Voltage build-up, critical resistance and speed

Voltage build-up in a DC shunt generator

A shunt generator is self-excited, so its voltage builds up from the residual magnetism in the poles.

1. The armature is driven at rated speed. Residual flux induces a small emf $E_r$ (about 1–3 V) in the armature.
2. This emf sends a small current $I_f = E_r/(R_f + R_a)$ through the shunt field winding.
3. If the field connections are correct (the field current aids the residual flux), the flux increases, which raises the emf, which raises the field current, and so on.
4. The build-up stops at the point where the field-resistance line ($V = I_fR_f$) cuts the open-circuit characteristic (OCC). Here the emf generated equals the voltage drop in the field circuit. This is the no-load terminal voltage.

 V (volts)          OCC
  |              _______---
  |           _-'    /  Rf line
  |  b      ,'      /
  |      ,-'      /
  |   ,-'       /   <- Rc (tangent)
  | ,'        /
  |/-- Er  /
  +-------------------------- If

Conditions for build-up: (i) residual magnetism, (ii) field winding connected so it aids the residual flux, (iii) total field circuit resistance less than the critical resistance.

Critical field resistance ($R_c$)

It is the maximum value of field circuit resistance with which the shunt generator will still build up at a given speed. Graphically, it is the slope of the field-resistance line that is tangent to the initial straight part of the OCC. If $R_f > R_c$, the line cuts the OCC only near the residual voltage, so the generator does not build up.

Critical speed ($N_c$)

It is the minimum speed below which a shunt generator will not build up voltage for a given field resistance. The OCC is for one speed; at lower speed the OCC drops (since $E \propto N$). The speed at which the OCC becomes tangent to the given field-resistance line is the critical speed.

Relation: $R_c \propto N$, i.e. $\dfrac{R_{c2}}{R_{c1}} = \dfrac{N_2}{N_1}$.