SUMMARY of The Skin Effect

• As the slip (speed) varies for constant voltage and frequency, the IM parameters: magnetization inductance (Lm), leakage inductances (Lsl, Lrl′), and rotor resistance Rr′ vary.

• In general, the magnetization flux decreases with slip to 55 to 65% of its full load value at stall.

• As the slip frequency (slip) increases, the rotor cage resistance and slot body leakage inductance vary due to skin effect: the first one increases and the second one decreases.

• Moreover at high slips (and currents), the leakage flux path saturate to produce a reduction of stator and rotor leakage inductance.

• In rotors with skewed slots, there is an uncompensated skewing rotor mmf which varies from zero in the axial center of the stack to maximum positive and negative values at stack axial ends. This mmf acts as a kind of independent magnetization current whose maximum is phase shifted by an angle slightly over 900 unless the rotor current is notably smaller than the rated value.

• At stall, the skewing magnetization current Imskew may reach values 3 times the rated magnetization current of the motor in the axial zones close to the axial stack end.

As the main flux is smaller than usual at stall, the level of saturation seems to be decided mainly by the skewing magnetization current.

• By slicing the stack axialy and using the machine magnetization curve Lm(Im), the value of Lm(Imskew) in each segment is calculated. Severe saturation of the core occurs in the marginal axial segments. The skewing introduces an additional notable component in the rotor leakage inductance. It reduces slightly the magnetization inductance.

• By including the main flux, slot neck flux, zig-zag flux, differential leakage flux, and skewing flux per tooth in the stator and rotor, for each axial segment of stack, the stator and rotor saturated leakage inductances are calculated for given stator, rotor, and magnetization current and slip frequency.

• The skin effect is treated separately for stator windings with multiple conductors in slots and for rotor cages with one bar per slot. Standard correction coefficients for bar resistance and leakage inductance are derived. For the general shape rotor bar (including the double cage), the multiple layer approach is extended both for the bar and for the end ring.

• The end ring skin effect is notable, especially for S ≥ 1 in applications such as freight elevators, etc.

• Skin and leakage saturation effects in the rotor cage are beneficial for increasing the starting torque with less starting current. However, the slot depth tends to be high which leads to a rather high rotor leakage inductance and thus a smaller breakdown torque and a larger rated slip. Consequently, the efficiency and power factor at full load are slightly lower.

• Skin effect is to be avoided in inverter-fed induction motors as it only increases the winding losses. However, it appears for current time harmonics anyway. Leakage saturation may occur only in servodrives with large transient (or short duration) torque requirements where the currents are large.

• In closed slot cage rotor motors, the rotor slot iron bridge saturates at values of rotor current notably less than the rated value.

• Skin and leakage saturation effects may not be neglected in line-start motors when assessing the starting, pull-up or even breakdown-torque. The larger the motor power, the more severe is this phenomenon.

• Skin and leakage saturation effects may be controlled to advantage by slot geometry optimization. This way, the 5 NEMA designs (A, B, C, D, E) have been born.

While skin and leakage (on load) saturation effects can be treated with modified 2D and 3D FEMs [19, 21], the computation time is still prohibitive for routine calculations. Rather sophisticated analytical tools should be used first with FEM and then applied later for final refinements.

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