JNTU B.Tech III ELECTRICAL MACHINES-III Previous Question Paper (March-2021 - R13/R15)

An alternator consists of two primary components: the stator and the rotor. The stator is the stationary part that houses the armature winding in slots on its inner periphery. It is constructed from laminated steel stampings to minimize eddy current losses. The rotor is the rotating part that provides the necessary magnetic field. It is typically one of two types: the salient pole rotor, used for low-speed machines, featuring projecting poles; or the cylindrical rotor, used for high-speed turbo-alternators, featuring a smooth, solid steel cylinder with slots for the field winding. Other essential parts include the exciter, which provides DC current to the rotor field windings, and the stator frame, which provides mechanical support and protection.

Given: P=8, f=50Hz, slots per pole per phase (m)=3, conductors per slot=6, coil span=150°, Φ₁=0.2Wb, Φ₃=0.1Φ₁=0.02Wb. Total slots = 8 poles × 3 slots/pole/phase × 3 phases = 72 slots. Conductors per phase (Zph) = (72 slots × 6 conductors/slot) / 3 phases = 144. Turns per phase (Tph) = 144 / 2 = 72.

Distribution factor (Kd): For m=3, Kd = sin(mβ/2) / (m sin(β/2)). Slot angle β = 180° / (slots/pole) = 180° / (72/8) = 20°. Kd = sin(3×20°/2) / (3×sin(20°/2)) = sin(30°)/(3×sin(10°)) = 0.5 / 0.5209 = 0.9598.

Pitch factor (Kp): Kp = cos(α/2). Coil span is 150°, so pitch deficiency α = 180° - 150° = 30°. Kp = cos(15°) = 0.9659. For 3rd harmonic, Kp3 = cos(3×15°) = cos(45°) = 0.7071. Kd3 = sin(3×3×20°/2) / (3×sin(3×20°/2)) = sin(90°)/(3×sin(30°)) = 1 / 1.5 = 0.6667.

Fundamental EMF (E1) = 4.44 × f × Φ1 × Tph × Kp × Kd = 4.44 × 50 × 0.2 × 72 × 0.9659 × 0.9598 = 2943.4V. 3rd Harmonic EMF (E3) = 4.44 × (3f) × Φ3 × Tph × Kp3 × Kd3 = 4.44 × 150 × 0.02 × 72 × 0.7071 × 0.6667 = 448.6V.