Energy Converters Guide for Computer Aided Design

Institut für Elektrische Energiewandlung

Energy Converters Guide for Computer Aided Design - Asynchronous Machine -

Issue SS 2011-2012

Dipl.-Ing. Oliver Magdun, M.Sc. Nam Anh Dinh Ngoc Professor Dr.-Ing. habil. Dr.h.c. Andreas Binder

Energy Converters: CAD and System Dynamics

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Asynchronous machines - design with PC-IMD

This guide is to facilitate the design of the asynchronous machine with the program PC-IMD. The design of the machine model from the lecture script “Energy Converters - CAD and System Dynamics” is presented. The input data, needed by the program, are bold printed indicated in the appropriate places (variable = value). In the program PC-IMD there are two important editors, where data have to be specified for the machine calculation. One of them is the template editor, where part of the geometric dimensions of the machine, calculation methods and further boundary conditions are chosen. The other one is the outline editor, where detailed geometric dimensions of stator, rotor and shaft are specified and also visualized with different view options. In the following the values that have to be specified in the template editor are printed as (TE: variable=value), while the values that have to be specified in the outline editor are printed as (OE: variable=value). Fig. 0 shows where to select the different editors.

Fig. 0: Screenshot PC-IMD menu bar – editor selection

Machine design: Given data: Asynchronous motor with squirrel-cage rotor (C-rotor) Rated power: P N = 500 kW Rated voltage: U N = 6 kV Rated frequency: fN = 50 Hz Number of poles: 2p = 4

(TE: Bar1 = Type2) (TE: PowrSh. = 500 000.0) (TE: Vs = 6000.0) (TE: Freq = 50.0) (TE: Poles = 4)

As the frequency and the power at shaft is given we choose the calculation method (TE: CalcMode=f/PowerSh) and (TE: TorqCalc = LR + Brk + NL) in the template editor. Aim is to design a machine with efficiency and a power factor as high as possible. By the design some conditions are to be kept: - Overload capability: 3 > M b /M N >1.6 - Starting current:

4 < I 1 /I N < 6

- Starting torque:

0,7 < M 1 /M N < 1.6

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(i.e. starting torque should not be too small, however not unnecessarily high) Institut für Elektrische Energiewandlung


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- Winding temperature rise: ISO-Kl. B 1. Calculation of main design geometry data 1.1. Electromagnetic and thermal utilization A time-dependent temperature rise calculation is not carried out (TE: TempCalc = fixed). The ambient temperature is 20 °C (TE: Ambient = 20.0), stator and rotor temperature according to ISO-Kl. B 75 °C (TE: WdgTemp = 75.0; TE: RoTemp = 75.0). At the beginning of the design several parameters have to be estimated, respectively initial values for these parameters must be chosen, which could change during the design process. For simplification, given curves of optimised machines will be used during the design. From Fig. 2.1-3 to Fig. 2.1-10 (see [1]) the following initial values are extracted: Table 1: Initial values of the design

Notation Number of poles Efficiency Power factor Pole pitch Equivalent iron stack length Current loading Air gap flux density Current density Air gap width Inner rotor diameter and shaft radius

Value 2p = 4  N = 0,94 cos  N = 0,868  p = 36 cm l e = 38 cm A s = 485 A/cm B ,av = 0,56 T ... 0,63 T J s = 5,5 A / mm2  = 0,14 cm d ri = 20 cm d rshaft  rri  ri 2

To insert as TE: Poles = 4

OE: Gap = 1.4 mm OE: RadSh = 100 mm

From the initial values (Table 1) we find: - Apparent power: PN 500  10 3 SN    610 kVA  N  cos  N 0.944  0.868 - Motor current: SN 610 10 3 IN    59 A 3 U sN 3  6 10 3 - Synchronous speed: nsyn  f s / p  1500 /min

-

Stator bore diameter:

d si  2 p p / π  458 mm.

Stator inner radius: rsi  d si / 2  229 mm. Rotor outer radius: rro  d si / 2    227.6 mm -

(OE: Rad1= 227.6 mm)

Internal apparent power for the stator stray coefficient  s = 0.08/2 = 0.04 : S δ  S /(1   s )  610  10 3 / 1.04  587 kVA

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587  10 3 Electromagnetic utilization: C  S δ /(d  l Fe  nsyn )   4.89 kVA.min/m3 2 0.458  0.38  1500 2 si

With the stator stray coefficient  s = 0,04 and winding factor k ws = 0,91 estimated as initial values, the air gap flux density results: π2  k w1  A  B C 2



2 C 2  4.89 10 3  60  0.954 T.  B  k w1  A  π 2 π 2  0.91  500 100

and the average:

B ,av 

2 2  B   0.954  0.6 T π π

Machines of this power class are equipped in axial direction with round cooling ducts. The lamination stack is divided into individual packages. According to [1] we will assume that both iron stacks, stator and rotor, consist of 9 sections with l 1 = 42 mm and 8 radial ducts (switch OE to axial view OE: NSDuct = 8 and OE: NRDuct = 8) with width l k = 10 mm (OE: WSDuct = 10 mm and OE: WRDuct = 10 mm). The iron stacks length results: l Fe  9  l1  9  42  378 mm. The total axial length will be extended in this case by the width of the cooling ducts: L  9  l1  8  l k  9  42  8 10  458 mm

(OE: Lstk = 458 mm)

