Interpolation–Differentiation Mismatch and Local Stability in FEA-Based Electrical-Machine Lookup Tables
- 1Department of Electricity and Energy, Bigadiç Vocational School, Balıkesir University, 10440 Bigadiç, Türkiye
Abstract
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.
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BibTeX
@article{karakaya2026interpolationdifferentiation,
title = {{Interpolation–Differentiation Mismatch and Local Stability in FEA-Based Electrical-Machine Lookup Tables}},
author = {Oktay Karakaya},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14213880},
url = {https://www.mdpi.com/2227-7390/14/21/3880},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Interpolation–Differentiation Mismatch and Local Stability in FEA-Based Electrical-Machine Lookup Tables
AU - Oktay Karakaya
PY - 2026
DA - 2026/10/24
JO - Mathematics
DO - 10.3390/math14213880
UR - https://www.mdpi.com/2227-7390/14/21/3880
AB - 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.
SN - 2227-7390
ER -