Design and Voltage Supply of High-Speed Induction - Aaltodoc

More documents

Recommendations

Info

110 of this is the use of linear and cubic spline functions as a replacement for a FEM model as illustrated in Bianchi and Bolognani (1999). One potential use for the solution data would be the teaching of a neural network system. This combined use of discretization and solution history is applicable to any algorithm but it is most efficient when used with stochastic optimization algorithms like GA, fuzzy logic (Bianchi and Bolognani, 1996) or simulated annealing. There, the reduction of calculation time is likely to be most significant. The use of solution history in surface fitting is also utilized best with stochastic algorithms, since the fitting requires large amounts of data in order to give a good estimation of the real behavior of the objective function. 9.2 Optimization of a squirrel cage rotor of the 60 kW 60000 1 /min motor A numerical optimization of the rotor design was performed for a squirrel cage solid steel rotor. The 16 bar and the 26 bar rotors compared in Chapter 5 were already designed and manufactured but the existence of better designs was checked. For the squirrel cage rotors seen in Fig. 9.3, the main variables are the number of cage bars and the width and height of a bar. The air gap was also taken as a free variable. The dimensions of stator and stator winding were kept constant. The objective was to minimize the temperature rise in the stator winding as this was considered the limiting factor for the utilization of the motor. The objective function for the temperature rise ∆T was of the following form: ( w p + w p + w p − ) S ∆ T = a 1 + , (9.1) s cus cus fes fes rot rot where as is a scaling factor and pcus, pfes and prot are the normalized power loss for the stator winding, stator iron and rotor, respectively. wcus, wfes and wrot are the corresponding weights. The normalization is done so that the losses of the initial 16 bar design yield zero as a value for the function. S is the penalty function term. The scaling factor and weights for the loss components were derived from the results of a sensitivity analysis for a thermal network model made by Saari (1995). The power loss components were calculated with the finite element model discussed in Chapter 7. The rotor design was optimized and the comparison was made at the nominal power of 60 kW at the rated speed of 60000 1 /min although speeds only up to 50000 1 /min could be tested, as discussed in Chapter 5. Designs were supplied with PAM. The model for the motor included stator end windings and rotor end rings.
Fig. 9.3 Cross sections of the 16, 26 and 22 bar squirrel cage rotors. The 22 bar rotor on the right is the result of optimization, giving a lowest temperature rise of the stator winding. The main constraint for the feasible design was the mechanical constraint limiting the height of the slot relative to the width of the solid iron tooth. This constraint was given by the manufacturer of the rotors. The constraint was not originally linear but for optimization purposes it was linearized, as can be seen from Fig. 9.4. There the constraint divides the search space into a feasible and a restricted domain. A penalty function was used to keep the designs in the feasible area. Because external penalty functions were used, the solutions of the optimization tend to be rather on the restricted side. This phenomenon indicates that the mechanical constraint due to the centrifugal forces and stress really prohibits otherwise optimal solutions. 9.2.1 Optimization results Table 9.2 shows the result of the optimization compared with the actual rotors tested in Chapter 5. The value of the objective function is shown in the last row of the table. The values were scaled so that the initial 16 bar design received a zero value. A positive value meant a hotter stator winding and a negative value for a cooler winding. The geometries of the squirrel cage rotors are shown in Fig. 9.3 and the progress of the optimization run is illustrated in Fig. 9.4. The result shows that a compromise has been made between the number of bars and the amount of copper. Large numbers of small bars induces less loss at the stator teeth because the permeance fluctuation is smaller. On the other hand, increasing the number of bars decreases the amount of copper because of the mechanical constraint. Fig. 9.5 shows that the bar height relative to the bar width is maximized as long as there is a balance between that ratio and the amount of copper. The importance of an adequate amount of copper was seen in Chapter 5. There the 26 bar rotor performed poorly because of the mistake in the manufacture. As is seen from Table 9.2, the amount 111
