State Of Charge Estimation Method Research Articles

Joint State of Charge (SOC) and State of Health (SOH) Estimation for Lithium-Ion Batteries Packs of Electric Vehicles Based on NSSR-LSTM Neural Network

Lithium-ion batteries (LIBs) are widely used in electrical vehicles (EVs), but safety issues with LIBs still occur frequently. State of charge (SOC) and state of health (SOH) are two crucial parameters for describing the state of LIBs. However, due to inconsistencies that may occur among hundreds to thousands of battery cells connected in series and parallel in the battery pack, these parameters can be difficult to estimate accurately. To address this problem, this paper proposes a joint SOC and SOH estimation method based on the nonlinear state space reconstruction (NSSR) and long short-term memory (LSTM) neural network. An experiment testbed was set up to measure the SOC and SOH of battery packs under different criteria and configurations, and thousands of charging/discharging cycles were recorded. The joint estimation algorithms were validated using testbed data, and the errors for SOC and SOH estimation were found to be within 2.5% and 1.3%, respectively, which is smaller than the errors obtained using traditional Ah-Integral and LSTM-only algorithms.

Hybrid deep learning model for efficient state of charge estimation of Li-ion batteries in electric vehicles

State of charge (SoC) estimation is critical for the safe and efficient operation of electric vehicles (EVs). This work proposes a hybrid multi-layer deep neural network (HMDNN)-based approach for SoC estimation in EVs. This HMDNN uses Mountain Gazelle Optimizer (MGO) as a training algorithm for the deep neural network. Our method leverages the intrinsic relationship between the SoC and the voltage/current measurements of the EV battery to accurately estimate the SoC in real time. We evaluate our approach on a large dataset of real-world EV charging data and demonstrate its effectiveness in comparison to traditional SoC estimation methods. Four diverse Li-ion battery datasets of electric vehicles are employed which are the dynamic stress test (DST), Beijing dynamic stress test (BJDST), federal urban driving schedule (FUDS), and highway driving schedule (US06) with different temperatures of 0oC,25oC,45oC. The comparison is made with Mayfly Optimization Algorithm based DNN, Particle Swarm Optimization based DNN and Back-Propagation based DNN. The evaluation indices used are normalized mean square error (NMSE), root mean square error (RMSE), mean absolute error (MAE), and relative error (RE). The proposed algorithm achieves 0.1% NMSE and 0.3% RMSE on average on all datasets, which validates the effective performance of the proposed model. The results show that the proposed neural network-based approach can achieve higher accuracy and faster convergence than existing methods. This can enable more efficient EV operation and improved battery life.

Combined State of Charge and State of Energy Estimation for Echelon-Use Lithium-Ion Battery Based on Adaptive Extended Kalman Filter

To ensure the safety and reliability of an echelon-use lithium-ion battery (EULIB), the performance of a EULIB is accurately reflected. This paper presents a method of estimating the combined state of energy (SOE) and state of charge (SOC). First, aiming to improve the accuracy of the SOE and SOC estimation, a third-order resistor-capacitance equivalent model (TRCEM) of a EULIB is established. Second, long short-term memory (LSTM) is introduced to optimize the Ohmic internal resistance (OIR), actual energy (AE), and actual capacity (AC) parameters in real time to improve the accuracy of the model. Third, in the process of the SOE and SOC estimation, the observation noise equation and process noise equation are updated iteratively to make adaptive corrections and enhance the adaptive ability. Finally, an SOE and SOC estimation method based on LSTM optimization and an adaptive extended Kalman filter (AEKF) is established. In simulation experiments, when the capacity decays to 90%, 60% and 30% of the rated capacity, regardless of whether the initial value is consistent with the actual value, the values of the SOE and SOC estimation can track the actual value with strong adaptive ability, and the estimated error is less than 1.19%, indicating that the algorithm has a high level of accuracy. The method presented in this paper provides a new perspective for estimating the SOE and SOC of a EULIB.

