How do aging state, initial SOC, current rate, and resting time nonlinearly influence charging polarization voltage? Optimize Your Battery Characterization

Charging polarization voltage is not determined by current alone. In lithium-ion characterization, it rises nonlinearly through the coupled effects of SOH, initial SOC, charging rate, and prior resting history. A practical model therefore modifies the baseline RC polarization response with SOC, current-rate, initial-state, and aging distortion factors rather than assuming a fixed resistance.

Core takeaway: The same charging current can produce very different polarization voltages depending on where the cell starts, how long it rested, what it was doing beforehand, and how much it has aged. Polarization is generally lowest at mid-range SOC and increases toward low and high SOC extremes, while aging raises the response across the operating range.

Why a Linear RC Model Is Not Enough

The baseline polarization response

A standard multi-order RC model commonly represents polarization as:

[ U_P(T)=U_P(0)+I\sum_{j=1}^{N}A_j ]

where the time-dependent contribution of each RC branch can be written as:

[ A_j=R_{Pj}\left(1-\exp\left(-\frac{T}{R_{Pj}C_{Pj}}\right)\right) ]

Here, (R_{Pj}) and (C_{Pj}) describe polarization processes with different time constants, (I) is charging current, and (T) is the charging or observation time.

Where the nonlinearity appears

The linear expression assumes that polarization voltage changes proportionally with current and that the RC parameters remain fixed. Real cells violate those assumptions because charge-transfer resistance, diffusion limitations, hysteresis, and aging mechanisms vary with operating condition.

A useful extended representation is:

[ U_P=U_P(0)+K_{SOC}K_I I\sum_{j=1}^{N}A_j+B_{P0-}+B_{SOH} ]

The factors do not necessarily represent independent physical mechanisms. Their interaction is important: a high current applied to an aged cell at high SOC can produce a much larger response than the sum of changes observed under each condition separately.

How Each Variable Changes Polarization

State of Health Changes the Baseline

Aging increases polarization at a given current

As SOH declines, the same charging current generally produces a larger polarization voltage. This reflects the cell’s increasing difficulty in accepting charge, including changes associated with internal resistance and transport limitations.

In the model, this effect is represented by an aging term such as (B_{SOH}). The term increases the predicted voltage response as capacity and electrochemical performance deteriorate.

Aging changes more than capacity

SOH should not be treated only as a remaining-capacity indicator. An aged cell can also exhibit altered resistance, slower relaxation, and stronger voltage excursions during charging.

Consequently, a model calibrated only on a fresh cell can underestimate both charging voltage and heat generation later in life.

Aging amplifies operating-condition sensitivity

The effect of current rate or high SOC can become more consequential as the cell ages. In practice, this means a fast-charge limit that is acceptable for a new cell may create excessive polarization or side-reaction risk in an aged cell.

Initial SOC Creates a Bowl-Shaped Response

Polarization is lowest in the middle SOC range

Under otherwise similar charging conditions, polarization voltage is typically relatively low and stable over the approximate 10%–70% SOC region. This corresponds to a range in which the cell generally has better charge-acceptance capability.

The exact boundaries depend on chemistry, temperature, cell design, and test conditions, so these ranges should be treated as characterization observations rather than universal limits.

Low SOC can still produce high polarization

Polarization can become high below approximately 10% SOC, with reported peaks near the low-SOC region. Low SOC does not automatically mean that the cell can accept unlimited charging current.

Transport and reaction conditions at the beginning of charging can still limit charge acceptance, producing a large transient or steady-state polarization response.

High SOC produces a stronger rise

Polarization increases significantly as the initial SOC approaches the upper charging range, particularly above approximately 80% SOC. During the constant-voltage stage, the current decreases while the voltage response evolves differently, so the polarization behavior should not be interpreted as a simple continuation of constant-current charging.

High SOC is especially important because elevated polarization can increase the risk of undesirable reactions, including lithium deposition and electrolyte degradation when charging current is excessive.

Charging Rate Produces Rate-Dependent Distortion

Higher current generally increases polarization

Increasing the charging rate—for example, from approximately 1/3C to 1C—increases the polarization voltage. The current-dependent term in the model captures the broad trend:

[ U_P \propto K_I I ]

However, (K_I) is not constant across all current levels.

The incremental response is nonlinear

The ratio of polarization-voltage increase to current increase changes with current magnitude. In other words, doubling the current does not necessarily double the incremental polarization voltage.

This occurs because reaction kinetics and diffusion limitations become increasingly influential as current demand rises. A rate factor (K_I) is therefore more realistic than a single fixed polarization resistance.

Rate and SOC interact

A moderate current at mid-range SOC may generate less polarization than the same current near the low- or high-SOC limits. High current combined with high SOC is therefore a particularly demanding condition, not merely two independent inputs.

