Efficient Approximation Procedure for Magnetization Characteristics Used in Performance Analysis of Highly Saturated Electrical Machines

The analytical and especially the numerical calculations of the magnetic fields of highly saturated electrical machines require a correctly given magnetizing curve. In practice, professional software may use many points of the magnetizing curve (sometimes 50 or more points). There is a high probability that a point will be entered or measured incorrectly. We have therefore set ourselves three objectives. The first is to reduce the number of points given. The second is to ensure that the curve is given analytically (in the form of orthogonal polynomials) and is as smooth as possible. This means that the derivatives of the reluctance are also as smooth as possible. Therefore, the Newton–Raphson iteration procedure in numerical calculations converges rapidly. The third objective was to make the magnetizing curve continue beyond a magnetic field density of 2 T up to about 3 T. Most professional programs simply limit the magnetizing curve to about 2.2 T. This limitation makes it impossible to calculate accurately the magnetic field in the bridges, especially when the slots in the rotor are closed. Local fields can exceed values of 2.2 T. A solution has been found. It uses higher order orthogonal polynomials. It has been shown that 12 given points of the magnetizing curve is enough to give a good approximation of the measured curve. However, one polynomial function is not enough. We need three functions and another exponential function for magnetic field densities above around 2 T up to a value of relative permeability equal to 1. In the numerical calculation of the field, we thus achieve the desired error (residual) vector of the Newton–Raphson iterative procedure in 10 ÷ 15 steps for semi-closed slots and 20 ÷ 30 steps for closed slots.