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REVIEW 3 major objections 5 minor 56 references

An Improved Approach to Estimate the Internal Resistance of a Battery During the HPPC Test

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Standard HPPC internal-resistance estimates are biased upward by the voltage shift caused by the pulse itself, and a least-squares OCV correction removes most of that bias.

desk verdict Solid, honest extension that fixes a real bias in HPPC resistance estimation, but the real-cell claims need an independent reference before they are taken as established. read the letter →

arxiv 2505.06410 v2 pith:4BRTCLYN submitted 2025-05-09 eess.SP

Prarthana Pillai , Smeet Desai , Krishna R. Pattipati , Balakumar Balasingam This is my paper · ORCID
classification eess.SP
keywords batteryinternalresistanceHPPCtestopen-circuitvoltageleast-squaresestimationstateofchargeequivalentcircuitmodellithium-ion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Standard HPPC internal-resistance measurement divides the voltage change by the discharge current, silently treating the battery's open-circuit voltage as frozen. The paper shows that for a 30-second, high-current pulse the OCV actually drops, so the quotient overstates resistance. It proposes a constrained least-squares observation model that fits terminal voltage as a linear function of current and cumulative ampere-seconds, yielding an estimate of the OCV drop with no need for SOC, capacity, or chemistry information. With that correction, simulated worst-case resistance error falls from 291.7% to 49.3% at low SOC and from over 100% to under 2% at full SOC; on four cylindrical cells the corrected estimates are up to 20 mΩ lower. The method's accuracy degrades where the OCV-SOC curve is strongly curved, between about 10% and 30% SOC.

What carries the argument

The load-bearing object is the linear observation model z = Hx + n (Eq. 30), whose columns are the constant discharge current, a constant '1', and the cumulative coulombs C{a(tx,t0)} drawn up to each sample. It collapses the OCV-SOC relationship into a single scalar κ under the assumption that the OCV-SOC slope is constant across the pulse, so the initial OCV E(s(t0)), resistance R0, and κ can be recovered together by nonnegative least squares. The corrected resistance (Eq. 36) subtracts the estimated OCV drift ΔÊ = κ̂LS C{a(t1,t0)} from the measured voltage drop before dividing by current.

What would settle it

Run the same HPPC pulse at SOC 0.15 and compare the corrected estimate (simulation predicts 7.47 mΩ at 22.5 A) against an EIS measurement or a 1 ms pulse resistance; if the true resistance is near 5 mΩ, the constant-slope assumption is the cause. More directly, split the 30 s pulse into early and late halves, fit κ separately to each, and check whether the two values differ by more than the estimation uncertainty — if they do, the model is misspecified in exactly the band the paper flags.

Watch

Extended reading notes

Core claim

The central claim is that the conventional HPPC resistance estimator, R0 = |Δv/Idis|, is biased upward by exactly ΔE/Idis, where ΔE is the open-circuit voltage change caused by the pulse, and that ΔE can be estimated from the same pulse data. The paper constructs a vector observation model in which each sampled terminal voltage during the pulse is expressed as Idis R0 + E(s(t0)) + κ times the cumulative coulombs drawn, with κ the ratio of OCV-SOC slope to capacity. Solving the nonnegative least-squares problem gives R0, the initial OCV, and κ simultaneously; the corrected resistance is (Δv - ΔÊ)/Idis. In controlled simulation with true R0 = 5 mΩ, the standard estimate ranged from 7.0 to 19.6 mΩ depending on SOC, while the corrected estimate stayed near 5 mΩ except at SOC 0.15 where it reached 7.47 mΩ.

Load-bearing premise

The method assumes the slope of the OCV-versus-SOC curve is constant across each 30-second pulse; when the curve bends sharply, as between roughly 10% and 30% SOC, the fitted κ is a biased average and the corrected resistance remains overestimated.

