Battery Thermal Model

Captures the bidirectional relationship between electrical behavior and heat generation. As current flows, internal resistance produces Joule heating, while electrochemical reactions generate entropic heat. The model links a battery's electrical equivalent circuit to its thermal mass, predicting how voltage sag under load simultaneously raises core temperature. This coupling is critical for accurately forecasting temperature spikes during high C-rate discharges or fast charging events.

Defines the model's geometric fidelity. A lumped-parameter model treats the entire cell as a single uniform temperature node, suitable for small cells or slow operations. A distributed-parameter model discretizes the cell into multiple nodes across its length, width, and thickness, solving partial differential equations to reveal internal thermal gradients. Distributed models are essential for large-format prismatic cells where a 5-10°C internal difference can accelerate localized degradation.

Models the three modes of heat exchange with the environment:

• Conduction: Heat flow through solid cell materials (electrodes, casing) and thermal interface materials.
• Convection: Heat transfer to surrounding air or liquid coolant, governed by a heat transfer coefficient (h) that varies with flow rate.
• Radiation: Typically negligible at normal operating temperatures but included in high-fidelity aerospace models. Accurate boundary condition definition is vital for predicting cooling system effectiveness.

Incorporates the reality that key battery properties shift with temperature. Internal resistance (both ohmic and polarization) increases sharply at low temperatures, causing greater heat generation. Entropic coefficient (dU/dT) changes sign depending on state of charge, leading to endothermic cooling or exothermic heating. A robust model uses lookup tables or Arrhenius equations to dynamically adjust these parameters, preventing prediction errors during cold-start or rapid-warmup scenarios.

Decomposes total heat output into constituent sources for precision:

• Irreversible heat: Always positive, from ohmic losses (I²R) and charge-transfer overpotentials.
• Reversible heat: Can be positive or negative, from the entropy change of the electrochemical reaction (I·T·dU/dT).
• Side reaction heat: From parasitic reactions like solid electrolyte interphase (SEI) formation, critical in degradation and thermal runaway models. This decomposition allows the model to predict cooling demands during both charge and discharge.

Extends the model into abuse conditions to predict catastrophic failure. When internal temperature exceeds a critical onset threshold (~80-120°C for Li-ion), exothermic decomposition reactions begin. The model chains these reactions: SEI decomposition → anode-electrolyte reaction → cathode decomposition. A self-heating rate exceeding 10°C/min indicates an unstoppable runaway. This predictive capability is mandatory for safety validation and battery management system (BMS) fault detection logic.

The hardware and software standards governing high-power energy transfer, which is the primary driver of Joule heating in cells. Protocols like CCS (Combined Charging System) and CHAdeMO require active thermal management negotiation. The thermal model predicts the maximum safe C-Rate the battery can accept at its current temperature without triggering degradation or safety cutoffs.

A mathematical representation of capacity fade, for which temperature is a primary acceleration factor. The Arrhenius equation governs the exponential relationship between temperature and chemical degradation rates. The thermal model provides the temperature history input; the degradation model outputs the resulting State of Health (SoH) impact. Key interactions:

• High-temperature operation accelerates Solid Electrolyte Interphase (SEI) growth
• Low-temperature charging causes lithium plating

The optimization routine that must treat the thermal model's output as a dynamic constraint. A naive scheduler might assign an agent to a fast charger immediately after a heavy-duty cycle. A battery-aware scheduler uses the thermal model to predict that the pack is already at an elevated temperature and will either:

• Derate the charge power to prevent overheating
• Insert a cooling delay before initiating the charge
• Route the agent to a less thermally stressed charger

Path planning that minimizes energy consumption, where the thermal model adds a critical dimension. High current draw on steep inclines generates significant I²R losses as heat. An energy-aware router informed by a thermal model can avoid routes that would cause thermal saturation of the pack, even if they are nominally shorter. This prevents the need for mid-route thermal derating.

The real-time data stream that provides the ground truth for model validation and state estimation. Telemetry includes cell-level voltage, pack current, and multi-point temperature readings. This data is used to:

• Run Kalman filters for internal state estimation
• Update the thermal model's heat generation parameters
• Detect anomalies like a faulty thermal interface