Cited by 160Battery Modeling and ManagementAdvancements in Battery MaterialsPower Systems and Renewable Energy

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A Practical Lithium-Ion Battery Model for State of Energy and Voltage Responses Prediction Incorporating Temperature and Ageing Effects

Open access

Li, Kaiyuan, Wei, Feng, Tseng, King Jet, Soong, Boon-Hee·2018·IEEE Transactions on Industrial Electronics

DOI 10.1109/tie.2017.2779411

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Abstract

The state of energy (SOE) is a key indicator for the energy optimization and management of lithium-ion (Li-ion) battery-based energy storage systems in smart grid applications. To improve the SOE estimation accuracy, a Li-ion battery model is presented in this study against dynamic loads and battery ageing effects. First, an electrical battery model is combined with an analytical model in order to take advantages of both models for accurate prediction of battery terminal voltage characteristics, SOE, and remnant runtime. Second, a novel method to separate the fast and slow dynamics of the electrical battery model is developed, and its superior performance is presented. Third, the effects of the battery initial SOC, load current rate and direction, operating temperature, and ageing level are systematically scrutinized and involved in the proposed model for robust SOE and terminal voltage prediction. Commercial Li-ion batteries are then tested under dynamic loads and at an arbitrary battery ageing level to validate the effectiveness and robustness of the proposed model. The laboratory-scale experimental test results show superb accuracy and reliability of the proposed battery model for estimating battery SOE and terminal voltage under dynamic loads and battery ageing conditions.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes a hybrid Li-ion battery model combining a 2nd-order RC electrical model with an analytical SOE/runtime model, incorporating temperature, load, initial SOC, and ageing effects. Validation on commercial LTO cells shows low voltage and SOE errors under dynamic loads and arbitrary ageing, though some high-current SOE error remains.

Key findings

Voltage prediction: for an aged cell at 18.7 Ah (93.5% SOH), maximum discrepancy occurred at 0–10% SOC with MAPE 0.17% and RMSPE 0.23%; over 95–10% SOC, MPE was about 0.09% and RMSPE within 0.15%. Under a dynamic smart-grid current profile from 50% initial SOC for 30 h, MAPE was less than 2% and RMSPE 1.2%.
SOE prediction: at 0.33 C constant current with dynamic temperature, MAPE was 2%, RMSPE 1.1%, and runtime error within 1%. Under pulse load with initial SOE 80%, MAPE was 3.2% and RMSPE 2.1%. Under a 5 h dynamic smart-grid profile with initial SOE 58%, the proposed model had MAPE 9.2% and RMSPE 4.7%, versus 26% and 10.9% for the prior model in [35].
MAE and RAE varied with operating conditions: at 5 °C, MAE dropped from 41.26 Wh to 38.12 Wh when current changed from 0.33 C to 3.0 C; at 0.33 C and 25 °C, MAE was 46.59 Wh for a fresh cell and 44.78 Wh, 42.1 Wh, and 37.9 Wh for aged cells. The RAE ratio at 40% versus 100% initial SOC decreased from 38.8% at 0.33 C to 33.4% at 5.0 C.
Internal resistance \(R_i\) was nearly constant at about 10 mΩ within 10–90% SOC, with abrupt increases near 0% and 100% SOC; it depended on SOC, temperature, and SOH, but was almost independent of current rate, direction, and switch on/off phases.

Methods

The model combines a 2nd-order RC Thevenin ECM—OCV, ohmic resistance \(R_i\), fast \(R_fC_f\), slow \(R_sC_s\), and a relaxation offset \(U_{\text{offset}}\)—with an analytical SOE/runtime model using \(SOE = E_{RAE|I,T,SOC,SOH} / E_{MAE|I,T,SOH} \times 100\%\), coupled by online SOC.
Commercial LTO cells were tested: nominal 20.0 Ah, 2.3 V; temperatures 5, 15, 25, 35, and 45 °C; SOHs 100%, 95%, 90%, and 85% corresponding to 20.0, 19.1, 18.1, and 17.0 Ah. MAE/RAE look-up tables used currents from 0.33 C to 5.0 C and initial SOCs from 5% to 95%; pulse tests used 3.0 C PC/PD pulses, with validation on a fresh cell and aged cells including an arbitrary 18.7 Ah cell (93.5% SOH).
Parameter extraction used pulse/relaxation data, derivative-based separation of fast, slow, and offset voltage components, and offline multidimensional look-up tables; validation compared simulated versus measured voltage and estimated SOE against brute-force actual SOE obtained via the power-integral method.

