In general, battery packs are monitored by the battery management system (BMS) to ensure the efficiency and reliability of the energy storage system. SOC and SOH represent the battery’s energy and lifetime, respectively. They are the core aspects of the battery BMS. The traditional method assumes that the SOC is determined by the integral of the current input and output from the battery over time, which is an open-loop-based approach and often accompanies by poor estimation accuracy and the accumulation of sensor errors. The contribution of this work is to establish a new equivalent circuit model based on the lithium battery external characteristic, and the battery parameters are identified by considering the influence of capacity fade, voltage rebound, and internal capacitance-resistance performance. The correlation between the ohmic internal resistance and real capacity is obtained by degradation test. Then, the dual extended Kalman filter (DEKF) is used to perform real-time prediction of the lithium battery state. And through the simulation analysis and experiments, the feasibility and precision of the estimation method are well proved.
Lithium battery has been widely used in the energy storage field due to its high energy density, long cycle life, high voltage, and outstanding security [
SOC and SOH represent the battery’s energy and lifetime, respectively. They are the core aspects of the battery BMS. The traditional method assumes that the SOC is determined by the integral of the current input and output from the battery over time. This is an open-loop-based approach, the result of which is often accompanied by poor estimation accuracy and the accumulation of sensor errors [
Traditional estimation methods, including the internal resistance method, coulomb counting (CC) method, open-circuit voltage method, and load charge method, have some limitations in practical application due to lack of abilities to correct errors and largely depending on high precision of sensors and low environment influences [
The contribution of this paper is to establish a new equivalent circuit model based on the lithium battery external characteristic, and the battery parameters are identified by considering the influence of capacity fade, voltage rebound, and internal capacitance-resistance performance. The correlation between the ohmic internal resistance and real capacity is obtained by degradation test. Then, the dual extended Kalman filter (DEKF) is used to perform real-time prediction of the lithium battery state. And through the simulation analysis and experiments, the feasibility and precision of the estimation method are well proved.
The rest of the paper is organized as follows. An equivalent circuit model is established, and the characteristic parameters of the battery are identified in Section
The battery performance is closely related to its internal parameters. And the change rule of characteristic parameters can be analyzed by establishing the reasonable equivalent model [
Equivalent circuit model of the lithium battery.
The voltage source is related with the SOC, SOH, and working conditions of the battery. Therefore, the equivalent voltage source
Hysteresis voltage
Therefore, the equivalent voltage source is
The capacitance and resistance performance of the battery are described by an equivalent impedance submodel, which consists of the ohmic internal resistance
Therefore, according to Thevenin's theorem, the complete equivalent circuit model of the lithium battery can be expressed as
Through the equivalent circuit model, the relations of internal parameters and external working characteristic, including EMF-SOC, voltage hysteresis, rebound effect, and impedance characteristic of the lithium battery, can be described clearly.
At the constant temperature of 25°C, a pulse discharge test for the max load 18650 lithium battery is performed to identify the model characteristic parameters. The battery capacity is 2900mAh, and the current is 2.9 A. The test current is shown in Figure
Pulse discharge test. (a) Test current. (b) Voltage and SOC.
Based on the test data of the balance electromotive force
The corresponding mathematical expression is
The
According to test data and equations (
The rebound characteristic curve.
The characteristic parameters.
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Battery state contains the state of charge (SOC) and the state of health (SOH). SOC is the remain charge that can be released from the battery, which is related with the initial charge state, actual capacity, and previous current [
SOH is evaluated based on the battery capacity. According to battery failure standard, the battery is invalid when its actual capacity drops to 80% of rated capacity [
The lithium ion in the electrolyte is hindered by the solid electrolyte interface (SEI) adhering to the electrode of the lithium battery. With continuous electrochemical reaction, SEI becomes thicker and thicker, which means hindrance to the lithium ion gets more serious. This can be seen from the increased ohmic internal resistance in the macroscopic view [
The corresponding mathematical expression is
According to the result analysis, SOC and SOH are closely related. The estimation accuracy of SOC can be improved by considering the influence of capacity degradation.
