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

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When 0.33 C and 25 oC were chosen, MAE was 46.59 Wh for fresh cell, and 44.78 Wh, 42.1 Wh and 37.9 Wh for each aged cell, respectively.

“Fig. 10(b) showed the MAE trajectory with SOH: when 0.33 C and 25 ºC were chosen, MAE was 46.59 Wh for fresh cell, and 44.78 Wh, 42.1 Wh and 37.9 Wh fo r each aged cell, respectively.”

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Calendar-ageing caused negligible effects on battery performance, so only cycling-ageing effects were considered in this study.

“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.”

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From 1.5-5 h when the cell was discharged at current rate as large as 3.0 C, the estimated SOE from the model in [35] deviated seriously from the actual one, while the SOE estimation of the proposed model was much closer to the actual one.

“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.”

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Experimental results validated the efficacy of the proposed model with voltage prediction error less than 2%, SOE error no more than 4.7%, and runtime error within 1% under dynamic load conditions at an arbitrary ageing level.

“The experimental results validated the efficacy of the proposed model with voltage prediction error less than 2%, SOE error no more than 4.7%, and runtime error within 1% under dynamic load conditions at an arbitrary ageing”

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Under a highly dynamic current profile from 50% initial SOC for 30 hours, simulated voltage results superimposed very well with measurements, with MAPE less than 2% (found at the 8.5th hour when online SOC was approximately 12%) and RMSPE of 1.2%.

“It could be observed from Fig. 22 that the simulated voltage results superimposed very well with the measurements, with the MAPE (found at the 8.5 th hour when the online SOC was approximately 12%) less than 2% and the RMSPE of 1.2%.”

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R_f and R_s values dropped with increasing current rate, and R_f was slightly larger than R_s.

“Meanwhile, R f and R s values dropped with increasing current rate, and the values of R f was slightly larger than that of R s .”

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For discharge regimes, battery voltage drop was more prominent at low SOCs when the cell was almost depleted due to build-up of concentration gradient, and R_f and R_s became very large due to slow mass transport and diffusion limitations.

“For the discharge regimes, the battery voltage drop was more p ro minent at low SOCs when the cell was almost depleted due to the build-up of concentration gradient, and R f and R s became very large due to the slow mass transport and diffusion limitations.”

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A downward trend with temperature of R_f and R_s values was observed, while C_f and C_s generally increased with rising temperature, more obvious for C_f than C_s.

“A downward trend with temperature of R f and R s values could be observed, while C f and C s generally increased with the rising temperature, and it was more obvious for the values of C f than that of C s .”

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SOE estimation at 0.33 C constant current load and temperature profile in Fig. 19 had MAPE 2% and RMSPE 1.1%, and runtime error within 1%, revealing the proposed model performed very well under constant load and dynamic temperature conditions.

“The MAPE and RMSPE o f the estimation results were 2% and 1.1%, and the runtime error was within 1%, revealing that the proposed model performed very well under constant load and dynamic temperature conditions.”

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The MAPE and RMSPE of the proposed model were 9.2% and 4.7%, while those of the model in [35] were 26% and 10.9%.

“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.”

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U_i was present during both charge and discharge events and was almost constant because R_i varied minimally with SOC and current rate variations.

“U i was present during both the charge and discharge events and it was almost constant because R i varied minimally with SOC and current rate variations.”

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Under the pulse current load profile of Fig. 18 and temperature profile in Fig. 19, during the 1-hour test, good superimposition of estimated SOE with actual was observed, and MAPE and RMSPE were 3.2% and 2.1%.

“During the 1-hour test, good superimposition of the estimated SOE with the actual one could be observed, and the MAPE and RM SPE were 3.2% and 2.1%, respectively.”

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A close agreement between simulated and measured voltage curves was observed, with maximum discrepancy at the end of discharge when the cell was nearly depleted (0-10% SOC), where MAPE was 0.17% and RMSPE was 0.23%.

“A close agreement between the two curves could be observed, and the maximu m discrepancy was found at the end of discharge when the cell was nearly depleted (0-10% SOC), where the maximu m absolute percentage error (MAPE) was 0.17% and the root mean square percentage error (RMSPE) was 0.23%.”