The length of the winding extension at each end of iron stack must be determined and inserted into the program. In dependence of the voltage (Table 2.8.3-2 [1]) the following value will be considered: l a =5.7 cm (TE: Ext=57.0). 1.2. Design of the stator winding The stator slot pitch  Qs changes with the number of coils per pole and phase q which is to be chosen. As q has an effect on the harmonic content of the winding it cannot be selected arbitrarily. The influence of q should be clarified within a table. The stator slot pitch consists of the tooth width b ds and the slot width b Qs . The tooth width may not be smaller than a minimum value for which the tooth flux density B ds becomes inadmissibly high. The minimum tooth width b ds,min is determined by linear calculation, without field flattening and for an iron fill factor of k Fe = 0,95 (OE: Stf = 0.95). π B , av  1    s 2 Qs bds, min  Bds, max k Fe

The maximum tooth flux density is assumed to 2.4 T (higher value because it is calculated without flattening). Thus the maximal permissible slot width can be indicated and the distribution and pitching factors can be calculated (see Table 2) with expressions:

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k d

    sin  2m s    ;     q sin   2m s q 

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 W   m qs     sin  k p  sin  s   2 2 m q s    p 

Table 2: Choice of number of coils per pole and phase and short-pitching of the stator winding

Number of slots per pole and phase q: Number of stator slots Q s = 2 p m s q: Slot pitch  Qs =  p / (m s q) in cm: Tooth width b dsmin in cm: Slot width b Qs = s -b dsmin in cm: Ratio b Qs / Qs : Pole pitch in slots  p : Distribution factor k d1 : Distribution factor k d5 : Distribution factor k d7 : Coil pitching with 1 Slot (s = 1): Pitching factor k p1 : Winding factor k w1 : Pitching factor k p5 : Winding factor k w5 : Pitching factor k p7 : Winding factor k w7 : Coil pitching with 2 Slots (s = 2): Pitching factor k p1 : Winding factor k w1 : Pitching factor k p5 : Winding factor k w5 : Pitching factor k p7 : Winding factor k w7 : Coil pitching with 3 Slots (s = 3): Pitching factor k p1 : Winding factor k w1 : Pitching factor k p5 : Winding factor k w5 : Pitching factor k p7 : Winding factor k w7 :

3 36 4,00 1.17 2.26 0,56 9 0,9598 0,2176 -0,1774 8 0,9848 0,9452 0,6428 0,1398 -0,3420 0,0607 7 0,9397 0,9019 -0,1736 -0,0378 0,7660 -0,1359 6 0,8660 0,8312 -0,8660 -0,1884 0,8660 -0,1536

4 48 3,00 1,31 1,17 0,56 12 0,9577 0,2053 -0,1576 11 0,9914 0,9495 0,7934 0,1629 -0,6088 0,0959 10 0,9659 0,9250 0,2588 0,0531 0,2588 -0,0408 9 0,9239 0,8848 -0,3827 -0,0786 0,9239 -0,1456

5 60 2,40 1,04 1,36 0,56 15 0,9567 0,2000 -0,1494 14 0,9945 0,9514 0,8660 0,1732 -0,7431 0,1111 13 0,9781 0,9358 0,5000 0,1000 -0,1045 0,0156 12 0,9511 0,9099 0,0000 0,0000 0,5878 -0,0878

6 72 2,00 0,87 1,13 0,56 18 0,9561 0,1972 -0,1453 17 0,9962 0,9525 0,9063 0,1787 -0,8192 0,1190 16 0,9848 0,9416 0,6428 0,1267 -0,3420 0,0497 15 0,9659 0,9236 0,2588 0,0510 0,2588 -0,0376

To insert as TE: CPP = 5 TE: Slots = 60

TE: Throw = 12

With the choice of q, we are trying to reduce the fifth harmonic wave amplitude of mmf. at an as small as possible value. From Table 2, it becomes evident that both q = 4 and q = 5 provide reasonable results and fulfil the conditions (see [1]): b Qs / Qs = 0.5 ... 0.6 and 1 cm < b Qs < 2 cm. Here q = 5 is selected with a short-pitching of s = 3. The winding diagram created by SPEED is W 12 presented in Fig.1 for the chosen case: q = 5 and  .  p 15 TU Darmstadt



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Fig. 1: Winding diagram created by SPEED (WdgType = Lap)

1.3. Choice of number of turns

The considered winding is a three-phase, double-layer winding (TE : Connex = 3-PhWye; TE: WdgType = Lap ; TE: CoilForm = None).

in

y-connection

The number of turns per phase is calculated as: Ns 

Uh 2 πf s  k w1  Φh



3330 2 π  50  0.91  83.12  10 3

 198 turns /phase

where the estimated induced voltage per phase is: Uh 

U N / 3 6000 / 3   3330 V 1s 1.04

and the main flux per pole of fundamental  = 1 is for the air gap flux density B , 1  0.954 T : Φh 

2 2   p  le  B , 1   0.36  0.38  0.954  83.12 mWb. π π

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By a roughly assumption we have considered, for a preliminary estimation, the stator iron length equal to the equivalent iron length: l Fe  le  380 mm. The number of turns per coil is: N c  N s  a /(2 pq)  198 1 /(2  2  5)  9.9 , so the integer value N c  10 (TE: TC = 10) for a = 1 (TE: Ppaths = 1) is chosen. The values for the number of turns per phase, flux, flux density and current loading are to be determined thereby again: Table 3: Corrected values

Number of turns per phase

N s  2 pqN c  200

Flux density

B  0,946 T Φˆ h  82.4 mWb 2ms N s I s A  491A/cm 2 p p

Air gap flux Current loading

The thermal utilization is A  J  491  5.5  2700.5 (A/cm)  (A  mm²) which is a permissible value for a 500 kW induction machine (see [1]). Obs: Since the terminal voltage is an effective constant value, the air gap flux density depends on the number of turns per phase. If the air gap flux density is selected too small, the machine is poorly used and a larger number of turns per phase will be necessary in order to come to the given voltage. Possibly the necessary place is not available in the slot for this number of turns. If the flux density is selected too big, the iron will be strongly saturated and the magnetisation demand becomes too high!

