the induction machine handbook chuong (16)

Chapter 16 INDUCTION MOTOR DESIGN ABOVE 100KW AND CONSTANT V/f 16.1 INTRODUCTION Induction motors above 100 kW are built for low voltage (480 V/50 Hz, 460 V/60 Hz, 690V/50Hz) or higher voltages, 2.4 kV to 6 kV and 12 kV in special cases. The advent of power electronic converters, especially those using IGBTs, caused the increase of power/unit limit for low voltage IMs, 400V/50Hz to 690V/60Hz, to more than 2 MW. Although we are interested here in constant V/f fed IMs, this trend has to be observed. High voltage, for given power, means lower cross section easier to wind stator windings. It also means lower cross section feeding cables. However, it means thicker insulation in slots, etc. and thus a low slot-fill factor; and a slightly larger size machine. Also, a high voltage power switch tends to be costly. Insulated coils are used. Radial – axial cooling is typical, so radial ventilation channels are provided. In contrast, low voltage IMs above 100 kW are easy to build, especially with round conductor coils (a few conductors in parallel with copper diameter below 3.0 mm) and, as power goes up, with more than one current path, a 1 > 1. This is feasible when the number of poles increases with power: for 2p 1 = 6, 8, 10, 12. If 2p 1 = 2, 4 as power goes up, the current goes up and preformed coils made of stranded rectangular conductors, eventually with 1 to 2 turns/coil only, are required. Rigid coils are used and slot insulation is provided. Axial cooling, finned-frame, unistack configuration low-voltage IMs have been recently introduced up to 2.2 MW for low voltages (690V/60Hz and less). Most IMs are built with cage rotors but, for heavy starting or limited speed- control applications, wound rotors are used. To cover most of these practical cases, we will unfold a design methodology treating the case of the same machine with: high voltage stator and a low voltage stator, and deep bar cage rotor, double cage rotor, and wound rotor, respectively. The electromagnetic design algorithm is similar to that applied below 100 kW. However the slot shape and stator coil shape, insulation arrangements, and parameters expressions accounting for saturation and skin effect are slightly, or more, different with the three types of rotors. Knowledge in Chapters 9 and 11 on skin and saturation effects, respectively, and for stray losses is directly applied throughout the design algorithm. © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… The deep bar and double-cage rotors will be designed based on fulfilment of breakdown torque and starting torque and current, to reduce drastically the number of iterations required. Even when optimization design is completed, the latter will be much less time consuming, as the “initial” design is meeting approximately the main constraints. Unusually high breakdown/rated torque ratios (t be = T bk /T en > 2.5) are to be approached with open stator slots and larger l i /τ ratios to obtain low stator leakage inductance values. lrlssc sc 2 1 ph 1 bk LLL ; L 1 V 2 p3 T +=         ω ≈ (16.1) where L sl is the stator leakage and L lr is the rotor leakage inductance at breakdown torque. It may be argued that, in reality, the current at breakdown torque is rather large (I k /I 1n ≥ T bk /T en ) and thus both leakage flux paths saturate notably and, consequently, both leakage inductances are somewhat reduced by 10 to 15%. While this is true, it only means that ignoring the phenomenon in (16.1) will yield conservative (safe) results. The starting torque T LR and current I LR are () 1 1 2 LR istart 2 1S r LR pIKR3 T ω ≈ = (16.2) () () () () () 2 1S rl 1S sl 2 1 2 1S rs ph1 LR LLRR V I = = = +ω++ ≈ (16.3) In general, K istart = 0.9 – 0.975 for powers above 100 kW. Once the stator design, based on rated performance requirements, is done, with R s and L sl known, Equations (16.1) through (16.3) yield unique values for ( ) 1S r R = , () sat 1S rl L = and () n SS rl L = . For a targeted efficiency with the stator design done and core loss calculated, the rotor resistance at rated power (slip) may be calculated approximately, () () 2 n1i mecstrayiron 2 n1s n n SS r IK3 1 pppIR3 P R n         −−−− η = = (16.4) with () nn1n1 n n1n1 n1 SS r i cosV3 P I ;2.0cos8.0 I I K n ηϕ =+ϕ≈= = (16.5) We may assume that rotor bar resistance and leakage inductance at S = 1 represent 0.80 to 0.95 of their values calculated from (16.1 through 16.4). © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… () ( ) () () r 2 1W1 bs bs 1S r 1S be N KWm4 K ; K R 95.085.0R =−= = = (16.6) () ( ) ( ) bs sat 1S rl 1S be K L 80.075.0L = = −= (16.7) Their values for rated slip are () ( ) ( ) bs SS r SS be K R 85.07.0R n n = = −= (16.8) () ( ) ( ) bs SS rl SS be K L 85.08.0L n n = = −= (16.9) With rectangular semiclosed rotor slots, the skin effect K R and K x coefficients are () () Al 01 SkinrSkin SS be 1S be R f ;h R R K n ρ µπ =ββ=ξ≈= = = (16.10) () () or or r r or or x r r SS be unsat 1S be b h b3 h 'b h K b3 h L L n + + ≈ = = (16.11) Apparently, by assigning a value for h or /b or , Equation (16.11) allows us to calculate b r because rskin x h2 3 K β ≈ (16.12) Now the bar cross section for given rotor current density j AL , (A b = h r ⋅b r ) is r 1w11 bi ALbi n1i Al b b N KWm2 K ; jK IK j I A === (16.13) If A b from (16.13) is too far away from h r ⋅b r , a more complex than rectangular slot shape is to be looked for to satisfy the values of K R and K X calculated from (16.10 and 16.11). It should be noted that the rotor leakage inductance has also a differential component which has not been considered in (16.9) and (16.11). Consequently, the above rationale is merely a basis for a closer-to-target rotor design from the point of view of breakdown, starting torques, and starting current. © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… A similar approach may be taken for the double cage rotor, but to separate the effects of the two cages, the starting and rated power conditions are taken to design the starting and working cage, respectively. 16.2 HIGH VOLTAGE STATOR DESIGN To save space, the design methodology will be unfolded simultaneously with a numerical example of an IM with the following specifications: • P n = 736 kW (1000HP) • Targeted efficiency: 0.96 • V 1n = 4 kV (∆) • f 1 = 60 Hz, 2p 1 = 4 poles, m = 3phases; Service: Si 1 continuous, insulation class F, temperature rise for class B (maximum 80 K). The rotor will be designed separately for three cases: deep bar cage, double cage, and wound rotor configurations.  Main stator dimensions As we are going to again use Esson’s constant (Chapter 14), we need the apparent airgap power S gap . n1ph1En1gap IVK3EI3S == (16.14) with K E = 0.98 – 0.005⋅p 1 = 0.98 – 0.005⋅2 = 0.97. (16.15) The rated current I 1n is nnn1 n n1 cosV3 P I ηϕ = (16.16) To find I 1n , we need to assign target values to rated efficiency η n and power factor cosϕ n , based on past experience and design objectives. Although the design literature uses graphs of η n , cosϕ n versus power and number of pole pairs p 1 , continuous progress in materials and technologies makes the η n graphs quickly obsolete. However, the power factor data tend to be less dependent on material properties and more dependent on airgap/pole pitch ratio and on the leakage/magnetization inductance ratio (L sc /L m ) as () m sc m sc loss zero max L L 1 L L 1 cos + − ≈ϕ (16.17) Because L sc /L m ratio increases with the number of poles, the power factor decreases with the number of poles increasing. Also, as the power goes up, the ratio L sc /L m goes down, for given 2p 1 and cosϕ n increases with power. © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… Furthermore, for high breakdown torque, L sc has to be small as the maximum power factor increases. Adopting a rated power factor is not easy. Data of Figure 16.1 are to be