✅ Power Flow in Induction Motor

Power in an induction motor flows in stages from stator input to mechanical output.

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🔹 Step-by-Step Power Flow

1️⃣ Stator Input Power

$$P_{in} = \sqrt{3} V_L I_L \cos \phi$$

Power supplied from the mains to stator.

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2️⃣ Stator Losses

These losses occur in stator:

(a) Stator Copper Loss

$$P_{sc} = 3 I_1^2 R_1$$

(b) Core (Iron) Loss

• Hysteresis loss

• Eddy current loss

$$P_{core}$$

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3️⃣ Air-Gap Power (Rotor Input Power)

$$P_g = P_{in} - (P_{sc} + P_{core})$$

This is the power transferred magnetically from stator to rotor across the air gap.

👉 Also called Rotor Input Power

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4️⃣ Rotor Copper Loss

$$P_{rc} = s P_g$$

where    s = slip

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5️⃣ Mechanical Power Developed

$$P_m = P_g - P_{rc}$$ $$P_m = P_g (1 - s)$$

This is the gross mechanical power developed in rotor.

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6️⃣ Mechanical Losses

• Friction loss

• Windage loss

$$P_{mech}$$

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7️⃣ Shaft Output Power (Final Output)

$$P_{out} = P_m - P_{mech}$$

This is useful mechanical power available at shaft.

Stator Input Power (Pin)

        ↓

   Stator Copper Loss

   Core Loss

        ↓

   Air Gap Power (Pg)

        ↓

   Rotor Copper Loss (sPg)

        ↓

   Mechanical Power Developed (1-s)Pg

        ↓

   Mechanical Losses

        ↓

   Shaft Output Power (Pout)