Voltage and Stoichiometry Limits

Distinguish cut-off voltages, OCV endpoints, and stoichiometry ranges used as simulation bounds and parameterization references.

When configuring a battery model, you may encounter several types of voltage and stoichiometry limits. This guide clarifies what each set of limits means, how they are used in simulation and parameter fitting, and why they all exist.

Voltage Limits

Voltage limits define the operating range of the cell. These values are critical for safety, model realism, and aligning with experimental protocols.

Cut-off Voltages

• Lower voltage cut-off / Upper voltage cut-off

These are the actual voltage limits of the cell, typically set by the manufacturer or safety requirements. They define the voltage range within which the cell is cycled and are used as hard simulation limits.

OCV at SOC Endpoints

• Open-circuit voltage at 0% / 100% SOC

These correspond to the stoichiometric endpoints of the electrodes. They define the open-circuit voltage at full lithiation or delithiation and are used to determine the stoichiometry range during parameterization. They should always lie within the upper and lower voltage cut-off values.

These two sets of voltage values often appear similar and typically take the same value, but serve different purposes:

• Cut-off voltages are operational bounds
• OCV endpoints are parameterization references for stoichiometry

Stoichiometry Limits

Stoichiometry describes the relative lithium content in each electrode and is central to determining electrode balancing and usable lithium.

Stoichiometry at 0%/100% SOC

• Negative/positive electrode stoichiometry at 0%/100% SOC

These define the electrode stoichiometries corresponding to 0% and 100% state of charge based on the full-cell OCV curve. They are used to compute:

• Initial lithium concentrations
• Electrode balancing

These are the main stoichiometry bounds used in simulations.

Stoichiometry at Min/Max SOC

• Negative/positive electrode stoichiometry at minimum/maximum SOC

These reflect the range of stoichiometry values observed in the data used for fitting. They are not used in simulation, only during parameter estimation.

These parameters provide better numerical convergence during fitting and help guide the optimization algorithm.

Lower/Upper Excess Capacity

• Negative/positive electrode lower/upper excess capacity

These are alternative fitting parameters that reflect unused lithiation capacity outside the typical operating range. Like min/max stoichiometry, they are internal to the fitting process and not exposed during model evaluation.

How These Fit Together

1. Start with OCV Data

   Obtain OCV data from the full cell

2. Determine Min/Max Stoichiometry

   Use OCV data to determine min/max stoichiometry for each electrode

3. Derive 0%/100% Stoichiometry

   Calculate the stoichiometry limits corresponding to OCV at 0%/100% SOC

4. Calculate Initial Conditions

   Use stoichiometry limits to compute initial concentrations and cyclable lithium

5. Define Operating Range

   Set cut-off voltages to define where the cell will actually be cycled

Stoichiometry Sign Convention

Key Design Principle: Stoichiometry always increases as voltage decreases for a given electrode.

Electrode	SOC	Stoichiometry	Reason
Negative	0%	Lower	Delithiated during discharge
Negative	100%	Higher	Lithiated during charge
Positive	0%	Higher	Lithiated during discharge
Positive	100%	Lower	Delithiated during charge

This consistent convention helps maintain orientation across models.

Summary Table

Parameter Type	Used In	Purpose
Cut-off voltages	Simulation	Operational safety bounds
OCV at 0%/100% SOC	Parameterization	Stoichiometry range reference
Stoichiometry at 0%/100% SOC	Simulation	Initial concentrations, electrode balance
Stoichiometry at min/max SOC	Fitting only	Numerical convergence, optimization guidance
Excess capacity	Fitting only	Unused lithiation capacity

While having multiple definitions may seem excessive, each serves a specific role in maintaining model fidelity, improving fitting stability, and aligning with experimental protocols.