Question

In a synchronous machine, the magnitude of magnetising reactance is:
1. directly proportional to air gap length
2. inversely proportional to air gap length
3. directly proportional to air gap length squared
4. constant

Answer 1

Correct Answer - Option 2 : inversely proportional to air gap length

Air gap length in a synchronous machine:

• The length of the air gap is a very important parameter because it greatly affects the performance of the machine.
• The air gap in a synchronous machine affects the value of short circuit ratio (SCR) which can affect many other parameters.

 

Magnetizing reactance:

The magnitude of magnetizing reactance is influenced by air-gap length as under:

Magnetizing reactance (X_ar) = ω L_ar

Where,

ω = angular frequency

L_ar = magnetizing inductance

And, L_ar ∝ (N_ph²) / (air-gap reluctance)

• So, a synchronous machine with a large air-gap has a low value of L_ar and X_ar.
• In other words, the magnitude of magnetizing reactance (X_ar) is inversely proportional to air-gap length.
• The armature leakage reactance X_al is usually treated as constant.
• As X_ar plays a dominant role on synchronous reactance (X_s). So it can be stated that X_s is inversely proportional to air-gap length.

 

Advantages of larger air-gap:

• As reactance is decreasing with the larger air-gap the stability limit will be increased.
• The smaller value of inherent regulation.
• Better cooling and noise reduction.
• The value of synchronizing power will be higher.
• Less value of unbalanced magnetic pull.

 

Disadvantages of larger air-gap:

• Larger diameter and hence larger size.
• More amount of field mmf is required.
• Increase in overall cost.