Equivalent circuit components of nickel-metal hydride battery at different states of charge

Equations that describe the voltage variations with time of rechargeable batteries during charging and discharging were used to determine the component values of the equivalent circuit of nickel-metal hydride batteries under different states of charge (SOC). The equivalent circuit of the battery was described as an ideal voltage source in series with a resistor and the parallel combination of a resistor and a capacitor. The battery model used different values of resistance and capacitance, in the parallel combination, during the different phases of the discharge-rest-charge-rest sequence. The results show that the resistances in the equivalent circuit are approximately constant with variations in the SOC. For the discharge and charge phases the capacitor value increased and decreased, respectively, as the SOC decreased. The value of the capacitor in the parallel RC circuit is an indicator of the battery SOC.     

Review of lithium-ion battery state of charge estimation

The technology deployed for lithium-ion battery state of charge (SOC) estimation is an important part of the design of electric vehicle battery management systems. Accurate SOC estimation can forestall excessive charging and discharging of lithium-ion batteries, thereby improving discharge efficiency and extending cycle life. In this study, the key lithium-ion battery SOC estimation technologies are summarized. First, the research status of lithium-ion battery modeling is introduced. Second, the main technologies and difficulties in model parameter identification for lithium-ion batteries are discussed. Third, the development status and advantages and disadvantages of SOC estimation methods are summarized. Finally, the current research problems and prospects for development trends are summarized.     

Research on parameter identification and state of charge estimation of improved equivalent circuit model of Li-ion battery based on temperature effects for battery thermal management

The performance and parameters of Li-ion battery are greatly affected by temperature. As a significant battery parameter, state of charge (SOC) is affected by temperature during the estimation process. In this paper, an improved equivalent circuit model (IECM) considering the influence of ambient temperatures and battery surface temperature (BST) on battery parameters based on second-order RC model have been proposed. The exponential function fitting (EFF) method was used to identify battery model parameters at 5 ambient temperatures including −10°C, 0°C, 10°C, 25°C and 40°C, fitting the relationship between internal resistance and BST. Then, the SOC of the IECM was estimated based on the extended Kalman filter (EKF) algorithm. Using the result calculated by the Ampere-hour integration method as the standard, the data of battery under open circuit voltage (OCV) test profile and dynamic stress test (DST) profile at different ambient temperatures has been compared with the ordinary second-order RC model, and the advantages of the SOC estimation accuracy with IECM was verified. The numerical results showed that the IECM can improve the estimation accuracy of battery SOC under different operating conditions.     

A comparative study of lumped equivalent circuit models of a lithium battery for state of charge prediction

Battery modeling plays an important role in remaining range prediction and battery management system development. An accurate and realistic battery model is essential to design an efficient electric storage system. The goal of this paper is to investigate the performance of different circuit topologies for diffusion process in the equivalent circuit models (ECMs). The theory of diffusion process approximation by using resistive‐capacitor (RC) networks is explained in frequency domain. The terminal voltage predictive capabilities of the ECMs are compared and validated with test data. The numerical simulation results show that model prediction accuracy and computation burdens increase along with the number of RC pairs. The ECM with three RC networks is the best choice in terms of the balance between accuracy and complexity for ternary lithium batteries. In addition, a novel method of combining unscented Kalman filter (UKF) algorithm with initial state of charge (SOC) acceleration convergence for SOC estimation is proposed. The results of urban dynamometer driving schedule (UDDS) show that ECM with three RC networks has the best comprehensive performance on calculation cost and SOC estimation accuracy.     

Composite electrodes of disordered carbon and graphite for improved battery state estimation with minimal performance penalty

Voltage based state of charge (SOC) estimation is challenging for lithium ion batteries that exhibit little open circuit voltage (OCV) change over a large SOC range. We demonstrate that by using a composite negative electrode composed of disordered carbon and graphite, we were able to introduce additional features to the OCV-SOC relationship that facilitate voltage-based SOC estimation. In contrast to graphite, the potential of disordered carbon is sensitive to the state of charge; this behavior, when manifested in a lithium ion battery, gives rise to additional beneficial features of the cell OCV-SOC relationship in terms of state estimation. We have demonstrated the effectiveness of the approach by comparing model simulations and corresponding experimental data of a cell composed of LiFePO₄ positives and graphite + disordered carbon composite negative electrodes. Last, we find that although the graphite material has a higher coulombic capacity, very little (dynamic) performance loss is manifest with the mixed graphite + disordered carbon composite is employed.     

