School of Electrical and Computer Engineering
Applied Electronics and Electrical
Machines
(ELEC 365)
Fall 2015
Synchronous Machines
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INTRODUCTION
 The bulk of electric power is generated by synchronous generators.
 They operate at constant speed (𝑁𝑠 ) and constant frequency under steadystate conditions.
 Can operate either as a generator or as a motor.
 Power ratings up to several hundred MVA are common.
 Many generators operate in parallel, even if one generator does not supply
any load, this m/c is kept on the bus.
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CONSTRUCTION DETAILS
Stator: Similar to induction motor, 3-phase distributed windings.
Rotor: Field winding (DC supply). Two types of m/c.
(a) High speed m/c
Round or cylindrical rotor. No protruding parts.
Used in turbo-generators (steam and gas turbines).
[e.g.: 2-pole, 60-Hz, 𝑁𝑠 = 3600 rpm].
(b) Low-speed m/c
Salient pole rotors.
Hydro-electric and diesel electric generators.
[e.g.: 12-pole, 60-Hz, 𝑁𝑠 = 600 rpm. Large number of poles to produce desired
frequency at low speed.]
Cooling: Air + coolant (water, hydrogen and helium).
To cool both windings and magnetic structures.
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CONSTRUCTION DETAILS
Basic structure of the three-phase synchronous machine.
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CONSTRUCTION DETAILS
Salient rotor
The rotating speed delivered to the 4-pole generator
needs to be 1500 RPM (50 hertz) or 1800 RPM (60
hertz).
Cylindrical rotor
15 MW 11 KV 3000 RPM 2 Pole rotor for Paper
Mills company.
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CONSTRUCTION DETAILS
Damper Bars:
Under steady-state m/c runs at synchronous speed (𝑁𝑠 ). However, synchronous
machine undergoes transients during starting and abnormal conditions – rotor
may undergo mechanical oscillations and speed may vary from synchronous
speed. This is not desirable. To overcome this problem: additional windings
(similar to cage of an induction motor) on the rotor, currents are induced in the
damper bars, producing a restoring torque to bring the speed to 𝑁𝑠 . They also
provide a starting torque,
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CONSTRUCTION DETAILS
Synchronous motor rotor with amortisseur winding.
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Field Supply
Field Supply:
(a) Supply through slip rings and brushes.
(i) DC excitation by self-excited DC m/c mounted on the same shaft.
(ii) In low speed machines (hydro-electric generator): A pilot exciter excites the
main exciter.
(iii) Solid state excitation systems: ac-to-dc or dc-to-dc power electronic
converters supply the field through brushes and slip rings.
(b) Rotating rectifier (Brushless system): no brushes or slip rings, rectifier on the
shaft.
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Field Supply
A brushless exciter circuit
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Field Supply
To make the excitation of
a generator completely
independent of any
external power source, a
small pilot exciter is
often added to the
circuit.
The pilot exciter is an AC
generator
with
a
permanent
magnet
mounted on the rotor
shaft and a 3-phase
winding on the stator
producing the power for
the field circuit of the
exciter.
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Example 1
In a factory a 3 phase, 4 kV, 400 kVA synchronous machine is installed along with
other induction motors. The following are the loads on the machines:
Induction motors: 500 kVA at 0.8 PF Lagging.
Synchronous motor: 300 kVA at 1.0PF.
a) Compute the overall power factor of the factory loads.
b) To improve the factory power factor, the synchronous machine is overexcited
(to draw leading current) without any change in its load. Without over loading
the motor, to what extent can the factory power factor be improved? Find the
current and power factor of synchronous motor for this condition.
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Example 1
Solution :
(a) Induction motors:
Power = 500 × 0.8 = 400 kW
Reactive Power = 500 × 0.6 = 300 kVAR
Synchronous motor:
Power = 300 kW
Reactive Power = 0.0
Factory :
Power = 700 kW
Reactive Power = 300 kVAR
Complex Power = 7002 + 3002 = 762 kVA
Power factor =
700
762
= 0.92 lagging
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Example 1
(b)The maximum leading kVAR that the synchronous motor can draw without
exceeding its rating is
4002 − 3002 = 264.58 kVAR
Factory kVAR = j300 – j 264.48 = j35.42 (i.e., lagging)
New factory kVA = 7002 + 35.422 = 700.9 kVA
700
Improved factory factor = 700.9 = 0.996
Synchronous motor current:
ISM =
400 kVA
3×4 kV
= 57.75 A
Synchronous motor power factor:
PFSM =
300 kW
400 kVA
= 0.75 lead
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SYNCHRONOUS GENERATOR OPERATION
Basis: Faraday’s law.
Flux linking the coil changes in time. Therefore, voltage is induced in a coil.
Voltage induced in Phase a:
φ = flux per pole; ω = 2πf rad/sec.;
f = frequency of induced voltage.
Voltage induced in Phase b:
Voltage induced in Phase c:
General: 𝐸0 = Kɸf (rms or peak).
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PERFORMANCE OF ROUND-ROTOR
SYNCHRONOUS GENERATOR
Fig.1: Per-phase equivalent circuit of armature.
where 𝑍𝑠 = synchronous impedance. = 𝑅𝑎 + j𝑋𝑠 Ω
𝑋𝑠 is called as synchronous reactance.
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VOLTAGE REGULATION IN GENERATOR
For the per-phase equivalent circuit shown in Fig.1:
Generally 𝑋𝑠 ≫ 𝑅𝑎 ∶ ∴ 𝑍𝑠 ≅ 𝑗𝑋𝑠
Percent voltage regulation=
𝐸0 −|𝑉𝑡 |
|𝑉𝑡 |
× 100
Regulation can be positive, zero or negative depending on the power factor (PF)
and the load.
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PHASOR DIAGRAMS (Neglecting Ra)
Per-phase armature equivalent circuit of a synchronous m/c neglecting the armature
resistance 𝑅𝑎 . 𝑋𝑠 is the per-phase synchronous reactance.
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PHASOR DIAGRAMS (Neglecting Ra)
Phasor diagram for a synchronous generator (neglecting 𝑅𝑎 ) with a lagging PF load.
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GENERATOR
From phasor diagram:
δ = angle between 𝐸0 and 𝑉𝑡 , called as POWER-ANGLE.
Here generator action is assumed (δ > 0): Terminal (here load) voltage, 𝑉𝑡 , lags
internal voltage, 𝐸0 , by δ.
Power developed (per-phase) 𝑃𝑑 , is applied to the load.
(Called as Power-Angle relation)
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MOTOR
Phasor diagram for a synchronous motor (neglecting Ra) with a lagging PF current
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MOTOR
Same as generator equation but with negative δ!
Terminal (here supply) voltage, 𝑉𝑡 , leads internal voltage, 𝐸0 , by δ.
Power developed, 𝑃𝑑 versus δ: δ < 0, motoring
and δ > 0, generator
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Taking the armature resistance Ra into account (GENERATOR)
Per-phase armature equivalent circuit of a synchronous generator including
the armature resistance 𝑅𝑎 . 𝑋𝑠 is the per-phase synchronous reactance.
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PHASOR DIAGRAM (Including Ra), Unity PF load
Phasor diagram for a synchronous generator (including 𝑅𝑎 ) with a unity PF load
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PHASOR DIAGRAM (Including Ra), Lagging PF (Generator)
Phasor diagram for a synchronous generator (including Ra) with a lagging PF load.
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PHASOR DIAGRAM (Including Ra), Leading PF (Generator)
Phasor diagram for a synchronous generator (including 𝑅𝑎 ) with a leading PF load
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EXPRESSIONS FOR ACTIVE AND REACTIVE POWERS
(Taking Ra into account)
Per-phase armature equivalent circuit of a
synchronous generator including the
armature resistance 𝑅𝑎 . 𝑋𝑠 is the per-phase
synchronous reactance
Phasor diagram for a synchronous generator
(including Ra) with a lagging PF load.
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EXPRESSIONS FOR ACTIVE AND REACTIVE POWERS
From the per-phase equivalent circuit:
*
From (*):
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EXPRESSIONS FOR ACTIVE AND REACTIVE POWERS
where
Using the definition of complex power,
where real power (per-phase) is given by
and reactive power (per-phase) is given by
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EXPRESSIONS FOR ACTIVE AND REACTIVE POWERS
If Xs >> Ra :
Torque (per-phase),
Reactive power:
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TORQUE – SPEED – POWER CHARACTEROSTICS
Power and torque angel characteristics
Torque – speed characteristic
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