An adaptive estimation method for state of charge of lithium-ion batteries

Abstract

This invention discloses a method for jointly estimating the state of charge (SOC) of lithium-ion batteries. The method comprises the following steps: establishing a second-order RC equivalent circuit model of the lithium-ion battery; obtaining the battery model's state-space equations; and estimating the SOC of the lithium-ion battery using an adaptive sliding mode observer based on the Adam algorithm. This method incorporates the Adam algorithm into the sliding mode observer to update the sliding mode observer matrix gain. Based on this, the system state variables are adaptively estimated to improve the algorithm's estimation performance and adaptability, thereby achieving accurate SOC estimation of the lithium-ion battery.

Description

Technical Field

[0001] The present invention belongs to the technical field of lithium-ion batteries, is applied to a lithium-ion battery management system, and particularly relates to a method for adaptively estimating the state of charge of a lithium-ion battery. Background Art

[0002] The core source of my country's carbon emissions comes primarily from energy activities, which account for 85% of total carbon emissions. Energy activities consist of two components: energy production and energy consumption. Energy production primarily involves the production of fossil fuels such as oil, coal, and natural gas. Within energy consumption, automotive fuel consumption already accounts for 55% of total oil consumption. To achieve its dual carbon goals, my country is vigorously developing wind and solar power stations for energy storage, replacing fossil fuels with clean energy to control carbon emissions from energy production. Regarding energy consumption, my country is primarily supporting the new energy vehicle industry. Lithium-ion batteries, due to their long cycle life, high energy density, and pollution-free nature, are widely used in new energy storage. Currently, lithium-ion batteries are the primary choice for research and manufacturing in energy storage power stations and new energy vehicle energy storage systems.

[0003] As a highly nonlinear system, the SOC of a lithium-ion battery cannot be directly measured and can only be estimated using methods based on battery-related physical quantities. Currently, SOC estimation methods are mainly divided into three categories: direct measurement, data-driven methods, and model-based estimation. Direct measurement methods primarily include the ampere-hour integration method and the open-circuit voltage method. The ampere-hour integration method is applicable to all batteries, is computationally simple, and does not rely on a battery model. However, its accuracy is limited by the accuracy of the battery's initial SOC value. During the calculation process, current sampling errors accumulate as the integration proceeds, leading to estimation bias, which increases with time. The open-circuit voltage method relies on the functional relationship between the battery's open-circuit voltage (OCV) and SOC. By repeatedly measuring different open-circuit voltages and corresponding SOCs, a battery SOC-OCV curve can be generated. Based on this curve, the battery's open-circuit voltage can be measured to estimate SOC. This method offers high accuracy, low cost, and computational simplicity, but it can only be used for static estimation, lacks real-time performance, and cannot meet the requirements of field estimation. Data-driven methods include neural networks and support vector machines. This type of method does not need to consider the dynamic characteristics of the battery's internal structure and can directly predict the SOC based on relevant parameters such as battery current and voltage. However, its disadvantage is that it requires a large amount of data for training and has high hardware requirements. Model-based estimation methods have become a hot topic in SOC estimation research at major universities because of their moderate computational complexity and ability to correct parameter perturbations and inaccurate initial values. The sliding mode observer is a common algorithm in model-based estimation methods. It has a low computational complexity and is robust against parameter perturbations. However, since this algorithm sets the sliding mode observer gain matrix to an ideal constant during application, its adaptability is limited. Summary of the Invention

[0004] In response to the problems existing in the above-mentioned prior art, the present invention provides a method for adaptively estimating the state of charge of a lithium-ion battery. The method introduces the Adam algorithm into the sliding mode observer to update the sliding mode observer gain matrix in real time, thereby enhancing the accuracy and robustness of the algorithm in estimating the SOC of a lithium-ion battery.

