Research methodology

Diffusion-limited calendar ageing with anode-potential SOC stress

Q_cal = A(T, SOC) * t^z. Varying conditions are combined with the equivalent-time method: the state S = Q^(1/z) grows at rate A^(1/z), so residence-weighted rates are additive in S. SOC stress follows the graphite anode potential (plateau behaviour) plus an optional cathode high-voltage term for layered oxides. Time-at-SOC residence drives the calculation, so reaching 100 % briefly is penalised far less than parking at 100 %.

Charging-curve based pack C-rate model

Battery input power is min(charger, vehicle AC limit or DC curve(SOC) x thermal derate). Pack C-rate = power / gross pack energy. A 350 kW charger never implies 350 kW into the battery: the vehicle curve, taper and pack temperature govern the session. Where no curve is known a generic curve is estimated from peak power and the 10-80 % time (LOW confidence).

LFP (olivine) / graphite

Dedicated LFP model. Never inherits NMC coefficients.

Lithium-ion - chemistry unknown (broad)

Used when the chemistry is unknown. Deliberately broad so that uncertain chemistry widens prediction intervals.

LMFP (manganese-doped olivine) / graphite

Fallback within the olivine family: LFP structure with 1.5x wider parameter spreads because public LMFP ageing data is scarce. Never uses NMC coefficients.

LMO / blended spinel-layered oxide / graphite

Spinel-containing chemistries (e.g. early compact EVs). Structure shared with layered oxides; Mn-dissolution makes temperature sensitivity higher.

Sodium-ion (hard-carbon anode)

Placeholder architecture for sodium-ion: hard-carbon anode (no graphite staging), very wide uncertainty.

NCA / graphite

Layered-oxide NCA. Shares the NMC functional form with NCA-specific stress amplitudes.

NMC (layered oxide) / graphite - generic

Generic NMC/graphite model used when the NMC sub-chemistry is unknown. Spreads cover sub-chemistry differences.

NMC111 / graphite

Sub-chemistry deltas relative to NMC-GENERIC are provisional.

NMC532 / graphite

Sub-chemistry deltas relative to NMC-GENERIC are provisional.

NMC622 / graphite

Sub-chemistry deltas relative to NMC-GENERIC are provisional.

Ni-rich NMC811 / NCMA / graphite(-Si)

Ni-rich deltas relative to NMC-GENERIC are provisional (oxygen release / surface reconstruction at high SOC).

Shared diffusion-limited SEI state + additive non-SEI pathways + knee

Calendar SEI and cycling-induced SEI share ONE diffusion-limited state (Q_sei = (S_cal + S_cyc)^z), so their combination is sub-additive: SEI that grew during storage slows SEI growth during cycling and vice versa. Active-material loss, plating and low-SOC damage add on top. A late-life knee term accelerates fade beyond an uncertain onset. An ADDITIVE option (superposition) is available for comparison. Attribution of interacting mechanisms is therefore approximate.

Two-pathway cycle ageing (cycling-induced SEI + active-material loss)

Each charging session and the following discharge form half-cycles (range, mean, max, min SOC, pack temperature, C-rate profile). Pathway 1 - cycling-induced SEI - adds equivalent reference time to the shared diffusion-limited SEI state. Pathway 2 - loss of active material / mechanical - follows a throughput power law with depth-of-discharge, high-SOC, low-SOC, temperature and C-rate stress factors. Equivalent full cycles are computed from battery discharge throughput, not from charging events.

Lithium-plating risk index (kinetic tolerance vs actual C-rate)

Plating tolerance C_safe(T, SOC) = margin x curve-peak C-rate x exp(-Ea/R(1/T - 1/Tref)) x psi(SOC). Dose = integral of max(0, C - C_safe) dt (excess charge throughput). Capacity loss is linear in dose. Preconditioning (see PACK-THERMAL) heats a pack that would otherwise start a DC session below the trigger temperature; the warmer session lowers the plating dose. Because a warmer session also speeds up temperature-driven SEI growth slightly, the net effect is evaluated by the full model: beneficial in cold conditions, negligible when the pack is already warm (a warm pack is not heated further).

Arrhenius temperature dependence on estimated pack temperature

Rates are evaluated at the estimated PACK temperature (never ambient directly). SEI pathways use Arrhenius acceleration on both sides of 25 degC; below cal_t_floor_c the calendar temperature factor is held constant instead of being extrapolated beyond the evidence. The active-material pathway is accelerated only above 25 degC; cold-temperature damage is handled by the lithium-plating model.

Pack temperature approximation

Parked pack temperature follows the damped daily mean of ambient, modified by the parking environment (garage, underground, carport, outdoor). Driving and charging add heat; active thermal management caps pack temperature while driving and - for liquid/refrigerant systems - while plugged in (grid-powered cooling, PROVISIONAL); heaters set a floor while driving; preconditioning heats a pack that would start a DC session below the trigger temperature (floor-at-target session profile). Uncertainty is represented by a per-sample offset and sampled plugged-in cooling parameters.