24/02/2018

Effect of Voltage and Frequency on Active Power of Load

The effect of variation in voltage and frequency on active power of load is summarized as below. The complex load power is given by

        S = P + jQ

           = VI

           = Y | V |2

           Where Y is admittance of load

        S = | V |2 Y

           = | V |2 / ( R – jX )

           = | V |2 ( R + jX ) / ( R – jX ) ( R + jX )

           = [ | V |2  R / ( R2 + X2 ) ] + j [ | V |2  X / ( R2 + X2 ) ]

           = P + j Q

Therefore

        P =  [ | V |2  R / ( R2 + X2 ) ]
       Q = [ | V |2  X / ( R2 + X2 ) ]

  • Therefore we can say that the active power and reactive power is directly proportional to square of the supply voltage.

Effect of change in supply voltage on active power of load

dP / dV

       = [  2 | V | R / ( R2 + X2 ) ]

( dP / dV ) / P

      = [  2 | V | R / ( R2 + X2 ) ] / [ | V |2  R / ( R2 + X2 ) ]

      = [  2 | V | R / ( R2 + X2 ) ] / [ | V |2  R / ( R2 + X2 ) ]

      = 2 / | V |

Therefore

       dP / P = 2 d | V | / | V |

  • We can say that change in voltage directly affect the change in real power of the load. If there is 10% change in supply voltage, 20% change in the real power of the load.

Effect of change in supply frequency on active power of load

The active power is given by

P = [ | V |2  R / ( R2 + XL 2 ) ]

Inductive reactance XL = 2πfL

P = [ | V |2  R / ( R2 + ( 2πfL ) 2 ]

dP / df  =

    [ ( R2 + ( 2πfL ) 2 ][ 0 ] – [ | V |2  R ][ 0 + 2( 2πfL )( 2πL) ] /

    [ ( R2 + ( 2πfL ) 2 ]2

[ dP / df ] / P =

    – [ | V |2  R ][ 2( 2πfL )( 2πL) ][ ( R2 + XL 2 ) ]  / 

       [ | V |2  R ] [ ( R2 + ( 2πfL ) 2 ]2

[ dP / P ] = – 2 XL 2 / [ ( R2 + XL 2 ) ]  [ df / f ]

Where SinΦ = XL 2 / [ ( R2 + XL 2 ) ]  

Therefore

        [ dP / P ] = { – 2 SinΦ [ df / f ] }

If the load power factor Cos Φ = 0.6, Sin Φ = 0.8

       [ dP / P ] = { – 2 SinΦ [ df / f ] }

                      = { – 1.28 [ df / f ] }

It means that if there is ten percentage drop in frequency, there will – 12.8 load increase.

Effect of change in frequency on the Induction motor

  • If the frequency drop / reduced, the induction motor draws more current from the supply source therefore the torque increases. 
  • If the load on the motor remains constant, the speed will increase. 
  • The torque is directly proportional to square of the supply voltage. 
  • If the supply voltage increases, the torque also increases. 
  • However the induction motor is a constant power device, the induction motor draw less current to compensate increase in the voltage. 
  • Therefore the change in the voltage does not affect the power output of the induction motor to some extent.

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    Parameters
    Squirrel Cage Induction Motor
    Slip Ring Induction Motor
    Rotor
    Copper bars are slotted in the rotor and these bars are short circuited from both ends by end rings
    Three phase winding is slotted in the rotor similar to stator winding

    End rings
    Two end rings are used on both side of rotor
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    Slip rings and brushes
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    High starting torque is achieved by adding external resistances to rotor side.

    Speed control
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    Speed control is possible from stator and rotor side. The speed control from rotor side is done by rotor resistance starter.
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    Cooling condition
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    Better overload capacity

    Low overload capacity as compared to squirrel cage induction motor

    Power factor
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    Comparatively high power factor
    Pull out torque

    High
    Low

    Maintenance
    Low
    High
    Construction
    Simple and robust

    Complicated
    Cost
    Low
    High
    Efficiency
    High
    Low as compared to Squirrel cage Induction Motor
    Applications
    Fan, printing machine, lathes, drill machine, blower etc

    Lift, compressor, crane, hoist etc.


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