**4.4. Fractional 2 levels factorial design**

Here, the DOE is applied to analyze the objective functions. The proposed approach uses tools of the experimental design method: fractional designs, notably of Box generators to estimate the performance of the induction motor. The interest is to save calculation time and to find a near global optimum. The saving of time can be substantial because the number of simulations needed is significantly reduced.

Since six parameters define the shape of the motor, it is advisable to determine the effect of each parameter on the objective functions. Thus, it is very important to provide proper parameter ranges. The considered parameters are listed in Table 5. There are two types of parameters; continuous parameters and discrete parameters.

Optimization of Induction Motors Using Design of Experiments and Particle Swarm Optimization 199

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**Resolution Design name Number of Runs Generators**

**Table 7.** Box generator of the fractional factorial design 26-2.

**Table 8.** Contrasts and contribution obtained.

**Figure 7.** Plot of effects for the efficiency.

87

87.2

87.4 87.6

87.8

Response

88 88.2

88.4 88.6

**4** 26-2 16 �� � �� � �� � ��

**Contrasts EFF kg/kW Tr I0/I Tst P** 13 2 9 45 7 **CDSW** 1 18 8 0 3 **Cdb** 3 1 0 0 5 **Spp** 4 10 2 25 41 **Tstrip** 34 24 36 0 14 **Zsw** 38 29 39 0 19 **P CDSW + Cdb Tstrip** 1 0 1 0 0 **P cdb + CDSW Tstrip** 2 2 1 0 0 **P Spp + Tstrip Zsw** 2 5 3 18 1 **P Tstrip + CDSW Cdb + Spp Zsw** 1 3 0 4 5 **P Zsw + Spp Tstrip** 1 3 0 4 5 **CDSW Spp + Cdb Zsw** 0 1 0 0 1 **Cdb Spp + CDSW Zsw** 1 2 1 0 0

The application of DOE identifies the effect of each parameter on each objective function. We can notice that for the efficiency Zsw, Tsrip, and P are the most significant factors with respectively 38% 34% and 13% of contribution on the objective function. Moreover, Fig. 7 gives more details. When P is low the efficiency is high and vice versa when P is high.

P CDSW cdb Spp Tstrip Zsw

Factors