Editorial extensions

If this is right

  • Battery management systems that run HPPC-style pulses can reduce resistance bias without adding sensors or prior knowledge of SOC or capacity.
  • Reported internal resistance values from standard HPPC tests, and the state-of-power and state-of-health conclusions built on them, are systematically high, especially under high current and low SOC.
  • The correction makes resistance estimates nearly independent of the pulse's SOC operating point, except in the 10-30% SOC band where OCV curvature remains.
  • Because the method needs only voltage, current, and time samples from the existing pulse, it can be retrofitted to past HPPC datasets.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Extending the model from one scalar κ to a piecewise-linear or quadratic OCV segment would likely close the residual 49% error at SOC 0.15; the data already collected contain the necessary samples.
  • The same bias argument applies to shorter or longer pulses: the correction term scales with pulse duration, so any standardized pulse with non-negligible coulomb throughput is affected.
  • A direct field test would be to compare corrected HPPC resistance against electrochemical impedance spectroscopy at the same SOC; the paper's claim implies the two should agree much more closely than uncorrected HPPC does.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper addresses internal resistance estimation in HPPC tests. The authors show that the conventional calculation R0 = |Δv/Idis| overestimates the true ohmic resistance because it neglects the open-circuit voltage change ΔE during the pulse. They propose a least-squares observation model (Eq. 30) that simultaneously estimates R0, the initial OCV, and an effective OCV slope κ from the sampled terminal voltage during the discharge pulse, assuming a constant OCV-SOC gradient. The corrected estimate is R0 = (Δv − κ̂C)/Idis. Simulation with a known 5 mΩ resistance shows the proposed method reduces estimation error from up to 291.7% to at most 49.3% across SOC, and the method is applied to four Molicel INR-21700-P42A cells, where it reduces the HPPC resistance estimates by 5–20 mΩ.

Significance. The paper's core derivation is sound, and the simulation benchmark against a known ground-truth resistance is a strength; it clearly demonstrates that the conventional HPPC resistance is inflated by the OCV drop, and the proposed correction is attractive because it requires no additional battery information such as SOC, capacity, or OCV parameters. If the accuracy on real cells were established, the method would be a low-cost improvement for BMS resistance estimation. However, the claimed accuracy is not yet established: the constant-gradient assumption fails substantially at low SOC, and the real-cell experiments lack an independent resistance reference, so the central quantitative claim is only partly supported.

major comments (3)
  1. [Section IV, Eqs. (26)–(29), and Table II] The central assumption of a constant OCV-SOC gradient over the pulse is load-bearing and it breaks down at low SOC. The authors' own Table II shows the proposed estimate has 49.31% error at SOC 0.15, versus 0.39% at SOC 0.5, and the conclusion acknowledges that the gradient changes significantly between 10% and 30% SOC. Since the paper claims accurate resistance estimation, this SOC dependence should be quantified and the valid operating range of the method should be stated; otherwise the reported 49.3% error is not an accuracy guarantee but a bound that is too large for many BMS applications.
  2. [Section VI, Fig. 11 and Table III] The real-cell results are not validated against any independent resistance reference. The proposed estimates are compared only to the biased HPPC ratio of Eq. (4), so the reported reduction of 5–20 mΩ cannot be distinguished from a systematic downward shift. The manufacturer datasheet quoted in Table III lists an internal resistance of 16 mΩ, but no comparison is made to this value. An independent measurement, such as EIS at a comparable frequency, a short sub-second pulse, or a manufacturer reference, is needed to establish that the corrected values are closer to the true resistance.
  3. [Section V, Remark 3, and Eqs. (23)–(30)] The observation model assumes an R-int circuit with no RC polarization. Over a 30 s HPPC pulse, real cells exhibit an exponential polarization transient; this unmodeled term will be absorbed by the κ regressor and the intercept, biasing the estimated R0. The simulation in Section V uses only R-int data, so the magnitude of this bias is not quantified. The authors should test the estimator on data with realistic RC dynamics, or restrict the method to timescales where the R-int model is a better approximation and provide evidence for that restriction.
minor comments (5)
  1. [Section IV, Eq. (32)] The optimization in Eq. (32) is written as an arg max of the squared residual norm, which is unbounded; it should be arg min to match the least-squares objective and the use of 'lsqnonneg'.
  2. [Section V.C] The 'gain' metric is defined as the difference between two percentage errors (e.g., 291.67 − 49.31 = 242.36 percentage points), but the abstract phrases this as a 'performance gain in the range of 30% to more than 250% in percentage estimation error', which is ambiguous and should be restated as a reduction in percentage-point error.
  3. [Section II.B, Algorithm 1] The initiation procedure states that the battery is discharged to Vmin, rested, charged to Vmax, and rested again, but the rest times are not consistently specified; clarifying that the first rest is one hour and the post-charge rest is one hour would improve reproducibility.
  4. [Section V, Fig. 5] Figures 5(b)–(d) show both terminal voltage and OCV, but the captions do not clearly identify which curve corresponds to E(s(k)) and which to v(k); adding labels to the figure or caption would remove ambiguity.
  5. [Section IV and Reference [52]] The observation model is attributed to the authors' own under-review paper [52]; although the model is written out in full here, citing a version with a preprint identifier or a self-contained derivation would help readers verify the provenance.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the proposed R0 and kappa are jointly estimated from measured voltage, with the simulation benchmarked against a known ground truth.