Limitations

The paper states that irreversible and reversible energy loss were not discussed; only RAE and MAE under a designated load condition were considered, with future work needed on energy loss and recovery rate including idle time. It also assumes SOH and initial SOC are already known, ignores calendar ageing because it had negligible effects in their tests, and ignores hysteresis and self-discharge due to ≤2 mV hysteresis and regular cycling.
The paper states there is no direct online SOE determination method; actual SOE was obtained by a time-consuming brute-force procedure, which limits practical online validation.
Evident from the text: validation used only commercial LTO cells, so generality to other Li-ion chemistries is not demonstrated; the dynamic smart-grid profile showed a relatively high SOE MAPE of 9.2% under currents up to 3.0 C, even though RMSPE was 4.7%.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1109/tie.2017.2779411

Cites

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Claims the paper makes

0 of 40 cited sources checked · 0 supported · 0 flagged

A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The laboratory-scale experimental test results show superb accuracy and reliability of the proposed battery model for estimating battery SOE and terminal voltage under dynamic loads and battery ageing conditions.”
- Also stated in: § I. INTRODUCTION · plain
  “a comprehensive hybrid Li-ion battery model is advocated in this paper, which is capable of pred icting the online battery SOE as well as the voltage characteristics accurately under various operating loads and battery ageing conditions.”
Load-bearingStrength:boosted· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- The authors state this as an assumption: The SOH and initial SOC of the battery were already known.
In the paper
“Moreover, according to our experimental results and that in [38], the extent of the cell degradation in capacity was not correlated with the ageing or cycling conditions.”
What the sources say
- Not checked yetcites [38] source
Load-bearingStrength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes

