23/11/2020

Compare Starting Torque and Full load Torque in Starter

Relation between starting torque and full load torque

                ( Tst / Tf )  = ( Ist / If )2 × Sf …… ( 1 )

Where

        Tst  = Starting Torque

        Tf  = Full load Torque

        Ist  = Starting Current

        If  = Full load current

        Sf  = Full load Slip

Direct ON Line Starter

  • When three phase induction motor is directly connected with three phase supply, the starting current is equal to short circuit current.

      Ist = Isc

    ( Tst / Tf )  = ( Isc / If )2 × Sf

                      = ( b2 ) × ( Sf )

       Where b = Isc / If

Let us consider that the starting current is 6 times that of full load current in the induction motor and slip is 4%,

        ( Tst / Tf )  = ( 6 )2 × 0.04

                         = 1.44

                   Tst = 1.44 Tf

  • When the induction motor is started with Direct ON Line starter and starting current is 6 times that of full load current, the starting torque is 1.44 times that of full load torque.

Star – Delta Starter

  • The induction motor is in star connection during starting condition and starting current

    Ist = Isc / 3…… ( 2 )

    From equation ( 1 ) and ( 2 )

    ( Tst / Tf )  = ( Isc / 3 If )2 × Sf …… ( 3 )

                      = ( 1 / 3 )( Isc / If )2 × Sf

                     = ( 1 / 3 )( b )2 × Sf ……( 4 )         (  Where b = Isc / If )

Let us consider that the starting current is 6 times that of full load current in the induction motor and slip is 4%,

( Tst / Tf )  = ( 1 / 3 )( b )2 × Sf    

                 = ( 1 / 3 ) ( 6 )2 × 0.04

                 = 0.48

           Tst = 0.48 Tf

Type of Starter

Starting current / Full load current

Slip

Starting torque / Full load torque

Direct ON Line starter

6

4%

1.44

Star Delta starter

6

4%

0.48

 

Auto transformer Starter

  • Let us consider that the induction motor winding is connected in star and each star connected winding get VL / 3 voltages.

       VPH = VL / 3

      IL = IPH = Ist = VL / 3Z

  • Let us consider that the tapping on the auto – transformer is K. Now each winding gets KVL / 3 voltage and starting current of motor Ist = KVL / 3Z

      I2 = KIsc

      Supply current I1 = KI2

                                   = K2Isc

Relation between starting torque and full load torque

( Tst / Tf )  = ( Ist / If )2 × Sf

                 = ( KIsc / If )2 × Sf

                 = K2b2× Sf ……… ( 5 )       (  Where b = Isc / If )

Comparing Star – delta starter and Auto transformer starter

From equation ( 4 ) and (5 )

Star delta starter

( Tst / Tf )  = ( 1 / 3 )( b )2 × Sf

Auto transformer starter

( Tst / Tf )  = K2 b2 × Sf

Therefore K2 b2 × Sf = ( 1 / 3 )( b )2 × Sf

K2 = ( 1 / 3 )

K = 1 / 3

    = 0.577

    = 57.8%

  • Therefore the star delta starter is equivalent to 57.8% tapping in the auto transformer starter. 
  • If we set 57.8% tapping in the auto transformer, it is simply as star delta starter.

You may also like :

Tertiary winding : construction and working

Crawling and Cogging in the Induction Motor

Working of Constant Voltage Transformer ( CVT )

Working of Constant Current Transformer ( CCT )

 

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