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Unformatted text preview: Module 8 Threephase Induction Motor Version 2 EE IIT, Kharagpur Lesson 31 Equivalent Circuit and Power Flow Diagram of IM Version 2 EE IIT, Kharagpur Instructional Objectives • determine the induced emfs, and the currents, per phase in the stator and rotor windings, • find the relation between the rotor input, rotor copper loss and rotor output, in terms of slip, • calculate the various losses – iron, copper and mechanical, in an IM, and • find where do the losses occur. Introduction In the previous, i.e. second, lesson of this module, the construction (the stator and two types of rotor − squirrel cage and wound (slipring) one), of the threephase induction motor (IM), has been described. Then, the principle of operation, i.e. production of torque, with the stator supplied from balanced threephase supply and the rotor winding terminals shortcircuited, is discussed. In this lesson, the equivalent circuit per phase of IM will be derived first, to be followed by the presentation of power flow diagram, wherein the various losses, and also where do they occur, are described. Keywords: The induced voltages (emfs) in stator winding and rotor bar/winding, the equivalent circuit per phase of IM, the fictitious resistance in the circuit, input power to stator and rotor, losses – iron loss, stator and rotor copper loss, mechanical losses, output power. The induced emf per phase, in the motor windings The induced emf per phase in the stator winding is nearly equal to the input voltage per phase, and is given by s ws s s w s s T f k Z f k E V ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ = ≈ φ 44 . 4 22 . 2 where, = Input voltage (V) per phase, to the stator winding s V = Induced emf (V) per phase, in the stator winding s E = Flux (Wb) per pole = Frequency (Hz or c/s) of the input voltage f = No. of stator conductors in series per phase s s T Z ⋅ = 2 = No. of stator turns or coils in series per phase s T = Stator winding factor ps ds ws k k k ⋅ = = Distribution factor of stator winding ds k = Pitch factor of stator winding ps k The above formula, not derived here, is a standard one available in any textbook. It is similar to the formula for the induced emf in a transformer, derived in the earlier module. As the winding in this case is stationary, with the rotating magnetic field rotating at a Version 2 EE IIT, Kharagpur speed of (also termed as the synchronous speed), the frequency of the induced emf in the stator winding is same as that of input frequency ( ), where, p f p f n s / ) 2 ( ) 2 / /( ⋅ = = s n p f ⋅ = ) 2 / ( = Speed of the rotating magnetic field (rev/sec) s n = No. of poles for which the stator winding of IM is designed p The induced emf per phase at standstill ( . = r ω , or . 1 = s ) in the rotor winding (assuming a wound or slipring one), is given by r r wr r r r w r T f k Z f k E ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ = φ 44 . 4 22 . 2 where, = Induced emf (V) per phase, in the rotor winding at standstill (...
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