Method and apparatus for estimating state of charge of battery, and device and storage medium

Abstract

Disclosed in the present application are a method and apparatus for estimating the state of charge of a battery, and a device and a storage medium. The method comprises: by means of a Thevenin equivalent circuit model, constructing a Thevenin equivalent circuit state space model for a lithium battery; on the basis of a preset high-order polynomial, performing fitting on the state of charge and open-circuit voltage of the lithium battery, and determining a non-linear relationship curve between the state of charge and the open-circuit voltage; collecting real-time operating state data of the lithium battery, and on the basis of the real-time operating state data, using an extended Kalman filter algorithm to perform online parameter identification on the Thevenin equivalent circuit state space model, so as to obtain an estimated state variable value; and constructing an adaptive double-power sliding mode observer, and inputting the non-linear relationship curve and the estimated state variable value into the adaptive double-power sliding mode observer, so that the adaptive double-power sliding mode observer calculates an estimated state-of-charge value of the lithium battery in real time. Compared with the prior art, the technical solution of the present application can improve the accuracy of estimating the state of charge of a lithium battery.

Description

A method, apparatus, device, and storage medium for estimating the state of charge of a battery.

[0001] Cross-reference to related applications

[0002] This application claims the benefit of Chinese Patent Application No. 202410782292.2, filed on June 18, 2024, the entire contents of which are incorporated herein by reference. Technical Field

[0003] This application relates to the technical field of lithium batteries, and in particular to a method, apparatus, device and storage medium for estimating the state of charge of a battery. Background Technology

[0004] Lithium-ion batteries (LiB) are widely used in consumer electronics, transportation, and energy storage due to their advantages such as high energy density, high power density, low self-discharge rate, and low cost. To ensure the safe, reliable, and effective use of lithium batteries, it is crucial to accurately estimate their state of charge (SOC).

[0005] However, when lithium batteries are used as power batteries in vehicles and other applications, estimating their state of charge requires considering many factors, such as high dynamic load, battery imbalance, self-discharge, aging, and hysteresis characteristics. Furthermore, lithium batteries are easily affected by nonlinearity between various physical quantities, electrothermal coupling, and uncertain external disturbances during operation, making it difficult to accurately estimate the state of charge of lithium batteries.

[0006] Application content

[0007] The technical problem to be solved by this application is to provide a method, apparatus, device and storage medium for estimating the state of charge of a battery, which can improve the accuracy of the state of charge estimation of lithium batteries.

[0008] To address the aforementioned technical problems, this application provides a method for estimating the state of charge (SOC) of a battery, comprising:

[0009] Based on the Thevenin equivalent circuit model, a Thevenin equivalent circuit state-space model of lithium battery is constructed.

[0010] Based on a preset high-order polynomial, the state of charge and open-circuit voltage of the lithium battery are fitted to determine the nonlinear relationship curve between the state of charge and the open-circuit voltage.

[0011] Real-time operating condition data of the lithium battery is collected. Based on the real-time operating condition data, the parameters of the Thevenin equivalent circuit state space model are identified online using the extended Kalman filter algorithm to obtain estimated values ​​of state variables.

[0012] An adaptive double-power sliding membrane observer is constructed, and the nonlinear relationship curve and the estimated value of the state variable are input into the adaptive double-power sliding membrane observer so that the adaptive double-power sliding membrane observer can calculate the estimated value of the state of charge of the lithium battery in real time.

[0013] In one possible implementation, a Thevenin equivalent circuit state-space model of a lithium battery is constructed based on the Thevenin equivalent circuit model, specifically including:

[0014] Based on the Thevenin equivalent circuit model, the state-of-charge equation of the lithium battery is determined.

[0015] Based on the Thevenin equivalent circuit model, the polarization voltage differential equation of the lithium battery is determined.

[0016] Based on the Thevenin equivalent circuit model, the terminal voltage equation of the lithium battery is determined, and the terminal voltage equation is converted into a terminal voltage differential equation.

[0017] Based on the state equation of charge, the differential equation of polarization voltage, and the differential equation of terminal voltage, the Thevenin equivalent circuit state-space model of the lithium battery is determined.

