• Besides main path lines which embrace stator and rotor slots, and cross the airgap to define the magnetization inductance L1m, there are leakage fields that encircle either the stator or the rotor conductors.
• The leakage fields are divided into differential leakage, zig-zag leakage, slot leakage, end-turn leakage, and skewing leakage. Their corresponding inductances are calculated from their stored magnetic energy.
• Step mmf harmonic fields through airgap induce emfs in the stator, while the space rotor mmf harmonics do the same. These space harmonics produced emfs have the supply frequency and this is why they are considered of leakage type. Magnetic saturation of stator and rotor teeth reduces the differential leakage.
• Stator differential leakage is minimum for y/τ = 0.8 coil throw and decreases with increasing q (slots/pole/phase).
• A quite general graphic-based procedure, valid for any practical winding, is used to calculate the differential leakage inductance.
• The slot leakage inductance is based on the definition of a geometrical permeance λs dependent on the aspect ratio. In general, λs ∈ (0.5 to 2.5) to keep the slot leakage inductance within reasonable limits. For a rectangular slot, some rather simple analytical expressions are obtained even for double-layer windings with chorded, unequal coils.
• The saturation of teeth tops due to high currents at large slips reduces λs and it is accounted for by a pertinent increase of slot opening which is dependent on stator (rotor) current (mmf).
• The zig-zag leakage flux lines of stator and rotor mmf snake through airgap around slot openings and close out through the two back cores. At high values of currents (large slip values), the zig-zag flux path, mainly the teeth tops, tends to saturate because the combined action of slot neck saturation and zig-zag mmf contribution.
• The rotor slot skewing leads to the existence of a skewing (uncompensated) rotor mmf which produces a leakage flux along the main paths but its maximum is phase shifted with respect to the magnetization mmf maximum and is dependent on slip and position along the stack length. As an approximation only, a simple analytical expression for an additional rotoronly skewing leakage inductance Lskew,r is given.
• Leakage path saturation reduces the leakage inductance.
• The a.c. stator resistance is higher than the d.c. because of skin effect, accounted for by a correction coefficient KR, calculated in Chapter 9. In most IMs, even at higher power but at 50 (60) Hz, the skin effect in the stator is negligible for the fundamental. Not so for current harmonics present in converter-fed IMs or in high-speed (high-frequency) IMs.
• The rotor bar resistance in squirrel cage motors is, in general, increased notably by skin effect, for rotor frequencies f2 = Sf1 > (4 − 5)Hz; KR > 1.
• The skin effect also reduces the slot geometrical permeance (Kx < 1) and, finally, also the leakage inductance of the rotor.
• The rotor cage (or winding) has to be reduced to the stator to prepare the rotor resistance and leakage inductance for utilization in the equivalent circuit of IMs. The equivalent circuit is widely used for IM performance computation.
• Accounting for leakage saturation and skin effect in a comprehensive way for general shape slots (with deep bars or double rotor cage) is a subject revisited in Chapter 9.
• Now with Chapters 5 and 6 in place, we have all basic parameters– magnetization inductance L1m, leakage inductances Lsl, Lrl′ and phase resistances Rs, Rr′.
• With rotor parameters reduced to the stator, we are ready to approach the basic equivalent circuit as a vehicle for performance computation.