1.4. Slot dimensions

The designed winding is a high-voltage winding. The slot flanks are parallel. The coils are inserted into the slot and then the conductor width must correspond to the slot opening. Because profile copper is used, rectangular conductors are specified in the winding parameters (TE: Wire_1=Rect). As can be seen from Table 2, for q = 5, the maximal permissible slot width is b Qs = 1.36 cm and the minimal calculate permissible slot is b Qs = 1.04 cm. The slot width is fixed here to b Qs = 1,25 cm and from this, further conductor dimensions and slot dimensions (Table 4 and Table 6) are determined according to the text script [1]. The initial value for the outer radius of the stator is with 50 mm much smaller than the already chosen radius of the rotor. In order to have a better overview of the change of the stator slots we set the outer radius of the stator arbitrarily to 400 mm (OE: Rad3 = 400). The final value of the stator outer radius will be later calculated. Table 4: Conductor and slot width dimensions

Slot geometry Slot width b Qs : Conductor insulation d ic : Slot-lining: Main insulation: Tolerance (slot play) b Tol : Insulation width b Is : Conductor width b L TU Darmstadt

Parallel flanks 12.5 mm 0.40 mm 0.15 mm 2.2 mm 0.3 mm 4.7 mm 7.1 mm

OE: S-Slots = PllSlot OE: SWid = 12.5

One-side One-side

TE: Liner = 0.15

2times slot-lining + 2times main ins. b L = b Qs - b Is - b Tol TE: wa_1 Institut für Elektrische Energiewandlung


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=7.1 Conductor cross section is checked: ATL  I s /( J s  a  ai )  59 /(5.5 1 1)  10.73 mm2 and for bL  7.1 mm and for the smallest admissible area of the conductor ATL  12.42 mm2 (see Table 5) the conductor height hL  1.8 mm is chosen. Table 5: Selection of available profile copper wire: dimensions without enamel coating and cross section (edges of wire rounded by 0.5 mm .... 1.0 mm radius)

bL (mm) 5 5.6 6.3 7.1 8 9 10 11.2 12.5 14 16

1.8 8.637 9.717 10.98 12.42 14.04 15.84 17.64 19.80 22.14 24.84 -

2 9.637 10.84 12.24 13.84 15.64 17.64 19.64 22.04 24.64 27.64 31.64

2.24 10.84 12.18 13.75 15.54 17.56 19.80 22.04 24.73 27.64 31.00 35.48

2.5 11.95 13.45 15.20 17.20 19.45 21.95 24.45 27.45 30.70 34.45 39.45

Conductor height h L (mm) 2.8 3.15 13.45 15.20 15.13 17.09 17.09 19.30 19.33 21.82 21.85 24.65 24.65 27.80 27.45 30.95 30.81 34.73 34.45 38.83 38.65 43.55 44.25 49.85

3.55 17.22 19.33 21.82 24.66 27.85 31.40 34.95 39.21 43.83 49.15 56.25

4 21.54 24.34 27.54 31.14 35.14 39.14 43.94 49.14 55.14 63.14

4.5 27.49 31.09 35.14 39.64 44.14 49.54 55.39 62.14 71.14

5 34.64 39.14 44.14 49.14 55.14 61.64 69.14 79.14

The wire insulation thickness is set to 0.15 mm (TE: InsThk1 = 0.150).

Table 6: Conductor and slot height dimensions

Cond. height h L : Inter-turn insulation: Conductor insulation d ic : Coated coil: Main insulation Insulated coil upper layer: Two coils per slot Inter-layer insulation: Slot-lining (3 times): Wedge: Top and Bottom lining: Vertical play: Slot height h Qs : Stator tang depth h 4s

1,80 mm 0.3 mm 0.4 mm 24.7 mm 4.4 mm 29.1 mm 58.2 mm 4,0 mm 0,45 mm 4,5 mm 0.8 mm 1.05 mm 69,0 mm 0 mm

TE: wb_1=1.80

N c (h L +d ic ) + (N c -1) inter-turn ins. 



