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Journal of Physics: Conference Series
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Study on SOC Estimation of Li-ion Battery Based
on the Comparison of UKF Algorithm and AUKF
Algorithm
To cite this article: Yi Guo and Yuhang Chen 2023 J. Phys.: Conf. Ser. 2418 012097
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EPEE-2022
Journal of Physics: Conference Series 2418 (2023) 012097
IOP Publishing
doi:10.1088/1742-6596/2418/1/012097
1
Study on SOC Estimation of Li-ion Battery Based on the
Comparison of UKF Algorithm and AUKF Algorithm
Yi Guo1, a*, Yuhang Chen1, b
1Electrical Engineering, Shanghai DianJi University, Shanghai, China
bemail:654367022@qq.com
*Corresponding author: aemail: 216004010202@st.sdju.edu.cn
Abstract: In this study, a state of charge (SOC) estimate technique for lithium-ion batteries is
presented using an adaptive traceless Kalman filter (AUKF). First, the battery’s second-order
RC equivalent circuit model is created, and its parameters are identified. Next, in contrast to the
traceless Kalman filter (UKF) algorithm, which ignores the time-varying characteristics of the
system noise when estimating the lithium-ion battery’s state of charge, the AUKF-based SOC
estimation method is formed from the perspective of adaptive noise adjustment (SOC). The
results of testing the AUKF algorithm in real-world settings demonstrate that it has great estimate
accuracy and stability and that its estimation outcomes outperform those of the UKF method.
1. Introduction
The primary direct measurement methods, data-driven approaches, and adaptive filter-based methods
are used in SOC estimation today. The open-circuit voltage approach and the ampere-time integration
method are both direct measuring techniques. The open-circuit voltage method necessitates leaving the
battery offline for a considerable amount of time, making it difficult to use for online estimation;
however, the ampere-time integration method is highly dependent on the determination of the initial
value of SOC, and the measurement error will gradually become larger [1]. The data-driven approach
establishes a mapping link between SOC and factors like voltage, current, and temperature, which are
quantifiable quantities outside of the battery, using machine learning techniques. For instance, the BP
neural network technique is frequently employed, although it requires a lot of processing and is highly
reliant on the accuracy and dependability of the training. The adaptive filter-based approach may limit
the error buildup during the process and fix errors brought on by the initial SOC value uncertainty, but
it is more dependent on the corresponding circuit’s characteristics.
2. Methodology
2.1 Second-order RC circuit model
SOC estimation is based on the battery model. It has been demonstrated that the comparable circuit
model can be used to estimate battery SOC, which properly reflects the physical and chemical changes
inside the battery and satisfies the needs of the battery management system. For a thorough analysis, the
battery model in Figure 1 is used [2].
EPEE-2022
Journal of Physics: Conference Series 2418 (2023) 012097
IOP Publishing
doi:10.1088/1742-6596/2418/1/012097
2
Figure 1 Second-order RC equivalent circuit model
The open circuit voltage, current, polarization capacitance, ohmic internal resistance, polarization
resistance, and terminal voltage are all shown in the figure as 𝑈
,𝐼,𝐶
,𝐶
,𝑅
,𝑅
,𝑅
and 𝑈
,
respectively. The model equation may be obtained by using the existing cell model and looks like this:
⎩
⎨
⎧
𝑈
𝑈
𝐼
𝑈
𝑈
𝐼
𝑈
𝑈
𝑈
𝑈
𝐼𝑅
(1)
The SOC expression is: 𝑆𝑂𝐶𝑡𝑆𝑂𝐶
, where: T is the sampling time; 𝜂 is the Coulomb
efficiency; 𝐶
is the cell capacity.
2.2 Parameter Identification
The NCR18650B ternary lithium-ion battery, with a rated capacity of 3A.H and a nominal voltage of
3.6V, is the experimental subject of this research. The constant current pulse test is used to determine
the parameters, and the following experimental steps are taken with the thermostat set to 25℃:
a. Leave the fully charged battery in the thermostat at room temperature for one hour while recording
the battery’s open circuit voltage;
b. Discharge the battery for three minutes at 1 C steady current;
c. After a 2-hour wait, note the battery’s resting voltage;
d. Keep going through steps 2 and 3 until the battery is dead.
