A self excited dc generator dc generator supplies its own field excitation . A self excited generator shown in figure is known as a shunt generator because its field winding is connected in parallel with the armature.thus, the armature voltage supplies the field current.
This generator will build up a desired terminal voltage. Assume that the generator in figure has no load connected to it and armature is driven at a certain speed by a prime mover. we shall study the condition under which the voltage buildup takes place. the voltage buildup in a dc generator. Due to this residual flux, a small voltage Ear will be generated.

It is given by                         

This voltage is of the order of 1V or 2V . It causes a current If to flow in the field winding in the generator.
the field current is given by                                           

This field current produces a magnetomotive force in the field winding, which increase the flux. this increase in flux increases the generated voltage Ea. The increased armature voltage Ea increases the terminal voltage V. with the increase in V , the field current If increases further. this in turn increases Φ  and consequently Ea increases further. the process of the voltage buildup continues. 

Figure shows the voltage buildup of a dc shunt generator.   
The effect of magnetic saturation in the pole faces limits the terminal voltage of the generator to a steady state value.
We have assumed that the generator is no load during the buildup process. the following equations describe the steady state operation.     
Since the field current If  in a  shunt  generator  is very small, the voltage drop If Ra can be neglected,
                                             and  V= Ea      
The Ea versus If curve is the magnetization curve shown in figure
For the field circuit                         V = IRf  
The straight line given by V =  If Rf  is called the field-resistance line.

The field resistance line is a plot of the voltage  If R across the field circuit versus the field If. the slop this line is equal to the resistance of the field circuit.

the no-load terminal voltage V0 of thr generator. thus, the intersection point P of the magnetization curve and the field resistance line gives the no-load terminal voltage V0 (bP) and the corresponding field current (Ob). Normally , in the shunt generator the voltage buildup to the value given by the point P
at this point   Ea = IRf V0.

If the field current corres-ponding to point P is increase further , there is no further increase in the terminal voltage.

The no-load voltage is adjusted by adding resistance in series with shunt field. this increase slope of this line causing the operating point to shift at lower voltage.

The operating point are graphical solution of two simultaneous equation namely , the magnetization curve and field resistance line . A graphical solution is preferred due to non-linear nature of magnetization curve.

Self excited generator are designed to obtain no-load voltage from 50% to 125% of the rated value while varying the added resistance in field circuit from maximum to zero value.

Show figure the voltage buildup in the dc shunt generator for various field circuit.

A decrease in the resistance of the field circuit reduces the slope of the field resistance line result in higher voltage. If the speed remain constant , an increase in the resistance of field circuit increases the slop of field resistance line, resulting in a lower voltage. If the field circuit resistance is increased to Rc which is terminal as the critical resistance of the field, the field resistance line becomes a tangent to the initial part of the magnetization curve. when the field resistance is higher than this value, the generator fail to excite.      

Figure shows the variation of no-load voltage with fixed Rf and variable speed of the armature.

The magnetization curve varies with the speed and its ordinate for any field current is proportional to the speed of the generator. all the points on the magnetization curve are lowered, and the point of intersection of the magnetization curve and the field resistance line moves downwards. at a particular speed, called the critical speed, the field resistance line becomes tangential to the magnetization curve. below the critical speed the voltage will not build up.

In Brief, the following condition must be satisfied for voltage buildup in a self-excited generator.

  1. There must be sufficient residual flux in the field poles.
  2. the field terminal should be connected such a way that the field current increases flux in the direction of residual flux.
  3. The field circuit resistance should be less than the critical field circuit resistance.
If there is a no residual flux in the field poles, Disconnected the field from the armature circuit and  apply a dc voltage to the field winding. this process is called Flashing the field. It will induce some residual flux in the field poles.        

                                       

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