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3/28/00 Electromechanical Dynamics 1
Chapter 17: Synchronous Motors
3/28/00 Electromechanical Dynamics 2
Starting a Synchronous Motor
• A synchronous motor can not start by itself– the motor is equipped with a squirrel case winding so as to
start as an induction motor
– during starting, the dc field winding is short circuited
– when the motor has accelerated close to synchronous speed, the dc excitation is then applied to produce the field flux
• Pull-in torque– if the poles on the rotor at the moment the exciting current is
applied happen to be facing poles of opposite polarity on the stator, a strong magnetic attraction is set up between them
• the mutual attraction locks the rotor and stator poles together
• the rotor is literally yanked into step with the revolving field
3/28/00 Electromechanical Dynamics 3
Motor under Load
• At no-load conditions, the rotor poles are directly opposite the stator poles and their axes coincide
• As mechanical load is applied, the rotor poles fall slightly behind the stator poles, but continues to turn at synchronous speed– greater torque is developed
with increase separation angle
– there is a limit when the mechanical load exceeds the pull-out torque; the motor will stall and come to a halt
– the pull-out torque is a function of the dc excitation current and the ac stator current
3/28/00 Electromechanical Dynamics 4
Motor under Load
δ∠=
°∠=
−−=
=−=
00
0
0
0
EE
EE
X
EEjI
EIjX
EEE
S
XS
X
3/28/00 Electromechanical Dynamics 5
Motor under Load
• Example– a 500 hp, 720 rpm synchronous motor connected to a 3980 V,
3-phase line generates an excitation voltage, E0 of 1790 V line-to-neutral when the dc exciting current is 25 A
• the synchronous reactance is 22 ohms
• the torque angle between E0 and E is 30°
– find• the value of EX
• the ac line current
• the power factor of the motor
• the developed horsepower
• the developed torque
3/28/00 Electromechanical Dynamics 6
Power and Torque
• When a synchronous machine operates as a motor under load, the converted power is given by the same equation used for the synchronous generator
• As far as torque is concerned, it is directly proportional the the mechanical power because of the fixed rotor speed
δsin0
SD X
EEP =
S
DD n
PT
55.9=
3/28/00 Electromechanical Dynamics 7
Maximum Torque
• The power equation shows that the mechanical power increases with the torque angle– its maximum value is reached when δ is 90°
– the poles of the rotor are then midway between the north and south poles of the stator
SX
EEP 0
max =
3/28/00 Electromechanical Dynamics 8
Power and Torque
• Example– 150 kW, 460 V, 1200 rpm, 60 Hz motor has a synchronous
reactance of 0.8 Ω per phase
– the excitation voltage is fixed at 300 V per phase
– determine the following:• the power versus the torque angle curve
• the torque versus the torque angle curve
• the pull out torque of the motor
3/28/00 Electromechanical Dynamics 9
Excitation and Reactive Power
• Consider a wye-connected synchronous motor connected to a power system with fixed line voltage VL
– the line current I produces a mmf in the stator
– the dc field current produces a dc mmf in the rotor
– the total flux Φ is created by the combined actions of the two mmf’s
• The total flux Φ induces the voltage Ea in the stator– neglecting the very small voltage drop IRa, Ea = VL
– because VL is fixed, the flux Φ is also fixed, as in a transformer
– the constant flux Φ may be produced either by the stator or the rotor or by both
3/28/00 Electromechanical Dynamics 10
Excitation and Reactive Power
• If the rotor exciting current Ix is zero– all the flux has to be produced by the stator
– the stator circuit absorbs considerable reactive power
• If the rotor exciting current is increased– the rotor mmf helps produce part of the flux
– less reactive power is drawn from the ac power system
• Eventually by raising the rotor exciting current gradually– the rotor produces all of the required flux
– the stator circuit draws no reactive power (unity power factor)
• If the exciting current exceeds this critical level– the stator delivers reactive power to the ac power system
3/28/00 Electromechanical Dynamics 11
Effects of Excitation
VT E
I
j XS
VT
E
I
j XS Iφδ
constantcos
constantsin
sinsin
0
00
==
==
==
T
TS
S
T
TS
V
PI
V
PXE
X
EVP
V
PXE
φ
φ
φφ
φ
δ
δδ
φφ
φδφδ
φδ
φ
φ
sin
cos
cossin0:
sincos:
0
0
0
0
IVQ
IVP
XIE
XIEV
XIjEV
T
T
S
ST
