Compare Starting Torque and Full load Torque in Starter

Relation between starting torque and full load torque

                ( T_st / T_f )  = ( I_st / I_f )² × S_f …… ( 1 )

Where

        T_st  = Starting Torque

        T_f  = Full load Torque

        I_st  = Starting Current

        I_f  = Full load current

        S_f  = 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.

      I_st = I_sc

    ( T_st / T_f )  = ( I_sc / I_f )² × S_f

                      = ( b² ) × ( S_f )

       Where b = I_sc / I_f

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

        ( T_st / T_f )  = ( 6 )² × 0.04

                         = 1.44

                   T_st = 1.44 T_f

• 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

    I_st = I_sc / √ 3…… ( 2 )

    From equation ( 1 ) and ( 2 )

    ( T_st / T_f )  = ( I_sc / √ 3 I_f )² × S_f …… ( 3 )

                      = ( 1 / 3 )( I_sc / I_f )² × S_f

                     = ( 1 / 3 )( b )² × S_f ……( 4 )         (  Where b = I_sc / I_f )

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

( T_st / T_f )  = ( 1 / 3 )( b )² × S_f    

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

                 = 0.48

           T_st = 0.48 T_f

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 V_L / √ 3 voltages.

       V_PH = V_L / √ 3

      I_L = I_PH = I_st = V_L / √ 3Z

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

      I₂ = KI_sc

      Supply current I₁ = KI₂

                                   = K²I_sc

Relation between starting torque and full load torque

( T_st / T_f )  = ( I_st / I_f )² × S_f

                 = ( KI_sc / I_f )² × S_f

                 = K²b²× S_f ……… ( 5 )       (  Where b = I_sc / I_f )

Comparing Star – delta starter and Auto transformer starter

From equation ( 4 ) and (5 )

Star delta starter

( T_st / T_f )  = ( 1 / 3 )( b )² × S_f

Auto transformer starter

( T_st / T_f )  = K² b² × S_f

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

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.

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