Efficiency of Dc generator
The efficiency of Dc generator … At normal conditions; when we hear efficiency our mind automatically think in output and input, of course you don’t need me to remind you that Dc generators convert mechanical power into electrical power as we had explained that previous in details in Working principle of Dc generator (Introduction to DC Generator), and of course you deduce that Efficiency of Dc generator depends on input mechanical power and output electrical power.
But in order to understand efficiency well, we must know losses which fortunately are less Compared to Dc motor
losses in Dc generator are:
Constant losses of Dc generator which are:
- Core or iron losses listed in hysteresis losses and eddy current losses
- And mechanical losses which are windage losses, friction losses (brush friction losses) and bearing friction losses
Variable losses of Dc generator which are:
- Copper losses listed in armature copper losses, field copper losses, and losses caused by brush contact resistance.
- Stray losses which are copper stray load losses and core stray losses.
And that explained by the power flow diagram of a Dc generator
After we listed all types of losses we need to understand why and when they happened surely to be more awareness about efficiency.
Core or iron losses:
these losses happen when the armature passes under the north and the south poles which lead to reverse of magnetization of the armature core, and this loses depends on the iron volume, flux density maximum value, and the frequency.
Eddy current losses:
these losses are a result of the flow of eddy currents which are sets of currents produced in the armature core when it cuts the magnetic flux.
Here you should be Conscious and tell me that we laminate, stack and revet the armature core to reduce these losses as much as possible, as when we laminated the armature core the magnitude of eddy current reduced and as a result eddy current losses reduced.
from the name these losses occur in the armature windings due to the brush contact resistance, these losses are a result of varying the load which produces a current pass through the armature winding resistance and raise the temperature.
and mathematically: armature copper losses=Ia^2 Ra
Field copper losses:
also from the name are a result of the flow of current in the field windings.
they expressed as field copper losses=If^2 Rf
Brush contact drop:
brush; when we hear this word we deduce that they are losses produced when a contact happens between the brush and the commutator and of course they are constant with the load.
Stray load losses:
In contrast, they are losses varying with the load and it’s difficult to account so we assume that they are 1% of the full load, and they contain:
Copper stray load losses:
they are a result of skin effect affected the conductor and also due to eddy currents passing through the conductor.
Core stray load losses:
these losses depend on the flux density, good; but how! When the load current passes through the armature conductor the flux density distorted in the teeth and the core and that results from a net increase in the core losses especially in the teeth and simply that is stray load losses.
Let’s be more definite with equations:
The main equation we all know is:
P (mechanical input) = P (Elec) + losses.
And the generating efficiency will be:
ƞ=P (out) /P (in)= P(Elec)/[P(Elec)+losses].
The constant losses can be expressed as Pi
The variable losses can also express as Pcu
So; ƞ= Pout/ (Pelec +Pcu+Pi)
To be more accurate the total resistance of the armature circuit including the resistance of the brush contact, the resistance of the series winding, and the resistance of inter-pole winding and compensating winding will be R
The output current= I
The shunt field current= Ish
The armature current= Ia = I+Ish
The terminal voltage= V
The total copper losses in the armature circuit= Ia^2 Rat.
The variable losses= Pcu
The constant losses= Pi
So the input power; Pin= Pout+Pcu+Pi
Maximum efficiency of dc generator
Without debate our total concentration is at maximum efficiency and the conditions for maximum efficiency:
We suppose that:
The output power= VI
And all losses are constant expect the armature copper losses so;
Losses= (I+Ish)^2 Ra +Pc = I^2 Ra+Pc
We neglect Ish because it’s little if we compare with the load current I
If you remember; to have the maximum we should differentiate so:
dƞ/(dI )=0=((VI+I^2 Ra+Pc)V-VI(V+2IRa))/(VI+I^2 Ra+Pc)^2
According to this equation, the efficiency will be maximized when variable losses= constant losses
This equation tells us that the efficiency is proportional to the load current when the load current increases the efficiency increases as it reaches its maximum value when the load current is as in the previous equation.
And it can be clear by the efficiency curve drawn between the efficiency and the load current: