An improved particle swarm optimization-adaptive square root Unscented Kalman filter algorithm for accurate state of charge estimation of lithium-ion batteries

Highly accurate state of charge (SOC) estimation of lithium-ion batteries is one of the key technologies of battery management systems in electric vehicles. The performance of SOC estimation directly influences the driving range and safety of these vehicles. Due to external disturbances, temperature variation and electromagnetic interference, accurate SOC estimation becomes difficult. To accurately estimate the SOC of lithium-ion batteries, this article presents a novel machine-learning method to address the risk of gradient explosion and gradient decent using the dynamic nonlinear auto-regressive models with exogenous input neural network (NARX) with long short-term memories (LSTM).The proposed hybrid NARX model embeds LSTM memory, which provides jump-ahead connections in the time-unfolded model. These jump-ahead connections provide a shorter path for the propagation of gradient information, therefore reducing long-term dependence on the recurrent neural network. Experimental results show that the estimation performance root mean square error (RMSE) of the proposed model is less than 1%, and this model has better multitime prediction performance. Finally, the hybrid NARX and LSTM model is compared with the standard back propagation neural network based on particle swarm optimization (BPNN-PSO), the least-squares support vector machine (LS-SVM) and LSTM existing models under urban dynamometer driving schedule (UDDS) and dynamic stress test (DST) conditions. The proposed hybrid NARX-LSTM model yield relative to other methods and can estimate the battery SOC with high accuracy. The RMSE of proposed model is improved by approximately 60% compared with the standard LSTM.

An optimized long short-term memory-weighted fading extended Kalman filtering model with wide temperature adaptation for the state of charge estimation of lithium-ion batteries

State of charge (SOC) of the lithium-ion battery is an important parameter of the battery management system (BMS), which plays an important role in the safe operation of electric vehicles. When existing unknown or inaccurate noise statistics of the system, the traditional unscented Kalman filter (UKF) may fail to estimate SOC due to the non-positive error covariance of the state vector, and the SOC estimation accuracy is not high. Therefore, an improved adaptive unscented Kalman filter (IAUKF) algorithm is proposed to solve this problem. The IAUKF is composed of the improved unscented Kalman filter (IUKF) that is able to suppress the non-positive definiteness of error covariance and Sage–Husa adaptive filter. The IAUKF can improve the SOC estimation stability and can improve the SOC estimation accuracy by estimating and correcting the system noise statistics adaptively. The IAUKF is verified under the federal urban driving schedule test, and the SOC estimation results are compared with IUKF and UKF. The experimental results show that the IAUKF has higher estimation accuracy and stability, which verifies the effectiveness of the proposed method.

State of charge is a significant indicator with respect to the remaining capacity for the lithium-ion battery. Nonetheless, strong nonlinearity and time-varying attributes resulting from the complicated electrochemical reactions incur the tremendous difficulty to acquire the accurate state directly. To address the above problems, a novel estimation method based on unscented Kalman filter and dual-filters scheme is proposed. Concerning the nonlinearity features of lithium-ion batteries and the advantages of unscented transformation technique to deal with nonlinearity problems, the unscented Kalman filter approach is applied for states estimation and simultaneously in order to guarantee parameters variation of models adaptively with changes of batteries performance, the dual filters scheme is established to estimate the parameters and state of charge collaboratively. Through the validation by two dynamic driving cycles, it is shown that the state of charge not only could approach to the true values fast, but also the estimated errors are kept within the boundary of 2%.