Resting Time and Previous History Set the Initial State

Rest does not simply “remove” polarization

After charging or discharging stops, the cell voltage relaxes as concentration gradients and electrochemical overpotentials decay. The voltage measured at the start of a subsequent charge therefore depends on how much relaxation occurred during the rest period.

This history-dependent behavior is commonly represented by an initial polarization-state term, (B_{P0-}).

Short rests preserve stronger history effects

During short rest periods—roughly 0 to 1 hour in the cited characterization context—polarization changes rapidly with additional rest time. Residual effects from the previous charge or discharge have not fully decayed, so repeated tests with different short rests can produce different initial polarization voltages.

The direction of the offset also depends on the preceding operation: a previously charging cell may be represented by (+B), a fully rested cell by approximately zero, and a previously discharging cell by (-B).

Longer rests improve repeatability

With extended rest—approximately 1 to 5 hours in the referenced observations—the voltage response approaches a more stable condition as relaxation progresses. This does not mean every cell is fully equilibrated after the same duration; relaxation time depends on chemistry, temperature, SOC, and cell construction.

For repeatable characterization, rest duration and preceding operating state must therefore be controlled and recorded.

Resting history is a form of hysteresis

Two cells with identical SOC and SOH can show different polarization voltages if one was previously charging and the other was previously discharging. The difference is not measurement noise; it is a state-history effect that a memoryless resistance model cannot represent adequately.

How the Four Effects Combine

A useful engineering interpretation

The extended expression can be read as four layers:

• (U_P(0)): the starting polarization state.
• (K_{SOC}): distortion caused by initial SOC.
• (K_I I): rate-dependent charging polarization.
• (B_{P0-}) and (B_{SOH}): offsets associated with prior history and aging.

The RC terms determine how polarization develops over time, while the distortion terms modify its amplitude and initial condition.

The interaction is more important than any single factor

Consider two tests at the same current. A fresh cell beginning near mid-range SOC after a long rest may show modest polarization, while an aged cell beginning near 90% SOC after a short prior charge may show a much larger response.

This is why a single “internal resistance” value is insufficient for fast-charging characterization. The measured voltage response is conditional on time, SOC, current, history, and SOH.

Time-domain measurements separate the mechanisms

A useful resting-identification method is to interrupt constant-current charging and observe the immediate voltage change and subsequent relaxation curve. The instantaneous drop and time-dependent recovery help distinguish faster resistance-like effects from slower polarization processes.

A practical full-rest criterion may be defined by a sufficiently low recovery rate, such as less than 10 mV per 180 seconds in the cited method. The threshold is a test-protocol choice and should be applied consistently rather than assumed to be universal.

Understanding the Trade-offs

Fast charging versus polarization control

Higher current reduces charging time but increases polarization and associated heat generation. The benefit is greatest where charge acceptance is high, generally in the middle SOC range.

Reducing current near low and high SOC can limit excessive polarization, but it lengthens the charging process.

Model complexity versus test effort

A simple RC model is easier to identify and implement. It can be adequate over a narrow SOC, temperature, SOH, and current range.

A distortion-aware model is more demanding because it requires testing across multiple rates, SOC starting points, rest durations, and aging states. It is justified when the model must support fast charging, lifetime prediction, or high-accuracy diagnostics.

Repeatability versus realistic operation

Long, standardized rests improve comparability between tests. However, they may not represent real-world charging, where cells often begin charging after irregular driving, regeneration, or partial rests.

A robust characterization program should use both controlled-rest tests for parameter identification and realistic-history tests for validation.

Avoiding false attribution

A higher polarization voltage should not automatically be attributed to SOH degradation. Temperature, initial SOC, current rate, and incomplete relaxation can produce similar changes.

SOH comparisons are meaningful only when these other conditions are controlled or explicitly included in the model.

Making the Right Choice for Your Goal

Use the model and test protocol according to the decision you need to make:

• If your primary focus is fresh-cell parameter identification: Control initial SOC, current rate, temperature, and rest history tightly before fitting the RC parameters.
• If your primary focus is fast-charging control: Use lower current near low and high SOC, and allow higher current mainly in the mid-SOC region where polarization is typically lower.
• If your primary focus is lifetime prediction: Re-identify or update polarization parameters as SOH declines instead of applying fresh-cell parameters across the entire life cycle.
• If your primary focus is repeatable impedance or polarization testing: Standardize the preceding charge/discharge operation and rest duration, and verify relaxation before each measurement.
• If your primary focus is real-world behavior: Include SOC, rate, rest history, and SOH as coupled inputs rather than validating the model at only one nominal condition.

Reliable lithium-ion characterization comes from treating polarization voltage as a dynamic, history-dependent state—not as a fixed resistance multiplied by current.

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