The modelling of any battery pack will cover the electrical-thermal performance attributes of the cells. This mathematical modelling is likely to initially be a simple spreadsheet based model, then over time as the data and requirements mature so will the model.
Full Index
A complete, always up to date index of every page in the Modelling section, organised by hierarchy. Click any heading to expand it.
This page is ordered as:
Materials => Cell Design => Cell Assembly => Cells => Modules => Pack => System => Recycling
Materials
Extending the Doyle-Fuller-Newman Model for Phase-Separating Materials — extends DFN to phase-separating materials (LFP-type) using phase-field methods rather than Fickian diffusion, capturing hysteresis and one-at-a-time particle filling.
Cell Design Models
Cell Analysis and Modelling System (CAMS)
CAMS was designed to rapidly assess the potential energy density of different cell chemistries and cell formats. The model could also be used as an educational tool to demonstrate how different cell components affect the energy density of the cell, and how the energy density of low TRL level electrode active materials would translate at an applicable scale. Case studies gives examples of how this tool could be used.
- Doyle Fuller Newman Battery Model, often abbreviated as the Newman mode, is the starting point for a lot of battery electrochemical models.
- Single Particle Model (SPM) is a simplified but physics‑based model of a lithium‑ion battery that represents each electrode (anode and cathode) as one “average” spherical particle rather than thousands of particles distributed through a porous electrode.
- Parameterisation of OCV and Diffusion Coefficient — parameter-fitting approach for DFN/SPM-style electrochemical models.
- Cylindrical Cell Electrode Estimation — geometric calculator for estimating electrode area/length in a cylindrical cell.
- Prismatic Cell Electrode Estimation — equivalent geometric calculator for prismatic cells.
- Equivalent Lithium Content — calculator for a cell’s equivalent lithium content.
Cell Manufacturing Models
Impact of Formulation and Slurry Properties on Lithium-ion Electrode Manufacturing
The combination of materials in the electrodes, including the active material, conductive additive, and binders, plays a crucial role in determining the characteristics and performance of LIBs.
- Slurry Viscosity & Solid Content Optimization — process optimisation modelling for electrode slurry formulation.
- Analysis Workflows for XCT Data — quantitative workflow for analysing X-ray CT defect data from manufactured cells.
Cell Electro-Thermal Models
Battery Cell Modelling
By conducting experiments to measure the battery voltage at various SoCs and temperatures it is possible to develop phenomenological models that relate the applied current and the voltage. An equivalent circuit model (ECM) is one such phenomenological model most widely used in industry to simulate the voltage response for subsequent Battery Management System control and state estimation.
Idealised Nyquist Plot of a Lithium-Ion Battery — feature-by-feature model interpretation of an EIS Nyquist plot (SEI, charge-transfer, Warburg diffusion), pairs with the existing LLM/EIS post.
Optimising Battery Models for Real-World Use Cases
Most lithium-ion cells are rated to operate from –40 to 80 °C, yet few ever experience the extremes for more than a few minutes. In real-world operation, temperature tends to converge within a much narrower band. This is typically between 30 and 50 °C. That reality should guide how battery models are trained if they are to provide insights that truly matter.
How well can an LLM Interpret Electrochemical Impedance Spectroscopy (EIS) Data?
The analysis of EIS data involves basically three stages/steps:
- Check for data quality or KK using tools such as Boukamp’s linKK [2]
- Fit of an equivalent circuit model (ECM) model to the data by means of complex non-linear least squares (CNLS)
- Analysis of the distribution of relaxation times (DRT)
This package uses an LLM workflow to automate the analysis.
Degradation & State Estimation Models
- Kalman Filter — intuitive, maths-light introduction to the Kalman filter and how it combines a predicted state with noisy measurements to estimate battery SoC.
- Enhancing Lithium-Ion Battery Management with Advanced Kalman Filter Tuning — practical tuning of Extended Kalman Filter parameters for more stable, accurate SOC estimation.
- Control-Oriented Reduced-Order Models — physics-based reduced-order and enhanced single-particle models for lithium-metal batteries, benchmarked against a full-order COMSOL model for real-time BMS use.
