• Conductor, core, frictional, and windage losses occur in IMs.
• Conductor and core losses constitute electromagnetic losses.
• Electromagnetic losses may be divided into fundamental and harmonic (space and/or time harmonics) losses.
• Fundamental conductor losses depend on skin effect, temperature, and the machine power and specific design.
• Fundamental core losses depend on the airgap flux density, yoke and teeth flux densities, and the supply voltage frequency.
• In a real IM, fundamental electromagnetic losses hardly exist separately.
• Nonfundamental electromagnetic losses are due to space or/and time harmonics.
• The additional (stray) losses, besides the fundamental, are caused by space airgap flux density harmonics or by voltage time harmonics (when PWM converters are used to feed the IM).
• The airgap flux density space harmonics are due to mmf space harmonics, airgap magnetic conductance space harmonics due to slot opening, and leakage or main flux path magnetic saturation.
• No-load stray losses are space harmonics losses at no-load. They are mainly: surface core losses, tooth flux pulsation core losses and tooth flux pulsation cage losses.
• For phase-belt (mmf first) harmonics, 5, 7, 11, 13 and up to the first slot opening harmonic (Ns/p1 ± 1), the skin depth in laminations is much larger than lamination thickness. So the reaction of core eddy currents on airgap harmonic field is neglected., This way, the rotor (stator) surface core losses are calculated.
• As the number of stator and rotor slots are different from each other Ns ≠ Nr, the stator and rotor tooth flux pulsates with Nr and Ns pole pairs, respectively, per revolution. Consequently, tooth flux pulsation core losses occur both in the stator and rotor teeth.
However, such tooth flux pulsations and losses are attenuated by the corresponding currents induced in the rotor cage.
• For the rotor slot skewing by one stator slot pitch, the reaction of cage currents to rotor tooth flux pulsation is almost zero and thus large rotor tooth flux pulsation core losses persist (undamped).
• For straight slot rotors, the rotor tooth flux pulsation produces, as stated above, no-load tooth flux pulsation cage losses. They are not to be neglected, especially in large power motors.
• All space harmonics losses under load are called stray load losses.
• Under load, the no-load stray losses are “amplified”. A load amplification factor Cload is defined and used to correct the stator and rotor tooth flux pulsation core losses. A distinct load correction factor is used for calculating rotor tooth flux pulsation cage losses. For full pitch stator winding when calculating stray losses, besides the first slot harmonics Ns ± p1, the first phase belt harmonics (5, 7) are contributing to losses. In skewed rotors, the load stray cage losses are also corrected by a special factor.
• Cast aluminum cages are used with low to medium power induction machines. Their bars are noninsulated from slot walls and thus a transverse (cross-path) resistance between bars through iron occurs. In this case, interbar current losses occur especially for skewed rotors. Thus, despite of the fact that with proper skewing, the stray cage losses are reduced, notable interbar current losses may occur making the skewing less effective.
• There is a critical transverse resistance for which the interbar current losses are maximum. This condition is to be avoided by proper design. Interbar current losses occur both on no-load and on load.
• A number of rules to reduce stray losses are presented. The most interesting is Ns > Nr where even straight rotor slots may be used after safe starting is secured.
• With the advent of power electronics, supply voltage time harmonics occur. With PWM static power converters, around carrier frequency, the highest harmonics occur unless random PWM is used. Frequencies up to 20 kHz occur this way.
• Both stator and rotor conductor losses, due to these voltage time harmonics, are heavily influenced by the skin effect (frequency). In general, as the frequency rises over 2 to 3kHz, for given time harmonic voltage, the conductor losses decrease slightly with frequency while core losses increase with frequency.
• The computation of core losses at high time frequencies (up to 20 kHz) is made accounting for the skin depth in iron δFe as all field occurs around slots and on the rotor surface in a thin layer (δFe – thick). These slot wall and rotor surface core losses are calculated. Only slot wall core losses are not negligible and they represent about 20 to 30% of all time harmonic losses.
FEM has been applied recently to calculate all no-load or load losses, thus including implicitly the space harmonics losses. Still the core losses are determined with analytical expressions where the local flux densities variation in time is considered. For field distribution computation, the laminated core electrical conductivity is considered zero. So the computation of time harmonic high frequencies (20 kHz) core losses including the iron skin depth is not available yet with FEM. The errors vary from 5 to 30%.
• However, the effect of skewing, interbar currents, magnetic wedges, and relative number of slots Ns/Nr has been successfully investigated by fieldcoupled circuit 2D FEMs for reasonable amounts if computation time.
• New progress with 3D FEM is expected in the near future.
• Measurements of losses will be dealt with separately in the chapter dedicated to IM testing.
11.16. REFERENCES
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1. L. Dreyfus, The Additional Core Losses in A.C. Synchronous Machines, Elektrotechnik und Maschinenbau, Vol.45, 1927, pp.737 – 756 (in German).
2. P.L. Alger, G. Angst, E.J. Davies, Stray Load Losses in Polyphase Induction Machines, AIEE Trans, Vol78, 1957, pp.349 – 357.
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17. S.L. Ho, H.L. Li, W.N. Fu, Inclusion of Interbar Currents in the Network Field-coupled Time-stepping FEM of Skewed Rotor Induction Motors, IEEE Trans. Vol.MAG – 35, No.5, 1999, pp.4218 – 4225.
18. T.J. Flack, S. Williamson, On The Possible Case of Magnetic Slot Wedges to Reduce Iron Losses in Cage Motors, Record of ICEM – 1998, Vol.1, pp.417 – 422.