State of Charge Estimation for Lithium-Ion Battery Based on Unscented Kalman Filter and Long Short-Term Memory Neural Network

State of charge (SOC) estimation is the core algorithm of the battery management system. However, the commonly used model-based, data-driven, or experiment-based methods struggle to independently achieve accurate SOC estimation under different working conditions and temperatures, which affects battery performance and safety. To this end, this paper proposes an online SOC estimation method that combines the model-driven and double-data-driven approaches. The unscented Kalman filter (UKF) based on the first-order RC model is used to achieve robust SOC estimation, while the data-driven long short-term memory (LSTM) neural network is used to achieve fast SOC estimation. The former model has an excellent dynamic performance and the latter has high steady-state accuracy. The SOC estimation results are input into the SOC estimation model of series LSTM so that the stable but inaccurate SOC values estimated by UKF in the first part and the accurate but fluctuating SOC values estimated by LSTM can be correlated and corrected, achieving a fast and accurate SOC estimation under various working conditions. The estimation results show that the above method has strong robustness and high accuracy, and effectively reduces model complexity and data redundancy. In addition, the root mean square error of SOC estimation under different working conditions is controlled within 1–2.3% at 0 °C, 25 °C, and 45 °C, which is better than the traditional single-SOC estimation method.

Identification of fractional-order equivalent circuit model of lithium-ion battery for improving estimation of state of charge

Accurate estimation of State of Charge (SOC) based on equivalent circuit model (ECM) of Lithium-ion batteries (LIBs) is an important research topic. Recent research has found that fractional-order model (FOM), as one kind of equivalent circuit model, can provide a better description of LIBs dynamics than the conventional integer-order ECMs. However, it is difficult to directly identify an FOM online. In this paper, a synergy of Beetle Antennae Search and Recursive Least Squares (BAS-RLS) is proposed to identify the parameters of an FOM for LIBs. Specifically, the BAS is adopted to determine the fractional order, while the remaining parameters of FOM are estimated via the well-established RLS algorithm. A comparison study will demonstrate that this method offers a similar modeling accuracy as the Particle Swarm Optimization (PSO), and the online estimated model is more accurate than offline estimated models. Based on the identified FOM, this article then explores the battery SOC estimation from two aspects: initial value effect of the SOC and the comparison of multiple estimation algorithms, thus verifying the advantage of the proposed method for LIBs modeling and SOC estimation.

State of charge estimation of lithium-ion battery based on improved adaptive boosting algorithm

State of charge (SOC) is a crucial battery state to calibrate the remaining charge of lithium-ion batteries in electric vehicles. Accurate battery SOC estimation is one of the keys and difficult issues for lithium-ion batteries. To achieve SOC estimation accurately, an improved adaptive boosting algorithm called AdaBoost.RT algorithm, which is a regression ensemble algorithm and uses the extreme learning machine (ELM) as weak learners, is applied to estimate the SOC of lithium-ion batteries in this paper. And a two-step method is also proposed to denoise experimental data, which are used as the input data of the proposed SOC estimation method, to further enhance the accuracy of SOC estimation. Firstly, a complementary ensemble empirical mode decomposition with adaptive noise method (CEEMDAN) is utilized to decompose the experimental data including battery voltage and current according to the frequency of the signals to form different frequency components. Secondly, a wavelet threshold denoising method (WTD) is combined to denoise these components. The denoised components trend to form a new battery signal by the linear superposition principle and input into the proposed SOC method in this paper. The combined SOC estimation method can be called CEEMDAN-WTD-AdaBoost-ELM (CWAELM) method. To verify the proposed method, experiments are conducted under Beijing dynamic stress test (BJDST), dynamic stress test (DST), federal urban driving schedule (FUDS), and highway driving schedule (US06) conditions at 0 °C, 25 °C and 45 °C temperatures, respectively. The results show that the proposed model has good robustness and accuracy in the SOC estimation of lithium-ion batteries under various working conditions at different temperatures.

Calendar Aging Effect on the Open Circuit Voltage of Lithium-Ion Battery

In recent years, lithium-ion batteries (LiBs) have gained a lot of importance due to the increasing use of renewable energy sources and electric vehicles. To ensure that batteries work properly and limit their degradation, the battery management system needs accurate battery models capable of precisely predicting their parameters. Among them, the state of charge (SOC) estimation is one of the most important, as it enables the prediction of the battery’s available energy and prevents it from operating beyond its safety limits. A common method for SOC estimation involves utilizing the relationship between the state of charge and the open circuit voltage (OCV). On the other hand, the latter changes with battery aging. In a previous work, the authors studied a simple function to model the OCV curve, which was expressed as a function of the absolute state of discharge, q, instead of SOC. They also analyzed how the parameters of such a curve changed with the cycle aging. In the present work, a similar analysis was carried out considering the calendar aging effect. Three different LiB cells were stored at three different SOC levels (low, medium, and high levels) for around 1000 days, and an analysis of the change in the OCV-q curve model parameters with the calendar aging was performed.