- Particle Swarm Optimization Based Battery Parameter Identification — fits equivalent circuit model parameters (R0, R1, C1, OCV-SOC) to measured drive-cycle data using PSO.
- Physics-Based Model-Informed Smooth Particle Filter — combines a physics-based degradation model with a smooth particle filter to predict remaining useful life (RUL), outperforming classical particle-filter and capacity-based approaches.
Modelling Thermal Runaway
A complex model that needs to take into account: thermal, electrical, chemical reaction, gas flow, particle ejection, mechanical failure and combustion.
Thermal Runaway Modeling and Calibration of an LFP Battery Cell
Build up of a thermal runaway model of an LFP cell and comparison to an ARC test.
CALBET: Estimating Heat Release During Thermal Runaway of Lithium-Ion Cells — distinct heat-release estimation method, complements the existing thermal runaway modelling posts.
Thermal Runaway Modelling at Cell Level — an overview of the lumped-kinetic and coupled electrochemical-thermal approaches used to model a single cell’s runaway, as distinct from pack-level propagation modelling above.
Modelling Groups of Cells
Digital Twin of a Battery Module
The capacity and resistance differences of cells amplify the inhomogeneity at a system level and results in accelerated aging and degradation.
For the module design, where many cells are in parallel, the BMS typically does not have access to individual cell currents and temperatures.
We aim to predict current, state of health and temperature of each cell in the module (or pack) via modelling the interaction between cell and busbar and weld quality.
Can we build a quite simple cell busbar thermal model? First thoughts are whether we can make some simple approximations and hence create a spreadsheet model.
We have a current [I] flow through the busbar (orange). The busbar has a resistance defined by it’s resistivity, cross-sectional area and length. Hence we can calculate the heating power.
Modelling Software
There are lots of packages available to model the electrochemistry, cell, module and pack level at electrical, thermal, mechanical, safety, control and even at the atomistic electrochemical level. We have listed the different packages available in a table so that you can search, sort and download it.
Battery Calculations Workbook
The Battery Calculations Workbook is a Microsoft Excel based download that has a number of sheets of calculations around the theme of batteries.
The Pack Sizing sheet gives you a simple way to estimate the nominal power capability of a battery pack.
Simple to use with estimates that get you into the right ballpark.
Pack Models
Tesla Model 3 Fast Charge Model
Building on the Tesla fast charge thermal model that was discussed in the Siemens post: Race to the clouds: Battery thermal behavior simulation of a Tesla Model 3.
This article looks at the cooling system and impact of a change in cooling direction. Starting with the model and the original Fast Charge Scenario.
Fast Charging of a Lithium-Ion Battery
This algorithm enhances the charging current in order to maintain the observed overpotential near the threshold potential while reducing the charging time and protecting the cell’s state-of-health SOH.
Using a Newman model to ensure the negative electrode potential <0V
- Example Pack Sizing Using Power Demand
- Battery Pack Mass Estimation — worked calculator: nameplate energy → mass of everything but cells, from benchmark regression.
- What is the Optimum Design of a Cooling Plate for Uniform Cooling?
- Performance Analysis of an Integrated BEV Thermal Management
- DC Arc Flash Hazard Calculations
System Models
In order to understand battery requirements it is often necessary to model the system. In this way the boundary conditions imposed on the battery pack will become apparent.
Road Vehicle Model
A look at the approach to calculating the forces and the resulting power demand of a vehicle.
System
- BESS Sizing — full sizing-chain derivation (nameplate energy, DoD, EoL retention, C-rate, round-trip efficiency, annual throughput) with calculator.
- Electric Vehicle Range Calculator — range estimator from capacity, SoC and drive-condition factors.
- Drone Power and Energy Estimation
- Bidirectional Buck-Boost DC-DC Converter Calculator
- Auxiliary Systems Power Consumption in Electric Vehicles
See also: Equivalent Circuit Model, Thevenin Model, Randles Circuit, Nernst Equation, Arrhenius Equation, Peukert’s Law, Pack Modelling Techniques, Digital Twin, The Bruggeman Myth: Why Cell Parameterization Must Move Beyond the 1.5 Assumption