Second-order Equivalent Circuit Research Articles

State of charge estimation under different temperatures using unscented Kalman filter algorithm based on fractional-order model with multi-innovation

In this study, a battery test platform is built to study and analyze the battery model. A fractional-order model (FOM) of battery is developed by combining the second-order equivalent circuit model with fractional calculus theory. By combining the multi-innovation with the unscented Kalman filter algorithm based on FOM, a fractional-order multi innovation unscented Kalman filter algorithm is proposed. Under different temperatures and dynamic conditions, the tracking of terminal voltage and the estimation results of SOC using the proposed algorithm are compared and analyzed. In order to verify the accuracy and robustness of the proposed algorithm, the tracking effect of the terminal voltage and the estimation results of SOC under different initial SOC values are investigated. The experimental results indicate that the FOM is more accurate than the integer-order model in reflecting the battery characteristics. Under different temperatures, dynamic conditions, and initial SOC values, the values of mean absolute error (MAE) and root mean squared error (RMSE) of the proposed algorithm are the lowest, which verifies the effectiveness of the proposed algorithm. The maximum values of MAE and RMSE of SOC estimation results of the proposed algorithm are 1.04 % and 0.9122 %, respectively, indicating that the proposed algorithm has high accuracy and good robustness.

State of charge estimation of ultracapacitor based on forgetting factor recursive least square and extended Kalman filter algorithm at full temperature range

State of charge (SOC) of ultracapacitor plays an important role in the energy management optimization of hybrid energy storage system for electric vehicles. In addition to the perfection of the model and the SOC estimation algorithm, the parameter identification method and temperature factor should also be considered. In this paper, an ultracapacitor test platform is established, the characteristic parameters of ultracapacitor at full temperature range are obtained. This paper uses the forgetting factor recursive least squares algorithm (FFRLS) to identify the parameters of the second-order equivalent circuit model of ultracapacitor online. The extended Kalman filter (EKF) algorithm is used to estimate the SOC of ultracapacitor cell. The results show that: (1) FFRLS algorithm can identify R0, R1, R2, C1, and C2 values of ultracapacitor at full temperature range. Under the hybrid pulse power characterization working condition, the average mean absolute error between the estimated voltage and the actual voltage is about 0.0132 V. (2) EKF algorithm has a good adaptability to estimate SOC of ultracapacitor under different temperatures and working conditions. The SOC estimation error under different working conditions is low. From the perspective of mean square error, the estimation error at −20°C is the lowest. (3) FFRLS and EKF joint estimation algorithm with good robustness and reliability can be used to estimate the SOC of ultracapacitor under different temperatures and working conditions. This study can provide a useful guidance for the parameter identification and SOC estimation of ultracapacitor for electric vehicle at different temperatures.

Mathematical Modelling and Simulation of Second Life Battery Pack with Heterogeneous State of Health

The service life of Lithium-ion batteries disposed from electric vehicles, with an approximate remaining capacity of 75–80%, can be prolonged with their adoption in less demanding second life applications such as buildings. A photovoltaic energy generation system integrated with a second life battery energy storage device is modelled mathematically to assess the design’s technical characteristics. The reviewed studies in the literature assume, during the modelling process, that the second life battery packs are homogeneous in terms of their initial state of health and do not consider the module-to-module variations associated with the state of health differences. This study, therefore, conducts mathematical modelling of second life battery packs with homogenous and heterogeneous state of health in module level using second-order equivalent circuit model (ECM). The developed second-order ECM is validated against experimental data performed in the lab on 3Ah NCM batteries. The degradation parameters are also investigated using the battery cell’s first life degradation data and exponential triple smoothing (ETS) algorithm. The second-order ECM is integrated with the energy generation system to evaluate and compare the performance of the homogenous and heterogeneous battery packs during the year. Results of this study revealed that in heterogeneous packs, a lower electrical current and higher SOC is observed in modules with lower state of health due to their higher ohmic resistance and lower capacity, compared to the other modules for the specific battery pack configuration used in this study. The methodology presented in this study can be used for mathematical modelling of second life battery packs with heterogenous state of health of cells and modules, the simulation results of which can be employed for obtaining the optimum energy management strategy in battery management systems.

