Non-linear optimization of the positions of the anodes in a DC-furnace

The positions of the anodes in a DC arc furnace is studied in order to minimize the deviating forces acting on the arc due to the magnetic field. The current distribution in the melt, in the anodes and in the cathode is calculated by using the control volume method. From the current distribution, a nonlinear relation is obtained between the total magnetic force and the anodes position. The optimal position is then calculated using the conjugate gradient method.