taken as purely orientative. Corroborating (16.1) with (16.17), for given breakdown torque, the maximum ideal power factor (cos ϕ ) max may be obtained. Figure 16.1 Typical power factor of cage rotor IMs For our case cosϕ n = 0.92 – 0.93. Rated efficiency may be purely assigned a desired, though realistic, value. Higher values are typical for high efficiency motors. However, for 2p 1 < 8, and P n >100 kW the efficiency is above 0.9 and goes up to more than 0.95 for P n > 2000 kW. For high efficiency motors, efficiency at 2000 kW goes as high as 0.98 with recent designs. With η n = 0.96 and cosϕ n = 0.92, the rated phase current I 1nf (16.16) is A 3 42.120 96.092.01043 10736 I 3 3 nf1 = ⋅⋅⋅⋅ ⋅ = − From (16.14), the airgap apparent power S gap becomes VA10307.80842.120400097.03S 3 gap ⋅=⋅⋅⋅=  Stator main dimensions The stator bore diameter D is may be determined from Equation (15.1) of Chapter 15, making use of Esson’s constant, 3 0 gap 1 1 1 1 is C S f pp2 D πλ = (16.18) From Figure 14.14 (Chapter 14), C 0 = 265⋅10 3 J/m 3 , λ = 1.1 = stack length/pole pitch (Table 15.1, Chapter 15) with (16.18), D is is © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… m4.0 10265 10307.808 60 2 1.1 22 D 3 3 3 is = ⋅ ⋅ ⋅π ⋅ = The airgap is chosen at g = 1.5⋅10 -3 m as a compromise between mechanical constraints and limitation of surface and tooth flux pulsation core losses. The stack length l i is m423.0 22 49.0 1.1 p2 D l 1 is i = ⋅ ⋅π = π ⋅λ=λτ= (16.19)  Core construction Traditionally the core is divided between a few elementary ones with radial ventilation channels between. Such a configuration is typical for radial-axial cooling (Figure 16.2). [1] Figure 16.2 Divided core with radial-axial air cooling (source ABB) Recently the unistack core concept, rather standard for low power (below 100 kW), has been extended up to more than 2000 kW both for high and low voltage stator IMs. In this case axial aircooling of the finned motor frame is provided by a ventilator on the motor shaft, outside bearings (Figure 16.3). [2] As both concepts are in use and as, in Chapter 15, the unistack case has been considered, the divided stack configuration will be considered here for a high voltage stator case. The outer/inner stator diameter ratio intervals have been recommended in Chapter 15, Table 15.2. For 2p 1 = 4, let us consider K D = 0.63. Consequently, the outer stator diameter D out is mm780m777.0 63.0 49.0 K D D D is out ≈=== (16.20) © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… Figure 16.3 Unistack with axial air cooling (source, ABB) The airgap flux density is taken as B g = 0.8 T. From Equation (14.14) (Chapter 14), C 0 is 1g11wiBo p2BAKKC πα= (16.21) Assuming a tooth saturation factor (1 + K st ) = 1.25, from Figure 14.13 Chapter 14, K B = 1.1, α i = 0.69. The winding factor is given a value K w1 ≈ 0.925. With Bg = 0.8T, 2p 1 = 4, and C 0 = 265⋅103J/m 3 , the stator rated current sheet A 1 is m/Aturns10565.37 48.0925.069.01.1 10265 A 3 3 1 ⋅= ⋅⋅π⋅⋅⋅ ⋅ = This is a moderate value. The pole flux φ is 1 is gii p2 D ;Bl π =ττα=φ (16.22) 0.0733Wb0.80.4230.3140.69 ;m314.0 22 49.0 =⋅⋅⋅=φ= ⋅ ⋅π =τ The number of turns per phase W 1 (a 1 = 1 current paths) is 8.207 0733.0925.0601.14 400097.0 KfK4 VK W 1w1B phE 1 = ⋅⋅⋅⋅ ⋅ = φ = (16.23) The number of conductors per slot n s is written as © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… s 111 s N Wam2 n = (16.24) The number of stator slots, N s , for 2p 1 = 4 and q = 6, becomes 723622mqp2N 111s =⋅⋅⋅== (16.25) So 31.17 72 8.207132 n s = ⋅⋅⋅ = We choose n s = 18 conductors/slot, but we have to decrease the ideal stack length l i to m406.0 18 31.17 423.0 18 31.17 ll ii ≈⋅=⋅= The flux per pole W07049.0 31.17 18 =⋅φ=φ The airgap flux density remains unchanged (B g = 0.8 T). As the ideal stack length l i is final (provided the teeth saturation factor K st is confirmed later on), the former may be divided into a few parts. Let us consider n ch = 6 radial channels, each 10 -2 m wide (b ch = 10 -2 m). Due to axial flux fringing its equivalent width b ch ’ ≈ 0.75b ch = 7.5⋅10 -3 m (g = 1.5 mm). So the total geometrical length L geo is m451.00075.06406.0'bnlL chchigeo =⋅+=+= (16.26) On the other hand, the length of each elementary stack is m056.0 16 01.06451.0 1n bnL l ch chchgeo s ≈ + ⋅− = + − = (16.27) As lamination are 0.5 mm thick, the number of laminations required to make l s is easy to match. So there are 7 stacks each 56 mm long (axially).  