Justify: series motor power; shunt motor for traction

a) Power drawn by a dc series motor varies as $\sqrt{T}$

In a series motor the field current is the armature current, so (below saturation) $\phi \propto I$:

$$T \propto \phi I \propto I^2 \Rightarrow I \propto \sqrt{T}$$

The supply voltage $V$ is constant, so the power drawn is

$$P = VI \propto I \propto \sqrt{T}$$

Example: if the load torque rises four times (steep gradient), the current and power drawn only double; speed falls automatically since $N \propto E/\phi \propto 1/I$.

For a shunt motor, $\phi$ is constant, so $T \propto I$ and $P \propto T$: a four-fold torque needs four-fold power. Hence a series motor puts much less strain on the supply and substation during heavy loads such as starting and climbing. This is a main reason dc series motors are used for traction.

b) Shunt motor is not suitable for traction

1. Power demand ∝ torque: since $T \propto I$ at constant flux and speed is nearly constant, heavy starting and gradient torques draw very large current and power from the supply (series motor: only $\sqrt T$).
2. Constant speed characteristic: traction needs a speed that falls on up-gradients and rises on light loads (falling characteristic). A shunt motor tries to keep the same speed, so power peaks are high.
3. Unequal load sharing: locomotives run several motors in parallel. Wheel diameters differ slightly by wear; with flat speed–torque curves, a small speed difference makes one shunt motor take a very large share of load, overloading it. Series motors with drooping curves share load nearly equally.
4. Supply voltage fluctuations: traction line voltage varies widely. In a shunt motor flux follows voltage; a sudden voltage rise or dip causes large current surges, since back emf cannot change instantly with speed. In a series motor the field current is the armature current, so surges are small.
5. Low starting torque per ampere: series motor torque rises with $I^2$, giving high starting torque with moderate current; a shunt motor gives only $T \propto I$.
6. Interruption of supply (e.g. pantograph bounce) is dangerous with shunt motors due to heavy current on reconnection.

(The shunt motor's only merit, easy regenerative braking, is outweighed by these drawbacks.)