Chapter Four

Synchronous Machines
 A synchronous machine rotates at a constant
speed in the steady state. Unlike induction
machines, the rotating air gap field and the rotor
in the synchronous machine rotate at the same
speed, called the synchronous speed.
 Like most rotating machines, a synchronous
machine can also operate as both a generator and
a motor. In large sizes (several hundred or
thousand kilowatts) synchronous motors are used
for pumps in generating stations and in small
sizes (fractional horsepower) they are used in
electrical clocks, timers, record turntables, and so
forth where constant speed is desired.
 Cont’d…
A synchronous machine is a doubly excited
machine. Its rotor poles are excited by a dc
current and its stator windings are connected to
the ac supply .
The air gap flux is therefore the resultant of the
fluxes due to both rotor current and stator
current.
In induction machines, the only source of
excitation is the stator current, because rotor
currents are induced currents.
 Construction of Three-phase Synchronous
Machines
 The stator of the three-phase synchronous machine has a
three-phase distributed winding similar to that of the
three-phase induction machine. Unlike the dc machine,
the stator winding, which is connected to the ac supply
system, is sometimes called the armature winding. It is
designed for high voltage and current.
 The rotor has a winding called the field winding, which
carries direct current. The field winding on the rotating
structure is normally fed from an external dc source
through slip rings and brushes.
 Synchronous machines can be broadly divided into two
groups as follows
 Cont’d…
High-speed
machines with
cylindrical (or
non-salient pole)
rotors.
 Low-speed
machines with
salient pole
rotors.
 Cont’d…
Salient pole syn machines Cylindrical rotor or Round
rotor or Non-salient type syn
machines
Uniform air gap

Salient pole
Non-uniform air gap, Cylindrical rotor
 Cont’d…
Poles > 4 Poles ≤ 4
Used in LOW speed machine HIGH speed machine

Small core length, large Long length, small diameter

diameter to accommodate to limit large centrifugal
large no of poles. forces due to high speed.

Under fault, there are Under fault, there are less

more chances of chances of deformation of
deformation of rotor due rotor due to uniform air gap.
to non-uniform air gap. Output waveform is more nearer
Output waveform is not to sine wave.
sinusoidal
(more harmonics)
 Synchronous Generators
 In Synchronous Generator, a DC current is applied to
rotor winding (produce rotor magnetic field).
 The rotor is turned by prime over producing a rotating
magnetic field.
 The rotating magnetic field produce three phase sets of
voltages within the stator.
Armature winding [in stator]
Field winding [in rotor]
 The rotating flux so produced will change the flux linkage
of the armature windings aa', bb', and cc' and will induce
voltages in these stator windings. These induced voltages,
shown in fig 4.1, have the same magnitudes but are phase-
shifted by 120°electrical degrees.
 Cont’d…

Fig 4.1 Excitation voltage in synchronous machines

They are called excitation voltages Ef. The rotor speed and
frequency of the induced voltage are related by
 Cont’d…
 Where n is the rotor speed in rpm
 P is the number of poles
 The excitation voltage in rms is

Where φf is the flux per pole due to the excitation Current If

N is the number of turns in each phase
Kw is the winding factor

The excitation voltage is proportional to the machine speed and

excitation flux, and the latter in turn depends on the excitation
current If.
 Cont’d…
 The variation of the excitation voltage with the field
current is shown in Fig 4.2. The induced voltage at If
= 0 is due to the residual magnetism. Initially the
voltage rises linearly with the field current, but as the
field current is further increased, the flux f does not
increase linearly with If because of saturation of the
magnetic circuit, and therefore Ef levels off. If the
machine terminals are kept open, the excitation
voltage is the same as the terminal voltage and can be
measured using a voltmeter.
 The curve shown in Fig 4.2 is known as the open-
circuit characteristic (OCC) or- magnetization
characteristic of the synchronous machine.
 Cont’d…

Fig 4.2 Open circuit characteristic (OCC) or

magnetization characteristic of a synchronous machine.
 Synchronous Motors
 When synchronous machine is used as a motor, one
should be able to connect it directly to the power supply
like other motors, such as dc motors or induction motors.
 However, a synchronous motor is not self-starting. If the
rotor field poles are excited by the field current and the
stator terminals are connected to the ac supply, the motor
will not start; instead, it vibrates.
 Two methods are normally used to start a synchronous
motor:
• use variable-frequency supply or
• start the machine as an induction motor.
 Start with Variable-Frequency Supply
• By using a frequency converter, a synchronous motor
can be brought from standstill to its desired speed.
The arrangement is shown schematically in Fig 4.3.
The motor is started with a low-frequency supply.
This will make the stator field rotate slowly so that
the rotor poles can follow the stator poles. Afterward,
the frequency is gradually increased and the motor
brought to its desired speed.
• The frequency converter is a costly power
conditioning unit, and therefore this method is
expensive. However, if the synchronous motor has to
run at variable speeds, this method may be used.
 Cont’d…

