📘 Induction Motor – Equivalent Circuit (Per Phase Model)
Induction motor equivalent circuit is similar to transformer equivalent circuit. It helps in torque, power and efficiency calculations.
🔹 1. Per Phase Equivalent Circuit
Components:- R₁ – Stator resistance
- X₁ – Stator leakage reactance
- R₂' – Rotor resistance referred to stator
- X₂' – Rotor reactance referred to stator
- Xm – Magnetizing reactance
- Rc – Core loss resistance
R₂'/s
This is very important.🔹 2. Why R₂'/s?
Rotor current depends on slip. At standstill (s = 1):Rotor resistance = R₂'
At small slip:Effective resistance increases → R₂'/s
🔹 3. Impedance Calculation
Total impedance:Z = R₁ + jX₁ + (R₂'/s + jX₂')
Used to calculate stator current.🔹 4. Example 1
Given: R₁ = 0.5 Ω X₁ = 1 Ω R₂' = 0.4 Ω X₂' = 1 Ω Slip = 0.04 Find rotor resistance term. Solution:R₂'/s = 0.4 / 0.04 = 10 Ω
Rotor resistance increases greatly at low slip.🔹 5. Example 2 – Rotor Current
If phase voltage = 230 V Total resistance:R_total = 0.5 + 10 = 10.5 Ω
Total reactance:X_total = 1 + 1 = 2 Ω
Impedance magnitude:Z = √(10.5² + 2²)
Then:I = V / Z
🔹 6. Important Observations
- Slip affects rotor resistance term
- At small slip → high effective resistance
- Equivalent circuit similar to transformer
- Used for torque derivation next
🎯 GATE Important Points
- Remember R₂'/s concept clearly
- Slip appears only in rotor resistance term
- Rotor frequency = s f
- Most torque problems use this model
Equivalent Circuit = Foundation for Torque-Slip Analysis
.png)
No comments:
Post a Comment