In this paper the equivalent sources methods, written in terms both of the actual and of the external field, are used for the computation of the total force in two-dimensional axisymmetric problems. A Finite Element modeling of the magnetizing currents as field sources is presented in order to improve the formulations using the external field. The numerical accuracy of all the proposed formulae is thoroughly checked on linear and nonlinear test examples.
The application of the equivalent source methods for the numerical calculation of the total magnetic force acting upon a permanent magnet is proposed. These methods are formulated in terms of the external field, which allows the complete avoidance of the numerical inaccuracies affecting force computation due to the singularity of the self‐field of the magnet on its edges. It is shown, with the help of some 2D and 3D test cases, that the proposed formulae provide reliable and stable results, even when the FEM mesh is not refined. Such results have also been compared with those derived from more traditional methods, such as the surface integration of the Maxwell’s stress tensor and the virtual work method, exhibiting better precision and lower computational costs.
The common approach to continuous and discrete optimisation problems in electromagnetics does not take into account uncertainties and variations of the design variables. Local sensitivity analysis is usually performed only after the optimisation run to study the behaviour of the objective function in the neighbourhood of the optimum. However, this procedure may prove inefficient if the optimum has to be rejected due to sensitivity considerations and a new run has then to be performed. In this paper an alternative approach, which takes into account uncertainties in the design variables and physical data, is presented, and an analytical function is used to highlight the features of the proposed method. The essence of the technique is to couple the optimisation with a series of worst case analyses which are embedded in the optimisation loop. The method is fully general and can be applied to any optimisation method. The additional computational costs associated with the procedure maybe relatively high, but in the authors' opinion the obtained gains in user confidence in the solution and the computational savings in some cases far offset the possible drawbacks of the method.
In this paper the results obtained in the realization of an automatic procedure for magnet design in 2D, plane and axisymmetric, will be presented. The proposed procedure combines mesh adaption, based on an “a-posteriori” error estimate, and deterministic optimization techniques. The use of an analysis module with mesh adaption capabilities gives the automatic design procedure a more stable behaviour in the evaluation of objective function. In particular, one of important features of this strategy is to allow wide variations in dimensional parameters, with high accuracy. The procedure has been realized with a modified version of the VF/OPERA 2d code, realized by the authors, and an optimization technique, based either on the “Response Surface” or on the “Pattern Search” algorithm, interacting with the analysis code using parametric command
The HVDC (High Voltage Direct Current) transmission system, although in use since about half a century, is gaining new popularity in recent years, as it can allow to transmit very large amounts of power over long distance at reasonable costs. Many plants are being commissioned and many others are in the design phase, both for mainland and submarine links. Ground/sea electrodes are normally used in such applications, either operated on a full time basis, or during partial failures of one pole of bipolar plants. Due to the adverse effects that stray currents dispersed by such electrodes may have in terms of corrosion to nearby structures, and to the growing concern for environmental issues, the design of sea electrode has to be defined with increasing attention. This paper deals with the technologies and with the design criteria that can be adopted to develop satisfactory sea electrodes.
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