First-principles physics behind every simulation

Thermal Physics

Heat generation and conduction in cylindrical cell arrays

A lithium-ion cell generates heat through two primary mechanisms: irreversible Joule heating from ohmic resistance, and reversible entropic heat from the thermodynamic entropy change of the intercalation reactions. Our model resolves both terms at each timestep.

The volumetric heat generation rate is modelled as:

q = I * (U_OCV - V_term) / Vol_cell  +  I * T * (dU/dT) / Vol_cell

where I is the current, U_OCV is the open-circuit voltage, V_term is the terminal voltage, T is the cell temperature in Kelvin, and dU/dT is the entropic coefficient measured experimentally for each chemistry.

Conduction across the pack is modelled using the lumped-thermal-node approach, with thermal conductivity tensors accounting for the anisotropy of wound cylindrical cells - axial conductivity (k_z ~ 30 W/m-K for INR18650) differs from radial conductivity (k_r ~ 0.8 W/m-K) by more than an order of magnitude. This asymmetry determines whether thermal runaway propagates along a row or remains localised - the central design question for high-density two-wheeler pack configurations.

Convective boundary conditions apply at the pack enclosure surface, parameterised by the natural or forced convection coefficient (h) derived from pack geometry and cooling channel configuration. Engineers can test passive air-cooling, directed airflow, and cold plate configurations within the same model run.

Model validation was performed against bench calorimetry on 3S4P INR18650 modules at 1C and 2C discharge rates, 25 C ambient. Peak temperature prediction error was 1.4 C RMS across 40 characterisation runs (June 2025 internal test report, e-TRNL Engineering Note EN-2025-04).

Degradation Model

Capacity fade from separable ageing mechanisms

Capacity fade in lithium-ion cells arises from multiple concurrent mechanisms. e-TRNL Energy's degradation model treats each mechanism as a separable contributor to total lithium inventory loss (LIL) and active material loss (AML), following the semi-empirical framework validated against NREL and KIT datasets.

The four primary mechanisms modelled are:

SEI growth (calendar ageing). The solid-electrolyte interphase on the anode grows as a square-root-of-time function of temperature and state-of-charge. The growth rate constant follows an Arrhenius temperature dependence (activation energy E_a ~ 50-75 kJ/mol depending on electrolyte formulation). SOC dependency is captured via a multiplier on the SEI ionic resistance.

Lithium plating. At low temperatures or high charge rates, lithium deposition on the anode competes with intercalation. The model tracks the negative electrode surface overpotential and flags conditions where plating onset potential is exceeded (eta_n < 0). Cumulative plated lithium contributes to irreversible capacity loss and, at high levels, poses a safety risk. This is the mechanism most relevant to fast-charge protocols during Indian winters.

Mechanical fatigue. Volume change during cycling induces stress in electrode particles. The model applies a crack-growth rate proportional to the depth-of-discharge swing and the number of cycles, contributing to progressive active material isolation.

Electrolyte oxidation (high-voltage). Sustained operation near the upper cut-off voltage accelerates cathode-side electrolyte decomposition. The model penalises protocols that hold terminal voltage above 4.15 V for extended periods.

The combined LIL and AML projections map directly to capacity and impedance trajectories, which the platform visualises as fade curves with uncertainty bands derived from a 20-sample Monte Carlo run over chemistry parameter distributions.