... This is the normal operating state of a slip-ring ** induction ** machine The second type of ** induction ** ** machines ** are so-called squirrel-cage ** induction ** ** machines ** Rotor winding is in this case cast into ... exclusively by electromagnetic ** induction;** therefore asynchronous ** machines ** are called ** induction ** ** machines ** End ring Rotor winding bars Fig – Squirrel-cage winding of a squirrel cage ** induction ** machine Rotating ... is the case in synchronous ** machines,** there is no way of exciting the ** induction ** machine in a manner similar to synchronous ** machines ** This is one of the main reasons why ** induction ** machine is mainly...

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... rotor resistance **6.** 2 Currents and Fluxes in ** Polyphase ** ** Induction ** ** Machines ** **6.** 3 ** Induction-** Motor Equivalent Circuit Only ** machines ** with symmetric ** polyphase ** windings exited by balanced ** polyphase ** voltages ... Tmech − Trot ωs = ωm **(6.** 24) **(6.** 25) **(6.** **26)** **(6.** 27) **(6.** 28) Figure ** 6.** 11 Equivalent circuits with the core-loss resistance Rc neglected corresponding to (a) Fig ** 6.** 9 and (b) Fig ** 6.** 10 **6.** 5 Torque and Power ... for a ** polyphase ** ** induction ** motor at slip frequency ˆ ˆ I 2s = I E s = sE ˆ ˆ E s = sE ˆ ˆ E s sE = = Z s = R2 + jsX ˆ ˆ I 2s I2 ˆ E R Z = = + jX ˆ s I2 **(6.** 12) **(6.** 13) **(6.** 14) **(6.** 15) **(6.** **16)** Fig ** 6.** 9...

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... 220 **460** 2300 2300 1710 1705 1773 17 **86 ** 11.9 198 1.98 × 103 8.9 × 103 5.8 **46.** 8 93 **.6 ** 421.2 0.435 0.087 0. **262** 0.029 0.754 0.302 1.2 **06 ** 0.2 **26 ** **26.** 13 13.08 **56.** 02 13.04 0.754 0.302 1.2 **06 ** 0.2 **26 ** 0.8 **16 ** 0.228 ... 2⎞ pWm = −Te ⎜ ⎟ pθ r ⎝ P⎠ **(6.** 6-11) Therefore, **(6.** 6 **-6)** can be written as ⎛ 2⎞ ⎛ 2⎞ ⎜ ⎟ pWe = pW f + Te ⎜ ⎟ pθ r ⎝ 3⎠ ⎝ P⎠ **(6.** 6-12) If we compare **(6.** 6-12) with **(6.** 6-8), and if we equate coefﬁcients ... ′ ′ **(6.** 6-8) Comparing **(6.** 6-8) with **(6.** 6 **-6)** , it is clear that the right-hand side of **(6.** 6-4) is pWf − pWm Now TORQUE EQUATION IN ARBITRARY REFERENCE-FRAME VARIABLES pWm = −Te pθ rm 231 **(6.** 6-9)...

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... **(9.** 5-21)– **(9.** 5-23) ** and ** solving the result for νng yields 350 ** UNBALANCED ** ** OPERATION ** ** AND ** ** SINGLE-** ** PHASE ** ** INDUCTION ** ** MACHINES ** vng = 1 (egb + egc ) + vas 2 **(9.** 5-24) Substituting **(9.** 5-24) into **(9.** 5-22) ** and ** **(9.** 5-23) ... **(9.** 5-8)– **(9.** 5-10), ** and ** we have vng = − ias z( p) **(9.** 5-11) 348 ** UNBALANCED ** ** OPERATION ** ** AND ** ** SINGLE-** ** PHASE ** ** INDUCTION ** ** MACHINES ** Equation **(9.** 5-11) is valid as long as ega + egb + egc is zero Substituting **(9.** 5-11) ... only ωe 346 ** UNBALANCED ** ** OPERATION ** ** AND ** ** SINGLE-** ** PHASE ** ** INDUCTION ** ** MACHINES ** ** 9.** 5 TYPICAL ** UNBALANCED ** STATOR CONDITIONS OF ** INDUCTION ** ** MACHINES ** Although it is not practical to consider all stator unbalanced...