Page 1 and 2:
El 108 ACTA POLYTECHNICA SCANDINAVI
Page 3 and 4:
PREFACE This thesis is the result o
Page 5 and 6:
5 Comparison of rotors for 60 kW 60
Page 7 and 8:
LIST OF SYMBOLS a Number of paralle
Page 9 and 10:
Rn Resistance of a parallel conduct
Page 11 and 12:
1 INTRODUCTION The need for high ro
Page 13 and 14:
Conventional (high-speed) drive Hig
Page 15 and 16:
Chapter 5 reports the comparison of
Page 17 and 18:
Some penetration depth values are c
Page 19 and 20:
2.2 Stator windings for high-speeds
Page 21 and 22:
⎛ π ⎞ sin⎜ν ⎟ ⎛ π ⎞
Page 23 and 24:
Table 2.3 Air gap characteristics o
Page 25 and 26:
Cooling of the stator could need ax
Page 27 and 28:
f sw N p = (2.9) fs The switching f
Page 29 and 30:
3 ROTOR CONSTRUCTIONS Starting from
Page 31 and 32:
and eddy-currents traveling on the
Page 33 and 34:
support the squirrel cage winding,
Page 35 and 36:
3.1.3 Rotor loss and friction loss
Page 37 and 38:
Table 3.1 High-speed induction moto
Page 39 and 40:
critical speeds are passed relative
Page 41 and 42:
Table 3.2 The free-free natural fre
Page 43 and 44:
Table 3.3 The free-free natural fre
Page 45 and 46:
4 COMPARISON OF ROTORS FOR 65 KW 30
Page 47 and 48:
Temperature [ºC] 110 109 108 107 1
Page 49 and 50:
Temperature rise [K] 120 100 80 60
Page 51 and 52:
improve the laminated design, more
Page 53 and 54:
The copper coated solid steel rotor
Page 55 and 56:
As reported in Lähteenmäki et al.
Page 57 and 58:
Temperature rise [K] 100 80 60 40 2
Page 59 and 60: Temperature rise [K] 140 120 100 80
Page 61 and 62: 6. The rest of the loss is defined
Page 63 and 64: Temperature rise [K] 100 80 60 40 2
Page 65 and 66: 5.2.7 About the mechanical robustne
Page 67 and 68: 6.1 Comparison of PAM and PWM for 6
Page 69 and 70: h d = , (6.2) I I h, PAM where Ih,P
Page 71 and 72: Fig. 6.4 Phase-to-phase voltage and
Page 73 and 74: Temperature rise [K] 120 100 80 60
Page 75 and 76: Machines loss [W] 12000 10000 8000
Page 77 and 78: considerably higher than expected.
Page 79 and 80: In order to improve the performance
Page 81 and 82: l = + , (7.2) sλs 2leλ e l wλ w
Page 83 and 84: gap of 1 mm would yield an effectiv
Page 85 and 86: Table 7.1 Calculated effective leng
Page 87 and 88: Input current [A] 170 160 150 140 1
Page 89 and 90: 8 CIRCULATORY CURRENTS IN A STATOR
Page 91 and 92: Table 8.1 Circulatory current loss
Page 93 and 94: Fig. 8.4 Strand currents in the two
Page 95 and 96: 8.2 Impedance of the circulatory cu
Page 97 and 98: Because Φ l is approximately at th
Page 99 and 100: Table 8.2 Circulatory current loss
Page 101 and 102: Power loss [W] 3500 3000 2500 2000
Page 103 and 104: k cc 600 500 400 300 200 100 0 0 50
Page 105 and 106: 9 OPTIMIZATION OF SOLID STEEL ROTOR
Page 107 and 108: whole solution space determined by
Page 109: the average time saving is 39 %. Th
Page 113 and 114: Height of bar slot [mm] 8 6 4 2 0 R
Page 115 and 116: The different rotor topologies were
Page 117 and 118: possible. The coating practically v
Page 119 and 120: Table 9.3. Optimization results for
Page 121 and 122: Fig. 9.11 Initial (left) and opt. (
Page 123 and 124: high-speed induction machine. Accor
Page 125 and 126: Foelsch K. 1936. Magnetfeld und Ind
Page 127 and 128: Pyrhönen J. and Kurronen P. 1994.
Page 129 and 130: APPENDIX 129
Page 131 and 132: currents in the solid iron flow mor
Page 133 and 134: where the C sw E is the loss coeffi
Page 135 and 136: B. CALCULATION OF THERMAL CHARACTER
Page 137 and 138: Axial cooling duct Frame R fr3 Stat
Page 139 and 140: Linear equalities Ax = b, (C3) wher
show all

Design and Voltage Supply of High-Speed Induction - Aaltodoc

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?