A Finite Element based State Model of Solid Rotor Synchronous Machines

Abstract

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. As an initial verification step, this method has been applied in two linear examples. The first involves a simplified geometric representation of the synchronous machine for which an analytical solution of the defining field equations can be obtained. The second involves a more detailed geometry which includes 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.