Electrification of a Class 8 Heavy-Duty Truck Considering Battery Pack Sizing and Cargo Capacity

The design and performance optimization of fully electric trucks constitute an integral goal of the transport sector to meet climate emergency measures and local air quality requirements. Most studies in the literature have determined the optimum pack size based on economic factors, without accounting for the details of pack behavior when varying the size. In this paper, the effect of battery pack sizing and cargo capacity of a class 8, 41-ton truck on its overall energy performance and technical parameters of its powertrain is investigated. For this purpose, the proposed electric truck is designed and mathematically modelled using AVL CRUISE M software. The second-order equivalent circuit model is developed to predict the battery packs’ parameters. The proposed battery pack model is extracted from experimental analysis on SONY VTC6 lithium-ion batteries performed in the lab. The weight changes due to adding the battery packs to the truck are also estimated and have been taken into account. The mathematical model of the powertrain is simulated in the long-haul driving cycle considering different cargo capacities and battery pack sizes. The results of this study revealed that the battery pack voltage reached its minimum value when the maximum cargo capacity was applied for the 399 kWh battery pack. In addition, increasing the occupied cargo capacity from 10% to 100% resulted in an increase in the regenerative brake energy of up to 9.87 kWh, while changing the battery size imposed minimal impacts on regenerative brake energy recovery as well as energy consumption.

SOC Estimation of Lithium-Ion Battery Based on Equivalent Circuit Model with Variable Parameters

The state of charge (SOC) of the battery is an important basis for the battery management system to perform state monitoring and control decisions. In this paper, by identifying the internal parameters of the battery model at different temperatures and SOCs of the lithium-ion battery, the specific factors that affect the change of the parameters are analyzed, the segmentation basis of the model and the fitting method of related parameters are discussed, the second-order equivalent circuit model of the lithium-ion battery whose parameters vary with SOC and temperature is established, the unscented Kalman filter (UKF) is used to estimate the SOC of the lithium-ion battery, and an improved SOC estimation method based on optimized equivalent circuit model is proposed. Simulation and experimental results show that the improved SOC estimation strategy can obtain high estimation accuracy in a wide temperature range.

Joint Estimation of SOC and SOH for Single-Flow Zinc–Nickel Batteries

The single-flow zinc–nickel battery (ZNB) is a new type of flow battery with a simple structure, large-scale energy storage, and low cost, and thus has attracted much attention in the battery field recently. The state of charge (SOC) and state of health (SOH) are key indicators of the battery, and their inaccurate estimation can damage the battery. However, little has been done so far to study how to jointly estimate SOC and SOH for the ZNB. In this paper, the method of adaptive IDUKF is proposed. A second-order equivalent circuit model is applied to improve the accuracy. At the same time, the double unscented Kalman filter (DUKF), which is optimized by the improved Harris hawk optimization (IHHO) algorithm, is used to estimate the SOC and parameters online. Then, the capacity update model is introduced to simulate the change in SOH. Finally, the proposed method is applied to a 16 Ah ZNB, and the experimental results confirm the validity of the proposed method.

State of charge estimation for lithium‐ion batteries based on square root sigma point Kalman filter considering temperature variations

The battery management system (BMS) in electric vehicles monitors the state of charge (SOC) and state of health (SOH) of lithium-ion battery by controlling transient parameters such as voltage, current, and temperature prevents the battery from operating outside the optimal operating range. The main feature of the battery management system is the correct estimation of the SOC in the broad range of vehicle navigation. In this paper, to estimate real-time of SOC in lithium-ion batteries and overcome faults of Extended Kalman Filter (EKF), the Square-Root Sigma Point Kalman Filter is applied on the basis of numerical approximations rather than analytical methods of EKF. For this purpose, the Hybrid Pulse Power Characterisation tests are combined with the non-linear least square method that acquired the second-order equivalent circuit model parameters. Then, the newly developed method is tested with an 18,650 cylindrical lithium-ion battery with a nominal capacity of 2600 mAh in four different ambient temperatures. Finally, the accuracy and effectiveness of the two proposed methods are verified by comparing with results of pulse discharge and dynamic driving cycle tests. The comparison results indicate the error of the proposed algorithm is about 0.02 under the most test conditions.

