The science
Equivalent-circuit cell. Each cell is a voltage source plus a series resistance and one RC pair (diffusion and charge-transfer lag):
V = OCV(SOC) + I R0(T, SOC) + V1 , dV1/dt = -V1/τ + I R1/τ
OCV is a generic NMC/graphite-like curve. Resistance follows an Arrhenius-type law, R(T) = R25 exp[Ea/R (1/T - 1/298 K)], so a cold cell has several times the resistance of a warm one. Series cells add voltage; parallel cells share current (pack = Ns x Np cells).
CC-CV and the charging curve. The charger asks for the smallest of: its power rating (I = P / V), the cable current limit (air-cooled cables carry less than liquid-cooled ones), and the battery management system (BMS) cell limit. Because the pack voltage climbs as SOC rises, a constant-power charger needs less current later; the BMS limit shrinks with SOC and falls steeply when cold. Once the cell terminal voltage reaches 4.2 V the charger holds voltage constant and the current decays (the CV taper):
ICV = (Vmax - OCV - V1) / R0 , C-rate = I / Qpack
Heat. Irreversible Joule heat plus a small reversible entropic term, minus cooling to ambient and the chiller (heating from a PTC heater when cold):
Q = I2R0 + V12/R1 + I T dU/dT , Cth dT/dt = Q + Qheater - UA (T - Tamb) - Qchiller
Above 45 C the BMS derates the current. Preconditioning warms the pack on the way to the charger, so R0 is already low when the session starts; the energy it costs is shown.
Lithium plating indicator. Charging pushes the graphite anode potential down. If it goes below 0 V versus Li/Li+, lithium metal can deposit instead of intercalating. The model uses
φan = Uan(SOC) - C-rate x ran(T) , ran rising steeply as temperature falls
The guard limits the C-rate so φan stays above +20 mV; switch it off to see the index climb in the cold. The index is 0 above +30 mV and 1 at -30 mV. It is a qualitative model indicator, not a measurement or a safety certification.
Ageing. An empirical illustration: a small base loss per session that grows with mean C-rate squared and peak temperature, plus a larger term proportional to the plating exposure. Coefficients are invented to be plausible; real ageing needs real cell data.
Simplifications. Generic NMC/graphite 5 Ah cell, one RC pair, uniform pack temperature (the coloured cells show an illustrative spread), no cell balancing, aging-dependent resistance or anode half-cell kinetics, constant coolant loop, charger efficiency not modelled. 400 V or 800 V class refers to 96 or 192 series cells. All designs are generic; no real vehicle, charger or standard is modelled. Background: Newman and co-workers on porous-electrode models; Thevenin-type battery models; Waldmann et al. 2018 (J. Power Sources) on lithium plating in commercial cells; Attia et al. 2020 (Nature) on optimising fast-charging protocols.