Synchronous Motor
Load Change
UCF
Synchronous Motor and Generator (1)
motor
generator
Tind  kB R  B net
Tind  kB R B net sin 
UCF
Synchronous Motor and Generator (2)
Motor
V  R A I A  jX s I A  E A
Generator
V   R A I A  jX s I A  E A
Torque of Synchronous Motor
UCF
V  E A  R A I A  jX s I A  E A  jX s I A
P  3V I A cos 
3
V E A
Xs
Tind 
P
m
sin  (for R A  X s )
3
V E A
m X s
sin 

jX s I A
Tind  kB R B net sin 
X s I A cos   3E A sin 
Pull-out torque: when sin=1, the maximum torque the machine can get.
Tmax  3
V E A
m X s
Tmax  kB R B net
Typically take Tmax  3T full  load in the design (leave margin).
sin   1 / 3 or   19.47 o
Effect of Load Change
UCF
P  3V I A cos   3
V E A
Xs
sin 
V : fixed (from electrical course)
E A : fixed (when I F fixed or using permanent magnets)
P  ( load increases)  sin    I A  more heat (3 I A2 R A )
   (leading  lagging)

jXsIA
P
UCF
Example 1 (1)
A 208 V, 45 kVA, 0.8 PF leading, delta connected 60Hz synchronous motor has a
synchronous reactance of 2.5 and a negligible armature resistance. Its friction and
windage losses are 1.5 kW, and its core losses are 1 kW. Initially, the shaft is supplying 1
15 hp load, and the motor’s power factor is 0.8 leading.
(1) Sketch the phasor diagram of this motor, and find the values of IA, IL and EA.
(2) Assume that the shaft load is now increased to 30 hp. Sketch the behavior of phasor
diagram in response to this change.
(3) Find IA, IL and EA after the load change. What is the new motor power factor?
Details in sm1.m
UCF
Example 1 (2)
Synchronous Motor
Field Current Change
Effects of Field Current Change
UCF
V  E A  R A I A  jX s I A
 E A  jX s I A

UCF
Underexcited Synchronous Motor
UCF
Overexcited Synchronous Motor
Behaves like a capacitor: can be used for power factor correction.
Called synchronous capacitor or synchronous condenser.
UCF
Synchronous Motor V Curves
UCF
Example 2 (1)
A 208 V, 45 kVA, delta connected, 60Hz synchronous motor of Example 1 has a
synchronous reactance of 2.5 and a negligible armature resistance. Its friction and
windage losses are 1.5 kW, and its core losses are 1 kW. Initially, the shaft is supplying 15
hp load, and the motor’s power factor is 0.85 lagging. The field current IF at these
conditions is 4 A.
(1) Sketch the initial phasor diagram of this motor, and find the values of IA and EA.
(2) If the rotor’s flux is increased by 25%, sketch the new phasor diagram in response to
this change. What are EA ,IA and power factor of the motor now?
(3) Assume that the flux in the motor varies linearly with the field current IF. Make a plot
of IA. versus IF. for the synchronous motor with 15 hp load.
sm2.m
UCF
Example 2 (2)
UCF
Example 2 (3)
UCF
Power factor Correction Using Overexcited
Synchronous Motor - Example 3
The infinite bus in the figure operates at 480V. Load 1 is an induction motor consuming
100 kW at 0.78 PF lagging, and load 2 is an induction motor consuming 200 kW at 0.8 PF
lagging. Load 3 is a synchronous motor whose real power consumption is 150 kW.
(1) If the synchronous motor is adjusted to operate at 0.85 PF lagging, what is the
transmission line current in this system?
(2) If the transmission line resistance is 1 , find the transmission line loss.
(3) If the synchronous motor is adjusted to operate at 0.85 PF leading, what is the
transmission line current in this system? How much is the transmission line loss?
sm3.m