vϕ
XS
(−Vϕ)
=
−3V
2
ϕ
XS
The field current is proportional to the
machine’s flux, and the flux is
proportional toEA=kϕω.
The length corresponding toEAon
the power diagram is
DE=
−3EAVϕ
XS
Any point that lies within both circles is a
safe operating point for the generator
By Yimam A. Chapter Five June 8, 2022
Synchronous generator capability curve
Cont...
On the voltage axes, the origin of the
phasor diagram is atVϕon the
horizontal axis, so the origin on the
power diagram is at
Q=
3Vϕ
XS
(−Vϕ)
=
−3V
2
ϕ
XS
The field current is proportional to the
machine’s flux, and the flux is
proportional toEA=kϕω.
The length corresponding toEAon
the power diagram is
DE=
−3EAVϕ
XS
Any point that lies within both circles is a
safe operating point for the generator
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous generator capability curve
Cont...
The operation limit is imposed due to armature current limit (Ia) and field current
limit (If).
The length of the phasorO
′
B
′
representing apparent power decides the limit of armature
current.
The length of the phasorC
′
B
′
representing maximum power decides the limit of field
current
The armature current cannot exceed the circular locus and the field current cannot
exceed the circular locus.
The operating region of the synchronous generator lies within the common region
between the two circular loci.
The synchronous generator capability curve is the overlapping region of the two
limiting circular loci.
By Yimam A. Chapter Five June 8, 2022
Synchronous generator capability curve
Cont...
The operation limit is imposed due to armature current limit (Ia) and field current
limit (If).
The length of the phasorO
′
B
′
representing apparent power decides the limit of armature
current.
The length of the phasorC
′
B
′
representing maximum power decides the limit of field
current
The armature current cannot exceed the circular locus and the field current cannot
exceed the circular locus.
The operating region of the synchronous generator lies within the common region
between the two circular loci.
The synchronous generator capability curve is the overlapping region of the two
limiting circular loci.
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous generator capability curve
Cont...
By Yimam A. Chapter Five June 8, 2022
Synchronous generator capability curve
Cont...
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Synchronous generator capability curve
Cont...
By Yimam A. Chapter Five June 8, 2022
Synchronous generator capability curve
Cont...
By Yimam A. Chapter Five June 8, 2022
Chapter Five
Questions
Thank You!
By Yimam A. Chapter Five June 8, 2022
Questions
Thank You!
By Yimam A. Chapter Five June 8, 2022
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