Shunt generator voltage build-up, critical resistance and speed

A self-excited DC shunt generator builds up its own field current from the small voltage due to residual magnetism, with no external DC source.

Voltage build-up process

     +---------+-----------o +
     |         |
   ( G )     [Rsh]  field         V
     |         |  winding
     +---------+-----------o -

1. The poles keep a little residual magnetism. When the armature is driven at rated speed, a small EMF $E_r$ (a few volts) is induced.
2. This EMF drives a small current through the shunt field winding (connected across the armature).
3. If the field is connected so that its MMF aids the residual flux, the flux increases, so the induced EMF increases.
4. The higher EMF drives more field current, which increases flux further, and so on (cumulative process).
5. Build-up stops where the OCC (magnetisation curve, $E$ vs $I_f$) meets the field resistance line ($V = I_fR_f$), because at that point the generated EMF just equals the drop across the field circuit. Saturation of the iron makes the OCC bend over, so the two curves intersect at a definite point.

  E ^           field resistance line
    |         /     (slope = Rf)
    |        /   ___....--- OCC
    |       / .-'
    |      /.'   <- operating point
    |     .'      (OCC meets Rf line)
    |   .'/
    |  / /  steps of build-up
    | / /
    |//
 Er +------------------------> If

Critical field resistance

The critical field resistance $R_c$ is the maximum shunt-field circuit resistance at which the generator will just build up voltage at a given speed. It equals the slope of the tangent to the linear part of the OCC drawn from the origin. If $R_f > R_c$, the field line lies above the OCC, they meet only near the residual voltage, and the machine fails to build up.

Critical speed

The critical speed $N_c$ is the minimum speed at which a shunt generator with a given field resistance $R_f$ will just build up. At that speed the slope of the OCC's initial tangent equals $R_f$. Since EMF ∝ speed:

$$\frac{N_c}{N} = \frac{R_f}{R_c} \quad\Rightarrow\quad N_c = N\,\frac{R_f}{R_c}$$

where $R_c$ is the critical resistance at speed $N$.

Example: if $R_c = 200\ \Omega$ at 1000 rpm and the field resistance is $150\ \Omega$, then $N_c = 1000 \times \frac{150}{200} = 750$ rpm.

Conditions for build-up

• Residual magnetism must be present.
• Field MMF must aid the residual flux (correct field connection / direction of rotation).
• Field circuit resistance must be less than critical resistance.
• Speed must be above critical speed.
• At start, load resistance should be high (no load), so the armature voltage is not pulled down.