Accurate online parameter identification and state of charge (SOC) estimation are both very crucial for ensuring the operating safety of lithium-ion batteries and usually the former is a base of the latter. To achieve accurate and stable SOC estimation results, this paper proposes a model-based method, which incorporates a vector forgetting factor least square (VFFLS) algorithm and an improved adaptive cubature Kalman filter (IACKF). Firstly, considering it is difficult for the traditional forgetting factor recursive least square (FFRLS) algorithm to balance the accuracy, convergence, and stability for multiple parameters with different time-varying periods, an improved VFFLS method is employed to determine the multiple parameters of the first-order RC battery model online. It supersedes the single forgetting factor in the FFRLS with multiple forgetting factors in a vector form for improving adaptive capability to multiple time-varying parameters. Secondly, aiming at the fact that the standard cubature Kalman filter (CKF) cannot operate properly when the error covariance matrix is non-positive definite, which is caused by disturbance, initial error, and the limit of the computer word length, the UR decomposition rather than the Cholesky decomposition is applied, thus improving the algorithm stability. In addition, an adaptive update strategy is added to the CKF to enhance accuracy and convergence speed. Finally, comparative experiments with different operating patterns, positive and non-positive definite error covariance matrices, and temperatures are carried out. Experimental results showed that the proposed method can estimate the SOC accurately and stably.

State of charge estimation for lithium-ion batteries based on adaptive dual Kalman filter

Accurate state of charge estimation is essential to improve operation safety and service life of lithium-ion batteries. This paper proposes a synthetic state of charge estimation method for lithium-ion batteries based on long short-term memory network modeling and adaptive H-infinity filter. Firstly, the long short-term memory network is exploited to roughly estimate state of charge with the input of voltage, current, operating temperature and state of health. Then, to mitigate the output fluctuation and improve the estimation robustness of long short-term memory network, the adaptive H-infinity filter is employed to flatten the estimation results and further improve the estimation accuracy. A main advantage of the proposed synthetic method lies in that precise battery modeling and burdensome model parameter identification tasks that are imperative in traditional observers or filters can be omitted, thus improving the application efficiency of the proposed algorithm. The proposed method is verified effective on two types of lithium-ion batteries under dynamic working scenarios including the varying temperature and aged conditions. The experimental results highlight that the estimation error of state of charge can be restricted within 2.1% in wide temperature range and different aging states, manifesting its high-precision estimation capacity and strong robustness.

The estimation of state of charge (SOC) is a critical issue in the energy management of electric vehicle (EV) power batteries. However, the current accuracy of SOC estimation methods does not meet the requirements of practical applications. Therefore, this study proposes an improved lithium-ion battery SOC estimation method that combines deep residual shrinkage network (DRSN) and bidirectional gated recurrent unit (BiGRU) to enhance the SOC estimation accuracy. First, we insert the bidirectional gated recurrent unit neural network between the global average pooling layer and the output fully connected layer of the deep residual shrinkage network. This improvement enhances the model’s expressiveness, robustness, and data learning effect. Second, we develop a new activation function called “∂_swish” to replace the original ReLU activation function in the deep residual shrinkage network. The ∂_swish activation function improves the accuracy of the deep network model and reduces the risk of overfitting by utilizing its regularization effect. Finally, we conduct experimental tests at three different temperatures using the FUDS driving cycle dataset and the DST-US06-FUDS continuous driving cycle dataset. The algorithm model’s convergence speed is verified by comparing it with other models. The results show that compared to other models, the proposed method significantly improves SOC estimation accuracy at three different temperatures. In addition, the method demonstrates a high convergence speed.

Improved adaptive feedback particle swarm optimization-multi-innovation singular decomposition unscented Kalman filtering for high accurate state of charge estimation of lithium-ion batteries in energy storage systems

State of charge (SOC) is one of the key indices for battery management system (BMS). Accurate estimation of SOC can greatly improve battery safety performance and service life. Due to the complex electrochemical reaction inside the battery, SOC is highly nonlinear and cannot be directly measured. This paper proposes a SOC estimation method based on recurrent neural network (RNN). The input current and terminal voltage are selected as input parameters to predict SOC. The information transfer of RNN is mainly divided into two steps: from the input layer to the hidden layer and from the hidden layer to the output layer. To identify the internal parameters of RNN, RNN is firstly opened the feedback loop, and then closed the feedback loop after the training using the improved gauss-newton backpropagation algorithm. Through the cycle charge and discharge experiment of Lithium-ion battery, this paper trained 8 neural networks based on different training sets and predicted them with corresponding verification sets respectively. It was found that the experimental data were consistent with the predicted data, which verified the effectiveness of the method.