The least squares approach is used to fit the voltage and current full cycle and one cycle fluctuation
curves from the CCP experiment to get the discriminative values for each parameter.
𝑈
𝑎
𝑎
ln𝑆𝑂𝐶𝑎
ln1𝑆𝑂𝐶
𝑎
𝑆𝑂𝐶 (2)
3. UKF and AUKF algorithms
When calculating SOC, the UKF method assumes the process and measurement noise as constant values,
however when the battery is functioning, the system environment is complicated and changing, and the
noise also has time-varying properties. The AUKF method is provided in this study to lessen the impact
of noise on the calculated SOC. To enhance the algorithm's capacity to estimate the SOC, the Sage-Husa
adaptive algorithm is added to the UKF in the AUKF algorithm [3].
3.1 UKF algorithm
The system’s measurement equation and equation of state are:
𝑥
𝑓𝑥
,𝑢
𝑤
𝑦
𝑔𝑥
,𝑢
𝑣
(3)
where: 𝑤
~0,𝑄
is the measurement noise, and 𝑣
~0,𝑅
is the process noise. The UKF functions
as described below:
a. Initialization: 𝑥
,𝑃
b. Calculation of the Sigma point sampling: The variance 𝑃
and 𝑥
at k-1 moments are used to
generate 2n-1 sigma points 𝑥
.
EPEE-2022
Journal of Physics: Conference Series 2418 (2023) 012097
IOP Publishing
doi:10.1088/1742-6596/2418/1/012097
3
𝑥,𝑥 𝑥𝑛𝜆𝑃 𝑥𝑛𝜆𝑃 (4)
c. Covariance time update and battery status for UKF. One-step predictions of the system state
𝑥𝑘1and the covariance 𝑃
𝑘1 are calculated using the obtained Sigma point set.
𝑥,𝑘1𝑓𝑥,,𝑢
𝑥𝑘1∑
𝜔𝑓𝑥,,𝑢𝑞 (5)
𝑃𝑘1𝑄∑
𝜔𝑥,𝑘1𝑥,𝑘1𝑥,𝑘1𝑥,𝑘1 (6)
d. UKF observational forecasts. A new Sigma point set is generated based on the results of 𝑥𝑘1
and 𝑃𝑘1.
𝑋,𝑘1𝑔𝑥,,𝑢 (7)
e. Determine the UKF's observed projected mean and covariance. By applying the recently acquired
Sigma point set observation predictions, the mean and covariance of the system predictions are
determined. The equations are provided below.
𝑦𝑘1∑
𝜔𝑔𝑥,,𝑢𝑟 (8)
𝑃,𝑅∑
𝜔𝜒,𝑘1𝑦𝑘1 (9)
𝑃,∑
𝜔𝜒,𝑘1𝑥,𝑘1𝜒,𝑘1𝑥,𝑘1 (10)
f. Calculate the gain matrix.
𝑘𝑔𝑃𝑃, (11)
g. Updates on battery condition and covariance measurement in UKF.
𝑥𝑥𝑘1𝑘𝑔𝑦𝑦𝑘1
𝑃𝑃
𝑘1𝑘𝑔𝑃
𝑘𝑔 (12)
The SOC value may be extracted from the updated battery status 𝑥 at instant k, allowing for the
SOC estimation to be made.
3.2 AUKF algorithm
The UKF method can estimate the system status in real-time, yet the following issues still exist [4].
Accurate values of the process noise covariance matrix and the measurement noise covariance matrix
are difficult to acquire because the nonlinear system has some uncertainty. Although the RC model’s
correctness is extensively relied upon by UKF, errors may inevitably occur when identifying the resistive
characteristics of the RC model. When the model error is substantial, a large state estimation error is
introduced through the measurement correction link. Unexpected events like variations in the SOC’s
starting value and unusual disruptions in measurement noise frequently occur in actual applications [5].