An equivalent circuit model of a deformed Li-ion battery with parameter identification

A new equivalent circuit model (ECM) of a Li-ion battery is developed in this study. The developed model is utilized to obtain the dynamic electrical response of the battery when it is deformed under external force. Compared with other models, this model is developed based on a modified Thevenin model, and the parameters of the developed model are relevant to state of charge, the battery surface temperature, and the deformation. In this study, to obtain the real electrical response of the battery when it deformed under external force, batteries that are compressed by different deformations from 0 to 5 mm are studied with pulse discharging tests. Then, the parameters of the circuit elements are identified by a differential evolution algorithm based on the data obtained from these tests. Moreover, the data from the pulse discharging tests of batteries compressed by 3.5, 4.25, and 4.5 mm and the data from the pulse charging tests of batteries compressed by 0 and 1 mm are used to verify the parameters. The results illustrate that the battery capacity should drop significantly when the battery is severely deformed, but the battery still can be charged and discharged. Most importantly, the discharging curves of these tested deformed batteries are similar to those of undeformed ones. Moreover, the developed new ECM can predict the dynamic electrical response of a deformed battery accurately.     

Equivalent circuit model parameters of a high-power Li-ion battery: Thermal and state of charge effects

Equivalent circuit model (EMC) of a high-power Li-ion battery that accounts for both temperature and state of charge (SOC) effects known to influence battery performance is presented. Electrochemical impedance measurements of a commercial high power Li-ion battery obtained in the temperature range 20 to 50 °C at various SOC values was used to develop a simple EMC which was used in combination with a non-linear least squares fitting procedure that used thirteen parameters for the analysis of the Li-ion cell. The experimental results show that the solution and charge transfer resistances decreased with increase in cell operating temperature and decreasing SOC. On the other hand, the Warburg admittance increased with increasing temperature and decreasing SOC. The developed model correlations that are capable of being used in process control algorithms are presented for the observed impedance behavior with respect to temperature and SOC effects. The predicted model parameters for the impedance elements R_s, R_ct and Y₀₁₃ show low variance of 5% when compared to the experimental data and therefore indicates a good statistical agreement of correlation model to the actual experimental values.     

Transient-boundary voltage method for measurement of equivalent circuit components of rechargeable batteries

A method is presented for measuring the equivalent circuit components of rechargeable batteries. The temporal discharge-rest-charge-rest sequence of a rechargeable battery is described, using the principles of transient circuit analysis, to derive equations for the battery voltage as a function of time during voltage transients and at the boundaries at transitions between transient phases. The equations lead to a new measurement method for battery characterization. The equivalent circuit of the battery is described as an ideal voltage source in series with a resistor and the parallel combination of a resistor and a capacitor. The battery model uses different values of resistance and capacitance, in the parallel combination, during the different phases of the discharge-rest-charge-rest sequence. The method is used to measure the circuit parameters of a nickel-cadmium battery.     

State of charge estimation method based on the extended Kalman filter algorithm with consideration of time-varying battery parameters

In developing battery management systems, estimating state-of-charge (SOC) is important yet challenging. Compared with traditional SOC estimation methods (eg, the ampere-hour integration method), extended Kalman filter (EKF) algorithm does not depend on the initial value of SOC and has no accumulated error, which is suitable for the actual working condition of electric vehicles. EKF is a model-based algorithm; the accuracy of SOC estimated by this algorithm was greatly influenced by the accuracy of battery model and model parameters. The parameters of battery change with many factors and exhibit strong nonlinearity and time variance. Typical EKF algorithm approximates battery as a linear, time-invariant system; however, this approach introduces estimation errors. To minimize such errors, previous studies have focused on improving the accuracy of identifying battery parameters. Although studies on battery model with time-varying parameters have been carried out, few have studied the combination of time-varying battery parameters and EKF algorithm. A SOC estimation method that combines time-varying battery parameters with EKF algorithm is proposed to improve the accuracy of SOC estimation. Battery parameter data were obtained experimentally under different temperatures, SOC levels, and discharge rates. The results of parameter identification are made into a data table, and the battery parameters in the EKF system matrix are updated by looking up the data in the table. Simulation and experimental results shown that, average error of SOC estimated by the proposed algorithm is 2.39% under 0.9 C constant current discharge and 2.4% under 1.3 C, which is 1.91% and 2.35% lower than that of EKF algorithm with fixed battery parameters. Under intermittent discharge with constant current (1.1 C) and capacity (10%), the average error of SOC estimated by the proposed algorithm is 1.4%, which is 0.3% lower than that of EKF algorithm with fixed battery parameters. The average error of SOC estimated by the proposed algorithm under the New European Driving Cycle (NEDC) is 1.6%, which is 0.2% lower than that of EKF algorithm with fixed battery parameters. Relative to the EKF algorithm with fixed battery parameters, the proposed EFK algorithm with time-varying battery parameters yields higher accuracy.     

