How do battery aging mechanisms affect ΔQ/ΔV curves and SOC estimation?

Battery aging changes both the shape and the meaning of incremental-capacity curves. In laboratory testing, loss of active lithium, electrode degradation, and rising resistance can reduce peak height and area, shift peak voltage, broaden peaks, and suppress secondary features in the ΔQ/ΔV curve. For SOC estimation, this means that models based on fresh-cell capacity, OCV curves, or fixed electrochemical parameters will progressively become biased unless they account for aging and test-condition effects.

The key implication is that ΔQ/ΔV curves are not only diagnostic fingerprints; they are aging-dependent inputs. Accurate SOC estimation across a cell’s life requires updated capacity, voltage, resistance, and—where appropriate—incremental-capacity features rather than a single static battery model.

How Aging Changes the ΔQ/ΔV Curve

Active lithium loss reduces available capacity

A major aging mechanism is loss of lithium inventory through irreversible side reactions, including continued SEI growth. Less cyclable lithium is available for intercalation, so the usable capacity decreases.

In the ΔQ/ΔV curve, this commonly appears as reduced peak area and changes in the voltage positions of reaction features. Because the curve is the derivative of capacity with respect to voltage, capacity loss can be more visible in the differential signal than in the original voltage-capacity curve.

Electrode degradation changes reaction utilization

Loss of active material and structural changes in either electrode reduce the amount of material participating in lithium intercalation and deintercalation. The associated reaction peak can therefore become shorter, narrower, broader, or partially absent.

The primary reference identifies a pronounced reduction in the second ΔQ/ΔV peak as a signature of reduced lithium-ion intercalation capability at the negative electrode. This interpretation is useful, but the exact peak affected depends on the cell chemistry, electrode design, SOC range, and test direction.

Resistance growth increases polarization

SEI thickening, contact degradation, electrolyte depletion, and electrode structural changes increase internal resistance and transport limitations. The measured terminal voltage then contains larger ohmic and polarization contributions in addition to its equilibrium voltage.

This causes differential-capacity peaks to shift in voltage, broaden, flatten, or merge. At sufficiently high current rates, a peak may appear to disappear even though the underlying electrochemical reaction has not completely vanished.

Peak changes are chemistry-dependent

A ΔQ/ΔV feature should not be assigned to a specific aging mechanism without considering the cell chemistry and electrode pairing. For example, LFP cells have a highly flat OCV region and closely spaced reaction features, making incremental analysis particularly valuable but also sensitive to measurement quality.

Other chemistries can show different peak counts, locations, and aging responses. Therefore, peak interpretation should be based on a validated baseline for the specific cell rather than on a universal peak map.

Why Laboratory Test Conditions Matter

Low-rate testing reveals the underlying electrochemical features

Low-rate constant-current charging, such as approximately 1/20 C to 1/5 C, reduces ohmic drop and polarization. The terminal voltage then more closely approximates the cell’s equilibrium voltage, allowing phase-transition and intercalation features to appear clearly.

This is especially important for aging comparisons. If a fresh cell is tested at low rate and an aged cell at high rate, differences in the ΔQ/ΔV curves may reflect test conditions rather than degradation.

High rates can mimic aging

At higher rates, polarization shifts voltage plateaus and flattens differential-capacity peaks. A secondary peak may become very small or disappear because the voltage response is broadened by kinetic and transport limitations.

Consequently, peak suppression is not, by itself, proof of irreversible electrode damage. It must be evaluated alongside current rate, temperature, hysteresis, relaxation time, and capacity measurements.

Data quality controls the usefulness of differentiation

Differentiation amplifies noise. Small voltage quantization errors, unstable temperature, current transients, and insufficient voltage resolution can create false peaks or obscure real ones.

Laboratory characterization should therefore use precise current and voltage measurement, thermal control, consistent cycling protocols, smoothing methods that do not distort peak locations, and repeatable SOC and voltage limits.

What ΔQ/ΔV Features Tell an SOC Model

Static nominal capacity becomes increasingly inaccurate

If an estimator continues to use the original nominal capacity after the cell has aged, its SOC calculation becomes inconsistent with the actual available charge. The resulting error can accumulate during coulomb counting.

For example, the same measured charge throughput represents a larger fraction of an aged cell’s available capacity than it did when the cell was new. Capacity must therefore be treated as an evolving state or periodically updated parameter.

The voltage-versus-SOC relationship can shift

Loss of lithium inventory changes the electrode stoichiometry corresponding to a given SOC. As a result, the apparent voltage-versus-SOC relationship may shift even when the cell’s chemistry has not fundamentally changed.

An SOC model using a fresh-cell OCV map can therefore interpret the same terminal voltage as the wrong SOC. Updating the maximum available capacity and relevant voltage maps at different aging stages helps preserve consistency.

Resistance changes distort voltage-based correction

Many SOC estimators use terminal voltage to correct accumulated coulomb-counting error. As resistance and polarization increase, terminal voltage becomes more dependent on current, temperature, and recent operating history.

