# Significance of Short Circuit Ratio of Alternator (Synchronous Machine)

In a synchronous machine, the short-circuit ratio (SCR) is an important factor. The SCR affects the physical size, operating characteristics and cost of the synchronous machine.

## Low Value of SCR

With a low value of SCR, the synchronous machine is very sensitive to the load variations, i.e., the alternator has a large variation in terminal voltage with a change in load. In order to keep the terminal voltage constant, the field current of the machine is to be varied over a wide range. Also, for a small value of SCR, the synchronising power of the machine is small. The synchronising power keeps the machine in synchronism, thus, the synchronous machine with a low value of SCR has a low stability limit. Therefore, an alternator with a low SCR is less stable when operating in parallel with other alternators. The armature current of the synchronous machine under short-circuit conditions is small for a low value of SCR

## High Value of SCR

With a high value of SCR, a synchronous machine has a better voltage regulation and improved steady-state stability limit, but the armature current under short-circuit conditions is high.

## Effect of SCR on the Size, Weight, and Cost of Machine

The physical size and cost of the synchronous machine are affected by the short-circuit ratio. The excitation voltage for a synchronous machine is given by,

$$\mathrm{Excitation\:voltage,\:𝐸_{𝑓} = 4.44\:𝑘_{𝑤}\:𝑓\:φ\:𝑇_{𝑓}… (1)}$$

Therefore,

$$\mathrm{𝐸_{𝑓}\:∝ field\:flux\:per\:pole}$$

$$\mathrm{𝐸_{𝑓}\:∝\frac{Field\:MMF\:per \:pole}{Reluctance\:of\:air\:gap}… (2)}$$

Also,

$$\mathrm{Synchronous\:inductance,\:𝐿_{𝑠} ∝ \frac{1}{Reluctance\:of\:air\:gap}… (3)}$$

And

$$\mathrm{SCR ∝\frac{1}{𝐿_{𝑠}}… (4)}$$

$$\mathrm{∴\:SCR ∝\:Reluctance\:of \:air\:gap\:or\:Length\:of\:air\:gap … (5)}$$

Hence, it is clear from eq. (5) that the SCR of the synchronous machine may be increased by increasing the length of air-gap. With the increased length of air-gap, the field MMF is to be increased for the same value of 𝐸𝑓 . To increase the field MMF, either the field current (𝐼𝑓) or the number of turns in field winding (𝑇𝑓) is to be increased and it requires greater height of the field poles. As a result, the overall diameter of the machine increases. Therefore, a high value of SCR will increase the physical size, weight, and cost of the machine.

Typical values of short-circuit ratio (SCR) of various types of synchronous machine are as follows −

• Cylindrical rotor synchronous machine – 0.5 to 0.9

• Salient-pole synchronous machine – 1.0 to 1.5

• Synchronous compensators – 0.4