Basic Formula & Performance Calculations of 3-Phase Induction Motor

 

 Basic Formula & Performance Calculations of 3-Phase Induction Motor 

 1.  Torque : 

  Torque in Kgm  =   ( kW x 974 ) / Full Load RPM

  Torque in Nm   =   Torque in Kgm x 9.81

  Starting Torque =   [ (Rated Voltage /Reduce Voltage )^2 ]  x Reduce Voltage

  Starting Torque % of Full Load Torque = ( Starting Torque /Rated Torque ) x100 

2.  Speed : 

Synchronous Speed (Ns)   =  ( 120 x Frequency ) / No. of Pole 

% Slip = [( Synchronous Speed - Full Load Speed  ) / Synchronous Speed] * 100

Speed at 50 Hz =  [ Speed ( Actual RPM ) x 50 ] / Frequency 

3.  Power : 

     Power in kW =  (√3 x Line Voltage x Line Current x p.f.) / 1000 

    Power Conversion : 

     A.  HP to kW  =  HP X 0.746

     B.  kW to HP  =  kW / 0.746  

4.  Current :    

   Full Load Current in Amp. = ( kW x 1000 ) / (√3 x Line Voltage x efficiency x p.f.)

     

 5.  Motor Starting Time :  

      Motor Starting Time   ∝  Motor Rated Speed  X ( Load GD²  +  Motor GD² )

                                                                         Accelerating Torque

    

    * Starting time is directly proportional to load  GD²

    * So higher the load GD²  (in case of fans), higher is the starting time

  

  6. Performance Calculations of 3 Phase Induction Motor 

      Where , 

        I0    :  No Load Current in Amp.

        Ifl    :  Load Current in Amp.

        W0  :  No load Power in Watts.

        Wfl  :  Load Power in Watts . 

         Ns   :  Synchronous Speed . 

         N     :  Full load Speed.  

       Ravg  : Average resistance 

      Resistance in STAR Connected motor    =  Ravg / 2

      Resistance in DELTA Connected motor  =  Ravg  x 1.5

 

      Resistance Per Phase ( Rph )  =  (RII*((235+95)/(235+T1)))

     Where , 

       RII  =  Resistance in STAR / DELTA

       T1   =  Initial Ambient Temp.

     No Load Loss Calculation : 

     No Load Cu Loss ( Vcuo )  =  I0*I0*Rph 

     Windage & Friction Loss  (Vr)  =  1 % of kW ( Assumption  )

     Constant Loss [ Iron Loss ] ( Vfe )  =  (Wo-Vcuo-Vr) 

    

     Load Loss Calculation :

     Stator Cu loss  ( Vcu1 )   =  (Ifl*Ifl*Rph)

     RPM @ 50 Hz   =  [ (RPM*50) / Frequency) ]

     Slip ( S )   =  (Ns-N)/Ns 

     Rotor Cu Loss ( Vcu2 )   =  (Wfl-Vcu1-Vfe)*Slip 

     Stray Loss  ( Vs )  =  (0.5/100)*Wfl  ( Assumption  )

     Total Loss  =  Vr+Vfe+Vcu1+Vcu2 +Vs

    Performance : 

      Output  =  (Input-losses)

     % Efficiency  =  (Output / Input) x 100 

      Power Factor  =  (Input) / (1.732*V*Ifl) 

      * The method of determining efficiency of machine or motor depends on number of    assumption. Now days IS: 15999- IEC -60034-2 std . use for performance calculation of motor. This will explain in future blog.