High-Precision and Robust SOC Estimation of LiFePO4 Blade Batteries Based on the BPNN-EKF Algorithm

The lithium iron phosphate (LiFePO4) blade battery is a long, rectangular-shaped cell that can be directly integrated into battery pack systems. It enhances volumetric power density, significantly reduces costs, and is widely utilized in electric vehicles. However, the flat open circuit voltage and significant polarization differences under wide operational temperatures are challenging for accurate voltage modeling of battery management systems (BMSs). In particular, inaccurate state of charge (SOC) estimation may cause overcharging and over-discharging risks. To accurately perceive the SOC of LiFePO4 blade batteries, a SOC estimation method based on the backpropagation neural network-extended Kalman filter (BPNN-EKF) algorithm is proposed. BPNN is a neural network model that utilizes the backpropagation algorithm to update model parameters, while EKF is an optimal estimation algorithm. Firstly, dynamic working condition tests, including the New European Driving Cycle (NEDC) and high-speed working (HSW) condition tests, are conducted under a wide temperature range (−25–43 °C). HSW conditions refer to a simulated operating condition that mimics the driving of an electric vehicle on a highway. The minimum voltage of the battery system is used as the output for training the BPNN model. We derive the Kalman gain by combining the BPNN output voltage. Additionally, the EKF algorithm is employed to correct the SOC value using voltage error information. Concerning long SOC calculation intervals, capacity errors, initial SOC errors, and current and voltage sampling errors, the maximum SOC estimation RMSE is 3.98% at −20 °C NEDC, 3.62% at 10 °C NEDC, and 1.68% at 35 °C HSW. The proposed algorithm can be applied to different temperatures and operations, demonstrating high robustness. This BPNN-EKF algorithm has the potential to be embedded in electric vehicle BMS systems for practical applications.

A Novel Method for SoC Estimation of Lithium-Ion Batteries Based on Kalman Filter in Electric Vehicle

In recent years, the energy crisis has become more and more serious. Li-ion batteries are used in grids because of their benefits such as contributing to the intermittent generation of renewable energy sources and stabilizing the grid. In addition, li-ion batteries are widely used in electric vehicles due to their long cycle life and high energy density. Li-ion battery state of charge (SoC) is an important indicator for safety. Therefore, the SoC estimation of li-ion batteries is important. Today, there are different methods to determine the state of the SoC in many applications. The traditional estimation method, the ampere-hour integration method and the coulomb counting method, has a cumulative error and cannot achieve good results in a working environment with Gaussian noise. For this purpose, in this study, firstly, the Thevenin equivalent model was created for battery SOC estimation, and then the Kalman filter algorithm was applied. Thus, the estimation error caused by Gaussian noise is eliminated. SoC estimation was simulated for the battery model created in the MATLAB/Simulink program using this method. Using these simulation results, the charge/discharge characteristics of the battery were obtained. However, the SoC estimation has been made for the charging and discharging processes of the battery. In the simulation, the charge value was recorded for 6 hours. The data recorded every 10 minutes gave results very close to the true value.

State of charge estimation for Li-ion batteries based on iterative Kalman filter with adaptive maximum correntropy criterion

Nonlinear filter methods are commonly employed for model-driven based battery state of charge (SOC) estimation because of their ability to suppress Gaussian noise. Due to the uncertainty of complicated operational conditions, the minimum mean square error (MMSE) criterion based Kalman filter (KF) methods may not guarantee sufficient SOC estimation accuracy in the presence of non-Gaussian noise. To enhance the anti-interference performance of the KFs based SOC estimation method, a novel methodology that combines the adaptive kernel width based maximum correntropy criterion (AMCC) with the Levenberg-Marguardt (L-M) principle based adaptive iterative extended KF (AIEKF) is proposed. Firstly, the MMSE criterion of the EKF is replaced by the MCC criterion and an adaptive kernel width strategy is designed to weaken the effect of anomalous data. Then, the AMCC-corrected covariance matrix and state are updated using an L-M optimized multi-step iterative filter during the measurement update phase. Finally, the combination of AMCC and AIEKF is devised to execute SOC estimation. Several sets of data from different temperatures and operational conditions are used to verify the validity of the proposed AMCC-AIEKF method. Compared with the adaptive EKF (AEKF) and the adaptive iterative EKF (AIEKF) method, the AMCC-AIEKF method has the advantage in terms of SOC estimation accuracy and robustness under different operational conditions with noiseless, Gaussian noise and non-Gaussian noise.

