Describe the Step by Step Procedure for Drawing Circle Diagram

What is Circle Diagram ?

     A circle diagram is a graphical method of representing an overall performance of an induction motor. Parameters like starting torque, the efficiency of the motor, losses in the motor, maximum power output, full-load electric current, power cistron, slip, maximum torque, etc. It is uncomplicated and easy to construct when compared to an equivalent circuit of consecration motor.

     A circumvolve diagram can be drawn by conducting no-load and blocked-rotor ( total-load ) tests on the induction motor. Merely it is a diagram drawn by taking the position ( locus ) of the current by an consecration motor for unlike atmospheric condition is known equally a circle diagram.

How to Describe a Circle Diagram ?

     This method aims at plotting the locus of input stator current I_ane for diverse values of skid. I_one is the phasor sum of I'_two ( i.e., rotor current every bit referred to stator ) and I_o .

     The phasor Eastward₂ / 10₂ denotes a constant electric current. Every bit seen from the above equation, current lagging E₂ by 90°, is equanimous of ii components viz. I₂ and - J R_ii I₂ / sX₂ . These two components are at correct angles to each other. Therefore the extremity of I_two lies on the circumference of a circle is shown in the figure below.

     Since I_ii & I'₂ are related by a abiding, the locus of I'_ii is also a circumvolve. Since I₁ is the phasor sum of I'₂ and I_o , we can displace this circle of I'₂ from the origin by the magnitude of I₀ . And so the extremity of I_i volition lie on the circumference of the circle is shown in the figure below.

Construction of Circle Diagram :

     The information available from the no-load and blocked-rotor tests are used for drawing the circle diagram. All quantities are per stage values.

     The no-load current I₀ and its ability cistron angle φ ₀ can be obtained from the no-load test. The Southward.C. ( blocked rotor ) current I_sc for voltage Five_sc and its power cistron angle φ _sc can be found out from the blocked rotor test. This current must be converted corresponding to the rated voltage, V₁ of the motor.

     S.C. current for normal voltage,

Knowing these information the circle diagram tin be drawn as follows.

1. Draw a vertical line representing the rated voltage V₁ ( reference phasor ).


2. Select a suitable scale for current. Draw line OA lagging V₁ past an angle φ ₀ equal to No-Load electric current I₀ .


3. Depict a line OB lagging 5₁ by an angle φ _sc equal to S.C. electric current for normal voltage. Vector OB represents the rotor current I'₁ as referred to the 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 Advertizing ( fatigued from A ) at bespeak C, which is the middle of the circumvolve. So with C equally a centre and CA every bit radius, describe the semi-circle ABD.


6. Draw a vertical line from betoken B, and so as to meet the line AD at the point F. Now divide BF in the ratio of rotor copper loss to stator copper loss at the point East.


7. At present draw a line from East to A known every bit torque line ( i.eastward., the torque generated by the motor ).

Parts of Circle Diagram :

     As the practical voltage V_i is drawn vertically, all vertical distances correspond the power or energy components of the currents. The vertical altitude AQ ( I_o cos φ _o ) represents the no-load input which supplies core loss, mechanical loss and a modest stator copper loss.

1. Torque line :

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

     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 equally torque line or rotor input line. Torque is proportional to the power input to the rotor. The rotor copper loss at standstill is Exist. Therefore the line Be is known as starting torque.

2. Location of Point 'East' :

For Cage Rotor :

     The input power under the blocked rotor condition is approximately equal to copper losses because the fe losses are very small and neglected. Let R₁ = stator resistance per stage ( plant from stator resistance examination )

Stator copper loss = three I_southward ^two R_ane

Rotor copper loss = 3 I_s ² R₁

For Wound Rotor :

Permit,

R₁ and R_ii = stator and rotor resistance per stage respectively

     I₁ and I₂ = stator and rotor resistance per stage respectively

     N₁ and N₂ = stator and rotor turns respectively

3. Operating Indicate or Full Load Point P :

     Draw a vertical line BL represents the full load output of the motor. From the point L describe a line parallel to the output line and it cuts the circle at ii points U and P. Since the normal operating skid is small, the point P volition be the operating signal.

4. Full Load Electric current and Power Gene :

     Bring together OP which represents the full load current of the motor. Corresponding power gene angle φ ₁ ( ∟ 5₁ 0 P ) gives the power factor at which the motor is operating.

5. Full Load Efficiency, Slip & Speed :

     Depict a vertical line from the point P. So PM and PK respectively represent the output and input of the motor. JK represents fixed losses, MN and NJ represent the rotor and stator copper losses respectively.

6. Maximum Output :

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

7. Maximum torque :

     It is also known as pull out torque. Depict a line the torque line AE tangent to the semi-circle. The actual point of contact R past cartoon a perpendicular to the tangent drawn from the center C. Now RS is the maximum torque. The slip at maximum torque, s_thousand = TS / RS

8. Maximum Input :

     Information technology occurs at the highest signal of the circle i.e., at point Five where the tangent to the circumvolve is horizontal. Now VW is the maximum input.

From the circle diagram, information technology tin be ended that,

Total-load current = OP

Full-load p.f. angle, φ ₁ = ∟ V_ane 0 P or Cos φ ₁ = PK/OP

Full-load slip, s = MN/PN

Total-load speed, N = N_s (ane-south)

Efficiency = PM/PK

Maximum output = HI

Maximum torque = RS

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

Starting torque or rotor copper loss at standstill = BE

Skid at maximum torque, s_m = TS/RS

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Source: https://www.electricaldeck.com/2020/10/circle-diagram-of-induction-motor.html

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