Design and Voltage Supply of High-Speed Induction - Aaltodoc

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106 Optimization (of electromechanical devices) - A design process for meeting the expectations of the decision maker - Goals, preferences - Objective function Predictions - Models Design process: 1. Setting goals 2. Creating models 3. Finding a solution 4. Realisation of a product Solving tools - Optimization algorithms Fig. 9.1 Division of the optimization process into different tasks. Reality - Prototypes Heavy models are considered to be numerical models which take a considerable amount of time and efficient computers to solve. These models are not very informative as far as the needs of deterministic optimization algorithms are considered. They miss the analytical presentation and first and second order derivatives of the objective function are often used by the optimization algorithms. Finite differences can be used instead of derivatives, but that may lead to case specific tuning of algorithm specific parameters. Using a stochastic algorithm like GA is justified for the following reasons: • The GA does not need the derivatives of an objective function. If the model includes a numerical computation such as in FEM, the objective function cannot be described explicitly as a function of the design variables. Hence, the derivatives of the function can only be estimated using finite differences. This is not good because the numerical model can include noise and the calculation of the finite differences means the calculation of many designs. Since the calculation of each design can take several minutes or tens of minutes, this should be avoided. • The objective function describing the goodness of a design may have several local optima. As the algorithms based on a calculation of gradients or a Hessian matrix often converge to a local minimum, the global solution may not be found. The GA searches for the solution from the
whole solution space determined by the limits for the variables and other constraints. Thus, it is more likely that the global optimum is found. • When designing new kinds of motors like high-speed motors, the optimal designs may be quite different from the conventional designs. The GA is not sensitive to the initial point of the design, which is often the case with the deterministic algorithms. The GA is more like an intelligent stochastic algorithm, combining the ‘freedom of prejudice’ of a stochastic algorithm with the ability of an deterministic algorithm to ‘concentrate on the relevant designs’. The downside of using a stochastic algorithm is that it takes a large number of function evaluations to get the result. Using a heavy model like FEM means that each function evaluation takes several or several tens of minutes to calculate. In order to decrease the optimization times and make more use of the time spent, a practical improvement not found in the literature review is suggested. This improvement is applicable to any algorithm but it is most efficient when used with a stochastic optimization algorithm running a heavy model. 9.1.1 Combination of discrete search space and solution history Solving heavy models like FEM can take most of the time used in optimization. In this work, the FEM model discussed in previous sections and Appendix A uses roughly 95 % of the computation time. Hence, the lower number of designs calculated the better. Unfortunately, this is contradictory to the nature of the stochastic optimization algorithms. The idea of the discretization of the search space is to avoid evaluation of designs that are practically the same. For example, an induction motor with an air gap of 2.0 mm is no different from a motor with an air gap of 2.001 mm. The discretization should be selected so that the smallest difference between two designs is noticeable and realizable. In the above example, the machine produced would probably have the air gap somewhere near 2.0 ± 0.05 mm. Higher tolerances would be possible but not necessarily cost-effective. For optimization algorithms using heavy models, the discretization is not a problem since the gradient and Hessian information of the objective function is unavailable anyway. Finite difference approximations could still be used. A proper discretization could actually improve the use of finite differences because of noise inherent in the models. However, the relation between discretization or relative perturbations and the accuracy of finite differences is a complicated issue (Palko 1996) and avoided by using stochastic algorithms. 107
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El 108 ACTA POLYTECHNICA SCANDINAVI
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PREFACE This thesis is the result o
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5 Comparison of rotors for 60 kW 60
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LIST OF SYMBOLS a Number of paralle
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Rn Resistance of a parallel conduct
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1 INTRODUCTION The need for high ro
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Conventional (high-speed) drive Hig
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Chapter 5 reports the comparison of
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Some penetration depth values are c
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2.2 Stator windings for high-speeds
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⎛ π ⎞ sin⎜ν ⎟ ⎛ π ⎞
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Table 2.3 Air gap characteristics o
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Cooling of the stator could need ax
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f sw N p = (2.9) fs The switching f
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3 ROTOR CONSTRUCTIONS Starting from
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and eddy-currents traveling on the
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support the squirrel cage winding,
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3.1.3 Rotor loss and friction loss
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Table 3.1 High-speed induction moto
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critical speeds are passed relative
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Table 3.2 The free-free natural fre
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Table 3.3 The free-free natural fre
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4 COMPARISON OF ROTORS FOR 65 KW 30
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Temperature [ºC] 110 109 108 107 1
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Temperature rise [K] 120 100 80 60
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improve the laminated design, more
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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: 9 OPTIMIZATION OF SOLID STEEL ROTOR
Page 109 and 110: the average time saving is 39 %. Th
Page 111 and 112: Fig. 9.3 Cross sections of the 16,
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
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