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... equations) around 1860 ** The ** knowledge was ripe for ** the ** invention of ** the ** ** induction ** ** machine ** which has two fathers: Galileo Ferraris (1885) and Nicola Tesla (1886) Their ** induction ** machines are shown ... manufacturing and testing for ** induction ** machines Integral ** induction ** motors: ** induction ** motors with ** the ** PWM converter integrated into one piece 1.3 ** INDUCTION ** MACHINES IN APPLICATIONS ** Induction ** motors are, ... invented ** the ** ** induction ** motor with ** the ** wound rotor and subsequently ** the ** cage rotor in a topology very similar to that used today He also invented ** the ** double-cage rotor Thus, around 1900 ** the ** induction...

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... cases ** the ** internal primary is ** the ** mover and ** the ** external secondary is at a standstill In most rotary IMs, ** the ** primary is ** the ** stator and ** the ** secondary is ** the ** rotor Not so for linear ** induction ** machines ... fact, it is 25 to 60% of ** the ** rated current depending on ** the ** ** machine ** airgap g to pole pitch τ ratio ** The ** higher ** the ** ratio τ/g, ** the ** smaller ** the ** magnetization current in p.u ** The ** stator and rotor currents ... (Figure 2.9) ** The ** slip rings are visible to ** the ** right ** The ** stator-placed brush system is not Single-phase-supply IMs have, on ** the ** other hand, in general, two windings on ** the ** stator ** The ** main winding...

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... to this combination ** The ** insulation of ** the ** coil conductors (turns) is applied before inserting ** the ** coils in slots ** The ** coils are vacuum also impregnated outside ** the ** ** machine ** ** The ** slot insulation ... All these insulation accelerated life tests involve ** the ** ageing of insulation test specimens until they fail at temperatures higher than ** the ** operating temperature of ** the ** respective motor ** The ** logarithms ... motor ** The ** logarithms of ** the ** accelerated ageing times are then graphed against their reciprocal Kelvin test temperatures (Arhenius graph) ** The ** graph is then extrapolated to ** the ** planed (reduced) temperature...

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... 6K1 + ** ****2(4) ** and 2p2 = 6K2 + 1, respectively, ** the ** mmf waves for ** the ** two pole counts travel in ** the ** same direction On ** the ** other hand, if 2p1 = 6K1 + ** ****2(4) ** and 2p2 = 6K2 + 4(2), ** the ** mmf waves for ** the ** ... layer and ** the ** other side in ** the ** second layer They are connected observing ** the ** inward (A, B, C) and outward (A’, B’, C’) directions of currents in their sides Connecting ** the ** coils per phase ** The ** Ns/2m ... ……… For ** the ** fundamental, ν = 1, we obtain ** the ** maximum amplitude ** The ** higher ** the ** order of ** the ** harmonic, ** the ** lower its amplitude in (4.8) While in principle such a primitive ** machine ** works, ** the ** harmonics...

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... and ** the ** mutual stator/rotor inductances are calculated for ** the ** fundamental airgap flux density This information prepares ** the ** ground to define ** the ** parameters of ** the ** equivalent circuit of ** the ** ** induction ** ... replaced by ** the ** actual (designed) maximum flattened flux density Bgm, at an angle θ = 30°/p1, which makes ** the ** length of ** the ** flux lines in ** the ** back core 2/3 of their maximum length Then finally ** the ** calculated ... have consequences in ** the ** phase current waveforms for ** the ** two connections Finally, ** the ** saturation produced third and other harmonics influence, notably ** the ** core loss in ** the ** ** machine ** This aspect...