Nonlinear estimator‐based state of charge estimation for lithium titanate oxide battery in energy storage systems

AbstractFuel savings, energy savings, and reduction of CO2 emissions are the key requirements in electric and hybrid electric vehicles (EVs and HEVs). These requirements are achieved through the usage of start‐stop systems, high‐rate energy boost during acceleration, and recovery of the energy during braking. Unfortunately, the commonly used lithium‐ion batteries are not a sufficient solution, although their performance is enhanced by supercapacitors. This hybrid system used is only a temporary solution. Therefore, lithium‐titanate‐oxide batteries (Li4Ti5O12—LTO), show high‐rate discharging and charging performance, high power capability, excellent cycle life, and improved cycle stability at wide‐rate temperatures and current rates are promising candidates for HEV and EV applications. There is a need to monitor the state of charge (SoC) for the reliability, performance, and safety of LTO batteries with the help of a battery management system. However, the conventional SoC estimation methods, such as open circuit voltage, Coulomb counting, artificial neural networks, fuzzy logic, and linear Kalman filter algorithm become insufficient. In this paper, a new nonlinear approach for the SoC estimation of an LTO battery is presented. The approach combines the static battery model and the sigma point Kalman filter (SPKF) algorithm while adapting to both constant load and dynamic load. The results show that the SPKF algorithm successfully estimated the SoC of the LTO battery under various initial SoC initialization values. It is also supported by various metric errors calculated.

OCV-SOC-Temperature Relationship Construction and State of Charge Estimation for a Series– Parallel Lithium-Ion Battery Pack

Accurate state of charge (SOC) estimation of a battery pack is more meaningful than that of a cell in practical applications. The existing methods are difficult to provide an accurate SOC of a battery pack under a wide range of temperature due to cell inconsistency. In this paper, a SOC estimation method for a series-parallel lithium-ion battery pack based on the newly constructed OCV-SOC-temperature relationship was proposed. In the proposed method, firstly the cosine similarity is used to quantify cell inconsistency and the representative cells in the battery pack are determined by the largest cosine similarity value. Secondly, the OCV-SOC curves of the representative cells at different temperatures are used to construct the OCV-SOC-temperature relationship of the battery pack. Finally, a multi-branch fusion method is developed to estimate the SOC of the battery pack through the SOC of each branch by means of a Bayesian probability formula. The effectiveness of the newly constructed OCV-SOC-temperature relationship and the proposed SOC estimation method of the battery pack is verified under various dynamic conditions. The estimated SOC error of the series–parallel battery pack is less than 1.5%, which is approximately 60% lower than the traditional methods.

A parameter identification and state of charge estimation method of lithium-ion battery considering temperature bias

To eliminate the impact of inaccurate initial parameter value on the parameter identification results of lithium-ion battery (LIB) model, a method for parameter identification of LIB combining Matlab and 1stOpt is proposed, fully utilizing the powerful global optimization ability of 1stOpt to obtain accurate initial parameter value. Moreover, this method can also efficiently heighten the precision of parameter identification results. The hybrid pulse power characteristic (HPPC) experiment is carried out on a LIB in the laboratory to obtain the relationship among state of charge (SOC), open circuit voltage (OCV), and ambient temperature, and the data required for parameter identification. To enhance the accuracy of SOC estimation, based on the obtained high-precision identification parameters, a dual-polarization dynamic thermal model of coupling temperature and SOC of the LIB is established. We find that the battery temperature tested is inconsistent with the ambient temperature, which causes inaccurate temperature input of the battery model, thus affecting the accuracy of the battery model. In this work, a particle swarm optimization (PSO) algorithm is introduced to obtain exact temperature differences to rectify the temperature input of the battery model. Then, the simulated terminal voltage of the battery is compared and validated against the experimental data. It is obtained that the maximum and minimum average errors considering temperature bias are only 0.962 % and 0.0075 %, respectively, while the maximum and minimum average errors without temperature bias are 3.622 % and 0.109 %, respectively, which commendably prove the accuracy of the established model. Finally, the extended Kalman filter (EKF) is adopted to estimate the SOC under the dynamic stress test (DST), and the maximum error is less than 0.8 %. The results strongly show that the established model in this work still has high accuracy in a wide temperature range. The results provide a theoretical reference for the related research on parameter identification and modeling of batteries.

