Series motor load start; shunt motor speed control

Why a series motor cannot be started without load

In a series motor the field winding carries the armature current, so the flux depends on the load: $\Phi\propto I_a$ (below saturation). The speed is

$$N \propto \frac{E_b}{\Phi} \approx \frac{V - I_a(R_a + R_{se})}{\Phi}$$

• At no load $I_a$ becomes very small, so the flux $\Phi$ becomes very small (only the residual value).
• The numerator $E_b\approx V$ stays nearly constant, so the speed $N\propto 1/\Phi$ rises to a dangerously high value (several times rated speed).
• This is called racing. The centrifugal forces can burst the armature, throw the winding out of the slots and damage the commutator and bearings.
• The torque $T\propto\Phi I_a\propto I_a^2$ is small at no load, so the motor has no load to hold the speed down.

Hence a series motor must always be started and run with a load connected (preferably directly coupled or geared, never by a belt that may slip or break).

Speed control of a DC shunt motor

From the motor equations:

$$N = \frac{V - I_aR_a}{K\Phi} \propto \frac{E_b}{\Phi}$$

So the speed of a shunt motor can be changed by varying the flux $\Phi$, the armature circuit resistance, or the applied voltage.

1. Armature (rheostatic) control

A variable resistance $R_x$ is connected in series with the armature (field kept constant at full value):

$$N = \frac{V - I_a(R_a + R_x)}{K\Phi}$$

• The speed is reduced below the normal (base) speed; the greater $R_x$, the lower the speed.
• Torque for a given $I_a$ is unchanged ($T\propto\Phi I_a$), so it suits constant-torque loads.
• Disadvantages: large $I_a^2R_x$ loss, poor efficiency, and poor speed regulation (the speed changes with load); it is used for small and short-time duty.

2. Field (flux) control

A rheostat $R_f$ is connected in series with the shunt field:

$$I_f = \frac{V}{R_{sh} + R_f}, \qquad N \propto \frac{1}{\Phi}$$

• Increasing $R_f$ lowers $\Phi$, so the speed rises above the base speed (typically up to 2:1 or 3:1).
• It is simple, cheap and efficient (field loss is small, since $I_f$ is small).
• Limits: commutation worsens and the machine can become unstable (armature reaction) at very weak fields; the torque for a given $I_a$ falls as $\Phi$ falls, so it suits constant-power loads.

   Speed
     ^       field control (N up)
     |      /
  base N ---+--- 
     |      \  armature control (N down)
     +--------------------> Rheostat setting

3. Armature voltage control (Ward-Leonard)

Varying the voltage applied to the armature (with a separate source) changes the speed smoothly from zero up to the base speed.

Comparison