State functions and bond graph dynamic models for rotary, multi-winding electrical machines

Abstract

The mathematical modeling and computer simulation of the dynamics of systems containing alternators, synchronous or induction motors or other polyphase machines is aided by the description of multi-winding rotary devices based on energy and coenergy state functions. The basic theory is reviewed including the formula for electromagnetic torque based on energy and coenergy state functions. The electrically linear—but geometrically nonlinear— case is then studied. As an example, an ideal, smooth rotor, two-axis, four-winding machine is discussed. Bond graph IC-storage field models are developed and the use of the d-q transformation as embodied in a modulated transformer structure is illustrated. This transformation removes the rotor angular dependence from the inductance matrix. However, the angle dependence remains in the transformation from the real coil variables to the d-q variables and in the multi-port transformer laws. The bond graph models of the basic transduction can be augmented to account for electrical and mechanical losses and other dynamic effects in the creation of a system model. Other multi-port transformers can be used to convert polyphase systems to the two-axis machine models described in the paper.