A fixed OCV or equivalent-circuit parameter set may then attribute an aging-related voltage drop to SOC. This produces systematic SOC bias, particularly during high-current operation and near voltage limits.

Differential-capacity features can support model adaptation

Peak voltage, height, area, width, and relative spacing can serve as aging indicators. These features can help estimate SOH, identify changes in lithium inventory or electrode activity, and select or update the appropriate SOC model parameters.

However, ΔQ/ΔV is usually most reliable as a diagnostic and calibration signal obtained under controlled conditions. It is not generally a direct real-time SOC measurement during arbitrary dynamic operation.

Model Strategies for Aging-Aware SOC Estimation

Recalibrate electrochemical or equivalent-circuit parameters

A practical approach is to periodically update capacity, resistance, relaxation, and OCV-related parameters using laboratory data from different aging stages. This maintains consistency between the model and the cell’s current condition.

The required updates depend on the model. A simple coulomb-counting estimator primarily needs available-capacity correction, while an equivalent-circuit or electrochemical model also needs updated resistance, polarization, and voltage relationships.

Use adaptive filters when parameters evolve

Adaptive Kalman-filter approaches can estimate SOC while simultaneously tracking selected parameters such as capacity or resistance. Their effectiveness depends on sufficient excitation in the operating data and on well-designed constraints.

The filter should not be expected to infer every aging mechanism from ordinary drive-cycle data. Laboratory ΔQ/ΔV results provide valuable priors and help define realistic parameter ranges.

Retrain data-driven models across aging states

Neural networks and other machine-learning estimators trained only on fresh-cell data may perform well initially but degrade as peak positions, capacity, and resistance change.

Training data should span relevant aging stages, temperatures, currents, and SOC ranges. ΔQ/ΔV-derived features can be included when they are available, but the model must distinguish genuine aging signatures from artifacts caused by rate or temperature.

Separate SOC estimation from SOH estimation

SOC describes the current charge state relative to the available capacity, whereas SOH describes how that available capacity and other characteristics have changed. Treating them as separate but coupled estimation problems is generally more robust than assuming a fixed SOH.

ΔQ/ΔV features are particularly valuable for SOH tracking and mechanism diagnosis. The resulting SOH estimate can then inform the capacity and parameter updates used by the SOC estimator.

Understanding the Trade-offs

Incremental-capacity analysis is sensitive but not uniquely diagnostic

A peak change can result from lithium inventory loss, active-material loss, resistance growth, temperature, current rate, or data-processing choices. The same visual feature may therefore have multiple possible causes.

Reliable diagnosis requires comparing multiple indicators, including capacity retention, charge and discharge curves, resistance measurements, temperature, and repeatability across test conditions.

High-resolution curves require slow and controlled testing

Low-rate testing produces clearer electrochemical features but is time-consuming and may not represent the conditions under which the battery operates. Faster tests are more practical but introduce polarization that complicates interpretation.

The appropriate test rate is therefore a compromise between diagnostic resolution, test duration, and application relevance.

More adaptive models require more calibration data

A model with aging-dependent capacity, resistance, OCV maps, and differential features can be more accurate, but it also requires more parameters and validation data. Poorly constrained adaptation can cause parameter drift or allow the estimator to fit measurement noise.

Adaptation should be limited to parameters that are observable from the available measurements and supported by laboratory characterization.

Peak suppression should not be overinterpreted

The reduction of a secondary peak is an important aging signature in the referenced test context, particularly when associated with reduced negative-electrode intercalation and increased polarization. It should not be treated as a universal indicator for every lithium-ion chemistry or operating condition.

The diagnostic meaning of each peak must be established for the specific cell and protocol.

Making the Right Choice for Your Goal

The most effective workflow combines controlled incremental-capacity testing with an SOC model that explicitly accounts for changing capacity and resistance.

• If your primary focus is laboratory degradation diagnosis: Track peak voltage, height, area, width, and disappearance across controlled low-rate tests while cross-checking the results against capacity and resistance measurements.
• If your primary focus is SOC accuracy over cell life: Update maximum available capacity and voltage-model parameters at multiple aging stages instead of retaining fresh-cell nominal values.
• If your primary focus is embedded BMS implementation: Use an adaptive filter or constrained parameter-update scheme, with laboratory data defining realistic aging trends and parameter limits.
• If your primary focus is machine-learning SOC estimation: Train and validate the model across aging states, temperatures, current rates, and cell-to-cell variation rather than using only beginning-of-life data.
• If your primary focus is LFP SOC estimation: Combine incremental-capacity or other model-based information with coulomb counting because the flat OCV plateau provides weak direct voltage sensitivity across much of the SOC range.

Aging-aware SOC estimation is most reliable when ΔQ/ΔV is treated as evidence of evolving cell behavior—not as a fixed curve that remains valid throughout the battery’s life.

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