**1. Introduction**

180 Induction Motors – Modelling and Control

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The level of prosperity of a community is related to its ability to produce goods and services. But producing goods and services is strongly related to the use of energy in an intelligent way. Energy can be exploited in several forms such as thermal, mechanical and electrical (Boldea & Nasar, 2002). Electrical energy, measured in kWh, represents more than 30% of all used energy and it is on the rise (Boldea & Nasar, 2002). The larger part of electrical energy is converted into mechanical energy in electric motors. Among electric motors, the induction motor is without doubt the most frequently used electrical motor and is a great energy consumer. About 70% of all industrial loads on a specific utility are represented by induction motors (Maljkovic, 2001). The vast majority of induction motor drives are used for heating, ventilation and air conditioning (Blanusa, 2010; Cunkas & Akkaya 2006).

The design of an induction motor aims to determine the induction motor geometry and all data required for manufacturing to satisfy a vector of performance variables together with a set of constraints (Boldea & Nasar, 2002). Because induction motors are now a well developed technology, there is a wealth of practical knowledge, validated in industry, on the relationship between their performance constraints and their physical aspects. Moreover, mathematical modeling of induction motors using circuit, field or hybrid models provides formulas of performance and constraint variables as functions of design variables (Boldea & Nasar, 2002).

The journey from given design variables to performance and constraints is called analysis, while the reverse path is called synthesis. Optimization design refers to ways of doing efficient synthesis by repeated analysis such that some single (or multiple) objective (performance) function is maximized and/or minimized while all constraints (or part of them) are fulfilled (Boldea & Nasar, 2002). The aim of this chapter is to present an optimal

© 2012 Anwari et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Anwari et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

design method for induction motors using design of experiments (DOE) and particle swarm optimization (PSO) methods.

Optimization of Induction Motors Using Design of Experiments and Particle Swarm Optimization 183

interactions between factors and, therefore, may lead to wrong conclusions (ReliaSoft

Let's assume, for instance, that we want to optimize an induction motor taking into account, for simplicity, only two factors: the length and the external radius. Hence, the length is the first factor and is denoted by �� while the external radius is the second factor and it is denoted by ��. Each factor can take several values between two limits, i.e. ������� ������ and ������� ������. We desire to study the influence of each of these factors on the system response or output for example the torque called Y. The classical or traditional approach consists of studying the two factors �� and���, separately. First we put �� at the average level ��������� and study the response of the system when �� varies between �����and ����� using for example 4 steps (experiments) as shown in Fig. 1. Similarly, we repeat the same procedure to study the effect of ��. Accordingly, the total number of tests is 8. However, we should ask a paramount question here, are these 8 experiments sufficient to have a good knowledge about the system? The simple and direct answer to this question is no. To get a better knowledge about the system, we have to mesh the validity domain of the two factors and test each node of this mesh as shown in Fig. 2. Thus, 16 experiments are needed for this investigation. In this example only two factors are taken into account. Therefore, if for example 7 factors are taken into account, the number of tests to be performed rises to

4� = 16384 experiments, which is a highly time and cost consuming process.

(Garcia, 2010), bioassay robustness studies (Kutlea, 2010) and many others.

method (Bouchekara, 2011; Uy & Telford, 2009).

**Figure 1.** Traditional method of experiments.

Knowing that it is impossible to reduce the number of values for each factor to less than 2, the designer often reduces the number of factors, which leads to incertitude of results. To reduce both cost and time, the DOE is used to establish a design experiment with less number of tests. The DOE, for example, allows identifying the influence of 7 factors with 2 points per variable with only 8 or 12 tests rather than 128 tests used by the traditional

Recently, the DOE technique has been adopted in the design and testing of various applications including automotive assembly (Altayib, 2011), computational intelligence

Corporation, 2008).

The outline of this paper is as follows. The current section is the introduction. Section 2 introduces and explains the DOE method. Section 3 gives an overview of the PSO method. In Section 4 the application of the DOE and PSO to optimize induction motors is explained and its results are also presented and discussed in detail. Finally, the conclusions are drawn in Section 5.
