Building a thermal model of a single cell is the foundational step in thermally-informed charge protocol design. But a two-wheeler battery pack is not a single cell operating in isolation. It is a collection of cells arranged in a module, with mutual thermal interactions, non-uniform cooling access, and a shared current path that distributes the charge load across the group. The thermal behavior of the pack is not the sum of isolated cell behaviors, and a charge strategy derived from a single-cell model needs explicit translation work before it can be applied to pack-level current control.
This translation is where a lot of practical protocol development work either does well or breaks down. The temptation is to take the single-cell model, declare it representative of the pack, and apply its protocol limits directly to pack-level charge control. Sometimes this is adequate. More often it misses the specific ways in which pack geometry creates thermal conditions that differ from the isolated cell assumption, and the protocol ends up either overly conservative or, less frequently but more seriously, insufficient to protect the cells in the worst-case thermal position.
The cell-in-pack thermal boundary condition
The most significant difference between an isolated cell and a cell in a pack is the thermal boundary condition. An isolated cell dissipates heat to the ambient from all of its external surfaces. A cell in the interior of a cylindrical cell array dissipates heat primarily through its contact with adjacent cells, the module housing wall, and any thermal interface material connecting the cells to a cooled surface.
For a cylindrical cell in the center of a three-by-four array (twelve cells total) with passive cooling through the module housing, the effective heat rejection path is longer and more restricted than for an isolated cell. Heat generated in the core must pass through the jelly roll to the can surface, then through the contact resistance between adjacent cells, then through the outer layer of cells to the housing wall, then through the housing to ambient air. Each thermal resistance in that series chain reduces the effective cooling rate.
The practical consequence: the center cell in a module runs hotter than the corner cells under the same charge protocol, and both run hotter than an isolated cell would under the same conditions. A single-cell model calibrated on an isolated cell in a temperature-controlled environment will predict temperatures that are systematically lower than what the center cell of the module actually reaches.
Quantifying the inter-cell thermal resistance
To extend the single-cell model to a module, you need to characterize the inter-cell thermal resistance: how much temperature drop exists between adjacent cells in the pack configuration. This depends on three factors: the cell-to-cell contact geometry (line contact for cylindrical cells, which is a poor conductor), any thermal interface material between cells (gap filler pads, thermal grease, or conductive foam inserts), and the contact pressure between cells.
For cylindrical cells in a typical two-wheeler pack without thermal interface material between cells, the inter-cell thermal resistance is high. Two adjacent 18650 cells in mechanical contact have a line contact of roughly 50 to 80 mm length (the length of the cell) and a contact width of fractions of a millimeter. The effective contact conductance is in the range of 0.1 to 0.5 W per Kelvin depending on contact pressure and surface finish. This is a significant thermal resistance, meaning that adjacent cells do not effectively share heat: a hot center cell cannot easily transfer its excess heat to a cooler neighbor.
With a thermal interface pad between cells (0.5 to 1 mm silicone gap filler, thermal conductivity around 2 W/m per Kelvin), the inter-cell resistance drops substantially. A 1 mm pad between two 18650 cells over their full surface contact area (roughly 50 mm length, a few millimeters of effective contact width) provides around 2 to 5 W per Kelvin of conductance, an order of magnitude better than dry contact. This significantly reduces the center-to-corner cell temperature differential in the module.
Position-dependent protocol limits
Once you have characterized the module thermal resistance network, the cell-level model extends to a module-level model by representing each cell as a heat source connected to its neighbors through the characterized inter-cell resistance. The module-level model has inputs of charge current (shared by all cells in a series string) and ambient temperature, and outputs temperature estimates for each cell position in the array.
The key output is the temperature of the hottest cell, typically the center cell in a passively cooled array. The charge protocol limit should be set to keep that hottest cell within the acceptable thermal envelope, not the average cell or the corner cell. Setting the limit based on the average cell temperature means the center cell regularly exceeds the desired temperature limit. Setting it based on the corner cell (the coolest) is overly conservative and leaves speed on the table.
In a well-parameterized module model, the temperature differential between the center and corner cells at a given charge rate and ambient condition is a predictable function of the pack geometry and thermal interface. For a passively cooled 12-cell array with no thermal interface material at 2C and 30 degrees Celsius ambient, the center-to-corner differential can reach 6 to 10 degrees Celsius. With a 1 mm gap filler pad between cells, this drops to 2 to 4 degrees Celsius. Knowing this differential, you can set the pack-level charge rate limit at the current that keeps the predicted center cell within the desired temperature bound, rather than applying a uniform margin on top of the single-cell limit that may or may not be sized correctly for the actual pack geometry.
Cell-to-cell variation and where it matters
Real packs contain cells with variation in capacity, internal resistance, and thermal resistance from the manufacturing process. This variation creates load imbalance in series strings: cells with higher resistance generate more heat per unit of charge current than lower-resistance cells. The hottest cells in a pack are therefore not purely determined by position in the array; they are the cells at the worst thermal position that also have the highest internal resistance.
For charge protocol design, this means the protocol limit derived from the nominal cell model has a statistical safety margin for manufacturing variation. If the variance in internal resistance across a cell lot is small (tight manufacturing control), the safety margin for cell variation can be narrow. If the variance is large, the margin must be wider to ensure the hottest-cell-in-the-worst-position is still within the thermal limit.
The way we address this in practice is to parameterize the cell model with a range of internal resistance values spanning the measured distribution from the cell lot, and set the protocol limit based on the 90th or 95th percentile cell temperature estimate rather than the nominal. This ensures the protocol is safe for the realistic population of cell resistances in the pack, not just the nominal cell.
From pack model to BMS implementation
The full module thermal model is too computationally expensive to run in real time inside most BMS microcontrollers in two-wheeler applications. The bridge from model to firmware is a simplification step: use the offline model to generate a reduced-order representation, typically in the form of a protocol lookup table indexed by ambient temperature and charge session start temperature, with current profiles for each condition that have been verified against the full model.
This is the same approach described in the context of single-cell models, just applied to the module-level model. The offline computation is done once during pack development; the BMS executes the result. The BMS needs to know ambient temperature (from an NTC thermistor on the module housing) and cell temperature at session start (from the pack thermistors, which read the outer cell layer), and it selects the appropriate protocol from the table.
The translation from single-cell model to pack-level firmware is not automatic. It requires understanding the specific thermal resistance structure of the pack, parameterizing it from measurement, and deriving the protocol limits that protect the hottest cell in the pack at the realistic distribution of ambient conditions. That is the engineering work that sits between a validated cell model and a deployed charge protocol.