Show all 40 claims

It may state two separate claims as one. 41
Probably not a substantial claim. 13

In the paper
“Nevertheless, based on our test results published elsewhere and in [37], the calendar-ageing caused negligib le effects on the battery performance, thus only the cycling-ageing effects were considered in this study.”
What the sources say
- Not checked yetcites [37]
Load-bearingStrength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
In the paper
“Fro m 1.5-5 h when the cell was discharged at current rate of as large as 3.0 C, the estimated SOE fro m the model in [35] deviated seriously fro m the actual one, while the SOE estimat ion of the proposed model was much closer to the actual one.”
What the sources say
- Not checked yetcites [35] source
Load-bearingStrength:plain· not yet calibratedCausal:correlational· not yet calibratedSingle case
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
In the paper
“Specifically, the MAPE and RMSPE of the proposed model were 9.2% and 4.7%, wh ile those of the model in [35] were 26% and 10.9%, respectively.”
What the sources say
- Not checked yetcites [35] source
Load-bearingStrength:plain· not yet calibratedSingle case
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
In the paper
“According to Fig. 26, fro m 0-1.5 h when the load current was moderate (within ±1.0 C), both the SOE estimation could achieve acceptable results, and our proposed model performed slightly better than the model in [35].”
What the sources say
- Not checked yetcites [35] source
Load-bearingStrength:plain· not yet calibratedCausal:correlational· not yet calibratedSingle case
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“A mong all the energy storage techniques, Li-ion based rechargeable batteries are deemed to be the most promising solution, due to their outperformed perfo rmance such as high gravimetric and volumetric energy density, great cycle life, enhanced safety and low self-discharge rate [1][2][3].”
What the sources say
- Not checked yetcites [1] source
- Not checked yetcites [2] source
- Not checked yetcites [3] source
Strength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passes
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“SOE was introduced in 2010 to directly delineate the energy state of batteries [12,13]”
What the sources say
- Not checked yetcites [12] source
- Not checked yetcites [13] source
Strength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passes
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“However, since SOC represents the capacity state instead of the energy state, it is no longer sufficient to describe the battery behavior in the ESS applications where the residual energy rather than the residual capacity of batteries is essential [4].”
What the sources say
- Not checked yetcites [4] source
Load-bearingStrength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“In [4,14], neural networks were used to predict the battery SOE variation, but the estimat ion exactness highly depended on the training data provided and the systematic co mplexity needed to be decreased to reduce the hardware costs.”
What the sources say
- Not checked yetcites [4] source
- Not checked yetcites [14] source
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
Probably not a substantial claim. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“These online estimators achieved acceptable results, but the intricate filtering algorith m produced heavy computational burdens for the micro-processors in the BMSs, wh ich were always with limited co mputational capability.”
What the sources say
- Not checked yetcites [18] source
- Not checked yetcites [19] source
- Not checked yetcites [20] source
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Additionally, due to the intrinsical peculiarities of ECMs, there is some deficiency in capturing the non -linear battery behaviors induced by the load variations and will undermine the SOE estimation accuracy if ECMs work alone under strenuous loads.”
What the sources say
- Not checked yetcites [30] source
- Not checked yetcites [31] source
- Not checked yetcites [32] source
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Last but not least, unfortunately, all of the above-mentioned research works only focused on the estimat ion of SOE but did not involve the prediction of the voltage responses of batteries: in the online SOE estimators [15][16][17][18][19][20][21], the voltage responses were taken as input factors.”
What the sources say
- Not checked yetcites [15] source
- Not checked yetcites [16] source
- Not checked yetcites [17]
Load-bearingStrength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.
In the paper
“Additionally, Lin et al. [22] proposed a mu lti-model-p robability-based approach to jointly estimate the battery SOE.Be that it might be, the weights of each model were kept the same under dynamic loads for simplicity, resulting in that the SOE estimation results achieved little improvement.”
What the sources say
- Not checked yetcites [22] source
Strength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes
It may state two separate claims as one.
In the paper
“In supplement, due to the fact that there was still some voltage variation after 1 hour's rest in the idle period, the interval of the rest time between current pulses was advocated to be 2 hours, instead of the short idle t ime of 5 -60 minutes.”
What the sources say
- Not checked yetcites [28] source
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
Probably not a substantial claim. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“However, the SOE estimat ion accuracy of these algorithms were totally dependent on the estimated SOC results, and the estimated SOE results were merely verified at load current of no mo re than 1.0 C.”
What the sources say
- Not checked yetcites [15] source
- Not checked yetcites [16] source
- Not checked yetcites [17]
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
It may state two separate claims as one.

