BATTLM: A Transmission-Line Modelling Realisation of nRC Equivalent Circuit Models for Lithium-Ion Batteries

Equivalent-circuit models (ECMs) are widely used in battery management systems. However, scheduled resistance and capacitance changes can make numerical histories inconsistent with physical polarisation states. This paper introduces BATTLM, a Transmission-Line Modelling (TLM) realisation of lithium-ion battery ECMs. Each capacitor in a resistor–capacitor (RC) branchcapacitor is represented by an open-circuit TLM stub using incident and reflected variables. When parameters change, the incident history is reconstructed from the endpoint polarisation voltage. The fixed-step algebraic formulation extends from 1RC to arbitrary nRC order and reproduces the corresponding trapezoidal update. Assessment uses Panasonic 18650PF and Stanford second-life cell data. Among 1RC, 2RC, 3RC, and 4RC candidates, frequency-point testing favours 4RC for all 180 Stanford spectra, whereas the corrected Akaike information criterion selects 4RC for 108 spectra and 3RC for 72. Median impedance test root-mean-square error (RMSE) values are 2.166, 1.146, 0.912, and 0.848 mΩ, respectively. Electrochemical impedance spectroscopy (EIS)-derivedparameters are applied to 177 measured pulses without pulse-domain fitting. Median voltage RMSE values, referenced to the measured pre-pulse voltage, are 5.359, 1.656, 0.884, and 0.623 mV. The results support state-consistent TLM implementation while identifying application-dependent model-order trade-offs. On a dedicated Panasonic temperature-rise record excluded from parameter identification, scheduling with measured battery temperature reduced terminal-voltage RMSE from 177.55 to 86.92 mV relative to freezing the temperature dependence at the initial condition.