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 𝐸_𝑓 . To increase the field MMF, either the field current (𝐼_𝑓) or the number of turns in field winding (𝑇_𝑓) 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