Dr. Akram I. Aly
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 Synchronous
machines cover the range from the
miniature permanent magnet synchronous motor in
wall-clocks, to the largest steam-turbine driven
generators of up to about 1500 MVA.
 Synchronous machines are one of two types: the
stationary field or the rotating field.
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 The
stationary field synchronous machine has
salient poles mounted on the stator.
 The poles are magnetized either by permanent
magnets or by a dc current.
 The armature, normally containing a 3-phase
winding, is mounted on the shaft.
 The armature winding is fed through three sliprings and a set of brushes sliding on them.
 This arrangement can be found in machines up to
about 5 kVA in rating.
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 The
field-winding wound on the rotating member.
 The armature wound on the stationary member.
 A dc current energizes the rotating field-winding.
 The rotor field is either of salient-pole or
cylindrical rotor
 Cylindrical rotors are utilized in two- or four-pole
machines. These are typically driven by steam or
combustion turbines.
 Salient-pole machines have six or more poles.
They include all synchronous hydro-generators.
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Two-pole salient pole generator concept
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Four-pole salient pole generator concept
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Two-pole cylindrical rotor generator concept
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View of a two-pole round rotor generator and exciter.
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Part (II)
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• The generator
is at no load.
• The armature is
open circuited .
• No current
flows in the
armature
windings
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Rotation produces flux linkage variation
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θ=ωt
link
f
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Part (III)
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A
balanced three phase load is connected to the
synchronous generator armature.
 The no load EMF produced by the rotating field
causes balanced sinusoidal three phase currents to
flow in the armature windings.
 Balanced three phase load currents in the 3 phase
armature winding result in rotating MMF, known
as the armature reaction MMF, ar.
 The armature reaction MMF rotates at the same
speed of the rotor.
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 Field
(Φf) and load generated (Φar) rotating fluxes.
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 The
armature reaction MMF cuts the armature
windings and induces a counter EMF, Ear
 The armature reaction flux at any point at an angle
θ from the axis of phase a is given by:
 The
induced EMF in armature phase (a) due to
armature reaction is given by:
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 Similarly
the induced EMF’s due to armature
reaction in phase b and c are given by:
 The
r.m.s. value of the EMF’s induced in the
armature due to the armature reaction is:
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 But:
 Where: Ia
is the amplitude of phase a current and
Laa is the self inductance of phase (a).
 Therefore:
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 But
 Xa
is the reactance of the armature winding, and
Ia/√2 = Ia-rms, thus:
 The
voltage at the armature terminals is therefore:
Va=no load EMF – armature reaction EMF
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 The
no load armature EMF is further reduced due
to the flux leakage between the field and armature,
this leakage flux is represented by the leakage
reactance Xl.
 The armature has a resistance Ra, therefore the
equivalent circuit of the synchronous generator is
given by:
Xs=Xa+Xl
Ra
Ea
Ia
Va
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 The
voltage at the terminals of a synchronous
generator is thus:
sum of the armature leakage reactance, Xl, and
the armature reaction reactance, Xa, is known as
the “synchronous reactance” Xs.
 Ra+jXs is known as the synchronous impedance Zs
 The
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Ea
jIaXa
Er
Va
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• In
all but small machines, the armature resistance is
usually neglected.
• With this simplification, the phasor diagram of the
synchronous generator is as shown below
Ea
Va
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Part (IV)
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Connection diagram
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 The
armature terminals are short-circuited through
a current-measuring circuit.
 By driving the machine at rated synchronous
speed, measurements of armature short-circuit
current are made for different values of dc field
excitation current.
 The field current is gradually increased until the
armature current is about 1.5 to 2 times the rated
current.
 The plot of short circuit armature current versus
the field current is known as the short-circuit
characteristic indicated by SCC
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Connection diagram
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
OCC and SCC on the same graph
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 The
unsaturated synchronous impedance per phase:
 The
saturated synchronous impedance per phase at
rated voltage:
 Since
the armature resistance is usually much smaller
than the synchronous reactance, the value of the
synchronous impedance is taken as the synchronous
reactance
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 The
short circuit ratio is: the ratio of the field
current required to generate rated voltage at rated
speed on open-circuit to the field current required
to produce rated armature current under a
sustained three phase short circuit.
 From figure:

 SCR
is the measure of the generator stability
characteristics.
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Part (V)
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 The
complex power output of the generator in
volt-amperes per phase is given by:
 taking
the terminal voltage as reference
Ea
 the
generated voltage
 the
armature current:
Va
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 The
conjugate of armature current:
 Therefore:
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 Equations
(6) and (7) hold good for a cylindricalrotor synchronous generator with negligible
armature resistance.
 To obtain the total power for a three-phase
generator, Equations (6) and (7) should be
multiplied by 3 when the voltages are line-toneutral.
 If the line-to-line magnitudes are used for the
voltages, these equations give the total three-phase
power.
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 The
maximum real electrical power output per
phase of the generator for a given terminal voltage
and a given excitation voltage is:
 Any
further increase in the prime-mover input to
the generator causes the real power output to
decrease, the excess power goes into accelerating
the generator, there by increasing its speed and
causing it to pull out of synchronism.
 steady-state stability limit is reached when δ = π/2.
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 For
normal steady operating conditions, the power
angle or torque angle is well under π/2 .
 The maximum torque or pull-out torque per phase
that a round-rotor synchronous machine can
develop for a gradually applied load is
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