47 of 47

The paper relies on this without support.
There existed only a few literatures on SOE estimation compared to SOC estimation.
“Co mpared to the SOC estimation, there existed only a few literatures on SOE estimation.”
The paper relies on this without support.
To date there is no unified determining equations for SOE.
“Firstly, to date there is no unified determin ing equations for SOE.”
The paper relies on this without support.
Most studies failed to obtain desirable SOE estimation against varying loads, ambient temperature and battery ageing conditions.
“What's worse, most studies failed to obtain desirable SOE estimation against varying loads, ambient temperature and battery ageing conditions.”
The authors state this as an assumption.
The SOH and initial SOC of the battery were already known.
“Herein we assumed that the SOH and initial SOC were already known.”
The authors state this as an assumption.
The expressions in (14) and (15) were also applicable at tpe when the load current just started to fall.
“Since t pe was only 1.0 s before the t ime of t 0 , we could assume that the expression in ( 14) and (15) were also applicable at t pe when the load current just started to fall.”
The authors state this as an assumption.
The fast and slow dynamics were both modeled as RC combinations.
“Because the fast and slow dynamics were both modeled as RC combinations, the following expressions could be stated:”
The paper relies on this without support.
All model parameters are multi-variable functions of SOC, current direction and rate, ambient temperature, self-discharge rate, hysteresis effects, and ageing levels of the batteries.
“Theoretically, all of the model parameters are mu lti-variab le functions of SOC, current direction and rate, amb ient temperature, self-d ischarge rate, hysteresis effects, and ageing levels of the batteries.”
The paper relies on this without support.
Electrical circuit models are among the most suitable candidates for battery parameters and terminal voltage prediction.
“Being the most intuitive and facile to handle, electrical circuit models (ECMs) have been pervasively used in circuit simu lators and alongside applications, and they are among the most suitable candidates for battery parameters and terminal voltage prediction.”
The paper relies on this without support.
Self-discharge can be ignored without noticeable effects on model accuracy.
“The batteries used in this study had hysteresis of no mo re than 2 mV [31][32][33] and were cycled regularly, thus hysteresis and self-discharge were ignored without any noticeable effects on model accuracy.”
The paper relies on this without support.
In smart grid applications, Li-ion batteries would scarcely be operated below 10% SOC.
“In the smart grid applications, Li -ion batteries would scarcely be operated below 10% SOC, thus the voltage disparities in this region was of trivial significance.”
The paper relies on this without support.
MAE is irrespective of the online SOC of the cell.
“In supplement, the MAE of the cell was extracted by interpolating the MAE look-up tables in the proposed model according to the online load current rate, temperature and SOH, since MAE was irrespective of the online SOC of the cell.”

11 of 11

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

Conclusion understates the reported SOE error
Major
The conclusion says the SOE error was no more than 4.7%, but the validation section reports a 9.2% maximum absolute percentage error for the proposed model. The 4.7% figure is its RMS percentage error, not an upper bound on the error.
Incorrect 1.0 C RAE ratio in Table II
Minor
At 1.0 C, the listed RAE values are 17.2 and 45.5. Their ratio is 37.8%, not the reported 38.8%.
Reported 38.8 · recomputed 37.802198
Reported maximum voltage error is below the RMS error
Minor
A maximum absolute percentage error cannot be smaller than the root mean square percentage error calculated from the same voltage errors. The reported maximum is 0.17%, while the RMS value is 0.23%.

3 of 3

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Authors: Li, K., Wei, F., Tseng, K. J., & Soong, B.-H.
Affiliations: Nanyang Technological University (SG)
Singapore Institute of Technology (SG)
ORCID: Li, Kaiyuan
Wei, Feng
Tseng, King Jet
Soong, Boon-Hee
Venue: IEEE Transactions on Industrial Electronics
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Published: 2018-08
Volume: 65
Issue: 8
Pages: 6696-6708
ISSN: 0278-0046 (ISSN-L)
1557-9948
DOI: 10.1109/tie.2017.2779411
OpenAlex: W2774519208
Semantic Scholar: d2b4ab26d4b1c2f16d7e7b4c51fef51a31090215
Cited by: 160
References: 39
Citations by year: 2026: 6 · 2025: 19 · 2024: 26 · 2023: 17 · 2022: 25 · 2021: 30 · 2020: 21 · 2019: 12 · 2018: 4
FWCI: 6.41
Type: journal article
Language: en
Open access: green
hdl.handle.net
Licence: ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)
Locations: IEEE Transactions on Industrial Electronics (publishedVersion)
DR-NTU (Nanyang Technological University) (submittedVersion)
Funders: National Research Foundation
National Research Foundation Singapore
Topics: Physical Sciences › Engineering › Automotive Engineering › Battery Modeling and Management
Physical Sciences › Engineering › Electrical and Electronic Engineering › Advancements in Battery Materials
Physical Sciences › Energy › Energy Engineering and Power Technology › Power Systems and Renewable Energy
Keywords: state of energy estimation, terminal voltage prediction, battery degradation, operating temperature effects, dynamic loading, battery energy storage, smart grid

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A Practical Lithium-Ion Battery Model for State of Energy and Voltage Responses Prediction Incorporating Temperature and Ageing Effects

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