TE: SD_S = 69.0 TE: TGD_S = 0.001*

(*Speed Software cannot handle h 4s = 0, therefore a small value is inserted)

The magnetic circuit computation assumes parallel-sided stator teeth. Simplified calculation takes H d on 1/3 of tooth length at the narrower side to calculate the mmf. Then:

 Qs ,1 / 3  (d si  (2 / 3)  lds )  π / Qs  (458  (2 / 3)  69)  π / 60  26.38 mm bds ,1 / 3   Qs ,1 / 3  bQs  26.38  12.5  13.9 mm TU Darmstadt



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1.5. Determination of the rotor winding parameters of the squirrel-cage rotor

Choice of rotor slot number Q r must be done with respect to stator number Q s . (see Lectures: “Motor development for electric drive systems”). We get as choice the slot numbers from Table 7. Table 7: Choice of rotor slot number Q r

According to the script for and number of pole pairs the following rotor slot numbers Q r Are permitted for unskewed rotor bars: Selected number of rotor slots:

Q s = 60 stator slots p=2 50, 54, 66, 70 Q r = 50 rotor slots

TE: Skew = 0 TE: R_Bars = 50

Rotor cage is designed according to rotor bar current: 2k m N 2  0.91 3  200 I r  I r / ü I  I s  cos  s  59  0.868  51.21 A, ü I  ws s s   21.84 Qr 50 I r  ü I  I r  21.84  51.33  1118 A

The rotor bar current density results: J r  I r / ACu  1118 / 200  5.6 A/mm Deep bar rotor to increase starting torque should respect the ratio h Cu /b Cu  8. Then: h Cu = 40 mm and b Cu = 5 mm with the cross section: A Cu = 200 mm2 . The necessary ring cross section: ARing  I Ring / J Ring  4462 / 5.6  798 A/mm2 Where: - Rotor ring current: I Ring  I r /(2  sin( pπ / Qr ))  1121 /(2  sin(2 / 50))  4462 A - Ring current density: J Ring  J r  5.6 A/mm2, Table 8. Rotor cage dimensions

Conductor dimensions: Winding factor k wr : Choice of bar height and bar width: Bar height h Cu : Bar width b Cu : Set-back h 4r : Rotor slot opening s Qr Ring height and axial width: Ring height h Ring Additional radial ring height: TU Darmstadt

1 by cage windings 40 mm 5 mm 3.5 mm acc. To text script [1] 2.5 mm 40 mm Ring height is usually at least bar height: h Ring > h Cu 0 mm h z = h Ring - h Cu

OE: BarDpth = 40 OE: BarWdth = 5 OE: SetBack = 3.5 mm

OE: SO_R = 2.5 mm

OE: ERLedge1 = 0 OE: ERLedge2 = 0



Ring width b Ring :

10


20 mm

OE: Erthk1 = 20 OE: Erthk2 = 20 The set-backs in the rotor are not filled with copper, therefore (TE: SBFull = false). As copper is used as rotor bars, the cage- and end-ring density is set to the one of copper which is 8900 kg/m³ (TE: CgDensity = 8900 kg/m³) (TE: ERDensity = 8900 kg/m³). 1.6. Yoke radii

The permissible flux density B y  1,7I1.8 T determines the thickness of the stator and rotor back. For stator: hys 

Φ  (1   s ) / 2 82.4 10 3  (1  0.04) / 2   70 mm, 0.378  0.95 1.8 l Fe  k Fe  Bys

value which can be increased according to motor performances. Let’s accept: h ys = 77 mm. Recalculate value of stator maximum flux density: Bys 

Φ  (1   s ) / 2  1.54 T hys  l Fe  k Fe

The stator outer diameter results: d so  d si  2lds  2hys  458  2  69  2  77  750 mm

(OE: Rad3= 375 mm)

Without flux penetration in shaft, the rotor height back is: hyr  d si  2  2ldr  d ri / 2  458  2 1.4  2  43.5  200/ 2  84.1 mm For axial cooling four ducts with a diameter of c 2 = 30 mm it results: hyr,e  hyr  (2 / 3)  c2  84.1  2 / 3  30  64.1 mm

(OE: NumHoles = 4) (OE: HoleDia=30 mm)

The radius for the circle, on which the axial cooling ducts lie (pitch circle), is is set to 286.5 mm (OE: PCDia = 286.5 mm).

Rotor maximum yoke flux density is: Byr 

(2 / π)  B , 1  p  le / 2 Φ / 2   1.85 T hyr,e  l Fe  k Fe hyr,e  l Fe  k Fe

In the reality this value will be much smaller due to the shaft presence (see [1]) and a round cooling duct with c 2 = 30 mm may be accepted. Now all values for the calculation of the machine with the PC-IMD program are available! In Fig.2 the geometry of the induction machine is given, as it has been generated by SPEED, with details of the stator and rotor slots.

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Fig. 2 Geometry of 500kW induction machine

1.7 Setting of calculation methods

Before performing the calculation several calculation method settings for simulation have to be set. Table 9: Calculation method settings

Method of calculating X diff SPEED End-winding leakage reactance calculation method: Richter Method of calculating deep-bar factors Classical Component of (rotor side) Carter factor Method for calculating iron losses

SPEED

TE: DiffLeak = SPEED TE: EndLeak = RICHTER TE: DeepBar = Classical TE: qC_R = 1 (for semi-closed slots) TE: WFeCalc: SPEED

2. Numerical computation of machine performances

For a better understanding, all the values, which are necessary for the input into the program, are again presented in Fig. 3 to 5. The calculated values for power factor (P.F.), torque (TorqSh), current densities (Jrms, Jrotor) etc., are located in design sheets. Beside the specification of a desired power (the program calculates then the associated slip) it is also possible to perform calculations for a given slip value. For this the parameter CalcMode (Figure1, Control Parameters) must be changed of f/PowerSh on f/slip and the appropriate slip (Slip) to be entered. Thus starting current / rated current ratios can be determined. The ratio pull-out torque / rated torque (TBrkpu) can be directly read! Are all values within the demanded range, the recalculation of the design with the values supplied by the program is to be performed. TU Darmstadt



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Fig. 3: Template Editor: Main specifications

