**5. Conclusion**

202 Induction Motors – Modelling and Control

**4.5. Optimization** 

posed as follows:

and (35) becomes:

��� = 1 can be posed in Eq.(35).

∑ �� �

attribute this to the Spp Tstrip interaction.

each one of these parameters is low the starting torque is low. Likewise, when these parameters are high, the starting torque is high. Furthermore, for this objective function there is two significant interaction between some factors 'P Tstrip + CDSW Cdb + Spp Zsw' (5%) and 'P Zsw + Spp Tstrip' (5%). Note that we have isolated all of the main effects from every 2-factor interaction. For the first contrast the two largest effects are Spp and Zsw. Thus, it seems reasonable to attribute this to the Spp Zsw interaction. While, for the second contrast the two largest effects are Spp and Tstrip. Hence, it is appropriate to

Two optimization approaches can be achieved. The first one is to treat 1 of the 5 objective functions (defined in the Objective Function section) at a time. Thus, every time a single objective function is taken into account regardless of the 4 others. The second approach is to consider a multi objective function where the 5 objective functions are taken into account at the same time. The resulted complicated multiple-objective function can be converted into a simple and practical single-objective function scalarization. Among scalarization methods we can find the weighting method. In this method, the problem is

F��������� =��� ��

�

(35)

(37)

���

where: �� = EFF, �� = −kg ⁄ kW , �� = −Tr, �� = −I0 ⁄ I, �� = Tst and �� is a constant indicating the weight (and hence importance) assigned to ��. By giving a relatively large value to �� it is possible to favor �� over other objective functions. Note that the condition

Nevertheless, since the 5 functions of the multi-objective function have different ranges, for instance �� varies from 85 to 91 and �� varies from 0.07 to 1.3. Thus, the values of these functions must be normalized between 0 and 1. The minimum of a given function is equal to

max(��) − min(��) (36)

0 and the maximum is equal to 1. The normalization operation is given by:

Normalized����� <sup>=</sup> ���t�al����� − min(��)�

F��������� =��� ������������ �

���

For this chapter we have chosen the first approach i.e. the single objective one.

This chapter investigated the optimal design of induction motor using DOE and PSO techniques with five objective functions namely, maximization of efficiency, minimization of kg/kW, minimization of temperature rise in the stator, minimization of I0/I ratio, maximization of starting torque. It has been shown that DOE and PSO based algorithms constitute a viable and powerful tool for the optimal design of induction motor. The main objective of the DEO here is to identify the effect of each parameter on the objective functions. This is of a paramount importance mainly because of two reasons. The first one and also the obvious one is the reduction of the number of parameters to be taken into consideration in the optimization stage called screening. This can be achieved by neglecting the parameters with less effect. This will reduce the computing time burden and simplify the analysis of the designed motor. The second reason is that among the influent parameters themselves we can classify the parameters in function of their calculated effect. This will help the designer to have a clear picture of the importance of each parameter. For instance, if two parameters having respectively 45% and 5% of influence on a given objective function are compared; it is obvious that even if both parameters have an effect on the given objective function, the first one is greatly more important than the second one.

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The approach developed here is universal and, although demonstrated here for induction motor design optimization, it may be applied to the design optimization of other types of electromagnetic device. It can be used also to investigate new types of motors or more generally electromagnetic devices. MATLAB code was used for implementing the entire algorithm. Thus, another valuable feature is that the developed approach is implementable on a desktop computer.