[0005] To achieve the above object, the present invention provides the following solution: The present invention provides a method for adaptively estimating the state of charge of a lithium-ion battery, comprising the following steps:

[0006] Step 1: Establish a second-order RC equivalent circuit model of the lithium-ion battery: collect open circuit voltage data and state of charge data, and obtain battery model parameters under different states based on the equivalent circuit model;

[0007] Step 2: Obtaining a battery model state space equation: Based on Kirchhoff's law, using the equivalent circuit model and battery model parameters, obtaining a model state space equation;

[0008] Step 3: Adaptive estimation: Based on the state-space equation of the model, an adaptive sliding mode observer based on the Adam algorithm is used to estimate the state of charge of the lithium-ion battery.

[0009] Preferably, the step 3 specifically includes:

[0010] Step 3.1, calculate the synovial surface z at time k k :

[0011] z k =u k -u k

[0012] Among them, u k is the observed value of the lithium-ion battery terminal voltage, u k is the predicted value of the lithium-ion battery terminal voltage;

[0013] Step 3.2: Update the system state variables based on the system state equation and the selected sliding surface. The update equation is:

[0014] x k+1 =f(x k )-L k *z k -r*sign(z k )

[0015] Where, f() is the system state equation, L, r is the sliding mode observer gain matrix;

[0016] Step 3.3, update the sliding mode observer gain matrix L based on the Adam algorithm;

[0017] Step 3.4: Loop through steps 3.1 to 3.3 to update the system state variables in real time.

[0018] Preferably, the method for jointly estimating the state of charge of a lithium-ion battery is characterized in that the updating process of the sliding mode observer gain matrix L is:

[0019] The algorithm error is defined as:

[0020] Taking the partial derivative of L in the above formula, we get: Where C is the output matrix of the system observation equation;

[0021] Calculate the partial first-order moment estimate m and the partial second-order moment estimate v:

[0022] m k =β1*m k-1 +(1-β1)*g k

[0023]

[0024] Among them, β1 and β2 represent the first-order exponential decay rate and the second-order exponential decay rate of the moment estimate, respectively. The default values are generally β1 = 0.9 and β2 = 0.999;

[0025] Update the sliding mode observer gain matrix L: Among them, α is the learning rate, and ε is a very small parameter to prevent zero division during the calculation process. Generally, the default values are α = 0.001 and ε = 10. -8 .

[0026] The present invention discloses the following technical effects:

[0027] The present invention proposes a method for adaptively estimating the state of charge (SOC) of a lithium-ion battery, which can effectively enhance the SOC estimation accuracy and environmental adaptability of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0029] Figure 1 The present invention provides a flow chart of a method for adaptively estimating the state of charge of a lithium-ion battery.

[0030] Figure 2It is the second-order RC equivalent circuit model of lithium-ion battery.

[0031] Figure 3 Current for the U.S. federal city driving cycle at 25°C.

[0032] Figure 4 Schematic diagram of SOC estimation error of two algorithms (sliding mode observer SMO and adaptive sliding mode observer ASMO based on Adam algorithm proposed in this invention) under 25°C U.S. federal city driving conditions.

[0033] Figure 5 Schematic diagram of SOC estimation error of two algorithms (sliding mode observer SMO and adaptive sliding mode observer ASMO based on Adam algorithm proposed in the present invention) using only battery model parameters identified at 20% SOC under 25°C US federal city driving conditions. DETAILED DESCRIPTION

[0034] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. However, it should be understood that the present invention may be implemented in various forms, and the following exemplary and non-limiting embodiments shown in the drawings and described below are not intended to limit the present invention to the specific embodiments described.

[0035] See also Figure 1 , Figure 1 A method for adaptively estimating the state of charge of a lithium-ion battery according to an embodiment of the present invention includes the following steps:

[0036] Step 1: Establish a second-order RC equivalent circuit model of the lithium-ion battery: collect open circuit voltage data and state of charge data, and obtain battery model parameters under different states based on the equivalent circuit model.

