3 phase Induction Motor Torque-slip characteristics and Related problems

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1. Three Phase Induction Motors – Torque-Slip Characteristics & Related Problems Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics Contents : Torque slip characteristics Power flow diagram Relationship between rotor power and losses Related Problems

2. Torque-Slip Characteristics The curve drawn between torque and slip from start (s=1) to Synchronous speed (s=0) is called torque slip characteristics of the induction motor Torque Equation Input voltage is constant (E 2 =C) Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

3. Torque-Slip Characteristics Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

4. Torque-Slip Characteristics Three Regions: Stable operating region Unstable operating region Normal operating region Stable Region (AB) ‘s’ is very small ( then, (sX 2 ) 2 <<< R 2 2 ) , Hence s 2 X 2 2 is neglected in this region as load ↑, T↑, s↑ Characteristics is approximately straight line Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

5. Torque-Slip Characteristics Unstable Region (BC) When s increases further from s m the region is unstable region, s is high (between s m and 1) , R 2 2 can be neglected as compared to s 2 X 2 2 in this region as load ↑, s↑, T↓ Characteristics is approximately rectangular hyperbola. When load further increases, N↓, s↑, leads motor to standstill condition , hence motor should not be operated at any point in this region. Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

6. Torque-Slip Characteristics Normal Region (AD) Low slip region, the motor can continuously operated in this region.   Three torques: Starting torque ( T st ) Maximum torque or pull out torque(T m ) Full load torque( T fl )   Starting Torque ( Tst ) The motor produces the torque when s=1 speed is zero. Maximum Torque or Pull out Torque(Tm) The torque produced at s= s m is called maximum torque. S m is slip at which maximum torque occurs. Also called breakdown torque of pull out torque .   Full Load Torque ( Tfl ) In the characteristics the torque corresponding to point D is called full load torque of motor. usually T fl < T m . Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

7. Torque-Slip Characteristics   Losses in An Induction Motor Three losses are Magnetic Losses (Constant) Mechanical Losses (Constant) Electrical Losses (variable)   Magnetic Losses Also called core losses or iron losses. Losses occur in stator core and rotor core because of rotating magnetic field Two types Eddy Current Losses Hysteresis Losses   Hysteresis Losses Occur due to alternate change in magnetic field in the stator core. Can be minimized by selecting high grade silicon steel as the material     Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

8. Torque-Slip Characteristics Eddy Current Losses Occur due to flow of eddy current through body of the stator core. Can be minimized by using laminated construction of the stator core   Two losses are depend on supply frequency , f stator = f supply , hence iron loss for stator is more f rotor <<, hence iron losses are also very small, neglected under running condition   Mechanical Losses Consists of frictional losses and windage losses Losses are <<< due to speed drop is very small Constant losses = Iron Losses + Mechanical Losses   Electrical Losses Due to resistance of stator and rotor winding. (stator and rotor copper losses) When load ↕ current ↕, so it is called variable losses Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

9. Power Flow Diagram Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

10. Power Flow Diagram Induction motor converts electrical power into mechanical power. 3ph supply is fed to stator, input power P in is Losses occur in stator called stator losses (P SL ) Remaining power is transferred to rotor magnetically, It is called output of the stator or input to the rotor (P 2 ) In rotor side, rotor copper losses occur ( P cu ) . Normally rotor iron losses are very small therefore it should be neglected. Remaining part is called mechanical power developed (P m )   Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

11. Power Flow Diagram Due to rotating part in motor mechanical losses ( P mL ) occur . Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

12. Relationship between rotor input (P 2 ), rotor copper loss ( P cu ) and gross mechanical power (P m ) In general Power in terms of torque is Power is transferred from stator to rotor Gross mechanical power developed by rotor (P m ) is Rotor copper loss Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

13. Relationship between rotor input (P 2 ), rotor copper loss ( P cu ) and gross mechanical power (P m ) Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

