Presentationon

Effect of Non sinusoidal waveform of A.C. Machine performance

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

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.

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

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.

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.

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.

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.

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.

The ratio (Ihar/I1) is a measure content of the harmonic content of the current wave.

The fundamental current I1 depends on the slip.

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.

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.

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.

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 speed with 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

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.

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.