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,

$$\mathrm{\text{Excitation voltage, } \: E_{f} \:=\: 4.44 \: k_{w} \: f \: \phi \: T_{f} \:\: \dotso \:(1)}$$

Therefore,

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

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

Also,

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

And

$$\mathrm{SCR \: \propto \: \frac{1}{L_{s}}\:\: \dotso \:(4)}$$

$$\mathrm{\therefore \: SCR \: \propto \: \text{ Reluctance of air gap or Length of air gap }\:\: \dotso \:(5)}$$

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