02/10/2020

DC Generator : Condition For maximum efficiency


The power stages of DC Generator is shown in the Figure



 

Commercial Efficiency

  • It is defined as the ratio of the electrical power output to the mechanical power input.

ηc = [ Electrical power input ] × 100% / [ Mechanical power input ]

Mechanical Efficiency

  • It is defined as the ratio of the armature power to the mechanical power input.

ηm = [ Armature power ] × 100% / [ Mechanical power input ]

Electrical Efficiency

  • It is defined as the ratio of the output power in mechanical to the armature power.

ηe = [ Output power in mechanical ] × 100% / [ Armature power  ]

Condition For Maximum Efficiency

Generator output power = VIL

Generator input power = Output power + Total losses

= VIL + Constant losses + Copper losses

= VIL + WC + Ia2Ra

= VIL + WC + ( IL + Ish )2 Ra

The value of shunt field current is very small as compared to load current therefore the shunt field current is neglected.

Generator input power = VIL + WC + ( IL )2 Ra

Generator efficiency = Output power / Input power

                                  = VIL  / VIL + WC + ( IL )2 Ra

                                  = 1 / [ 1 + (  WC / VIL2 + IL  Ra / V ) ]

The load current is variable parameter therefore the generator efficiency becomes maximum when

dη / dIL = 0

d / dIL  [(  WC / VIL2 + IL  Ra / V ) ] = 0

( WC / V ) ( 1 / – IL2 ) + (  Ra / V ) ( 1 ) = 0

IL2 Ra = WC

Therefore the variable losses is equal to constant losses is condition for maximum efficiency in the DC Generator.

IL2 Ra = WC

Load current for maximum efficiency

                       IL  = √ (  WC / Ra )

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