The stator winding For high voltage IMs, the winding is made of form-wound (rigid) coils. The slots are open in the stator so that the coils may be introduced in slots after prefabrication (Figure 16.4). The number of slots per pole/phase q 1 is to be chosen rather large as the slots are open and the airgap is only g = 1.5⋅10 -3 m. The stator slot pitch τ s is m02137.0 72 49.0 N D s is s = ⋅π = π =τ (16.28) The coil throw is taken as y/τ = 15/18 = 5/6 (q 1 = 6). There are 18 slots per pole to reduce drastically the 5 th mmf space harmonic. © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… Figure 16.4 Open stator slot for high voltage winding with form-wound (rigid) coils The winding factor K w1 is 9235.0 6 5 2 sin 66 sin6 6 sin K 1w = π ⋅ π ⋅ π = The winding is fully symmetric with N s /m 1 a 1 = 24 (integer), 2p 1 /a 1 = 4/1 (integer). Also, t = g.c.d(N s ,p 1 ) = p 1 = 2, and N s /m 1 t = 72/(3⋅2) = 12 (integer). The conductor cross section A Co is (delta connection) 36.69I ;mm/A3.6J ,1a ; Ja I A 1nf 2 Co1 Co1 nf1 Co ==== (16.29) cc 2 Co bamm048.11 33.61 42.120 A ⋅== ⋅ = A rectangular cross section conductor will be used. The rectangular slot width b s is () () mm7.107.75.036.0021375.05.036.0b ss ÷=÷⋅=÷⋅τ= (16.30) Before choosing the slot width, it is useful to discuss the various insulation layers (Table 16.1). The available conductor width in slot a c is mm6.54.40.10bba inssc =−=−= (16.31) © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… Table 16.1 Stator slot insulation at 4kV thickness (mm) Figure 16.4 Denomination tangential radial 1 conductor insulation (both sides) 1⋅04 = 0.4 18⋅0.4 = 7.2 2 epoxy mica coil and slot insulation 4 4⋅2 = 8.0 3 interlayer insulation - 2⋅1 = 2 4 wedge - 1⋅4 = 4 Total b ins = 4.4 h ins = 21.2 This is a standardised value and it was considered when adopting b s = 10 mm (16.30). From (16.19), the conductor height b c becomes mm2 6.5 048.11 a A b c Co c ≈== (16.32) So the conductor size is 2×5.6 mm×mm. The slot height h s is written as mm2.572182.21bnhh csinss =⋅+=+= (16.33) Now the back iron radial thickness h cs is mm8.872.57 2 490780 h 2 DD h s isout cs =− − =− − = (16.34) The back iron flux density B cs is T988.0 0878.0406.02 07049.0 hl2 B csi cs = ⋅⋅ = φ = (16.35) This value is too small so we may reduce the outer diameter to a lower value: D out = 730 mm; the back core flux density will now be close to 1.4T. The maximum tooth flux density B tmax is: T5.1 1037.21 8.037.21 b B B ss gs maxt = − ⋅ = −τ τ = (16.36) This is acceptable though even higher values (up to 1.8 T) are used as the tooth gets wider and the average tooth flux density will be notably lower than B tmax . The stator design is now complete but it is not definitive. After the rotor is designed, performance is computed. Design iterations may be required, at least to converge K st (teeth saturation factor), if not for observing various constraints (related to performance or temperature rise). © 2002 by CRC Press LLC [...]