SOC Estimation for Electrical Vehicle lithium Batteries base on Simplified-spherical Un-scented Kalman Filtering

In order to develop electric vehicles, it is vital to be able to accurately estimate the state charge (SOC) of a lithium battery. To address the problem that the Extended Kalman Filter (EKF) algorithm leads to the Taylor expansion truncation of the higher-order system. In this paper, a system of state-space equations is established based on the second-order equivalent circuit model, and a simplified-sphere sample approach is used to improve the Unscented Kalman Filter (UKF) algorithm. The SOC estimation performance of the three algorithms is tested under constant current discharge, pulse discharge conditions, and UDC conditions, respectively. The simulation results show that Simplified-spherical Unscented Kalman Filtering (SUKF) has smaller errors between SOC estimation and theoretical reference values than EKF and UKF. The SUKF is less computationally intensive than UKF and has better timeliness in the onboard battery management system.

State of charge estimation for lithium-ion batteries connected in series using two sigma point Kalman filters

This paper proposes a method to estimate state of charge (SoC) for Lithium-ion battery pack (LIB) with 𝑁 series-connected cells. The cell’s model is represented by a second-order equivalent circuit model taking into account the measurement disturbances and the current sensor bias. By using two sigma point Kalman filters (SPKF), the SoC of cells in the pack is calculated by the sum of the pack’s average SoC estimated by the first SPKF and SoC differences estimated by the second SPKF. The advantage of this method is the SoC estimation algorithm performed only two times instead of 𝑁 times in each sampling time interval, so the computational burden is reduced. The test of the proposed SoC estimation algorithm for 7 samsung ICR18650 Lithium-ion battery cells connected in series is implemented in the continuous charge and discharge scenario in one hour time. The estimated SoCs of the cells in the pack are quite accurate, the 3-sigma criterion of estimated SoC error distributions is 0.5%.

Parameter identification and co-estimation of state-of-charge of Li-ion battery in real-time on Internet-of-Things platform

An accurate estimate of the battery’s state-of-charge (SoC) is important for extending its service life and ensuring its protection. Based on a second-order equivalent circuit model, a joint estimator of online parameter identification and an improved adaptive extended Kalman filter (AEKF) for Li-ion battery SoC is developed, which tackles the problem of ill-conditioning while estimating the SoC in real-time. A three-state decoupled parameter estimation approach is designed to compute the best parameters:(i) ohmic resistance estimator with recursive least square (RLS) method, (ii) Tikhonov regularization has been introduced with the Kalman filter (KF) for the estimation of the fast time constant which improves the conditioning of the system and (iii) the measure of the slow time constant using lookup table-based method. Finally, an improved AEKF with fading weight factor mechanism is used to achieve closed-loop feedback of SOC estimation with parameter estimation, confirming the algorithm’s correctness and speed of convergence. The Chi-square test is incorporated into the AEKF to improve the rationale of the adaptive measurement covariance introduction timing. A variety of experimentally generated trending current patterns were used to validate the approach under various complex operating conditions. Furthermore, the proposed model-based diagnostic techniques have been integrated into a cloud-based system in this article, ensuring continuous and accurate battery state monitoring. All battery-related data is measured and transmitted to the cloud via the Internet of Things (IoT), where the proposed diagnostic algorithms analyze the data and estimate the SoC. As the proposed estimation approach features a low computational expense, it can be used in real-time industrial applications.