Fig. 4: Template Editor: Winding settings

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Fig. 5: Template editor: Rotor settings

Fig. 6: Template editor: Loss calculation settings

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Fig. 7: Template editor: Thermal calculation settings

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Fig. 8: Template editor: Calculation method settings

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Make sure that the correct material curves are loaded:

After all settings were made, start the calculation by clicking on Steady State analysis:

Finally see the calculation results in the Design sheet:

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PC-IMD 4.1 (4.1.1.26) 26-Sep-2011 15:55:15 TU Darmstadt IEE PC-IMD Design sheet 1 Dimensions : ----------------------------------------------------------------Slots StatorOD StatorID

60 750.0000 mm 458.0000 mm

Poles RotorOD RotorID

4 455.2000 mm 200.0000 mm

Lstk Gap MConfig

STATOR.. Rad3 S-slot SD_S STOH NSDuct SWedge

375.0000 mm PllSlot 69.0000 mm 0.0000 mm 8 NonMag

R1g ASlot SWid SBWid WSDuct muWedge

229.0000 863.5539 12.5000 12.5000 10.0000 1.0000

mm mm^2 mm mm mm

ASlotLL TGD_S SYoke LFeS

ROTOR.. Rad1 Bar1 Skew ARslot muPlug Rotor slot BarDpth SetBack Dbar

227.6000 mm Type2 0.0000 SSlots 208.7557 mm^2 1.0000 dimensions.. 40.0000 mm 3.5000 mm 411.6966 mm

Rad0 R_Bars LB Abar SBFull

0.0000 mm 50 458.0000 mm 200.0000 mm^2 false

RadSh DblCage BarExt Shrink RYoke

Rotor end-rings and ERType1 Type C ERType2 Type C ERLedge1 0.0000 ERLedge2 0.0000 ERArea1 800.0697 NRDuct 8 ROH 0.0000 Shaft.. RadSh AxExSh1

BarWdth

5.0000 mm

SO_R

458.0000 mm 1.4000 mm Int

839.0786 1.0000E-03 77.0000 359.1000

mm^2 mm mm mm

100.0000 mm false 0.0000 mm 0.0000 84.0966 mm 2.5000 mm

fins..

mm mm mm^2 mm

ERthk1 ERthk2 ERArea2 WRDuct LFeR

100.0000 mm 0.0000 mm

RadSh2 AxExSh2

4.8000 mm 0.0000 mm

XStf_R

1.0000

Stacking factors.. Stf 0.9500

20.0000 20.0000 800.0697 10.0000 359.1000

mm mm mm^2 mm mm

ERID1 ERID2 EROD

RadSh3 AxExSh3

368.1931 mm 368.1931 mm 448.2001 mm

3.6000 mm 0.0000 mm

2 Winding Data : --------------------------------------------------------------General Connex PC SFill MaxSFg ACL PCSlot EndFill Ax1md

3-Ph Wye 100.0000 %Cu 0.2960 0.2960 69006.2284 mm^2 1.8401 0.5000 54.0000 mDeg

Stator winding.. WdgType Lap Throw 12 Tph 200.0000 MLT 2186.8835 mm Wire_1 Rect TU Darmstadt

TCC SFillHBL MaxSFn LCL XPCslot LaxPack Ax2md

T_wdg CPP PPaths XET

0.3930 0.4716 0.4716 150.6686 1.0000 712.0051 114.0000

%/°C

mm

WireDens ACu ASlotLL Liner

mm mDeg

LAYERS Ax3md

2.0000 174.0000 mDeg

RLL_Amb TC Tph1 Ext

1.1800 ohm 10 181.9708 57.0000 mm

75.0000 °C 5.0000 1 1.0000

8900.0000 255.6000 839.0786 0.1500

kg/m³ mm^2 mm^2 mm



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wa_1 wb_1 NSH_1 BWDia_1 BWArea_1 InsThk_1 HBWDia_1

40.3386 4.0339 mm 12.7800 mm^2

7.1000 1.8000 1 4.0339 12.7800 0.1500 4.4482


mm mm mm mm^2 mm mm

EWG EWDia ACond

Winding factors.. kw1 0.9099 kw7 -0.0878 kw13 -0.0601 kw19 0.1041 ks1 1.0000

kw3 kw9 kw15 kw21 kr_RS

-0.3804 0.2351 0.0000 -0.2351 7947.2112

kw5 kw11 kw17 kw23 zSlot

Rotor cage CgDens 8900.0000 kg/m³ PC1 100.0000 %Cu PCEndR 100.0000 %Cu Kring1 0.9619 PRSlot 4.1267

ERDens TCC1 TCCEndR Kring2 XPRslot

8900.0000 kg/m³ 0.3750 %/°C 0.3750 %/°C 0.9619 1.0000

SBFull RhoBar RhoEndR

0.0000 -0.1041 0.0601 0.0878 20

false 2.0796E-08 ohm-m 2.0796E-08 ohm-m

3 Control Data : -------------------------------------------------------------CalcMode Freq rpmS Vs

f/PowerSh 50.0000 Hz 1500.0000 rpm 6000.0000 V

PowrSh.. 5.0000E+05 W rpm 1486.6834 rpm Drive AC_Volts

Slip

0.0089 p.u.

