Molicel P45B ECM: Open-Source Equivalent Circuit Model
Updated: Sep 18
About:Energy believes battery modelling is held back by how much of it stays hidden. Most vendors treat their methodology as proprietary, leaving engineers to choose models on trust rather than evidence, and leaving the field to re-derive the same testing and parameterisation problems in isolation. We do the opposite: we publish our testing methods, model structure, assumptions and limitations, and the raw validation data behind them, so anyone can check our working. This paper is the first in an ongoing series doing exactly that, and it's the same approach we bring to joint development with customers, moving faster because the methodology is visible to both sides from the start.
Molicel P45B Equivalent Circuit Model
About:Energy has published the first in a series of open-source battery model papers, starting with a full industry-standard equivalent circuit model (ECM) parameterisation of the Molicel P45B, a 4.5 Ah high-power 21700 cell used across eVTOL, motorsport and drone platforms. Where most academic ECM papers optimise for accuracy alone, this paper treats accuracy, build cost and run cost as equally important, since a model that only wins on accuracy rarely gets used downstream in industry. Read the preprint.
Molicel P45B Open-source Validation
The testing methodology is built around plausible real-world operation rather than discrete pulse loads from quasi-equilibrium conditions, and uses conductive surface-controlled thermal testing to hold the cell close to isothermal. That separates electrical and thermal effects cleanly, so voltage error can be attributed to the electrical model rather than a moving thermal target. The model itself uses two RC pairs, reversible heat generation and OCV hysteresis, and is validated across the full SOC, current and temperature envelope, including representative eVTOL missions and drive cycles with regenerative charging under aggressive surface cooling.
Around 30 validation conditions were run across four temperatures and the cell's full current envelope, with RMSE voltage error binned in 10% SOC increments rather than reported as a single average, so performance across the range is visible rather than hidden. The full parameter sets, validation data, validation metrics workbook and documentation are released on the Zenodo data repository under CC-BY 4.0, continuing About:Energy's approach of publishing methodology in the open rather than treating it as a black box. The same testing and validation approach is used across the rest of the Voltt cell library.
FAQs
What is an equivalent circuit model?
An equivalent circuit model represents a cell as a voltage source with resistive and RC elements that reproduce its terminal behaviour. It does not resolve internal physics, which makes it fast enough for pack simulation, control development and long duty cycles. It is the most widely deployed battery model format in industry.
How many RC pairs does a battery ECM need?
Two is the usual answer for high-power cells. One RC pair misses the slower diffusive response and under-predicts voltage recovery after a load step. Three or more adds fitting complexity and run cost for diminishing accuracy gain. The P45B model uses two RC pairs alongside reversible heat generation and open-circuit voltage hysteresis.
How do you parameterise an equivalent circuit model?
By characterising open-circuit voltage, resistance and time constants across the full state-of-charge, current and temperature envelope, then fitting the circuit elements to that data. The quality of the result depends more on the test conditions than the fitting routine. Testing under plausible real-world loads produces a model that holds up in application, unlike pulse tests from quasi-equilibrium.
Why does isothermal testing matter for ECM parameterisation?
Because if cell temperature moves during a test, voltage error cannot be attributed cleanly to the electrical model. Conductive surface-controlled thermal testing holds the cell close to isothermal, separating electrical and thermal effects. Without that separation you end up fitting an electrical model against a moving thermal target and carrying the error forward.
What is OCV hysteresis and does it need modelling?
Open-circuit voltage differs slightly between charge and discharge at the same state of charge. Ignoring it introduces persistent voltage error, particularly in applications with regenerative charging where the cell repeatedly swaps direction. Any model intended for eVTOL, motorsport or drive-cycle use should include it.
What voltage RMSE is acceptable for a battery model?
It depends on the application, but a single average RMSE figure hides more than it shows. Reporting error binned by state of charge reveals where the model is weak, which is usually at the extremes where designs actually operate. The P45B model was validated across around 30 conditions and four temperatures with error reported in 10% state-of-charge bins.
How do you validate a battery model?
Against real duty profiles, not against the same pulse data used to fit it. Validation should cover the full current, temperature and state-of-charge envelope the cell will see, including regenerative charging if the application has it. Publishing the validation dataset lets anyone reproduce the result, which is a reasonable thing to ask of any model vendor.
Can an ECM model temperature rise?
Only with a heat generation term attached. Irreversible heating from overpotential is straightforward. Reversible entropic heating matters at low C-rate and during long constant-current phases, where it can flip the sign of heat generation. The P45B model includes both, which is what allows it to be coupled to a thermal model.
Is an equivalent circuit model good enough for eVTOL or drone pack design?
For sizing, mission simulation and control development, yes. It captures voltage under load, heat generation and end-of-discharge behaviour at a run cost that allows thousands of missions to be simulated. What it will not give you is internal state: plating margin, electrode utilisation or the reason behind a failure. That is where a physics-based model is added.
