Shunt generator build-up conditions, critical speed and resistance

Process of voltage build-up

A self-excited shunt generator uses its own output to supply its field.

1. The field poles retain a small residual flux $\phi_r$. When the armature is driven, a small EMF $E_r = \frac{P\phi_rZN}{60A}$ (a few volts) appears.
2. $E_r$ drives a small current through the shunt field, which is connected across the armature.
3. If this current's MMF aids the residual flux, flux rises, so EMF rises.
4. Higher EMF gives more field current, which gives more flux and more EMF: the voltage builds up cumulatively.
5. Build-up stops at the point where the OCC cuts the field resistance line ($V = I_fR_f$). Beyond that point, the EMF generated is less than that needed to drive more field current, so the voltage settles there.

  E ^           Rf line
    |          /
    |         /   ___---- OCC
    |        / .-'
    |       /.'  <-- operating voltage
    |     .'/
    |   .' /
    | .'  /
 Er +'---/------------------> If

Conditions for voltage build-up

1. Residual magnetism must be present in the poles. (If lost, "flash" the field from a battery.)
2. Correct field connection: field MMF must aid the residual flux; otherwise the residual flux is wiped out. If wrong, reverse field terminals or the direction of rotation.
3. Field resistance less than critical resistance $R_c$.
4. Speed above critical speed $N_c$ for the given field resistance.
5. No load or high-resistance load at starting (load resistance above critical load resistance), so that the terminal voltage is not pulled down.
6. Brushes on the correct neutral axis with good contact.

Finding critical field resistance and critical speed

No numerical OCC data is given, so the standard graphical method is described.

Critical field resistance: plot the OCC at rated speed $N$. Draw a tangent from the origin to the initial straight part of the OCC. Its slope is the critical resistance:

$$R_c = \frac{\Delta E}{\Delta I_f}\Big|_{\text{tangent}}$$

Critical speed: for the actual field resistance $R_f$, draw the field line of slope $R_f$. Take any current $I_f$ on the linear part; read the tangent voltage $E_c$ (= $R_cI_f$) and the field-line voltage $E_f$ (= $R_fI_f$). Since EMF ∝ speed:

$$N_c = N\,\frac{E_f}{E_c} = N\,\frac{R_f}{R_c}$$

Example: OCC at 1000 rpm gives 120 V at $I_f = 0.6$ A on the linear part, so $R_c = 120/0.6 = 200\ \Omega$. With $R_f = 160\ \Omega$, $N_c = 1000 \times 160/200 = 800$ rpm. The generator builds up only above 800 rpm, or at 1000 rpm only if $R_f < 200\ \Omega$.