A dynamic programming-finite element procedure for the design of nonlinear magnetic devices

A novel procedure for the optimum design of nonlinear magnetic circuits is presented. The optimum choice of a set of geometry is based on that 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, as well as the specified current in the coil. The first step in the procedure is to express the nodal coordinates as Newton-Raphson unknowns using local Jacobian derivatives. Following the specifications of flux density and current in the coil, a set of nodal coordinates are found. The obtained set of nodal coordinates identify an initial topology and outline of the magnetic circuit. The obtained topology is then perturbed. The difference in flux density in the core due to topology changes is determined and minimized using least squares. Since this step is obtained due to 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 be picked utilizing a backward dynamic programming procedure. This method was implemented in the design of a single-phase transformer and the results were verified using standard finite-element analysis