4 Magnetic design : ----------------------------------------------------------SSteel RSteel ShSteel MagCalc XBsy

WWN 230-50 WWN 230-50 Luft Classical 1.0000

PPitch qC_S kC_s kC_sd muPlug Bstpk Brtpk Bsypk Brypk Bshpk Bg1L Bgm

359.7124 0.0000 1.5018 1.1307 1.0000 2.0330 1.3280 1.4496 1.3273 0.0000 0.7643 0.4866

XBst XBry mm

T T T T T T T

Ag qC_R kC_r kC_rd PCplug ATst Atrt ATsy ATry ATsh ATgap Bgpk

1.0000 1.0000 0.0000 1.0000 1.0372 1.1307 1.4000 733.9806 35.2505 95.8747 28.1934 0.0000 1695.8217 0.7643

mm^2

A A A A A A T

XBrt XBsh IncShaft Lge XkC kC

MMFst MMFrt MMFsy MMFry MMFsh kXm Phi1L

1.0000 1.0000 No shaft 2.7881 mm 1.0000 1.9915

0.4328 0.0208 0.0565 0.0166 0.0000 1.5268 80.1649

p.u. p.u. p.u. p.u. p.u. mWb

5 Equivalent circuit parameters : --------------------------------------------R1 R2 Rc Rbar R_rotor EQcct DeepBar

0.7175 0.5418 9207.5856 0.3791 6.8174E-05 SPEED Classical

EndLeak

Richter

DiffLeak LkSat TU Darmstadt

SPEED None

ohm ohm ohm ohm ohm

X1 6.6658 X2 6.4149 Xm0 234.8003 REndRing 0.1627 X_rotor 8.0719E-04 RcLoc GapFlux K_r 1.0016 XKr_DB 1.0000 CoilFill 1.0000 XX1end 1.0000 NHDiff 1000 kXL1 1.0000

ohm ohm ohm ohm ohm

X1unsat X2unsat Xm Erb XErb K_x XKx_DB kEndCoil XX2end DiffSat kXL2

6.6658 6.4149 158.3289 0.0000 1.0000

ohm ohm ohm V

0.9996 1.0000 1.0000 1.0000 false 1.0000


Energy Converters: CAD and System Dynamics kzz Xkzz XXm

1.0000 1.0000 1.0000

kX1slot XkX1slot XXL1

Unsaturated reactance components.. X1slot 1.8672 ohm X1end X2slot 4.8918 ohm X2end L-circuit parameters.. alpha_TL 1.0405 XL_L 13.8811 ohm R2_L 0.5866 ohm

uX1oX2 Rc_L Xm_L

19


1.0000 1.0000 1.0000

kX2slot XkX2slot XXL2

1.0000 1.0000 1.0000

4.5180 ohm 1.2782 ohm

X1diff X2diff

0.2806 ohm 0.2448 ohm

X1oX2

1.0391

1.0000 9968.8143 ohm 164.7438 ohm

6 Performance : --------------------------------------------------------------OpMode Motoring Vt 6000.0000 V Pshaft 4.9997E+05 W PshaftHP 670.4711 h.p. Currents.. Iph1 Imc

58.6643 A rms 20.4703 A

rpm PElec P.F. WTotal IL1 IMag

Equivalent circuit voltages.. E1 3240.5650 V VR1 ER2 3194.1983 V VR2 Losses and related parameters.. WCuS 7408.3039 W WCuR SLLCalc ANSIC50 WSLL Jrms 4.5903 A/mm^2 JBar1 5.7658 A/mm^2 J_ER Other performance parameters.. PGap 5.1058E+05 W EMTorque Locked-rotor.. TLR 3219.1352 ILR 343.5242 PLR 7.1454E+05 pTWdg 3.6533 C_Cu 57.1755 T_wdg_S 20.0000 XXL1s 1.0000

Nm A W C/sec kJ/C °C

Breakdown.. TBrk 7958.7126 IBrk 187.9838 rpmBrk 1445.6086 T_wdg_B 20.0000 XXL1b 1.0000

Nm A rpm °C

TLRpu ILRpu pTBar C_cage T_rtr_S XXL2s

TBrkpu IBrkpu PBrk T_rtr_B XXL2b

1486.6834 rpm 5.2140E+05 W 0.8552 21435.0875 W 58.6643 A rms 20.4673 A

I2 Ic

42.0943 V 28.6113 V

VX1 VX2

4532.7666 W 6072.5137 W

WIron Wwf

5.7499 A/mm^2 JRotor

0.0089 3211.4200 95.8893 82.0084

p.u. Nm % %

52.8085 A 0.3519 A

391.0422 V 338.7613 V

3421.5033 W 0.0000 W 5.7329 A/mm^2

3250.4251 Nm

1.0024 5.8558 9.5613 C/sec 52.8862 kJ/C 20.0000 °C 1.0000

2.4783 3.2044 1.3302E+06 W 20.0000 °C 1.0000

No-load.. INL 22.0592 A INLpu 0.3760 T_wdg_NL 20.0000 °C PNL 4418.0537 W

NLTorque TNLpu T_rtr_NL XLL_NL

0.0000 Nm 0.0000 20.0000 °C 314.0145 ohm

Test data.. Wrated 0.0000 W V_Test 6000.0000 V s_Test 0.0000

Irated I_Test T1_Test

0.0000 A 0.0000 A 20.0000 °C

TU Darmstadt

Slip Tshaft Effcy Eff_X_PF

sLR PFLR

1.0000 p.u. 0.2002

XErbs

1.0000

sBrk PFBrk

0.0363 p.u. 0.6809

sBrkType XErbb

Search 1.0000

NLPF NLrpm rpmNL INLX1

P_Test T2_Test

0.0193 1500.0000 rpm 1500.0000 rpm true

0.0000 W 20.0000 °C



20


7 Core losses, Harmonic losses, and Stray Load Losses : ----------------------WFe0S WFeS Wst Wsy WstWkg WFeR Wrt Wry WrtWkg WFeCalc