A Comparative Study on the Parameter Identification of an Equivalent Circuit Model for an Li-ion Battery Based on Different Discharge Tests

An effective model of battery performance is important for battery management systems to control the state of battery and cell balancing. The second-order equivalent circuit model of a lithium-ion battery is studied in the present paper. The identification methods that include the multiple linear regression (MLR), exponential curve fitting (ECF) and Simulink design optimization tool (SDOT), were used to determine the model parameters. The aim of this paper is to compare the validity of the three proposed algorithms, which vary in complexity. The open circuit voltage was measured based on the pulse discharge test. The voltage response was collected for every 10% SOC in the interval between 0–100% SOC. The battery voltages calculated from the estimated parameters under the constant current discharge test and dynamic discharge tests for electric vehicles (ISO and WLTP) were compared to the experimental data. The mean absolute error and root mean square error were calculated to analyze the accuracy of the three proposed estimators. Overall, SDOT provides the best fit with high accuracy, but requires a heavy computation burden. The accuracy of the three methods under the constant current discharge test is high compared to other experiments, due to the nonlinear behavior at a low SOC. For the ISO and WLTP dynamic tests, the errors of MLR are close to that of SDOT, but have less computing time. Therefore, MLR is probably more suitable for EV use than SDOT.

A novel feedback correction-adaptive Kalman filtering method for the whole-life-cycle state of charge and closed-circuit voltage prediction of lithium-ion batteries based on the second-order electrical equivalent circuit model

Accurate state of charge (SOC) and closed-circuit voltage (CCV) prediction is essential for lithium-ion batteries and their model performance. In this study, a novel feedback correction-adaptive Kalman filtering (FC-AKF) method is proposed for the online battery state co-prediction, which is adaptive to the whole-life-cycle of the lithium-ion battery based on the improved second-order equivalent circuit model (SO-ECM). For the feedback correction strategy, the optimized iterative state initialization is conducted using the uncertainty covariance matrix of the prior three-time points with the convergence of the updating process. The experimental results show that the SOC prediction error of the proposed FC-AKF method is 0.0099% and 0.975% compared with the ampere-hour integral method under the dynamic stress test (DST) and the Beijing bus dynamic stress test (BBDST) working conditions, respectively. Also, the CCV traction by the SO-ECM is 0.80 V and has fast initial convergence and quick prediction error reduction characteristics. The constructed iterative calculation model promotes the accurate SOC and CCV co-prediction effect, improving the safety and longevity of lithium-ion batteries with high precision and fast convergence advantages.

Alternative combined co-estimation of state of charge and capacity for lithium-ion batteries in wide temperature scope

This study develops a combined method for co-estimation framework for state of charge and capacity of lithium-ion batteries considering wide temperature scope. In this framework, a second-order equivalent circuit model incorporating temperature compensation is established to characterize the battery's electrical performance. Next, the particle swarm optimization algorithm integrating data accumulation and dynamic updating technique is exploited to adaptively identify the model parameters. Then, the charging duration is selected as the health feature, and the long short-term memory recurrent neural network is leveraged to predict battery capacity with high accuracy. Moreover, the dynamically updated model parameters and capacity value are inputted to estimate the state of charge based on the square root cubature Kalman filter. Experimental validations are conducted considering different voltage ranges, data lengths, temperatures and aging status to illustrate the feasibility and superiority of the designed estimation framework, and the results highlight that the proposed co-estimation framework can supply precise state of charge estimation with the error of less than 2% under time-varying temperatures, and the capacity can be predicted efficiently with less than 0.071 A h.

Online SoC Estimation of Lithium-Ion Batteries Using a New Sigma Points Kalman Filter

The accurate state of charge (SoC) online estimation for lithium-ion batteries is a primary concern for predicting the remaining range in electric vehicles. The Sigma points Kalman Filter is an emerging SoC filtering technology. Firstly, the charge and discharge tests of the battery were carried out using the interval static method to obtain the accurate calibration of the SoC-OCV (open circuit voltage) relationship curve. Secondly, the recursive least squares method (RLS) was combined with the dynamic stress test (DST) to identify the parameters of the second-order equivalent circuit model (ECM) and establish a non-linear state-space model of the lithium-ion battery. Thirdly, based on proportional correction sampling and symmetric sampling Sigma points, an SoC estimation method combining unscented transformation and Stirling interpolation center difference was designed. Finally, a semi-physical simulation platform was built. The Federal Urban Driving Schedule and US06 Highway Driving Schedule operating conditions were used to verify the effectiveness of the proposed estimation method in the presence of initial SoC errors and compare with the EKF (extended Kalman filter), UKF (unscented Kalman filter) and CDKF (central difference Kalman filter) algorithms. The results showed that the new algorithm could ensure an SoC error within 2% under the two working conditions and quickly converge to the reference value when the initial SoC value was inaccurate, effectively improving the initial error correction ability.