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In the SOC range from 95% to 10%, MPE was approximately 0.09% and RMSPE was confined within 0.15%.

“In the SOC range fro m 95% to 10%, MPE was appro ximately 0.09% and RMSPE was confined within 0.15%.”

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R_i values increased when the temperature was lower and battery ageing was more severe.

“Basically, R i values increased when the temperature was lower and battery ageing was more severe.”

Probably not a substantial claim: may not pass S3 (load-bearing).

U_s decayed more slowly in about 2600 s.

“U s decayed more slowly in about 2600 s.”

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From 0-1.5 h when load current was moderate (within ±1.0 C), both SOE estimations could achieve acceptable results, and the proposed model performed slightly better than the model in [35].

“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].”

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R_i values were almost irrespective of current rate and direction and switch on/off phases, but depended on SOC, temperature, as well as SOH.

“Conclusion could be derived that: R i values were almost irrespective of current rate and direct ion and switch on/off phases, but depended on SOC, T, as well as SOH.”

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U_offset (about 11 mV), modeled as a linear function, decayed much more slowly and vanished in about 1.7 hours.

“U offset (about 11 mV), which was modeled as a linear function in the proposed model, decayed much more slowly and vanished in about 1.7 hours.”

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As the battery aged progressively, R_f and R_s increased on the whole, and the dependence on SOC was more pronounced.

“As the battery aged progressively, R f and R s increased on the whole, and the dependence on SOC was mo re pronounced.”

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The parameters under charge and discharge regimes were not equal to each other and varied with different SOCs and load current rate.

“It could be seen that the parameters under charge and discharge regimes were not equal to each other and they varied with different SOCs and load current rate.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Li-ion rechargeable batteries are the most promising energy storage solution due to high gravimetric and volumetric energy density, great cycle life, enhanced safety and low self-discharge rate.

“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].”

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SOE was introduced in 2010 to directly delineate the energy state of batteries.

“SOE was introduced in 2010 to directly delineate the energy state of batteries [12,13]”

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SOC represents the capacity state rather than the energy state, so it is no longer sufficient to describe battery behavior in ESS applications where residual energy rather than residual capacity is essential.

“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].”

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Classified as probably not a substantial claim. May combine two claims.

Neural-network-based SOE prediction methods' estimation exactness highly depended on the training data provided, and their systematic complexity needed to be decreased to reduce hardware costs.

“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.”

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Online SOE estimators using filters achieved acceptable results, but their intricate filtering algorithms produced heavy computational burdens for BMS microprocessors with limited computational capability.

“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.”

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Due to intrinsic peculiarities of ECMs, there is deficiency in capturing non-linear battery behaviors induced by load variations, which will undermine SOE estimation accuracy if ECMs work alone under strenuous loads.

“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.”

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All above-mentioned research works only focused on SOE estimation and did not involve prediction of voltage responses of batteries; in online SOE estimators, voltage responses were taken as input factors.

“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.”

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The proposed method was capable of improving the model accuracy and offering a good trade-off between the model accuracy and computational burden.

“In conclusion, the proposed method was capable of improving the model accuracy and offering a good trade-off between the model accuracy and computational burden.”

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Battery SOH, ambient temperature, and load conditions all influence discharging performance, inducing quantitative change of RAE and MAE and further SOE.

“The battery SOH, amb ient temperature, and load conditions would all influence the discharging performance thus inducing quantitative change of RA E and MA E and further the SOE.”

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Introducing Uoffset increases model accuracy but keeps the additional increase of computational complexity to a minimal level.

“This would increase the model accuracy but keep the additional increase of the computational complexity to a minimal level.”

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The proposed generic modeling method is concise but useful since it allowed accurate online prediction of battery performance using data gleaned from laboratory-scale tests.

“This proposed generic modeling method was concise but useful since it allowed accurate online prediction of battery performance using data gleaned fro m the laboratoryscale tests.”

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Prolonged rest time guaranteed the battery to completely reach equilibrium, thus the entire transient voltage could be captured, and the accuracy was improved.

“This prolonged rest time guaranteed the battery to completely reach equilibriu m thus the entire transient voltage could be captured, and the accuracy was improved.”