[0037] The second-order RC equivalent circuit model of the lithium-ion battery in step 1 is as follows: Figure 2 As shown, it consists of a controlled voltage source, two RC links and an ohmic internal resistance R0 in series. The controlled voltage source represents the open-circuit voltage of the battery. The RC link (R1, C1, R2, C2) is the polarization internal resistance and polarization content, which are used to simulate the battery electrochemical polarization and concentration polarization. The battery ohmic internal resistance is used to simulate the battery ohmic polarization process.

[0038] Step 1 is implemented as follows:

[0039] Step 1.1, static method: The fully charged battery is discharged intermittently at a constant rate and allowed to stand for a long time (with 10% SOC as the interval) to obtain the open circuit voltage U of the battery. oc and SOC data;

[0040] Step 1.2: Use the least squares method to fit the open circuit voltage Uoc The relationship between SOC and the 9th order polynomial U oc =a1*SOC 9 +a2*SOC 8 +a3*SOC 7 +a4*SOC 6 +a5*SOC 5 +a6*SOC 4 +a7*SOC 3 +a8*SOC 2 +a9*SOC+a 10 Perform fitting to obtain the open circuit voltage U oc Functional relationship with SOC;

[0041] Step 1.3, calculate the ohmic internal resistance by dividing the sudden voltage value at the moment of pulse discharge of the battery by the sudden current value;

[0042] Step 1.4, by formula Obtain the electrochemical polarization time constant τ1 and concentration polarization time constant τ2; by the formula Obtain the electrochemical polarization internal resistance R1, and the concentration polarization resistance R2. The ratio of the electrochemical polarization time constant τ1 to the electrochemical polarization internal resistance R1 is the first polarization capacitance C1, and the ratio of the concentration polarization time constant τ2 to the concentration polarization internal resistance R2 is the second polarization capacitance C2. Wherein, U1 is the terminal voltage of the first RC link, U2 is the terminal voltage of the second RC link, and U oc is the open circuit voltage of the battery, I is the operating current of the battery, and U is the terminal voltage of the battery;

[0043] Step 1.5: Execute steps 1.3 to 1.4 according to different states of charge to obtain battery model parameters under different states of charge.

[0044] Step 2: Obtaining a battery model state space equation: Based on Kirchhoff's law, obtain a model state space equation through the equivalent circuit model and the battery model parameters.

[0045] The model state space equation established in step 2, including the state equation and observation equation, is as follows:

[0046]

[0047] U k =U oc,k -U 1,k -U 2,k -R0I k +v k

[0048] Where T is the sampling period, w kis the process noise, v k To measure noise, C N is the rated capacity of the battery, soc represents the state of charge of the battery, and k represents the number of iterative calculation steps at the current moment.

[0049] The state space equation can be simplified to:

[0050] x k =Ax k-1 +BI k-1 +w k-1

[0051] U k =U oc,k -U 1,k -U 2,k -R0I k +v k

[0052] in,

[0053] Step 3: Adaptive estimation: Based on the state-space equation of the model, an adaptive sliding mode observer based on the Adam algorithm is used to estimate the state of charge of the lithium-ion battery.

[0054] Step 3 is implemented as follows:

[0055] Step 3.1, set the initial value of the state variable x0 and the synovial observer gain matrix L,r;

[0056] Step 3.2: Calculate the battery model parameters based on the current state of charge (SOC) of the battery.

[0057] Step 3.3, calculate the synovial surface z at time k k :

[0058] z k =u k -u k

[0059] Among them, u k is the observed value of the lithium-ion battery terminal voltage, u k is the predicted value of the lithium-ion battery terminal voltage;

[0060] Step 3.4: Update the system state variables based on the system state equation and the selected sliding surface. The update equation is:

[0061] x k+1 =f(x k )-L k *z k -r*sign(z k )

[0062] Where, f() is the system state equation, L, r is the sliding mode observer gain matrix;

[0063] Step 3.5: Update the sliding mode observer gain matrix L based on the Adam algorithm;

[0064] Step 3.6: Loop through steps 3.3 to 3.5 to update the system state variables in real time.