State of charge estimation method by using a simplified electrochemical model in deep learning framework for lithium-ion batteries

To ensure the secure and healthy usage of lithium-ion batteries, it is necessary to accurately estimate the state of charge (SOC) in battery management systems. The development of deep learning (DL) provides a new solution for battery SOC estimation. However, the directly measured physical quantities contain less useful information and have low estimation accuracy. This paper proposes a method of integrating the mechanism knowledge of the battery domain into the DL framework. Firstly, the simplified electrochemical model is utilized to obtain the mechanism-related physical variables to expand the input of the DL model. Secondly, the long short-term memory (LSTM) network is used with the Bayesian optimization, and the variables with high correlation are identified. The best SOC estimation performance can be obtained by adding all the selected highly-correlated variables to the input for training together. The results show that the proposed method can improve the SOC estimation performance with only a slight increase in computation cost. Finally, other DL models are utilized to further validate the effectiveness, to reveal the universality. These results show that the performance of the DL model can be effectively improved by using the knowledge of the battery domain.

State-of-Charge Estimation of Ultracapacitor Based on H Infinity Filter Considering Variable Temperature

Abstract The performance and service life of ultracapacitors are highly dependent on accurate modeling and state-of-charge (SOC) estimating. To overcome the model parameter errors caused by the various temperatures and different SOC intervals, the H infinity filter (HIF) is employed to estimate the ultracapacitor SOC based on a variable temperature model. For the application of the HIF method, the Thevenin model is first developed with a small terminal voltage estimation error. Then, the model parameters are optimally identified using the ant colony optimization (ACO) algorithm. Next, a variable temperature model is established to improve the adaptability of the ultracapacitor model, and the HIF is utilized for the ultracapacitor SOC estimation. Finally, to verify the performance of the variable temperature model and the proposed SOC estimation method, a series of experiments are conducted. The analysis results illustrate that the mean absolute error (MAE) of the SOC estimation values based on the variable temperature model is decreased by 39.62% compared to the one based on the nonvariable temperature model. Meanwhile, the proposed state estimation scheme based on the variable temperature model is accurate with estimation values maximum error (ME) and root-mean-squared error (RMSE) less than 0.80% and 0.60%, respectively. The HIF-based SOC estimation method also shows a good robustness with a short convergence time within 90.00 s when the SOC initial error is set to 0.20.

Multistate joint estimation of ultracapacitor based on trans-scale dual extended Kalman filter

Accurate ultracapacitor state of charge (SOC) estimation directly affects safety, durability and reliability of hybrid energy storage system. For that, this paper presents a multistate joint estimation method of ultracapacitor based on trans-scale dual extended Kalman filter to predict SOC and model parameters in real-time. Firstly, an ultracapacitor model is established by using experimental data. Then, the model is combined with two Kalman filters, one of which is used to estimate SOC, and another one is applied to achieve trans-scale update the model parameters. Finally, the effectiveness of the method is verified in the urban dynamometer driving schedule at different temperatures. The validation results show that the mean absolute errors of voltage, SOC and capacity estimation are within 0.49 mV, 0.63% and 0.04 Ah, respectively. Moreover, compared with the other two traditional SOC estimation methods, whose results show that the proposed algorithm has higher estimation accuracy and more stable convergence ability.