ST
=
=−=ℑ
+=ℜ∠+∠=°∠
3/28/00 Electromechanical Dynamics 12
Effects of Excitation
φm
VT
E0 Im j XS Im δ
VT
E0
Im
j XS Im
φm
δ
VT
E0
Im
j XS Im δ
Unity Power Factor
Lagging Power Factor Leading Power Factor
Constant Power Locus
Constant Power Locus
3/28/00 Electromechanical Dynamics 13
Power Factor Rating
• Most synchronous machines are designed to operate at unity power factor– may be operated at full-load with a 0.8 leading power factor
– this is equivalent to a 0.6 leading reactive power factor
– the motor can deliver a reactive power equal to 75% of the rated mechanical power
3/28/00 Electromechanical Dynamics 14
V-Curves
• Consider a synchronous motor operating at rated mechanical load– examine the behavior as the excitation is varied
• mechanical power remains constant
• at unity power factor the motor current is at a minimum
• at unity power factor the total power equals the active power
• as excitation increases or decreases
– the motor current increases
– the total power increases
– by varying the excitation, a plot of total power, S, with respect to the excitation voltage E0 is generated for a fix load
• the family of active power curves are shaped as the letter V
3/28/00 Electromechanical Dynamics 15
V-Curves
3/28/00 Electromechanical Dynamics 16
Effects of Excitation
• Example– 3000 kW, 200 rpm, 6600 V synchronous motor operates at
full-load at a 80% leading power factor• synchronous reactance is 11 Ω
– calculate the following• the apparent power of the motor
• the ac line current
• the value and phase angle of the induced voltage, E
• draw the phasor diagram
• determine the torque angle, δ
3/28/00 Electromechanical Dynamics 17
Stopping the Synchronous Motor
• Synchronous motors with their loads have large inertia– may take several hours to stop after power has been
disconnected from the power line
– to stop faster, electrical or mechanical braking can be applied• maintain full dc excitation on rotor and short the 3-phase
armature windings (stator windings), or
• maintain full dc excitation on rotor and connect the armature (stator windings) to a bank of external resistors, or
• apply mechanical braking
– with electrical braking, the motor slows because the stored energy is dissipated into the resistive elements of the circuit
– mechanical braking is usually applied only after the motor has reached half speed or less
3/28/00 Electromechanical Dynamics 18
Stopping the Synchronous Motor
• Example– a 1500 kW, 4600 V, 600 rpm motor is stopped by using the
short-circuit method• E0 = 2400, XS = 16 Ω and RA = 0.2Ω, per phase
• moment of inertia = 275 kg m2
– calculate• the power dissipated in the armature at 600 rpm
• the power dissipated in the armature at 150 rpm
• the kinetic energy at 600 rpm
• the kinetic energy at 150 rpm
• the time required for the speed to fall from 600 rpm to 150 rpm
3/28/00 Electromechanical Dynamics 19
Machine Comparison
• Induction machines have excellent properties– when speeds are above 600 rpm
– simple construction and maintenance
– at lower speeds induction machines become heavy and costly with relatively low power factors and efficiencies
• Synchronous motors are particularly attractive for low-speed drives– power factor can always be adjusted to 1.0 with high
efficiencies and reduced weight and costs
– can improve the power factor of a plant while carrying its rated load
– can be designed to deliver a higher starting torque
3/28/00 Electromechanical Dynamics 20
Machine Comparison
a squirrel-cage induction motor and a synchronous motor, both rated at 4000 hp, 1800 r/min, 6.9 kV, 60 Hz.
comparison of the efficiency
comparison of the starting torque
3/28/00 Electromechanical Dynamics 21
Synchronous Condenser
• A synchronous condenser (synchronous capacitor) is a synchronous motor running at no load– only purpose is to absorb or deliver reactive power in order to
stabilize the system voltage
– the machine acts as an enormous 3-phase capacitor or inductor
– the reactive power is varied by changing the dc field excitation
3/28/00 Electromechanical Dynamics 22
Synchronous Condenser
• Example– a synchronous condenser is rated at 160 MVar, 16 kV, and
1200 rpm, and is connected to 16 kV line
– the machine has a synchronous reactance of 0.8 Ω per phase
– calculate the value of E0 so that the machine • absorbs 160 Mvar
• delivers 120 Mvar
3/28/00 Electromechanical Dynamics 23
Synchronous Motors
• Homework– 17-14, 17-15, 17-19, and 17-20