Effect of Non sinusoidal waveform of A.C. Machine performance
Nonsinusoidal Waveforms
Key Similarities and Differences between Sinusoidal and Nonsinusoidal Waveforms
Effect of harmonics in motor drives
Square wave inverter with 180° mode
Effect of leakage reactance on the harmonic content of current
Parasitic torques due to non-sinusoidal voltages
2. Introduction
Nonsinusoidal Waveforms
Key Similarities and Differences between
Sinusoidal and Nonsinusoidal Waveforms
Effect of harmonics in motor drives
Square wave inverter with 180° mode
Effect of leakage reactance on the harmonic
content of current
Parasitic torques due to non-sinusoidal voltages
3. We have to use some kind and inverter to provide a
variable stator voltage, variable frequency stator
supply more the induction motor.
If the square wave voltage source inverter is used,
with 180° mode then it produce a rectangular or
stepped voltage waveform independent of the load
current.
The performance of the induction motor depends
upon the type of inverter.
There is an important major effect of non sinusoidal
stator voltage on the performance of induction
motor I.e. Production of harmonic currents.
4. In many electronic applications, other waveforms
besides sine and cosine are important. Some of those
forms are shown below.
Square wave
Sawtooth wave
Pulse wave
Common in digital
electronic circuitry
Used in timing
and control
circuitry
Used in digital
and control
circuitry
5. For all waveforms, the cycle is measured
between two points having the same amplitude
and varying in the same direction.
Peak amplitude is measured from the zero
axis to the maximum positive or negative
value.
Peak-to-peak amplitude is better for
measuring nonsinusoidal waveshapes
because they can have unsymmetrical peaks.
6. The rms value 0.707 applies only to sine
waves.
Phase angles apply only to sine waves.
All the waveforms represent ac voltages.
Positive values are shown above the zero axis,
and negative values are shown below the axis.
7. 1).Torque pulsations:
Each harmonic component present in the stator
voltage will produce its own rotating magnetic
field in the air gap between the stator and the
rotor.
The field strength of the effective RMF will not
remain constant but it will keep changing.
The torque produce by the motor is proportional
to the air gap flux.
Hence this torque also will fluctuate with changes
in the strength of RMF. this is called as Torque
pulsations.
8. The hysteresis and eddy current losses are
proportional to square of frequency.
So the presence of high frequency harmonics will
increase these losses.
Due to this power loss the motor gets heated up.
9. The performance of induction motor with different
types of inverters on the basis of these two
factors:
1). Square wave inverter with 180° mode.
2). Effect of leakage reactance on the harmonic
content of current.
10. The ratio (Ihar/I1) is a measure content of the harmonic
content of the current wave.
The fundamental current I1 depends on the slip.
11. Peak current :
The harmonic distortion not only increase the rms stator
current but it also increases the peak value of the current
wave.
The thyristors connected in the inverter will have to handle
these increase peak current.
The fundamental component of current is dependent on
load whereas the harmonic currents are dependent of the
load variations.
12. Machine losses :
1. Additional copper losses
2. Additional core losses
3. Additional stray load losses
Total additional loss & motor efficiency:
Due to increase in the additional losses the efficiency of
induction motor decreases.
The reduction in efficiency is 5 to 7% with the six step
inverter & 2 to 3% with the 12 pulse or PWM inverter.
13. Torque behaviour of the motor :
The effect of harmonic currents on the torque behaviour of
an induction motor are similar to those of magnetic field
space harmonics resulting which exist due to the non-
sinusoidal field distribution in the air gap.
These effect are known as secondary effects and also as
parasitic or additional torques.
14. Parasitic torques due to non-sinusoidal voltages:
The motor produces torque due to interaction of stator &
rotor mmfs.
When a stator winding with 2p poles is excited by a three
phase supply of frequency a rotating stator magnetic field is
developed, this field rotates
Each of these fields induces harmonic currents in the 2 pole
rotor. These currents produce rotor mmfs which rotate at a
speedwith respect to stator are constant.
The torques developed due to the interaction between stator
and rotor fields having the same speed with respect to stator
are constant.
Torques are of two types :
1. Useful torque 3. Pulsating torques
2. Parasitic torque
15. 1. Useful torque :
The useful torque is produced due to the reaction of
fundamentals mmfs produced by the stator and rotor
windings.
2. Parasitic torques :
These are the torque produced due to the reaction of the
stator and rotor harmonic mmfs of the same order.
These torques are steady asynchronous torques. They can
be either motoring or braking torques.
However these torques are normally very small and hence
can be neglected.
16. 3. Pulsating torques :
Pulsating torques are produced due to interaction of stator
and rotor field produced by harmonics of different order.
The torque pulsations are independent of load. The amplitude
of pulsations depends upon the harmonic content of the
voltage waveform.
The sixth harmonic torque pulsations may pose problems at
low speeds of operation. Hence its amplitude should be
reduced.
This is achieved by using 12-step inverter or a PWM inverter.