State of Charge Estimation for Batteries Based on Common Feature Extraction and Transfer Learning

The state of charge (SOC) of a battery is a key parameter of electrical vehicles (EVs). However, limited by the lack of computing resources, the SOC estimation strategy used in vehicle-mounted battery management systems (V-BMS) is usually simplified. With the development of the new energy vehicle big data platforms, it is possible to obtain the battery SOC through cloud-based BMS (C-BMS). In this paper, a battery SOC estimation method based on common feature extraction and transfer learning is proposed for C-BMS applications. Considering the diversity of driving cycles, a common feature extraction method combining empirical mode decomposition (EMD) and a compensation strategy for C-BMS is designed. The selected features are treated as the new inputs of the SOC estimation model to improve the generalization ability. Subsequently, a long short-term memory (LSTM) recurrent neural network is used to construct a basic model for battery SOC estimation. A parameter-based transfer learning method and an adaptive weighting strategy are used to obtain the C-BMS battery SOC estimation model. Finally, the SOC estimation method is validated on laboratory datasets and cloud platform datasets. The maximum root-mean-square error (RMSE) of battery SOC estimation with the laboratory dataset is 2.2%. The maximum RMSE of battery pack SOC estimation on two different electric vehicles is 1.3%.

A novel combined online method for SOC estimation of a Li-Ion battery with practical and industrial considerations

Estimation of the state of charge (SOC) in the battery management systems (BMS) is very crucial. However, the BMS consistently suffers from inaccuracy of SOC estimation and high computational burden in industrial applications. Herein, we propose a novel combined SOC estimation approach with high accuracy, simplicity in implementation and, robustness that can be implemented on the low-cost microcontrollers. The basis of the method is to online identification the open circuit voltage (OCV) value of the battery simultaneously with other unknown parameters of the battery equivalent circuit model (ECM). Using this identified OCV, SOC is extracted from the OCV-SOC curve, directly. This direct method is an open-loop estimation method and tends to get lower SOC accuracy compared with known methods. To overcome this disadvantage, a combined method is proposed. Hence, to estimate SOC in this method, in the middle part of the OCV-SOC curve (linear part) and after identifying OCV from recursive least square algorithm (RLS) method with a forgetting factor, SOC is estimated directly via OCV-SOC curve. Furthermore, in the other parts of the curve especially non-linear parts, SOC is estimated with the EKF algorithm. In summary, not only estimation accuracy will increase, but also the computational burden of the EKF will decrease. In this paper, voltage and current samples of the battery at each sample time are the inputs of the algorithms and gained from the known “LA-92 dynamic driving cycle” test. To validate the efficiency of the presented method, results are compared with the EKF algorithm and direct method. The experimental results show that the proposed method reduces the EKF calculations by almost 15 % and guarantee high accuracy SOC estimation. The maximum error of the proposed method is <2.5 %.

Multi-dimensional features based data-driven state of charge estimation method for LiFePO4 batteries

The flat open-circuit voltage (OCV) curve of LiFePO4 (LFP) batteries poses a significant challenge to state of charge (SOC) estimation. To solve this problem, this paper proposes a data-driven SOC estimation method based on multi-dimensional features, especially incorporating force signals. The significant force variation at the middle SOC region section compensates for the flat OCV problem. A long short-term memory (LSTM) neural network model is established to estimate SOC. Battery voltage, current, temperature, and force data sampled only in 5 s are taken as input. The proposed method is validated under different dynamic testing profiles and different temperatures. Experimental results indicate that this method can highly improve SOC estimation accuracy in the middle SOC region, with less than 0.5% root mean square errors and less than 2.5% maximum errors. The validation results at different temperatures also maintain high accuracy with the same model, showing strong robustness and excellent generalization performance. Additionally, the model training process of this method only takes 1.5 h, and the online estimation time is less than 1 s, considerably reducing time cost.

Assessing the Limits of Equivalent Circuit Models and Kalman Filters for Estimating the State of Charge: Case of Agricultural Robots

The battery State of Charge (SoC) is critical information to overcome agricultural robots’ limitations related to battery and energy management. Although several SoC estimation methods have been proposed in the literature, the performance of these methods has not been validated for different battery chemistries in agricultural mobile robot applications. Compared to previous work, this paper evaluates the limits of the SoC estimation using the RC model and the Thevenin model for a Lithium Iron Phosphate (LFP) battery and a Sealed Lead Acid (SLA) battery. This evaluation used a custom agricultural robot in a controlled indoor environment. Consequently, this work assessed the limitations of two ECM-based SoC estimation methods using battery packs, low-cost sensors and discharge cycles typically used in agricultural robot applications. Finally, the results indicate that the RC model is not suitable for SoC estimation for LFP battery; however, it achieved a mean absolute error (MAE) of 2.2% for the SLA battery. On the other hand, the Thevenin model performed properly for both chemistries, achieving MAE lower than 1%.