Theme images by Storman. Powered by Blogger.

Recent in Sports

Home Ads



Random Posts

Saturday, 28 December 2019

Power Flow Diagram of DC Generator


Power flow diagrams give the stages of power in the case of a dc generators showing clearly the losses that occur at various stages of generation of power. The input to a generator is mechanical power a hydel, steam, diesel or nuclear source in the form of rotational power. The power flow diagram is shown in figure below.


Efficiency, η = Output/Input

In the case of a dc generator the output is a known factor from which input can be found. Thus the formula gets modified as,

Efficiency, η = Output/[Output +  Losses]
= Output/[Output +  Copper loss + Stray losses]

The following three types of efficiencies can be determined for a DC generator.

(a) Mechanical efficiency (ηm)

ηm = B/A = Total watts generated in armature/ Mechanical power supplied
= EgIa/Output of driving engine

(b) Electrical efficiency (ηe)

ηe = C/B = Watts available in load circuit/Total watts generated
= VI/EgIa

(c) Overall or Commercial efficiency (ηc)

ηc = C/A = Watts available in load circuit/Mechanical power supplied
= VI/Output of driving engine

Overall efficiency can also be found by

ηc = ηm x ηe


Let the generator,

Output = VI watts
Input = Output + Losses

The losses comprises of constant losses and variable losses.

Constant Losses (WC) = Stray losses + Shunt Field copper losses

In the case of shunt field,
Field copper losses = Ish2 Rsh

The variable losses occur in the armature winding and series field winding and are equal to
I2aRa + I2seRse


Generator Input = Output + Variable losses + Constant losses
= VI + I2aRa + I2seRse + WC

η = Output/Input
= VI/( VI + I2aRa + I2seRse + WC)

Since shunt field current (Ish) is supplied by armature. Ia > 1 but in practice the shunt field current is negligible as compared to line current. Therefore Ia = I (approx).

η = Output/Input = VI/(VI + I2Ra + WC)

Dividing numerator and denominator by VI,

η = 1/{1 + (IRa/V + WC/VI)}

Efficiency shall be maximum when the denominator is minimum. Differentiating the denominator with respect to I and equating to zero.

d/dI(IRa/V + WC/VI) = 0

We get,

Ra/V – WC/VI2 = 0   
Or Ra/V = WC/VI2
Or I2Ra = WC 

That is, when the variable losses is equal to constant losses, the efficiency of a DC generator is maximum. The load current corresponding to maximum efficiency is given by,

I2Ra = WC 

Or I = (WC/Ra)

0 on: "Power Flow Diagram of DC Generator"