Optimal design of nonlinear magnetic circuits by finite elements and a dynamic programming approach

A novel procedure for the design of nonlinear magnetic circuits is presented. The optimum choice of a set of geometries is based on the set which gives the minimum size of the magnetic circuit topology. At the same time, the chosen set of geometries should not violate the specified flux density in the core, or the specified current in the coil. In the proposed method, the nodal coordinates are expressed as Newton-Raphson unknowns using local Jacobian derivatives. A set of nodal coordinates is found to identify an initial topology and outline of the magnetic circuit. The obtained topology is then perturbed. The difference (error) in flux density in the core due to topology changes is determined and minimized by using least squares. Since this step is obtained because of the change of one of the geometries defining the outline of the circuit, it is repeated every time a different geometry is perturbed. The optimum geometries can then be picked by utilizing a backward dynamic programming procedure. This technique was implemented in the design of a single-phase-transformer as an example. The results were verified using standard finite-element analysis on empirical design data.<
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