Online management of lithium-ion battery based on time-triggered controller area network for fuel-cell hybrid vehicle applications

This paper introduces a state of charge (SOC) estimation algorithm that was implemented for an automotive lithium-ion battery system used in fuel-cell hybrid vehicles (FCHVs). The proposed online control strategy for the lithium-ion battery, based on the Ah current integration method and time-triggered controller area network (TTCAN), incorporates a signal filter and adaptive modifying concepts to estimate the Li₂MnO₄ battery SOC in a timely manner. To verify the effectiveness of the proposed control algorithm, road test experimentation was conducted with an FCHV using the proposed SOC estimation algorithm. It was confirmed that the control technique can be used to effectively manage the lithium-ion battery and conveniently estimate the SOC.     

System dynamic model and charging control of lead-acid battery for stand-alone solar PV system

The lead-acid battery which is widely used in stand-alone solar system is easily damaged by a poor charging control which causes overcharging. The battery charging control is thus usually designed to stop charging after the overcharge point. This will reduce the storage energy capacity and reduce the service time in electricity supply. The design of charging control system however requires a good understanding of the system dynamic behaviour of the battery first. In the present study, a first-order system dynamics model of lead-acid battery at different operating points near the overcharge voltage was derived experimentally, from which a charging control system based on PI algorithm was developed using PWM charging technique.The feedback control system for battery charging after the overcharge point (14 V) was designed to compromise between the set-point response and the disturbance rejection. The experimental results show that the control system can suppress the battery voltage overshoot within 0.1 V when the solar irradiation is suddenly changed from 337 to 843 W/m². A long-term outdoor test for a solar LED lighting system shows that the battery voltage never exceeded 14.1 V for the set point 14 V and the control system can prevent the battery from overcharging. The test result also indicates that the control system is able to increase the charged energy by 78%, as compared to the case that the charging stops after the overcharge point (14 V).     

Active cell balancing of lithium-ion battery pack based on average state of charge

Differences in the environment and parameters of lithium-ion battery (LiB) cells may lead the residual capacity between the battery cells to be inconsistent, and the battery cells may be damaged due to overcharging or overdischarging. In this study, an active balancing method for charging and discharging of LiB pack based on average state of charge (SOC) is proposed. Two different active balancing strategies are developed according to the different charging and discharging states of LiB pack. When the LiB pack is charging, charging balance strategy is performed, wherein the battery cells whose SOC is higher than the average SOC of the LiB pack are balanced to increase the charging capacity of the entire LiB pack. When the LiB pack is discharging or static standing, discharging balance strategy is performed, wherein the batter cells whose SOC is lower than the average SOC of the LiB pack are balanced to increase the discharging capacity of the entire LiB pack. The experimental results show that the proposed active balancing method can reduce the inconsistency of residual energy between the battery cells and improve the charging and discharging capacity of the LiB pack.     

Combustibility and hazard of lithium iron phosphate power battery components in different aging states

选用四种衰退状态,容量保持率（capacity retention ratio,CRR）分别为100%、85%、75%及65%的磷酸铁锂动力电池为研究对象,采用锥形量热仪（CONE）对电池关键组件（含电解液的正极片、负极片及隔膜）的燃烧性和生烟性进行了研究,并运用层次分析法（analytic hierarchy process,AHP）综合评价了不同衰退状态电池组件的火灾危险性。结果表明,随着电池容量保持率的下降,电池组件中负极的有效燃烧热值有所下降,并且电池组件的CO₂产率和总生烟量逐渐降低;容量保持率100%~85%的电池组件的归一化危险性指数要明显大于75%~65%的电池组件。     

State of charge estimation in Ni-MH rechargeable batteries

In this work we estimate the state of charge (SOC) of Ni-MH rechargeable batteries using the Kalman filter based on a simplified electrochemical model. First, we derive the complete electrochemical model of the battery which includes diffusional processes and kinetic reactions in both Ni and MH electrodes. The full model is further reduced in a cascade of two parts, a linear time invariant dynamical sub-model followed by a static nonlinearity. Both parts are identified using the current and potential measured at the terminals of the battery with a simple 1-D minimization procedure. The inverse of the static nonlinearity together with a Kalman filter provide the SOC estimation as a linear estimation problem. Experimental results with commercial batteries are provided to illustrate the estimation procedure and to show the performance.     

