## 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

Ist  = Starting Current

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.

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