# Electromagnetic optimization problems (Electrical Machine)

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## Numerical optimisation

The design process of electromagnetic devices reflects an optimisation procedure. The construction and step by step optimisation of technical systems in practice is a trial and error-process. This design procedure may lead to sub-optimal solutions because its success and effort strongly depends on the experience of the design engineer (Fig. 7.1).

Fig. 7.1. Parameters affecting the design.

To avoid such individual parameters and thus to achieve faster design cycles, it is desirable to simulate the physical behaviour of the system by numerical methods. In order to get an automated optimal design, numerical optimisation is recommended to achieve a well defined optimum.

Optimisation of electromagnetic devices turns out to be a task of increasing significance in the field of electrical engineering. The term of Automated Optimal Design (AOD) describes a self-controlled numerical process in the design of technical products.Recent developments in numerical algorithms and more powerful computers offer the opportunity to attack realistic problems of technical importance (Pahner M).

The distinctive feature of this type of optimisation problem is its complexity, which results from a high number of design parameters, a complicated dependence of the quality on design parameters and various constraints. Often the direct relation of the desired quality of the technical product on the objective variables is unknown. Stochastic optimisation methods in combination with general numerical field computation techniques such as the finite element method (FEM) offer the most universal approach in AOD. This section discusses methodology, characteristic features and behaviour of optimisation methods.

To be able to select the appropriate optimisation algorithms to form an overall design tool together with the numerical field computation, the properties of typical electromagnetic optimisation problems will be discussed (Rao , Pahner M). Electromagnetic design and optimisation problems reflect mainly the following categories:

• constrained

• problem type:

.parameter- or static optimisation,

trajectory, or dynamic problem,

• non-linear objective function

• design variables:

real

mixed real/integer

• multi-objective function

• interdependences of the quality function and the design variables are unknown; no derivative information available

• the quality function is disturbed by stochastic errors caused by the truncation errors of the numerical field computation method.

Nowadays optimisations are performed mainly as static problems. Numerical optimisations require huge amounts of computation time. Therefore, the optimisation as aimed at here, combined with the FEM, of the dynamic system behaviour is not yet performed. For transient problems an evaluation of the quality function by numerical methods (FEM) is too time consuming. Considering mixed real/integer design variables results in long computation times as well. The tick boxes in the list that are not marked, represent developments for the future. The optimisation problems that can be solved will grow with increasing computer performance as well.