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.

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

Mechanical Efficiency

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

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

Electrical Efficiency

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

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

Condition For Maximum Efficiency

Generator output power = VI_L

Generator input power = Output power + Total losses

= VI_L + Constant losses + Copper losses

= VI_L + W_C + I_a²R_a

= VI_L + W_C + ( I_L + I_sh )² R_a

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

Generator input power = VI_L + W_C + ( I_L )² R_a

Generator efficiency = Output power / Input power

                                  = VI_L  / VI_L + W_C + ( I_L )² R_a

                                  = 1 / [ 1 + (  W_C / VI_L² + I_L  R_a / V ) ]

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

dη / dI_L = 0

d / dI_L  [(  W_C / VI_L² + I_L  R_a / V ) ] = 0

( W_C / V ) ( 1 / – I_L² ) + (  R_a / V ) ( 1 ) = 0

I_L² R_a = W_C

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

I_L² R_a = W_C

Load current for maximum efficiency

                       I_L  = √ (  W_C / R_a )

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