Battery algorithm verification and development using hardware-in-the-loop testing

Battery algorithms play a vital role in hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs), extended-range electric vehicles (EREVs), and electric vehicles (EVs). The energy management of hybrid and electric propulsion systems needs to rely on accurate information on the state of the battery in order to determine the optimal electric drive without abusing the battery.In this study, a cell-level hardware-in-the-loop (HIL) system is used to verify and develop state of charge (SOC) and power capability predictions of embedded battery algorithms for various vehicle applications. Two different batteries were selected as representative examples to illustrate the battery algorithm verification and development procedure. One is a lithium-ion battery with a conventional metal oxide cathode, which is a power battery for HEV applications. The other is a lithium-ion battery with an iron phosphate (LiFePO₄) cathode, which is an energy battery for applications in PHEVs, EREVs, and EVs.The battery cell HIL testing provided valuable data and critical guidance to evaluate the accuracy of the developed battery algorithms, to accelerate battery algorithm future development and improvement, and to reduce hybrid/electric vehicle system development time and costs.     

Effect of charge rate on capacity degradation of LiFePO4 power battery at low temperature

Limited by the current power battery technology, electric vehicles show extremely poor duration performance and potential risk at low temperature, which is mainly caused by poor charging performance of lithium-ion batteries. To explore the impact of charging process on cycle degradation at low temperatures, a cycle aging experimental scheme with different charging C-rate (0.3C and 0.5C) under −10°C and −20°C was designed for the commercial LiFePO₄ battery. The experimental batteries showed severe degradation after a few of cycles. The phenomenon of reduced internal resistance and up-shift of the charging curve was found during the early cycle stages (0th-20th cycle). The influence of low-temperature cycle on battery was analyzed by the increment capacity analysis (ICA); the fast decreasing intensity of ①*II showed sharp loss of lithium ions. Those lithium ions mainly transformed into lithium plating and built up dendrites instead of reintercalating into the anode crystal structure, causing the further degradation of capacity and ohmic resistance. Degradation law was obtained by curve regression analysis in the end.     

Robust polynomial approach for state of charge estimation in NiMH batteries

In this work we estimate the state of charge (SOC) of NiMH rechargeable batteries using a robust optimal filter based on a simplified electrochemical model. The robust filter guarantees that the supremum of the error variance - difference between real and estimated SOC - with respect to all admissible uncertainties be minimum. The results are compared with those obtained using the linear Kalman filter. We conclude that both estimations have similar performance, although the robust filter is easier to tune. Experimental results with commercial batteries are provided to illustrate the estimation procedure and it performance.     

电动汽车电池的充电状态和健康状况评估：关键问题和挑战

使用电动汽车（EV）进行运输被视为实现可持续发展和解决环境问题的必要组成部分。当前对环境的关注,例如化石燃料的快速消耗,空气污染的增加,能源需求的加速增长,全球变暖和气候变化,为交通运输部门的电气化铺平了道路。电动汽车可以解决上述问题。电源已成为电动汽车发展的关键,尤其是锂离子（Li-ion）电池。由于其能量密度、功率...     

Two‐layer online state‐of‐charge estimation of lithium‐ion battery with current sensor bias correction

Because of the harsh working condition in electrified vehicles, the measured current and voltage signals typically contain non‐ignorable noises and bias, which potentially decline the accuracy of state‐of‐charge estimation. In this regard, the noise and bias corruption should be well addressed to maintain sufficient accuracy and robustness. This paper improves the existing methods in the literature from two aspects: (a) A novel offset‐free equivalent circuit model is developed to remove the current bias; and (b) based on the offset‐free equivalent circuit model, a two‐layer estimator is proposed to estimate the state of charge using real‐time identified model parameters. The robustness of the two‐layer estimator against model uncertainties and the aging effect is further evaluated. Simulation and experimental results show that the proposed two‐layer estimator can effectively attenuate the current bias and estimate the state of charge accurately with the error confined to ±4% under different levels of current bias and model uncertainties.     

Simulation study of electrical dynamic characteristics of lithium-ion battery

The electrical dynamic characteristics of a lithium-ion battery have been simulated by an equivalent circuit, which is derived from the measured impedance. The transient voltage response to the various kinds of applied current waves such as single pulse, single rectangular, triangle, and sawtooth waves is experimentally examined and calculated by using the numerical Laplace transform with the equivalent circuit. The experimental and calculated results are compared and discussed, focusing on the range of current where the linear relationship is valid. Changing the time range, the state of charge (SOC) and the battery temperature as parameters, their influence on the linear range of the applied current has been investigated.