Modified dual extended Kalman filters for SOC estimation and online parameter identification of lithium-ion battery via modified gray wolf optimizer

In order to achieve accurate state of charge (SOC) estimation of Lithium-Ion Battery, A method that dual Extended Kalman filters (DEKF) optimized by PSO-based Gray Wolf optimizer (MGWO) is proposed. A second-order equivalent circuit model with two resistor-capacitor branches is applied. The battery parameters are determined by battery test. Dual Extended Kalman filters are divided into state filter and parameter filter. Parameter filter is applied to adjust battery parameters online, state filter is applied to SOC estimation. Meanwhile, MGWO is applied to optimize the noise covariance matrix to improve the state estimation accuracy of SOC which reduces the linearization error from EKF. The results shows that the accuracy of algorithm is improved by adding online parameter identification and the optimization of the noise covariance matrix, meanwhile, the proposed method can adapt to the initial error well.

Improved gray wolf particle filtering and high‐fidelity second‐order autoregressive equivalent modeling for intelligent state of charge prediction of lithium‐ion batteries

The rapid development of new energy vehicles puts forward higher requirements for the lithium-ion batteries model construction, high-efficiency condition monitoring and collaborative estimation. An improved high-fidelity second-order autoregressive model is proposed and constructed, and the autoregressive model is integrated with the second-order equivalent circuit model, which can achieve an accurate and reliable description of the batteries internal dynamic change process. To achieve the accurate expression of the battery's external characteristics and internal state, the forgetting factor is combined with the recursive least square algorithm to improve the parameter identification accuracy and optimality while reducing the space complexity of the algorithm. A novel gray wolf particle filtering algorithm is proposed, which eliminates the particles severe degradation in traditional algorithms and enhances the ability of particles to resist degradation. The algorithm superiority and generalization are verified under complex working conditions. The experimental results show that the accuracy of the high-fidelity second-order autoregressive model can reach 99%, which can well simulate the complex chemical reaction process inside the lithium-ion battery. Experimental simulation is performed under constant current conditions. Compared with the extended Kalman filter, unscented Kalman filter, and particle filter algorithms, the gray wolf particle filter algorithm has reduced the root mean square error by 3.39%, 0.90%, and 2.84%, and the mean absolute error has reduced by 1.95%, 0.51%, and 2.22%. Under dynamic stress test conditions, the root mean square error is reduced by 1.54%, 0.33%, and 0.78%, and the average absolute error is reduced by 1.4%, 0.22%, and 0.76%. In addition, when tested under different environmental conditions, although the improved algorithm has a relatively long running time, the estimation accuracy of the algorithm is greatly improved and the execution efficiency is high. The improved algorithm provides a theoretical basis for the reliability and stability of the onboard operation of lithium-ion batteries. Highlights A novel lithium-ion battery high-fidelity second-order autoregressive equivalent model is proposed. The gray wolf particle filter is employed to improve the observation accuracy. A recursive calculation method is derived by the time-based parameters.

