Equivalent circuit of Induction Motor
- 1. EQUIVALENT CIRCUIT OF THREE PHASE INDUCTION MOTOR PER PHASE EQUIVALENT CIRCUIT OF STATOR PER PHASE EQUIVALENT CIRCUIT OF ROTOR To study & predict the performance of Induction Motor ITS SIMILAR TO TRANSFORMER That’s why IM called as ROTATING TRANSFORMER! = 𝟐𝛑𝐟 𝟏 𝐋 𝟏 “Operates @ stator/ supply frequency 𝐟 𝟏”
- 2. PER PHASE EQUIVALENT CIRCUIT OF ROTOR Slip rpm S* Ns= Ns- N Rotor circuit frequency 𝐟 𝟐 = 𝐒𝐟 𝟏 So, frequency dependent parameters such as reactance and EMF will be 𝐒𝐄 𝟐 & 𝐒𝐗 𝟐 S S = 𝟐𝛑𝐟 𝟐 𝐋 𝟐 We Cant Combine Stator & rotor equivalent circuit directly! Problem 1 : Stator & rotor circuit are operating @ different frequency Problem 2 : Air-gap is between the stator and rotor “Operates @ rotor frequency 𝐟 𝟐”
- 3. To overcome the problem 1 𝐈2 = 𝐒𝐄2 𝐑2 2 + ൯ሺ 𝐒𝐗2 2 𝐈2 = 𝐒𝐄2 𝐒 𝐑2 𝐒 2 + 𝐗2 2 “Operates @ rotor frequency 𝐟 𝟐” “Operates @ stator frequency 𝐟 𝟏”
- 4. To overcome the problem 2 (Speaker resistance referred to the primary side) Air gap Air gap 𝐑 𝟐 ′ = 𝐚 𝟐 ∗ 𝐑 𝟐 𝐈 = 𝟏𝟎 𝟏 + 𝟏 = 𝟓 𝐀𝐦𝐩𝐬 𝐑 𝟐 ′ = 𝐍 𝟏 𝐍 𝟐 𝟐 ∗ 𝐑 𝟐 ⇒ 𝟏 𝟑 ∗ 𝟗 ⇒ 𝟏
- 5. PER PHASE TOTAL EQUIVALENT CIRCUIT OF IM REFERRED TO STATOR SIDE Air gap (a = S to R turns ratio) ሺ𝐑 𝟐 ′ = 𝐚 𝟐 𝐑 𝟐)
- 6. The air-gap power associated with the equivalent circuit is 𝐏𝐚𝐠 = 𝐈 𝟐 𝟐 𝐑 𝟐 ′ 𝐒 𝐏𝐚𝐠 = 𝐈2 2 𝐑2 ′ + 𝐑2 ′ 𝐒 − 𝐑2 ′ 𝐏𝐚𝐠 = 𝐈 𝟐 𝟐 𝐑 𝟐 ′ + 𝐑 𝟐 ′ 𝐒 ሺ𝟏 − 𝐒) Rotor copper loss Pcu2 = 𝐈 𝟐 𝟐 𝐑 𝟐 ′ Mechanical Power Pmech = 𝐈 𝟐 𝟐 𝐑 𝟐 ′ 𝐒 (1-S) Power Flow Diagram of IM 𝐏𝐚𝐠 Pcu2 Pmech P electric Pcore + Pcu1
- 7. Ratio of Air-gap power , Rotor copper loss & Mechanical power developed Pag : Pcu2 : Pmech = 1 : S : (1-S) 𝐈 𝟐 𝟐 𝐑 𝟐 ′ 𝐒 : 𝐈 𝟐 𝟐 𝐑 𝟐 ′ : 𝐈 𝟐 𝟐 𝐑 𝟐 ′ 𝐒 (1-S) Dividing By 𝐈 𝟐 𝟐 𝐑 𝟐 ′ 𝐒 1 : S : (1-S) Pag : Pcu2 : Pmech Important Note By operating at low slip rotor copper loss can be minimized & mechanical power can be increased or in other words Efficiency of IM will increase
- 8. IMPORTANT POINTS TO REMEMBER IN TORQUE- SLIP CHARACTERISTICS • Torque is directly proportional in low slip region of IM • Torque is inversely proportional in high slip region of IM • Low slip region is called stable region • Maximum torque obtained is called pull out torque in IM • The slip @ which the pullout torque occurs is called critical slip • Critical slip = R2/X2 • By increasing the resistance in rotor it is possible to increase the starting torque (This is possible only in slip ring IM!!). Maximum torque is irrespective to Rotor resistance!
- 9. IMPORTANT POINTS TO REMEMBER IN EQUIVALENT CIRCUIT OF AN INDUCTION MOTOR • Equivalent circuit of IM is used to study and predict the performance of IM • From solving the equivalent circuit we understand that, from the total air-gap power, a fraction of “slip power” S is dissipated in the resistance of the rotor circuit (rotor copper loss) • A fraction of (1-S) is converted into mechanical power • So we understand the lower the slip – higher the mechanical power and lesser the rotor copper loss or higher efficiency. • All Equivalent circuit parameters (E, I, R, X) can be found from No load test and Blocked rotor test (Document given in the description!)