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Lin et al.'s multi-model-probability-based SOE estimation kept the weights of each model the same under dynamic loads for simplicity, resulting in little improvement in SOE estimation.

“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.”

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Classified as probably not a substantial claim. May combine two claims.

The pulse test profile was optimized, and R_i values were calculated at a higher resolution from more SOCs in both charge and discharge directions and switch on/off phases.

“Thirdly, the pulse test profile was optimized, and R i values were calculated at a higher resolution fro m mo re SOCs in both charge and directions and switch on/off phases.”

Classified as probably not a substantial claim. May combine two claims.

The interval of rest time between current pulses should be 2 hours instead of the short idle time of 5-60 minutes because there was still some voltage variation after 1 hour's rest.

“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.”

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Classified as probably not a substantial claim.

This work advocates equations (16) and (17) for R_f and R_s through the V-I values at t_pe, when the pulse current just began to fall.

“In this work, we advocated ( 16) and ( 17) for R f and R s through the V-I values at t pe instead, when the pulse current just began to fall.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

The proposed approach had good generality and was highly versatile to simulate any cell materials without deep insights into the chemistry itself.

“This proposed approach had good generality and were highly versatile to simulate any cell materials without deep insights into the chemistry itself.”

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SOE estimation algorithms that extract the relationship between SOC and SOE had accuracy totally dependent on estimated SOC results, and their estimated SOE results were merely verified at load current no more than 1.0 C.

“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.”

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The proposed SOE determination approach took thorough consideration of all influencing factors on discharging performance and further online SOE.

“This proposed SOE determination approach took thorough consideration on all the influencing factors on the discharging performance and further the online SOE of batteries.”

Classified as probably not a substantial claim.

Following previous studies on online SOC and SOH co-evaluation, this work provides a holistic understanding on the discharging behavior, terminal voltage and online SOE variation of Li-ion batteries exploited as ESSs in smart grids.

“Follo wing our previous studies on the online SOC and SOH co-evaluation of Li-ion batteries, this work provides a holistic understanding on the discharging behavior, terminal voltage and online SOE variation of Li-ion batteries explo ited as ESSs in smart grids.”

Classified as probably not a substantial claim.

The actual SOE values were obtained through brute force according to the determining equation in (1).

“It was worth noting that SOE results obtained from any algorith ms had errors more or less; thus, in this work, the actual SOE values were obtained through brute force according to the determining equation in (1).”

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A novel method to extract the parameters of the electrical model is proposed and it is capable of identifying the parameters with outperformed fidelity and acceptable computational burden.

“In specific, the key contributions of this work are summarized as: (1) a novel method to ext ract the parameters of the electrical model is proposed and it is capable of identifying the parameters with outperformed fidelity and acceptable co mputational burden;”

Classified as probably not a substantial claim. May combine two claims.

The proposed model is based on Matlab/Simulink and computationally light, thus it has the potential to be implemented in the BMSs of the ESSs in the smart grids applications.

“Last but not least, the proposed model is based on Matlab/Simulink and computationally light, thus it has the potential to be implemented in the BMSs of the ESSs in the s mart g rids applications.”

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The proposed model achieved a significant improvement over the previous model for estimating SOE, and was capable of predicting the SOE and runtime of an arbitrary aged cell under dynamic load and temperature conditions with high fidelity and reliability.

“The test results denoted that the proposed model achieved a significant imp rovement over the previous model for estimating SOE, and it was capable of predict ing the SOE and runtime of an arbitrary aged cell under dynamic load and temperature conditions with h igh fidelity and reliability.”

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Test results on commercial Li-ion batteries validated the robustness and effectiveness of the proposed battery model against varying load, temperature and battery ageing influences, comparing to most models in the literature that were only verified on fresh cells under moderate loads and from fully charged states.

“(3) test results on commercial Li-ion batteries validated the robustness and effectiveness of the proposed battery model against varying load, temperature and battery ageing influences, comparing to that most models in the literature were only verified on fresh cells under moderate loads and from fully charged states.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The brute-force method for obtaining actual SOE was a little bit time-consuming, but the results were almost 100% accurate.

“This method was a little bit time-consuming, but the results were almost 100% accurate.”