Interpolation–Differentiation Mismatch and Local Stability in FEA-Based Electrical-Machine Lookup Tables

Finite-element analysis (FEA) flux maps are widely used in reduced electrical-machine lookup-table (LUT) models. However, the local dynamics of an implemented LUT representation need not match those inferred from separately interpolated derivative maps. This study develops a representation-aware numerical analysis workflow for a 100 kW externally excited synchronous machine. A formal atlas of 10,230 grid–knot matrices is compared with the audited trilinear representation at grid knots and at 5000 strictly off-grid cell-center equilibria. Although interior-knot constructions agree closely, the Jacobian of the implemented LUT representation is non-Hurwitz at 488 of 5000 within-cell equilibrium centers (9.76%), whereas the derivative-consistent comparator is Hurwitz at all centers. An extended nine-point audit of 1660 center-admissible geometric cells at five speeds (8300 cell-speed groups) retains 73,900 current-limit-valid design locations; within this finite design, 16,526 of 73,900 implemented-model Jacobians (22.36%) are non-Hurwitz, compared with 0% for the derivative-consistent representation. Interpolation-family and grid-resolution sensitivities preserve the qualitative operator-order effect. On the 832-point common strict-domain subset, Heun and classical fourth-order Runge–Kutta (RK4) remain markedly more accurate than Euler-based alternatives. The results show that interpolation–differentiation consistency should be established before interpreting model-predicted local continuous-time stability and fixed-step numerical admissibility. These percentages describe two distinct finite designs and do not estimate continuous-domain prevalence.