Half-Order Modeling of Saturated Synchronous Machine

Non-integer-order systems are used to model diffusion in conductive parts of electrical machines as they lead to more compact knowledge models and also to improve their precision. In this paper, a linear half-order impedance model of a ferromagnetic sheet deduced from the diffusion of magnetic field is briefly introduced. Then, from physical considerations and finite-element simulation, the nonlinear half-order impedance model of a ferromagnetic sheet is proposed, taking into account both saturation and diffusion effects. Next, it has been proved that this model can be successfully included in the equivalent circuits of a synchronous machine (SM), taking into account eddy currents in massive parts of the rotor or damper bars and of small-signal saturation. The new SM equivalent circuit is validated by stand-still frequency response tests performed on the solid salient-pole SM of 125 kVA for variable field excitation conditions. An example of the SM transfer function computation in relation to different magnetization levels indicates the usefulness of this modeling approach for robust control issues.