full rationale

The derivation chain is self-contained. The claimed overestimation of the standard HPPC resistance estimate follows algebraically from the R-int model in Eqs. (7)–(13): the measured voltage difference includes both the ohmic drop and the OCV change, so ignoring the OCV change inflates the resistance estimate. The proposed observation model in Eq. (30) regresses measured terminal voltage on regressors [I, 1, C] to jointly estimate R0, E(s(t0)), and kappa; these parameters are separately identifiable from the data because the regressor columns are distinct, so R0 is not forced to equal any fitted ratio by construction. The simulation section provides an external ground truth: the simulator is configured with a known true R0 = 5 mΩ, and the proposed estimator recovers values close to that truth (e.g., 5.0784 mΩ at full SOC), so the claimed performance gain is a genuine quantitative comparison against a known reference, not a renaming of inputs. The constant-gradient assumption in Eq. (26) is explicit and its violation at low SOC is acknowledged in the conclusion as a limitation; this is a modeling approximation, not a circular step. The self-citations to [52] and [45] supply context and an observation-model reference, but the model is fully written and derived in this paper, so those citations are not load-bearing. The real-cell results lack an independent resistance reference, but that is a validation gap rather than circularity: the paper does not claim to have independently verified the absolute accuracy of the corrected real-cell values, only that they are lower than the HPPC estimates. Overall, no step in the derivation reduces by definition or by fitted-parameter renaming to its own input.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The method introduces no new physical entities. Its load-bearing axioms are the R-int model without polarization, the local constancy of the OCV slope, and equilibrium at pulse start. The only fitted quantity is kappa, which is an output of the least-squares estimator rather than a hand-chosen free parameter, but the simulation truth curve is an external input that shapes the reported gains.

