A Synchronous Machine Transient Model Based upon an Algebraic Loop Accounting for Nonlinearity and Cross-Magnetization

The purpose of this paper is to carry out an alternative to the present transient models for field wound synchronous machines, which is able to take into account the nonlinearity of the magnetic materials as well as the cross-magnetization. After presenting the principal model structures according to the state variables, a model based on two lookup tables for the magnetizing flux linkages is introduced and built step by step. The resulting signal flowchart shows an algebraic loop within the model, where the main flux linkage rapidly converges to its instantaneous value by simple iteration. The proof of this convergence is given for both saturated and unsaturated machine. Even though the proposed model uses the total linkage flux as state variable, as many alternative models do, it does not require the inversion of the current to flux linkage function (i.e., of lookup tables). This can spare a heavy computational task, especially with very large lookup tables. In the proposed model, the computational effort in the worst case scenario is reduced to few iterations (<10). Finally, the nonlinear behavior of the model is verified in four different transient scenarios by comparing its outcomes with those of a linear model for the same test machine