14. Problem - 1 A 6pole, 3phase induction motor develops a power of 22.38kW, including mechanical losses, which total 1.492kW at a speed of 950rpm on 550V, 50Hz mains. The power factor is 0.88. Calculate for this load ( i ). Slip, (ii). The rotor copper loss, (iii). The total input iif the stator losses are 2000W, (iv). The efficiency, (v). The line current, (vi). The number of complete cycles of the rotor electromotive force per minute. Solution ( i ). Slip s Given: P=6, P m =22.38kW, P mL =1.492kW, N=950rpm, V=550V, f=50Hz, PF =0.88 ; Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

15. Problem - 1 Solution (ii). Rotor copper loss P cu Given: P=6, P m =22.38kW, P mL =1.492kW, N=950rpm, V=550V, f=50Hz, PF =0.88 ; (iii). The total input (P in ) (iv). Efficiency Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

16. Problem - 1 Solution (v). The line current (IL) Given: P=6, P m =22.38kW, P mL =1.492kW, N=950rpm, V=550V, f=50Hz, PF =0.88 ; (vi). The number of complete cycles of the rotor electromotive force per minute. Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

17. Problem - 2 A 37.3kW, 4pole, 50Hz induction motor has friction and windage losses of 3320 watts. The stator losses equal the rotor losses. If the motor is deleiverig full load power output at a speed of 1440rpm, calculate, ( i ). Synchronous speed, (ii). Slip (iii). Mechanical power developed by the motor, (iv). Rotor copper loss, (v). Power transferred from stator to rotor, (vi) Stator power input, (vii). Efficiency . Solution ( i ). Synchronous speed(N s ) Given: P out =37.3kW; P=4; f=50Hz; friction and windage losses P ml =3320W; Stator losses P SL =Rotor Loss P cu ; N=1440rpm. ; (ii). Slip s Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

18. Problem - 2 Solution (iii). Mechanical power developed by the motor (P m ), Given: P out =37.3kW; P=4; f=50Hz; friction and windage losses P ml =3320W; Stator losses P SL =Rotor Loss P cu ; N=1440rpm. ; (iv). Rotor copper loss ( P cu ), (v). Power transferred from stator to rotor (P 2 ), Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

19. Problem - 2 Solution (vi) Stator power input (P in ), Given: P out =37.3kW; P=4; f=50Hz; friction and windage losses P ml =3320W; Stator losses P SL =Rotor Loss P cu ; N=1440rpm. ; (vii). Efficiency Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

20. Problem - 3 An 18kW, 4pole, 50Hz, 3phase induction motor has friction and windage loss 500W. The full load slip is 4%. Compute for full load, ( i ). Rotor copper loss. (ii). Rotor input. (iii). The shaft torque and (iv). The gross torque. Solution ( i ). Rotor copper loss ( P cu ), Given: P out =18kW, P=4; f=50Hz; P mL =500W; s=4%; Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

21. Problem - 3 Solution (ii). Rotor input (P 2 ). Given: P out =18kW, P=4; f=50Hz; P mL =500W; s=4%; (iii). The shaft torque ( T sh ), (iv). The gross torque( T g ) Kongunadu college of Engineering & Technology Three phase Induction Motor – Torque slip characteristics

22. S.No Book s / Web Sources 1 A.E. Fitzgerald, Charles Kingsley, Stephen. D. Umans , ‘Electric Machinery’, Tata Mc Graw Hill publishing Company Ltd, 2003. 2 D.P. Kothari and I.J. Nagrath , ‘Electric Machines’, Tata McGraw Hill Publishing Company Ltd, 2002. 3 P.S. Bhimbhra , ‘Electrical Machinery’, Khanna Publishers, 2003. 4 M.N.Bandyopadhyay , Electrical Machines Theory and Practice, PHI Learning PVT LTD., New Delhi, 2009. 5 K. Murugesh Kumar, ‘Electric Machines’, Vikas Publishing House Pvt. Ltd, 2002. 6 Syed A. Nasar , Electric Machines and Power Systems: Volume I, Mcgraw -Hill College; International ed Edition, January 1995. 7 J. Ganavadivel , ‘Electrical Machines II’, Anuradha publications, Fourth edition, 2015. 8 U.A.Bakshi & M.V.Bakshi , ”Electrical Machines II,” Technical Publications, Second revised edition, 2016. 9 Google and Wikipedia REFERENCES