A FINITE ELEMENT BASED STATE MODEL OF SOLID ROTOR SYNCHRONOUS MACHINES (DIFFUSION EQUATION, EDDY CURRENTS, SATURATION, MAGNETIC VECTOR POTENTIAL)

In this work, a state model which portrays the dynamic electromagnetic characteristics of a synchronous machine is derived based upon the first order finite element method. The method of finite elements is used to determine the axial component of magnetic vector potential throughout the cross section of the machine. Algebraic relationships between the winding voltages and the magnetic vector potentials are derived. These are used to establish a state model which admits winding voltages as inputs. The resulting model consists of a set of first order, ordinary differential equations which predict vector potentials at grid nodes along with the winding currents as time proceeds following arbitrary disturbances in stator or rotor voltages. The technique has been applied in two linear examples. The first involves a simplified geometric representation of a synchronous machine for which an analytic solution can be obtained. The second involves a more detailed geometry including stator and rotor slots. Numerical solutions are shown to be in excellent agreement with analytical solutions for the simplified structure. In the detailed geometry, numerical solutions are shown to compare favorably with the classical equivalent circuit representation. The finite element model is also used to investigate the effectiveness of an equivalent circuit representation for which a modification is incorporated in an attempt to model the effects of magnetic saturation. It is shown that the modified equivalent circuit approach may produce inaccurate results for both the steady state and transient response if rotor nonlinearities are included