GATE Electrical Engineering - Complete Master Library

 

📘 Induction Motor – Power Flow & Efficiency

Power flow diagram explains how input power is divided into different losses and output power. Very important for numerical problems.

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🔹 1. Power Flow Stages

Input Electrical Power (P_in) ↓ Stator Copper Loss ↓ Core Loss ↓ Air Gap Power (P_g) ↓ Rotor Copper Loss ↓ Mechanical Power Developed (P_m) ↓ Mechanical Losses ↓ Output Power (P_out)

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🔹 2. Air Gap Power (P_g)

Air gap power is power transferred from stator to rotor. Very important relation:

Rotor Copper Loss = s × P_g

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🔹 3. Mechanical Power Developed

P_m = (1 − s) P_g

This is one of the most important formulas.

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🔹 4. Rotor Efficiency

Rotor Efficiency = (1 − s)

If slip = 4%, Rotor efficiency = 96%. Very commonly asked.

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🔹 5. Example 1

Given: Air gap power P_g = 50 kW Slip = 0.04 Find: 1️⃣ Rotor copper loss 2️⃣ Mechanical power developed Solution: Rotor copper loss:

= s × P_g = 0.04 × 50 = 2 kW

Mechanical power:

= (1 − s) P_g = 0.96 × 50 = 48 kW

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🔹 6. Example 2

If rotor copper loss = 1 kW Slip = 0.05 Find air gap power. Using:

Rotor copper loss = s × P_g

1 = 0.05 × P_g P_g = 20 kW

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🔹 7. Important Observations

• Rotor loss proportional to slip
• At standstill (s=1) → All power lost as rotor copper loss
• At synchronous speed (s=0) → No rotor loss
• Motor operates at small slip → High efficiency

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🎯 GATE Important Points

• Remember P_m = (1 − s) P_g
• Rotor efficiency = 1 − s
• Slip directly affects rotor loss
• Power flow diagram very important

Slip = Determines Rotor Loss & Mechanical Power