Extended Kalman filter (EKF) is an improved method based on the traditional Kalman filter that can be used for the estimation of nonlinear state variables [
The battery state estimation based on the DEKF method is shown in Figure
DEKF procedure for state estimation.
According to the result of the last cycle, the battery capacity at time
The estimated values obtained by state equations cannot avoid the accumulation of process errors. Besides, the initial errors that may exist is hard to be recognized and corrected [
The error corrections depend on the difference value of observational variable
The real cycle test is time consuming. And it is more efficient for the algorithm analysis to simulate the battery working conditions with the help of computer simulation technique [
The battery simulation model.
The SOC estimation is performed by using the DEKF method in the 1C intermittent discharge working condition as shown in Figure
The simulated discharge condition.
The simulation results. (a) SOC. (b) Estimation errors.
In Figure
To verify the feasibility and accuracy of the DEKF method in the real SOC estimation, the experiments are performed by the BMS circuit. The circuit structure consists of a lithium battery pack, the battery monitoring circuit (BMC), the battery control unit (BCU), and the upper computer, as shown in Figure
Experimental circuit and its structure. (a) The circuit structure. (b) Experimental setup.
The SOC estimation experiments are performed by, respectively, using the traditional CC method and DEKF method in the working conditions of the open-circuit state, constant-current discharge state, and intermittent discharge state.
When the initial charge is 92%, the SOC estimation is performed in the open-circuit state. The measuring voltage nearly remains constant due to the zero working current, as shown in Figure
Measuring voltage in the open-circuit state.
SOC estimation in the open-circuit state. (a) 0 initial error. (b) 2% initial error.
The measuring voltage constantly decreases in 1.5 C constant-current discharge state, as shown in Figure
Measuring voltage in the constant-current discharge state.
SOC estimation in the constant-current discharge state. (a) 0 initial error. (b) 10% initial error.
The change of measuring voltage in 1C intermittent discharge state is shown in Figure
Measuring voltage in the intermittent discharge state.
When initial errors are 0 and 10%, the estimation results of SOC are shown in Figure
SOC estimation in the intermittent discharge state. (a) 0 initial error. (b) 10% initial error.
In the open-circuit state, the accuracy of the CC method completely depends on initial error because of zero working current, while DEKF can correct error within a short time. In working conditions, even if the initial error is 0, the maximum errors of CC, respectively, reach 8% and 12%, while the DEKF method is less than 2%. In terms of situation that 10% initial error is introduced, and the error of the CC method is still very big in all of the experiment processes. But, the DEKF method has good convergence, and the initial error can gradually be decreased by correction of the state equation and observational equation.
The average errors of two methods in different conditions are shown in Table
The average estimation error.
Open-circuit state | Constant-current discharge state | Intermittent discharge state | ||||
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0 initial error (%) | 2% initial error (%) | 0 initial error (%) | 10% initial error (%) | 0 initial error (%) | 10% initial error (%) | |
DEKF | 0.2 | 0.2 | 0.8 | 1.3 | 1.8 | 2.7 |
CC | 0 | 1.8 | 4.2 | 11.4 | 6.5 | 13.3 |
A new equivalent circuit model that can describe the working characteristics of the lithium battery is established based on Thevenin’s theorem. The internal parameters, including capacity, the ohmic internal resistance, polarization resistance, and capacitance, are identified by fitting characteristic curve. The relation of equivalent internal resistance and capacity is obtained by battery life experiments. The DEKF principle using in battery state estimation is analyzed based on the relation of SOC and SOH. A simulation model is established to analyze the estimation ability with the influence of different initial errors. The SOC estimation experiments are performed by, respectively, using the traditional CC method and DEKF method in three different working conditions. By comparison with the estimation results of the CC method, the results of DEKF are still near the real values, even if the errors of sensors exist. When 10% initial errors are introduced, the DEKF can correct the errors, and the estimation can fast converge to real values. The average errors are less than 3% in all kinds of working conditions, which verifies the feasibility of the algorithm.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors would like to acknowledge the support of the National Key R&D Program of China (Grant no. 2016YFC0802900) and the Fundamental Research Funds for the Central Universities.