# Speed Regulation of DC Motor

On application of load the speed of a dc motor decreases gradually. This is not at all desirable. So the difference between no load and full load speed should be very less. The motor capable of maintaining a nearly constant speed for varying load is said to have good speed regulation i.e the difference between no load and full load speed is quite less. The speed regulation of a permanent magnet DC motor is good ranging from 10 - 15% whereas for dc shunt motor it is somewhat less than 10 %. DC series motor has poor value of regulation. In case of compound DC motor the speed regulation for dc cumulative compound is around 25 % while differential compound has its excellent value of 5 %.

## Speed of a DC Motor

The emf equation of DC motor is given by

$E\; =\;\frac{N P \phi Z}{60A}$

Here N = speed of rotation in rpm.

P = number of poles.

A = number of parallel paths.

Z = total no. conductors in armature.

$Thus,\; speed\; of\; rotation\;N\; =\; \frac{60A}{PZ}X\frac{E}{\phi}$

$\Rightarrow \; N\; =\; \frac{E}{k\phi}\;\;\;Where\;k\;=\;\frac{PZ}{60A}\; is\;a\;constant$

Hence, speed of a DC motor is directly proportional to emf of rotation (E) and inversely proportional to flux per pole (φ).

## Speed Regulation of a DC Motor

The speed regulation is defined as the change in speed from no load to full load, expressed as a fraction or percentage of full load speed.

Therefore, as per definition per unit (p.u) speed regulation of DC motor is given as,

$Speed\; Regulation_{pu}\; =\; \frac{N_{no\;load} -N_{full\;load}}{N_{full\;load}}$

Similarly, percentage (%) speed regulation is given as,

$Speed\; Regulation(\%)\; =\; \frac{N_{no\;load} -N_{full\;load}}{N_{full\;load}}X100\%$

Where Nno load = no load speed and Nfull lod = full load speed of DC motor.

Therefore, Percent speed regulation = Per unit (p.u) speed regulation X 100 %.

A motor which has nearly constant speed at all load below full rated load, have good speed regulation.