An Immune Genetic Extended Kalman Particle Filter approach on state of charge estimation for lithium-ion battery

In this paper, based on the lithium-ion battery parameter identification by Immune Genetic Algorithm, An Extended Kalman Particle Filter approach is proposed to estimate the state of charge. Immune Genetic Algorithm was designed to identify the second-order equivalent circuit model parameters of lithium-ion battery. Combining Extended Kalman Filter with Particle Filter, Extended Kalman Particle Filter is designed to estimate the lithium-ion battery state of charge. This method is especially for the nonlinear and time variant lithium-ion battery system, and it can improve the calculation accuracy and stability of State of Charge estimation. An Immune Genetic Extended Kalman Particle Filter approach is validated by some experimental scenarios on the test bench. Experimental results show that Immune Genetic Extended Kalman Particle Filter has better adaptability, robustness and accuracy than Extended Kalman Filter under both UDDS and ECE conditions. Both theoretical and experimental results illustrate that Extended Kalman Particle Filter is a good candidate to estimate the lithium-ion battery state of charge.

A comparative study of equivalent circuit models for a Li-ion battery pack of an electric Tuk-Tuk

This paper presents developments and validations of Lithium Nickel Manganese Cobalt Oxide (NMC) battery cell and battery pack models. A 7.4 kWh NMC battery pack is installed on an electric Tuk-Tuk equipped with a 3 kW motor. The battery pack is configured of four cells connected in parallel and 20 sets of the four cells connected in series. Based on the first-order and the second-order equivalent circuit models, battery cell and battery pack models are developed in Matlab/Simulink environment. For parameter identifications of the cell model, pulse discharge tests are performed at room temperature with 10% State of Charge (SOC) interval. The lumped heat capacitance method is applied to the battery models. The battery cell model is validated with SOC, cell center temperatures and terminal voltage using the experimental data of constant current discharge tests. With the battery pack configuration, the battery cell model is scaled up to match the battery pack voltage and its capacity. The dynamics of the battery pack models are validated with the vehicle testing data using the no-load, wide-open throttle and real road tests. The simulation results show good agreement with the test data. Using the developed battery models, vehicle performance and its energy consumption can be improved by optimizing battery cell and pack configurations.

Modeling and validation of lithium-ion battery with initial state of charge estimation

The modeling of lithium-ion battery is an important element to the management of batteries in industrial applications. Various models have been studied and investigated, ranging from simple to complex. The second-order equivalent circuit model was studied and investigated since the dynamic behavior of the battery is fully characterized. The simulation model was built in Matlab Simulink using the Kirchhoff Laws principle in mathematical equations, while the battery's internal parameters were identified by using the BTS4000 (Battery tester) device. To estimate the full state of charge (SOC), the initial state of charge (SOC0) must be identified or measured. Hence, this paper seeks for the SOC estimation by using experimental terminal voltage data and SOC with Matlab lookup table. Then, the simulated terminal voltage, as well as the SOC of the battery are compared and validated against measured data. The maximum relative error of 0.015 V and 2% for terminal voltage and SOC respectively shows that the proposed model is accurate and relevant based on the error analysis.

Thermal performance of honeycomb-like battery thermal management system with bionic liquid mini-channel and phase change materials for cylindrical lithium-ion battery

To improve the working performance of the lithium-ion battery, a novel honeycomb-like battery thermal management system (BTMS) integrated hexagonal cooling plate with bionic liquid mini-channel and phase change materials is proposed. The bionic liquid mini-channel in the cooling plate is inspired by the structure of the spider web and honeycomb. The thermal performance of battery module is numerically investigated with computational fluid dynamics (CFD) and second-order equivalent circuit model. Base on the structural design of the battery module, the single cooling plate with the hexagonal shape is applied, and the width of the mini-channel and the amount of tube joints are fixed at 2.5 mm and two, respectively. When the discharge current, inlet flow rate, and ambient temperature are 32.2 A, 0.001 kg·s−1, and 298.15 K, respectively, the battery module adapted the internal-flow scheme has the maximum temperature of 309.15 K and the temperature difference of 3.8 K with a pressure drop of 11.95 Pa. Furthermore, the back propagation (BP) neural network is used to estimate the appropriate inlet flow rate according to the driving cycle condition and ambient temperature. The maximum temperature and temperature difference of the battery module are stabilized within 312.0 K and 3.5 K after a period of fluctuations by using the estimated value of BP model. The battery module proposed in here avoids the failure of temperature control when the phase change material is melted completely.