... pursue the whole design methodology to prove the performance For the wound rotor, the efficiency, power factor (cosϕn = 0.92), and the breakdown p.u torque tbk = 2.5 (in our case) are the key performance parameters The starting performance is not so important as such a machine is to use either power electronics or a variable resistance for limited range speed control and for starting, respectively The. .. larger than the equivalent starting resistance Rstart The difference is notable and affects the sizing of the starting cage © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… The value of Rbes includes the influence of starting end ring The starting cage bar resistance Rb is approximately R bs ≈ R bes (0.9 ÷ 0.95) = 0.9 ⋅ 5.648 ⋅10 −4 = 5.083 ⋅10 −4 Ω (16.89) The cross section of the starting... in this case the leakage inductance of the rotor bar field in the radial channels is to be considered The two phenomena are lumped into lgeo (the geometrical stack length) The lengths of bars outside the stack are ls and lw, respectively First we approach the starting cage, made of brass (in our case) with a resistivity ρbrass = 4ρCo = 4⋅2.19⋅10-8 = 8.76⋅10-8 (Ωm) We do this based on the fact that,... 4, because the ratio τ/g = 314/1.5 = 209.33 (pole-pitch/airgap) is rather large and the saturation level is low, the magnetization current is lower than 20% of rated current The machine has slightly more iron than needed or the airgap may be increased from 1.5⋅10-3m to (1.8−2)⋅10-3m As a bonus the additional surface and tooth flux pulsation core losses will be reduced We may simply reduce the outer... WOUND ROTOR DESIGN For the stator, as in previous paragraphs, we approach the wound rotor design methodology The rotor winding has diametrical coils and is placed in two layers As the stator slots are open, to limit the airgap flux pulsations (and, consequently, the tooth flux pulsation additional core losses), the rotor slots are to be half – open (Figure 16.13) This leads to the solution with wave-shape... on the rated bar current Ib = 1213.38A (16.66), to the detailed design of the rotor slot (bar), end ring, and rotor back iron Then the teeth saturation coefficient Kst is calculated If notably different from the initial value, the stator design may be redone from the beginning until acceptable convergence is obtained Further on, the magnetization current equivalent circuit parameters, losses, rated efficiency... S.A.Nasar………… ……… The size of end rings is visible in Figure 16.13 It is now straightforward to calculate Rbes and Rbew based on lrs and lrw, the end ring segments length of Figure 16.13 The only unknowns are (Figure 16.13) the stator middle neck dimensions an and hn From the value of the working cage reactance (Xrlw 16.88), if we subtract the working end ring reactance (Xrlel, (16.84)), we are left with the working... This is the same as for the aluminum deep bar cage, though it is copper this time The reason is to limit the slot area and depth in the rotor Working cage sizing The working cage bar approximate resistance Rbe is R be ≈ (0.7 ÷ 0.8) (R r )S=S K bs n = 0.75 ⋅ 0.6861 = 0.6905 ⋅10− 4 Ω 7452.67 (16.75) From (16.6), Kbs is 4m(W1K w1 ) 4 ⋅ 3 ⋅ (12 ⋅18 ⋅ 0.923) = = 7452.67 Nr 64 2 K bs = 2 (16.76) The working... in Chapter 9 (paragraphs 9.2 and 9.3) Aside from these small differences, the stator design follows the same path as high voltage stators This is why it will not be further treated here 16.4 DEEP BAR CAGE ROTOR DESIGN We will now resume the design methodology in paragraph 16.2 with the deep bar cage rotor design More design specifications are needed for the deep bar cage breakdown torque Tbk = = 2.7... all calculated Most of these calculations are to be done with the same expressions as in Chapter 15, which is why we do not repeat them here 16.5 DOUBLE CAGE ROTOR DESIGN When a higher starting torque for lower starting current and high efficiency are all required, the double cage rotor comes into play However, the breakdown torque and the power factor tend to be slightly lower as the rotor cage leakage . taken for the double cage rotor, but to separate the effects of the two cages, the starting and rated power conditions are taken to design the starting. ratio increases with the number of poles, the power factor decreases with the number of poles increasing. Also, as the power goes up, the ratio L sc /L m