For these circumstances, the traditional UKF has a limited capacity for adaptation. The Sage-Husa
adaptive method is used in the UKF algorithm to update the 𝑞,𝑄,𝑟,𝑅 noise parameters in real-
time to increase the accuracy of the estimated SOC since the noise of the system model is unknown and
will vary over time. The AUKF algorithm equation is as follows:
a. Determine the process noise's estimated mean and covariance.
𝑞1𝑑𝑞𝑑𝑥∑
𝜔𝑓𝑥,,𝑢
𝑄1𝑑𝑄𝑑𝑘𝑔𝑦𝑦𝑦𝑦𝑘𝑔𝑃𝑃,𝑃, (13)
b. Calculate the measurement noise’s estimated mean and covariance.
EPEE-2022
Journal of Physics: Conference Series 2418 (2023) 012097
IOP Publishing
doi:10.1088/1742-6596/2418/1/012097
4
𝑟
1𝑑
𝑟
𝑦
∑
𝜔
𝑔𝑥
,
𝑘1,𝑢
𝑅
1𝑑
𝑅
𝑑
𝑦
𝑦𝑦
𝑦
𝑃
,
𝑃
,
(14)
The Simulink simulation of AUKF is shown in Figure 2.
Figure 2 Simulink simulation diagram
4. Experiment and analysis
The thermostat was set to 25°C, and a 3𝐴⋅ℎ, 18650B ternary lithium-ion battery with a nominal voltage
of 3 V was used. The battery’s voltage and current curves were recorded while it was fully charged and
drained under dynamic stress test circumstances [6].
Figure 3 UKF estimated SOC results Figure 4 UKF estimation error
The outcomes and relative mistakes of the UKF method for SOC estimation are displayed in Figures
3 and 4. As can be observed, there are significant estimating errors in the early half of the experimental
phase and the anticipated SOC values do not closely match the real values. This is because the filter is
in a divergent state, at which point a smaller measurement noise covariance is selected, and the UKF
converges at later points, at which point a larger measurement noise covariance is selected. Additionally,
the fitting residuals of the end voltages have large deviations and the initial SOC error is present.
EPEE-2022
Journal of Physics: Conference Series 2418 (2023) 012097
IOP Publishing
doi:10.1088/1742-6596/2418/1/012097
5
Figure 5 AUKF estimated SOC results Figure 6 AUKF estimation error
Figures 5 and 6 display the SOC estimate results and the AUKF algorithm’s relative mistakes. In the
first half of the experiment, it can be seen that there is a similar issue of a poor fit between the predicted
and true values as with the UKF algorithm, but in the second half of the experiment, the predicted values
are closer to the true values than with the UKF algorithm, and the estimation error is also smaller. When
the observed residuals in the process of SOC estimation are bigger than the threshold owing to flaws in
sensor measurement accuracy or the RC model itself, R is set to infinity, and only state prediction
without state correction is carried out at those points [7].
To further verify the effect of different initial values of SOC estimation on the two algorithms, SOC
= 0. 5 was taken and the results were verified using the port voltage to obtain Figure 7 and Figure 8.
Figure 7 End voltage prediction Figure 8 End voltage prediction error
The findings are depicted in the figure, which demonstrates that when using smaller initial values for
SOC estimation, both methods’ convergence times lengthen, and the subsequent coefficient rises. The
UKF method is less robust against the uncertainty of the starting value, as seen by the larger increase in
the subsequent coefficient. Although compared to its original value of 0.8, the AUKF algorithm’s
estimation inaccuracy somewhat rises. The MAE and RMSE estimate errors are still minimal.
5. Conclusion
The general convergence criterion of the filter is introduced into UKF and the method adapts the
measurement noise covariance R, process noise covariance Q, and Kalman gains K by adjustment,
improving the stability and convergence of the filtering algorithm. The AUKF algorithm is used to
estimate SOC using UKF while proposing an AUKF algorithm for the problems of conventional UKF.
Finally, real test results are used for experimental validation. The findings demonstrate that, when
compared to the traditional UKF method, the suggested AUKF algorithm has greater estimation
accuracy, lower following coefficients, and smoother estimation curves under various test settings.
EPEE-2022
Journal of Physics: Conference Series 2418 (2023) 012097
IOP Publishing
doi:10.1088/1742-6596/2418/1/012097
6
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