3.5086 3414.1815 1702.4924 1711.6891 6.0128 7.3218 2.7773 4.5445 0.0190 SPEED

W/kg W W W W/kg W W W W/kg

WFe0R WFeSe Wste Wsye WsyWkg WFeRe Wrte Wrye WryWkg XFe

3.5086 884.0935 457.9210 426.1726 3.3026 0.0209 0.0079 0.0130 0.0190 1.0000

W/kg W W W W/kg W W W W/kg

WFe0Sh WFeSh Wsth Wsyh

3.6719 2530.0879 1244.5715 1285.5165

W/kg W W W

WFeRh Wrth Wryh

7.3009 W 2.7694 W 4.5315 W

Bd_slot

0.5951 T

8 Thermal data : -------------------------------------------------------------TempCalc Ambient T_wdg

Fixed 20.0000 °C 75.0000 °C

HeatFlux T_rtr

7.7389 kW/m²

TempRise

55.0000 °C

75.0000 °C

9 Miscellaneous parameters : -------------------------------------------------Wt_Cu 149.2443 kg WtFeS 717.0246 kg WtFesy 518.2904 kg Wt_Al 59.0248 kg WtShaft 183.7832 kg RotJ 13.9842 kg-m² C_cage 52.8862 kJ/C WtFrame 54.0323 kg Ecc 0.0000 FrThk 10.0000 mm FrLgthM Actual TRV 43086.1054 Nm/m3 Wf0 0.0000 W CanStyle None NumHoles 4 RTC_OC 2.0256 sec

Wt_Fe WtFeR WtFest WtAl_RB

1092.8759 375.8514 198.7318 40.7620

JL C_main WtCap UMP LFrame FrLgth T/Wt RPM0

0.0000 57.1755 2.8416 2.0010E-13 750.0000 750.0000 2.4681 1500.0000

PCDia RTC_SC

kg kg kg kg

Wt_Tot

p.u. kJ/C kg kg mm mm Nm/kg rpm

JFan

0.0000 p.u.

CapThk

5.0000 mm

286.5000 mm 0.1083 sec

WtTri WtAl_ER

P/Wt NWFT HoleDia

1301.1450 kg 84.4109 kg 18.2628 kg

384.2541 W/kg 1.0000 30.0000 mm

End of Design sheet------------------------------------------------------------

3. Speed – exercise

1) The number of turns per coil will be decreased from 10 to 9. Decreasing the number of turns per coil allows increasing the cross-section of cupper (h L from 1.8 mm to 2 mm). Calculate the new motor impedances, the starting current and the starting torque! Do the motor impedances change? How do starting torque and current vary in comparison to the initial data? 2) How do the air-gap induction, the primary current at rated slip and the electric loading change?

References: [1] A.Binder, Energy Converters: CAD and System Dynamics, Text book – TU Darmstadt, 2009 [2] A.Binder, CAD and System Dynamics of Electrical Machines, Text book – TU Darmstadt, 2006 ÷ 2008 [3] A.Binder, Motor Development for Electric Drive Systems, Text book – TU Darmstadt, 2006 ÷ 2009 [4] A.Binder, CAD and System Dynamics of Electrical Machines, Tutorial for Exercise– TU Darmstadt, 2006- 2008 [5] A.Binder, Energy Converters: CAD and System Dynamics, Tutorial for Exercise – TU Darmstadt, 2009 [6] ****, User’s Manual for PC-IMD 2.5, University of Glasgow, 1998 [7] A.Binder, M. Aoulkadi, CAD and System Dynamics of Electrical Machines: Design of an Asynchronous Machine, Tutorial for Exercise, 2006 [8] O.Magdun, A.Binder, Energy Converters - Asynchronous Machine, Guide for Computer Aided Design, 2009 TU Darmstadt



21


Abbreviations PC-IMD Symbol hr

mm

Rotorbar depth

Leiterhöhe des Rotorstabes

BarWdth

br

mm

Rotorbar width

Leiterbreite des Rotorstabes

ERLedge

mm

Additional endring length

Zusätzliche radiale Endringlänge

Erthk

mm

Endring thickness

Endringdicke (1=linker, 2=rechter)

