Induction motor characteristics part-2

AIM -

• Discuss about the equivalent circuit network of induction motor MATLAB model.
• 3 phase, 50 Hz induction motor, represented by equivalent circuit constants X1 = X2 = 0.1 ohm and R1 = R2 = 0.2 ohm is operated at half of rated voltage and frequency. Calculate the ratio of starting torque at half voltage & frequency to rated values.
• Make a comparison of square wave inverter output voltage with sine modulated one.

STUDY-1>

Equivalent circuit network of induction motor

Equivalent circuit of induction motor enables the performance characteristics which are evaluated for the steady state conditions. A induction motor is based on the inductor of voltage and current. The voltage and current is induced in the rotor circuit from the stator circuit for the operation. Three phase induction motor acts as a generalized transformer. because three phase AC supply is given to the stator winding of induction motor and due to the rotating magnetic field resultant flux will be produced and due to resultatnt flux, EMF is induced in the rotor winding and it produces the current . Here electromagnetic induction acts as a transformer.

Fig: 

Here R1 and L1 are resistance and inductance of stator winding and X1 is the stator leakage reactance. V and I is supply voltage and current which is flowing through stator. Stator current is divided into two parts  magnetising current(Im) and rotor current(I2). I=Im+I2 As we know that there is an airgap between stator and rotor , Magnetic reactance is required to cross the airgap represented by Xm. Rotor reistance and reactance is represented by  R2 and X2. Rotor behaviour is observed by a parameter called slip, which is represented by [R2(1-s)/s].

Synchronous speed (Ns) is given by supply frequency and number of poles of the motor. [Ns=120*f/p]

For the equivalent circuit model , slip is defined as s=1-(pwm/f) 

where, p= number of poles 

          wm=motor speed

           f =supply frequency

Torque speed relation of induction motor is 

T=(npR2/sw) *(Vrms)^2/[R1+R2+(1-s)/s*R2]^2+(X1+X2)^2

where, n=number of phases 

          X1=stator inductance

          R1= stator resistance

          X2= rotor inductance

          R2= rotor resistance

        Vrms= Rms voltage

         s= slip

STUDY-2>

Given:

3 phase induction motor with a frequency of 50Hz, represented by equivalent circuit constant, i.e X1=X2=0.1ohm and R1=R2=0.2ohm .

Here we have to calculate the ratio of starting torque at half voltage and frequency to rated voltage and frequency.

Calculations:

RESULT :

The ratio of starting torque (T1) at half rated voltage and frequency and starting torque (T2) of rated voltage  and frequency is 0.5.

STUDY-3>

Comparision of square wave inverter output and sine modulated inverter output.

As we know that the main purpose of an inverter is to convert the DC electricity into AC electricity. An inverter converts DC current to either square wave AC current or sine wave AC current. In comparision with the square wave output the sine wave output is purer, Output voltage wave form of the true form inverter is a pure sine wave which we get through utility usage in out home for the electric loads.In pure wave of sine distortion is approximately zero just like electricity obtained from supply. But in square wave, harmonics produce distortions which can destroy and damage our equipment while running on square wave we also know that if we use square wave inverters in household devices it gets heated up , So in many european countries it is banned. Most of the time we use inductive loads in our homes, while we are using such loads we have to use pure sine wave than square wave. Inductive load can be microwaves, motors, coolers etc. So pure sine wave is better than square wave.

Nowadays ,we have a new type of inverter that is called  "Modified sine wave inverter" . This type of inverter is better than the square wave inverter and less costlier than the sine wave inverter. It can also be utilized in simple systems such as : 

• Laser printers
• photo copiers
• Appliances with microprocessor controls
• Home automation systems
• Medical equipments