Piecewise Affine Modeling of Wound-Rotor Synchronous Machines for Real-Time Motor Control

High-performance control of wound rotor synchronous machines motor drives requires a nonlinear magnetic model that captures magnetic saturation and cross saturation. This research proposes a generalized piece-wise affine (PWA) magnetic and state-space model that divides the current and flux space into simplices. PWA functions are obtained from experimental or finite element analysis data leveraging the Delaunay triangulation. Error margins and memory requirements can be optimized for given applications by varying the number of PWA functions. The PWA domains can be irregular and an algorithm to optimize accuracy for a given number of PWA domains is proposed. The PWA performance is compared with a high-fidelity magnetic model. Irregular PWA functions have lower error than regularly gridded tables at reduced size: Average error is improved from 15% to 1%; peak error is improved from 20% to 9%. Finally, the PWA state-space model is validated on an experimental testbench with a real-time microcontroller unit. The state-space equations are verified using steady state and dynamic tests.