Gap



mm

Airgap length

Luftspaltweite

Lstk

l

mm

Rotor and Stator stack length

Blechpaketlänge

Poles

p

-

Number of Poles

Polzahl

mm

Shaft radius

Radius der Welle

Dimensional

R-Bars

Qr

-

Number of rotor bars or slots

Rotornutzahl

SD-S

hS

mm

Stator slot depth

Statornuttiefe

mm

Set-Back

Rotorstreusteghöhe

SetBack Skew

k sq

-

Rotor skew

Schrägung des Rotors um x – Nuten

Slots

Qs

-

Number of stator slots

Statornutzahl

SO-R

mm

Rotor slot opening

Nutöffnung Rotor

SO-S

mm

Stator slot opening

Nutöffnung Stator

S-slot

-

Shape of Stator slot bottom

Statornutform

-

Stacking factor

Stapelfaktor

TGD-R

mm

Rotor tang depth

Streusteghöhe Rotor

TGD-S

mm

Stator tang depth

Streusteghöhe Stator

mm

Stator tooth width

Statorzahnbreite

-

Winding connection

Anschlussart

-

Number of coils per pole

Nuten je Pol und Strang

Ext

mm

Winding extension at each end

Gerader Leiter außerhalb Eisen

LAYERS

-

Number of layers

Anzahl der Spulenlagen pro Nut

Liner

mm

Thickness of stator slot-liner

Dicke der Nutauskleidung

Stf

TW-S

k Fe

b ds

Connex Coils/P

Winding

Denotation

BarDpth

RadSh

q

NSH

b

-

No. of strands in hand

Anzahl der parallelen Teilleiter

PPaths

a

-

No. of parallel paths

Anzahl der parallelen Zweige

TC

Nc

-

Turns per coil

Spulenwindungszahl

Throw

y

-

Throw

Spulenweite

WdgTemp 

°C

Winding temperature

Wicklungstemperatur

WdgType

-

Type of winding

Wicklungsart

Wire

mm

Wire size or gauge

Leiterdurchmesser

Freq Control

Unit

rpm

f n

Hz

Fundamental line frequency

Speisefrequenz

min

-1

Actual shaft speed

Drehzahl

-1

Synchronous speed

Synchrondrehzahl

rpmS

nS

min

Slip

s

-

Slip

Schlupf

Vs

U

V

RMS AC line voltage

Spannung

TU Darmstadt


Equivalent

Magnetic


Performance Core Loss Miscellaneous


Bg1L

B 1

T

Peak fundamental flux-density

Maximalwert Luftspaltflussdichte

Bgm

B av

T

Mean airgap flux-density

Mittlere Luftspalt Flussdichte

Bstpk

B ds

T

Peak Stator tooth flux-density

Statorzahn Flussdichte

Brtpk

B dr

T

Peak rotor tooth flux-density

Rotorzahn Flussdichte

Bsypk

B ys

T

Peak stator yoke flux-density

Statorrücken Flussdichte

Brypk

B yr

T

Peak rotor yoke flux-density

Rotorrücken Flussdichte

Bshpk

Bs

T

Peak shaft flux-density

Rotorwelle Flussdichte

KC_s

k Cs

-

Carter coefficient for stator slot

CARTER-Faktor

R1

Rs



Primary resistance/phase

Statorwiderstand

R2

Rr



Secondary resistance/phase

Rotorwiderstand

X1

X s



Primary stray reactance

Statorstreureaktanz

X2

X r



Secondary stray reactance

Rotorstreureaktanz

Xm

X hges



Saturated magnetising reactance

Hauptreaktanz (gesättigt)

Xm0

X hung



Unsaturated magnetising

Hauptreaktanz (ungesättigt)

Effcy



%

Efficiency

Wirkungsgrad

IL1

I

A

RMS line current

Statorstrom

I2

I

A

Rotor current

Rotorstrom

Imag

Im

A

Jrms

Thermal

22

J

Magnetising current

Magnetisierungsstrom

2

RMS current-density main wind.

Statorstromdichte

2

A/mm

Jbar1

J

A/mm

RMS current-density rotor cage

Rotorstabstromdichte

P.F.

cos 

-

Power factor

Leistungsfaktor cos

Pelec

Pe

W

Mean electrical power

Elektrische Leistung

PowerSh

Pm

W

Shaft power

Mech. Leistung

TbrkR

mb

-

Ratio Breakdown/rated Torque

Verhältnis Kipp-/Nennmoment

WcuR

P Cur

W

Rotor copper losses

Kupferverluste Rotor

WcuS

P Cus

W

Stator copper losses

Kupferverluste Stator

Wiron

P Fe

W

Iron (Core) loss

Eisenverluste

Wwf

PR

W

Windage and friction loss

Ventilations- & Reibungsverluste

WFeS

P Fes

W

Stator Iron (Core) loss

Eisenverluste Stator

WFeR

P Fer

W

Rotor Iron (Core) loss

Eisenverluste Rotor

WstWkg

W/kg

Specific stator teeth core losses

Spezifische Stator-Zahn Eisenverluste

WsyWkg

W/kg

Specific stator yoke core losses

Spezifische Stator-Joch Eisenverluste

Shaft speed at no load

Leerlaufdrehzahl

-1

RPM0

n0

min

Wt_Al

mr

kg

Weight of rotor cage

Gewicht Rotorkäfig

Wt_Cu

ms

kg

Weight of copper in stator wind.

Wicklungsgewicht Stator

Wt_Fe

m

kg

Weight of iron stator / rotor lams

Gesamteisengewicht Stator/Rotor

Wt_Tot

m

kg

Total active weight

Gesamtgewicht (Al+Cu+Fe)

Wf0

PR

W

Windage and friction loss

Ventilations- & Reibungsverluste

Ambient

a

°C

Ambient

Umgebungstemperatur

RoTemp

r

°C

Rotor cage temperature

Rotortemperatur

Temperature calculating method

Temperatur-Berechnungsmethode

TempCalc WdgTemp  Wi

°C

Stator winding temperature

Wicklungstemperatur Stator

Rad1

mm

Rotor surface Radius

Außenradius des Läufers

Rad3

mm

Stator outer radius

Außenradius Stator

R-Cage

-

Rotor-cage

Nutform des Rotors

TU Darmstadt


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