Fig 4.3 Starting of a synchronous motor using a

variable-frequency supply.
 Start as an Induction Motor
 If the frequency converter is not available, or if the
synchronous motor does not have to run at various speeds, it
can be started as an induction motor.
 For this purpose an additional winding, which resembles the
cage of an induction motor, is mounted on the rotor. This cage-
type winding is known a damper or amortisseur winding
 To start the motor the field winding is left unexcited; often it is
shunted by a resistance.
 If the motor terminals are now connected to the ac supply, the
motor will start as an induction motor because currents will be
induced in the damper winding to produce torque. The motor
will speed up and will approach synchronous speed. The rotor
is then closely following the stator field poles, which are
rotating at the synchronous speed.
 Now if the rotor poles are excited by a field current from a dc
source, the rotor poles, closely following the stator poles, will
be locked to them.
 The rotor will then run at synchronous speed.
 Cont’d…
 If the machine runs at synchronous speed, no current will
be induced in the damper winding. The damper winding
is therefore operative for starting.
 Note that if the rotor speed is different from the
synchronous speed because of sudden load change or
other transients, currents will be induced in the damper
winding to produce a torque to restore the synchronous
speed. The presence of this restorative torque is the
reason for the name "damper" winding.
 Also note that a damper winding is not required to start a
synchronous generator and parallel it with the infinite
bus. However, both synchronous generators and motors
have damper windings to damp out transient oscillations.
 Cont’d…

Fig 4.4 cage-type damper (or amortisseur) winding in a

synchronous machine
 Equivalent Circuit Model
 We can now develop an equivalent circuit model that can
be used to study the performance characteristics with
sufficient accuracy.
 The equivalent circuit will be derived on a per-phase basis.
 The current If in the field winding produces a flux f in the
air gap. The current Ia in the stator winding produces flux
a. Part of it, al, known as the leakage flux, links with the
stator winding only and does not link with the field
winding. A major part, ar, known as the armature reaction
flux, is established in the air gap and links with the field
winding.
 The resultant air gap flux r is therefore due to the two
component fluxes, f and ar. Each component flux induces
a component voltage in the stator winding.
 Cont’d…
 Ef is induced by f , Ear by ar , and the resultant voltage Er by the
resultant flux r. The excitation voltage Ef can be found from the
open-circuit curve. However, the voltage Ear, known as the
armature reaction voltage, depends on ar (and hence on Ia).


If the two reactances Xar and Xal are combined into one reactance, the
equivalent circuit model reduces to the form
 Cont’d…

Equivalent circuit of a synchronous machine

 Cont’d…
The synchronous reactance Xs takes into
account all the flux, magnetizing as well as
leakage, produced by the armature (stator)
current.
 Power and Torque Characteristics
 A synchronous machine is normally connected to a fixed-voltage
bus and operates at a constant speed. There is a limit on the power
a synchronous generator can deliver to the infinite bus and on the
torque that can be applied to the synchronous motor without
losing synchronism.
 The per-phase equivalent circuit is shown again in Figure 4.5 for
convenience , where Vt is the constant bus voltage per phase and
is considered as the reference phasor.

Figure 4.5 Per-phase equivalent circuit

 Cont’d…

 The per-phase complex power S at the terminals is

 The conjugate of the current phasor Ia is used to conform with

the conversion that lagging reactive power is considered as
positive and leading reactive power as negative.
Cont’d…
 Cont’d…
• If Ra is neglected, then Zs = Xs and s =90.

Because the stator losses are neglected in this analysis, the power
developed at the terminals is also the air gap power.
 Cont’d…
The developed torque of the machine is

Both power and torque vary sinusoid ally with the

angle , which is called the power angle or torque
angle.
Example 4.1 A 3, 5 kVA, 208 V, four-pole, 60 Hz, star
connected synchronous machine has negligible stator
winding resistance and a synchronous reactance of 8 
per phase at rated terminal voltage. The machine is first
operated as a generator in parallel with a 3, 208 V, 60 Hz
power supply.
a) Determine the excitation voltage and the power
angle when the machine is delivering rated kVA at
0.8 pf lagging.
b) What are the corresponding values of the stator (or
armature) current, power factor, and reactive power
at this maximum power transfer condition?
The maximum power transfer occurs at  = 90.