In the battery management system, it is important to accurately and efficiently estimate the state of charge (SOC) of lithium-ion batteries, which generally requires the establishment of a equivalent circuit model of the battery, whose accuracy and rationality play an important role in accurately estimating the state of lithium-ion batteries. The traditional single order equivalent circuit models do not take into account the changes of impedance spectrum under the action of multiple factors, nor do they take into account the balance of practicality and complexity of the model, resulting the low accuracy and poor practicability. In this paper, the theory of electrochemical impedance spectroscopy is used to guide and improve the equivalent circuit model. Based on the analysis of the variation of the high and intermediate frequency range of the impedance spectrum with the state of charge and temperature of the battery, a variable order equivalent model (VOEM) is proposed by Arrhenius equation and Bayesian information criterion (BIC), and the state equation and observation equation of VOEM are improved by autoregressive (AR) equations. Combined with the unscented Kalman filter (UKF), a SOC online estimation method is proposed, named VOEM-AR-UKF. The experimental results show that the proposed method has high accuracy and good adaptability.

To realize accurate estimation of SOC (state of charge) and SOH (state of health), Li-ion battery’s operating characteristic is analyzed in this paper while fully considering temperature, degree of aging and other practical factors that could impact their operating status. On the basis of nonlinear autoregressive with exogenous inputs (NARX) architecture, an improved dynamic recurrent neural network (DRNN) with ability of dynamic mapping is established, which is more suitable than static network for estimating the batteries’ state with strongly nonlinear and dynamic behaviors. Meanwhile, a self-adaptive weight particle swarm optimization (SWPSO) algorithm is introduced for training the network. Compared with gradient descent algorithm, the SWPSO algorithm could improve error convergence speed and avoid falling into local optimum. Validation results highlights that the presented method is able to improve the estimation accuracy of the SOC and SOH under different conditions including temperature, current and degree of aging, and has strong robustness and ability of generalization.

State of charge (SOC) estimation of lithium-ion batteries is a problem of time series. In deep learning methods, both convolutional neural network (CNN) and recurrent neural network (RNN) can be used to solve such problems. In this paper, based on deep learning, a hybrid neural network model is proposed to estimate the SOC of lithium-ion batteries by taking the sequence of sampling points of voltage, current and temperature as input. The model is mainly composed of three modules, namely, convolutional module, ultra-lightweight subspace attention mechanism (ULSAM) module and the gated recurrent unit (GRU) module. Convolutional module and ULSAM module are responsible for extracting the feature information from the sequence of sampling points and outputting feature maps. GRU module is responsible for processing the sequences of the feature maps and outputting the value of SOC. The proposed model is tested on the public NASA Randomized Battery Usage dataset and Oxford Battery Degradation dataset. The experimental results show that the proposed model can obtain a relatively accurate SOC estimation at unknown aging state and complex operating conditions.

An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time.