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... respectively As ** the ** pole pitch of ** the ** harmonics is τ/ν, their fields not reach ** the ** back cores and thus their saturation factor Ksν is smaller then Ks ** The ** higher ν, ** the ** closer Ksν is to unity In a ... fields ** The ** airgap flux does not reach ** the ** other slotted structure (Figure 6.10a) while ** the ** zig-zag flux “snakes” out through ** the ** teeth around slot openings In general, they may be treated together ... rotor phases In reality ** the ** flux in ** the ** rotor varies at Sf1 frequency, while in ** the ** stator at f1 frequency ** The ** amplitude is ** the ** same and, with respect to each other, they are at stall Now we...

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... S.A.Nasar………… ……… ** The ** lower ** the ** power factor at ideal no-load, ** the ** lower ** the ** core loss in ** the ** ** machine ** **(the ** winding losses are low in this case) In general, when ** the ** ** machine ** is driven under load, ** the ** value ... ** the ** value of Pelm is zero, so ** the ** ** machine ** driven at that speed absorbs power in ** the ** stator to cover ** the ** winding and core loss Motor no-load mode is when there is no-load torque at ** the ** shaft ** The ** ... means that either n < and n1(f1) > or n > and n1(f1) < In both cases, as S > (S > 0), ** the ** electromagnetic power Pelm > and thus flows from ** the ** power source into ** the ** ** machine ** On ** the ** other hand, with...

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... constant under steady state and ** the ** ** machine ** behaves like a synchronous ** machine ** with ** the ** torque dependent on ** the ** power angle δ (S = f2/f1 = ct) On ** the ** other hand, ** the ** frequency f2 may be varied ... frequency f1 and ** the ** other at frequency f2 from a limited power frequency converter ** The ** ** machine ** speed n is n= f1 ± f p1 + p (8.71) ** The ** smaller f2, ** the ** smaller ** the ** rating of ** the ** corresponding ... single ** induction ** motions If ** the ** ** induction ** motor remains at stall for a long time, ** the ** rotor and stator temperatures become too large, so there is a maximum stall time for each ** machine ** design On the...

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... IN ** THE ** END RINGS VIA ** THE ** MULTILAYER APPROACH As ** the ** end rings are placed in air, although rather close to ** the ** motor laminated stack, ** the ** skin effect in them is routinely neglected However, there ... On ** the ** other hand, if slot leakage saturation occurs only on ** the ** teeth top and ** the ** teeth, additional saturation due to skewing does not influence ** the ** flux lines distribution within ** the ** slot, ** the ** ... calculate ** the ** final values of leakage inductances Now if ** the ** skewing flux occurs both in ** the ** stator and in ** the ** rotor, when ** the ** leakage inductance is calculated, ** the ** rotor one will include ** the ** skewing...

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... components close their flux lines axially through ** the ** stator frame then radially through ** the ** end frame, bearings, and axially through ** the ** shaft (Figure 10.3) ** The ** factor ch accounts for ** the ** magnetic ... order is a multiple of ** the ** number of slots (10.12) ** The ** stator (rotor) mmfs may produce harmonics of ** the ** same order either as sourced in ** the ** mmf or from ** the ** interaction with ** the ** first airgap magnetic ... in general, 6c1 ± 1, while ** the ** stator slotting introduces harmonics of ** the ** order c1 N s ± ** The ** higher ** the ** harmonic order, ** the ** lower its mmf amplitude ** The ** slip p1 Sν of ** the ** νth harmonic is Sν =...

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... when ** the ** IM is static converter fed, and thus ** the ** voltage time harmonics content depends on ** the ** type of ** the ** converter and ** the ** pulse width modulation used with it ** The ** space harmonics in ** the ** stator ... associated with them, but ** the ** higher frequency flux harmonics may lead to larger core loss On ** the ** other hand, ** the ** commutation losses in ** the ** PWM converter increase with carrier frequency ** The ** optimum ... means that ** the ** skin effect is not significant Therefore we may neglect ** the ** rotor lamination-induced current reaction to ** the ** stator field That is, ** the ** airgap field harmonics (11.6) penetrate ** the ** rotor...

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