Condition for Maximum Efficiency in DC Machine

The DC generator efficiency is perpetual but varies with load. Think through a shunt generator supplying a load current I_L at a terminal voltage V.

Then Generator output  =  VI_L

Generator input  =  Output + Losses

                           =  VI_L + Variable losses + Constant losses

                           =  VI_L + I2_a R_a + W_c

                           =  VI_L + (I_L + I_sh²)R_a + W_c 

                    ( ∵  I_a = I_L + I_sh)

The shunt field current I_sh is generally small as compared to I_L and, therefore, can be neglected.

                Generator input   =  VI_L + I²_a R_a + W_c

Now                Efficiency   η  =  output / Input

                                            =  VI_L / (VI_L + I²_a R_a + W_c

                                            =  1 / {1+[(I_LR_a/V)+(W_c/VI_L)]}

• EMF Equation of a Generator

The efficiency is always maximum when the denominator of Eq.(1) is minimum i.e.,

                                              d/dI_L {( I_LR_a/V) + (W_c+VI²_L)} =0

                                                        Or

                                             (R_a/V) – (W_c/ VI²_L) =0

                                                        Or

                                              Ra/V = Wc/VI²_L

                                                       Or

                                               I²_LR_a = W_c

I.e. Variable loss = Constant loss (I_L ≈ I_a)

The load current corresponding to maximum efficiency is given by;

                                             I_L = √ W_c/R_a

Therefore, the efficiency of a DC generator will always be maximum once the load current is such that variable loss is the same to the constant loss. The fig shows the deviation of efficiency with load current.

CSV Nov 24, 2014

SHARES

Share

Pin it

Tweet

Share

Share

Share

Buffer

Print