This paper deals with the state of charge (SOC) estimation of lithium-ion battery (LIB) in electric vehicles (EVs). In order to accurately describe the dynamic behavior of the battery, a fractional 2nd-order RC model of the battery pack is established. The factional-order battery state equations are characterized by the continuous frequency distributed model. Then, in order to ensure the effective function of nonlinear function, Lipschitz condition and unilateral Lipschitz condition are proposed to solve the problem of nonlinear output equation in the process of observer design. Next, the linear matrix (LMIS) inequality based on Lyapunov’s stability theory and H∞ method is presented as a description of the design criteria for non-fragile observer. Compared with the existing literature that adopts observers, the proposed method takes the advantages of fractional-order systems in modeling accuracy, the robustness of H∞ method in restricting the unknown variables, and the non-fragile property for tolerating slow drifts on observer gain. Finally, The LiCoO2 LIB module is utilized to verify the effectiveness of the proposed observer method in different operation conditions. Experimental results show that the maximum estimation accuracy of the proposed non-fragile observer under three different dynamic conditions is less than 2%.

In order to improve the accuracy of the battery state of charge (SOC) estimation, in this paper we take a lithium-ion battery as an example to study the adaptive Kalman filter based SOC estimation algorithm. Firstly, the second-order battery system model is introduced. Meanwhile, the temperature and charge rate are introduced into the model. Then, the temperature and the charge rate are adopted to estimate the battery SOC, with the help of the parameters of an adaptive Kalman filter based estimation algorithm model. Afterwards, it is verified by the numerical simulation that in the ideal case, the accuracy of SOC estimation can be enhanced by adding two elements, namely, the temperature and charge rate. Finally, the actual road conditions are simulated with ADVISOR, and the simulation results show that the proposed method improves the accuracy of battery SOC estimation under actual road conditions. Thus, its application scope in engineering is greatly expanded.

Dynamic ultrasonic response modeling and accurate state of charge estimation for lithium ion batteries under various load profiles and temperatures

Accurate state of charge estimation and robust cell equalization are vital in optimizing the battery management system and improving energy management in electric vehicles. In this paper, the passive balance control based equalization scheme is proposed using a combined dynamic battery model and the unscented Kalman filter based state of charge estimation. The lithium-ion battery is modeled with a 2nd order Thevenin equivalent circuit. The combined dynamic model of the lithium-ion battery, where the model parameters are estimated depending on the state of charge, and the unscented Kalman filter based state of charge, are used to improve the performance of the passive balance control based equalization. The experimental results verified the superiority of the combined dynamic battery model and the unscented Kalman filter algorithm with very tight error bounds. Furthermore, these results showed that the presented passive balance control based equalization scheme is suitable for the equalization of series-connected lithium-ion batteries.

Accurate state of charge (SOC) estimation is a fundamental guarantee for effective development of lithium-ion power battery in electric vehicles. To improve the SOC estimation precision and robustness, a novel model-based estimation approach has been proposed. Fully giving consideration to the effect of measurement errors, the dynamic external electrical property of lithium-ion battery is approximated by a controlled auto-regressive and moving average (controlled ARMA)-based equivalent circuit model. An improved adaptive extended Kalman filter approach is developed for SOC estimation based on the multi-innovation principle. Meanwhile, the different weighting factor is added into each innovation to reduce cumulative influence of historical interference. Since the flat characteristic in OCV-SOC fitting curve enlarges the OCV-based SOC estimation error, a feedforward compensation method is introduced to reduce OCV identification error to improve OCV-based SOC estimation. The simulation and experimental results verify the validity of the proposed methodology over other estimation methods. Besides, simulated current noise is added to the condition data to prove the high precision and strong robustness of the proposed algorithm.