free parameters (1)
  • Combined+3 OCV model coefficients u0..u7 = u0=-9.082, u1=103.087, u2=-18.185, u3=2.062, u4=-0.102, u5=-76.604, u6=141.199, u7=-1.117
    These coefficients set the simulated truth OCV curve in Section V and therefore determine the reported error percentages; they are taken from [53], not fitted in this paper, but the performance gain numbers depend on this specific curve.
assumptions (5)
  • domain assumption Battery terminal voltage follows the R-int model v(k)=E(s(k))+i(k)R0 with no RC/polarization dynamics over the pulse.
    Used in Section III Eq. 6 and in the proposed observation model; Remark 3 acknowledges only Ohmic resistance in simulation, and real-cell interpretation inherits this assumption without validation.
  • ad hoc to paper The OCV-SOC gradient f'_em(s) is constant during the pulse.
    Stated in Eq. 26 and used to collapse kappa(tx,t0) to a single scalar in Eqs. 27-29; the paper's conclusion admits this fails between 10% and 30% SOC.
  • domain assumption The terminal voltage at t0 equals the OCV E(s(t0)), i.e., the cell is at rest equilibrium before the pulse.
    Used in Eq. 20; in HPPC a rest period precedes the pulse, but residual relaxation may remain.
  • standard math Charge removed is computed by rectangular (constant-current) integration with known Idis and sampling time Ts.
    Eq. 16; valid for constant current pulses in the HPPC profile.
  • domain assumption The OCV-SOC curve is monotonically non-decreasing and all unknowns are nonnegative.
    Remark 2 and constraint Eq. 33; used to justify the nonnegative least squares solver.

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Pith. "Pith review of An Improved Approach to Estimate the Internal Resistance of a Battery During the HPPC Test." pith.science (2026). https://pith.science/paper/4BRTCLYN

@misc{pith2026250506410,
  author       = {Pith},
  title        = {Pith review of: An Improved Approach to Estimate the Internal Resistance of a Battery During the HPPC Test},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4BRTCLYN}},
  note         = {Machine review of arXiv:2505.06410}
}
read the original abstract

This paper considers the problem of resistance estimation in electronic systems including battery management systems (BMS) and battery chargers. In typical applications, the battery resistance is obtained through an approximate method computed as the ratio of the voltage difference to the applied current excitation pulse or vice versa for admittance. When estimating the battery resistance, this approach ignores the change in the open circuit voltage (OCV) as a result of the excitation signal. In this paper, we formally demonstrate and quantify the effect of the OCV drop on the errors in internal resistance estimation. Then, we propose a novel method to accurately estimate the internal resistance by accounting for the change in OCV caused by the applied current excitation signal. The proposed approach is based on a novel observation model that allows one to estimate the effect of OCV without requiring any additional information, such as the state of charge (SOC), parameters of the OCV-SOC curve, and the battery capacity. As such, the proposed approach is independent of the battery chemistry, size, age, and the ambient temperature. A performance analysis of the proposed approach using the battery simulator shows significant performance gain in the range of 30% to more than 250% in percentage estimation error. Then, the proposed approach is applied for resistance estimation during the hybrid pulse power characterization (HPPC) of cylindrical Li-ion battery cells. Results from tested batteries show that the proposed approach reduced the overestimated internal resistance of the batteries by up to 20 m{\Omega}.

Figures

Figures reproduced from arXiv: 2505.06410 by the authors.

Figure 2
Figure 2. Current profile for HPPC pulse and discharge to next [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Standard HPPC pulse [46]. Each pulse consists of three regions: (i) Discharge Pulse. This pulse is the first region between time instances t0 and t1 where a discharge current Idis is applied for 30 seconds. The magnitude of Idis is decided based on the low-current or high-current HPPC test to be performed. (ii) Rest period. The battery is rested for 40 seconds between times t1 and t2. (iii) Charge (Regenerative) Pul… view at source ↗
Figure 3
Figure 3. Full HPPC test current profile [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: R-int equivalent circuit model of a battery. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 6
Figure 6. Figure 6: Error in resistance computed using the existing ap [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 8
Figure 8. Figure 8: Existing (HPPC) and proposed approaches’ resistance [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 9
Figure 9. Figure 9: Molicel INR-21700-P42A batteries. TABLE III: Molicel INR-21700-P42A battery specifications. Specification Battery Nominal voltage 3.6V Minimum capacity, C 4.2 Ah Discharge current 45A Height 70.2 mm Diameter 21.7 mm Weight 70g Internal resistance 16 mΩ Maximum voltage,…
Figure 10
Figure 10. Figure 10: HPPC test current and voltage data from Molicel INR [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 11
Figure 11. Figure 11: Resistance values computed for the previous(HPPC) [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.