Circle Diagram of Induction Motor



What is Circle Diagram :


     Circle diagram is a graphical method to analyse the performance of a 3-phase induction motor. We can also compute the operation of induction motor using equivalent circuit, but it is easy and simple by using the circle diagram. If we neglect the parallel branch of the equivalent circuit of an induction motor, it reduces into a simple series circuit having a constant voltage supply. A diagram giving the locus of the current drawn by an induction motor is referred to as a ' Circle Diagram '. 


     The circle diagram can be drawn by using no-load and blocked-rotor test data. From the circle diagram it is possible to on obtain graphically a considerable range of information like full-load current and power factor, maximum power output, pull-out torque, full-load efficiency, etc.



Theory :


     This method aims at plotting the locus of input stator current Ifor various values of slipIis the phasor sum of I'( i.e., rotor current as referred to stator ) and Io.


     The phasor  EXdenotes a constant current. As seen from the above equation current lagging Eby 90°, is composed of two components viz.  I and  -  J R2 I2 / s X2. These two components are at right angles to each other. Therefore the extremity of Ilies on the circumference of a circle is shown in figure below.

Circle Diagram of Induction Motor

     Since  II'are related by a constant, the locus of I'is also a circle. Since Iis the phasor sum of I'and Io, we can displace this circle of I'from origin by the magnitude of Io. Then the extremity of Iwill lie on the circumference of the circle is shown in figure below.

Circle Diagram of Induction Motor


Construction :


     The data available from the No. Load and Blocked Rotor Tests is used for drawing the circle diagram. All quantities are per phase values.

     The No-load current Iand its power factor angle Φcan be obtained from the No-Load test. The S.C. (blocked rotor) current Isc for voltage Vsc and its power factor angle Qsc can be found out from the blocked rotor test. This current must be converted corresponding to the rated voltage, Vof the motor.

     S.C. current for normal voltage,

ISN  =  Isc ( V1 / Vsc )


     Knowing these data the circle diagram can be drawn as follows.


1. Draw a vertical line representing the rated voltage V( reference phasor ).

2. Select a suitable scale for current. Draw line 'OA' lagging Vby an angle Φequal to No-Load current Io.

3. Draw a line 'OB' lagging Vby an angle Φsc equal to S.C. current for normal voltage.

     Vector 'OB' represents the rotor current I'as referred to stator.

4. Join 'AB' which represents the output line of the motor.

5. A perpendicular bisector of the line 'AB' is drawn cutting the horizontal line 'AD' ( drawn from A ) at the point 'C', which is the centre of the circle. Then with 'C' as centre and 'CA' as radius, draw the semi circle 'ABD'.

6. Draw a vertical line from the point 'B', so as to meet the line 'AD' at the point 'F' Divide 'BF' in the ratio of rotor copper loss to stator copper loss at the point 'E ' i.e.,



Then 'AE' represent the torque line.

Circle Diagram of Induction Motor


Computation of Performance :   


     As the applied voltage V1  is drawn vertically, all vertical distances represent the power or energy components of the currents. The vertical distance AQ ( =  Io CosΦ) represents the no-load input which supplies core loss, mechanical loss and a small stator copper loss.



1. Torque line :


     Under blocked rotor conditions at rated voltage, the power input is 'BG'. This represents core loss and copper losses The intercept 'FG'  the ( = AG ) is approximately equal to core loss because through the mechanical losses are absent slightly increased under blocked rotor conditions. 

     Hence the intercept 'BF' represents the sum of stator and rotor copper losses.

     The line 'AE' which separates the stator and rotor copper loss as known as torque line or rotor input line.

     Torque is proportional to power input to rotor. The rotor copper loss at stand still is 'BE'.

     Therefore Starting torque = BE


2. Location of Point 'E' :


Cage Rotor :


     The input power under blocked rotor conditions is approximately equal to copper losses because the iron losses are very small and neglected. Let R1 = stator resistance / phase ( found from stator resistance test )


Stator copper loss =  3  Is2  R1

Therefore,

Rotor copper loss = S. C. input power  - 3  Is2  R1 


Wound rotor :


 Let,

      Rand R= stator and rotor resistance / phase respectively

     Iand I2  =  stator and rotor resistance / phase respectively



3. Operating Point or Full Load Point 'P' :

 

     Draw a vertical line 'BL' represents the full load output of the motor. From the point 'L' draw a line parallel to the output line and it cuts the circle at two points 'U' and 'P'. Since the normal operating slip is small, the point 'P' will be the operating point.



4. Full Load Current and Power Factor :


     Join 'OP' which represents the full load current of the motor. Corresponding power factor angle  φ1  ( = ∟ V1 O P ) gives the power factor at which the motor is operating.



5.  Full Load Efficiency, Slip & Speed :


     Draw a vertical line from the point 'P'. Then 'PM' & 'PK' respectively represent the output and input of the motor. 'JK' represents fixed losses. 'MN' & 'NJ' represent the rotor and stator copper losses.


Efficiency,


 Full load slip,


Full load rotor speed,  N  =  Ns ( 1 - s )



6. Maximum Output :


     Draw a line parallel to the output line 'AB' tangent to the semicircle. The actual point of contact 'H' is obtained by drawing a perpendicular to the tangent drawn from the centre 'C'. Now 'HI' is the maximum output.



7. Maximum torque :


     It is also called as stalling or pull out torque. Draw a line the torque line 'AE ' tangent to the semi-circle. The actual point of contact 'R ' by drawing a  perpendicular to the tangent drawn from the centre 'C'. Now 'RS' is the maximum torque.


The slip at maximum torque,

sm  =  TS  / RS



8. Maximum Input :


     It occurs at highest point of the circle i.e., at point 'V' where the tangent to the circle is horizontal. Now 'VW' is the maximum input.



From the circle diagram, it can be concluded that


Full current  =  OP


Full-Load power factor angle,

φ1  =  ∟V10P  or  Cos φ1  =  PK / OP

Full-Speed,


Full-Load speed,   N  =  Ns ( 1 - s )


Maximum output  =  HI

Maximum torque  =  RS

       Full-load torque  =  Full-load rotor input  =  PN

       Starting torque  =  Rotor copper loss at Standstill  =  BE

Slip at maximum torque,

sm  =  TS  / RS



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