[0065] The updating process of the sliding mode observer gain matrix L in step 3 is:

[0066] The algorithm error is defined as:

[0067] Taking the partial derivative of L in the above formula, we get: Where C is the output matrix of the system observation equation;

[0068] Calculate the partial first-order moment estimate m and the partial second-order moment estimate v:

[0069] m k =β1*m k-1 +(1-β1)*g k

[0070]

[0071] Among them, β1 and β2 represent the first-order exponential decay rate and the second-order exponential decay rate of the moment estimate, respectively. The default values are generally β1 = 0.9 and β2 = 0.999;

[0072] Update the sliding mode observer gain matrix L: Among them, α is the learning rate, and ε is a very small parameter to prevent zero division during the calculation process. Generally, the default values are α = 0.001 and ε = 10. -8 .

[0073] In order to verify the effectiveness of the present invention in estimating SOC, a simulated operating condition experiment was conducted using a ternary lithium-ion battery NCR18650B with a rated capacity of 3.2Ah produced by Panasonic. The simulated operating condition was the Federal Urban Driving Schedule (FUDS) at 25°C. The charge and discharge currents were as follows: Figure 3 shown.

[0074] Figure 4 The figure is a schematic diagram of the SOC estimation error of two algorithms (sliding mode observer SMO and adaptive sliding mode observer ASMO based on Adam algorithm proposed in this invention) under 25℃ FUDS conditions. It can be seen that compared with the SMO algorithm, the ASMO algorithm exhibits higher SOC estimation accuracy throughout the entire SOC discharge cycle, proving that the proposed method can effectively improve the SOC estimation accuracy of the algorithm.

[0075] Figure 5 Figure 2 shows the SOC estimation errors of two algorithms (the sliding mode observer (SMO) and the adaptive sliding mode observer (ASMO) based on the Adam algorithm proposed in this paper) under 25°C FUDS operating conditions with sampling model errors. The battery model only uses parameters identified at 20% SOC. It can be seen that the ASMO algorithm maintains superior estimation accuracy to the SMO algorithm even in the presence of model errors, demonstrating that the proposed method can effectively improve the algorithm's robustness to model parameter perturbations.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for adaptively estimating the state of charge of a lithium-ion battery, characterized in that: The method mainly includes the following steps: Step 1: Establish a second-order RC equivalent circuit model of the lithium-ion battery: collect open circuit voltage data and state of charge data, and obtain battery model parameters under different states based on the equivalent circuit model; Step 2: Obtaining a battery model state space equation: Based on Kirchhoff's law, using the equivalent circuit model and battery model parameters, obtaining a model state space equation; Step 3, adaptive estimation: based on the state space equation of the model, an adaptive sliding mode observer based on the Adam algorithm is used to estimate the state of charge of the lithium-ion battery; The step 3 specifically includes: Step 3.1, calculate the synovial surface z at time k k : Among them, u k is the observed value of the lithium-ion battery terminal voltage, is the predicted value of the lithium-ion battery terminal voltage; Step 3.2: Update the system state variables based on the system state equation and the selected sliding surface. The update equation is: x k+1 =f(x k )-L k *z k -r*sign(z k ) Where f() is the system state equation, L and r are the sliding mode observer gain matrices; Step 3.3, update the sliding mode observer gain matrix L based on the Adam algorithm; Step 3.4: Loop through steps 3.1 to 3.3 to update the system state variables in real time.

2. The method for adaptively estimating the state of charge of a lithium-ion battery according to claim 1, wherein: The updating process of the sliding mode observer gain matrix L is: The algorithm error is defined as: Taking the partial derivative of L in the above formula, we get: Where C is the output matrix of the system observation equation; Calculate the partial first-order moment estimate m and the partial second-order moment estimate v: m k =β1*m k-1 +(1-β1)*g k Among them, β1 and β2 represent the first-order exponential decay rate and the second-order exponential decay rate of the moment estimate, β1 = 0.9, β2 = 0.999; Update the sliding mode observer gain matrix L: Among them, α is the learning rate, ε is a very small parameter to prevent zero division during the calculation process, α = 0.001, ε = 10 -8 .

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