[0018] The Thevenin equivalent circuit state-space model is shown below:

[0019] In the formula, U t For terminal voltage, U oc U is the open-circuit voltage, I(t) is the charging / discharging current, and U is the charging / discharging current. p Polarization voltage, C p For polarization capacitor, R p Q is the polarization resistor, SOC is the state of charge, and Q is the polarization resistor. n Let κ be the nominal capacitance of the battery, R0 be the derivative of the open-circuit voltage, Δf1 be the uncertainty caused by the unknown nonlinear term terminal voltage, Δf2 be the uncertainty caused by the unknown nonlinear term, where the nonlinear term represents the nominal capacitance deviation, temperature coefficient, and unknown uncertain disturbance, and Δf3 be the uncertainty caused by the unknown nonlinear polarization voltage term. This is the differential form of the battery terminal voltage. This is the differential form of the battery's state of charge. This is the differential form of the battery polarization voltage.

[0020] In one possible implementation, the state of charge (SOC) and open-circuit voltage of the lithium battery are fitted based on a preset high-order polynomial to determine a nonlinear relationship curve between the SOC and the open-circuit voltage, specifically including:

[0021] Obtain multiple states of charge of the lithium battery and the open-circuit voltage corresponding to each state of charge;

[0022] Based on a pre-defined high-order polynomial, an expression for the relationship between state of charge and open-circuit voltage is constructed.

[0023] Substitute the multiple states of charge and the open-circuit voltage into the state-of-charge-open-circuit voltage relationship expression, and perform fitting processing on the state-of-charge-open-circuit voltage relationship expression based on the fitting algorithm to obtain the nonlinear relationship curve between the multiple states of charge and the open-circuit voltage;

[0024] The nonlinear relationship curve is shown below: U oc (SOC)=a0+a1SOC+a2SOC 2 +…+a 11 SOC 11 +a 12 SOC 12 ;

[0025] In the formula, a i i = 0, 1, 2, ..., 11, 12 are the fitting coefficients, and SOC is the battery state of charge. 2 SOC is the square of the battery's state of charge. 11 SOC is the 11th power of the battery's state of charge. 12 It represents the 12th power of the battery's state of charge.

[0026] In one possible implementation, based on the real-time operating data, the extended Kalman filter algorithm is used to perform online parameter identification on the Thevenin equivalent circuit state-space model to obtain estimated values ​​of state variables, specifically including:

[0027] Select the state variables to be identified, and establish the online parameter identification state space equation based on the state variables and the real-time operating data;

[0028] The state-space equations of the parameters are linearized online to obtain the state transition matrix and the system output matrix.

[0029] Set initial filtering conditions, calculate initial estimates of the state variables based on the initial filtering conditions, and calculate the initial error covariance matrix based on the initial filtering conditions;

[0030] The initial estimate of the state variable is updated based on the state transition matrix to obtain the prior estimate of the state variable, and the initial error covariance matrix of the state variable is updated based on the state transition matrix to obtain the error covariance matrix.

[0031] Calculate the gain matrix based on the system output matrix, calculate the posterior estimate of the state variable based on the gain matrix, and update the error covariance matrix based on the gain matrix;

[0032] Based on the posterior estimate of the state variable, the estimated value of the state variable is determined.

[0033] In one possible implementation, constructing the adaptive double-power sliding membrane observer specifically includes:

[0034] An adaptive double-power sliding mode observer is constructed, and a switching gain is set for the adaptive double-power sliding mode observer. The adaptive double-power sliding mode observer includes an end voltage adaptive double-power sliding mode observer, a battery charge state adaptive double-power sliding mode observer, and a polarization voltage adaptive double-power sliding mode observer.

[0035] Set the terminal voltage observation error, state of charge observation error, and polarization voltage observation error;

[0036] Based on the terminal voltage observation error, the terminal voltage sliding mode function is determined, and based on the terminal voltage sliding mode function, the terminal voltage Lyapunov function is determined.

[0037] Based on the state of charge observation error, the state of charge sliding mode function is determined, and based on the state of charge sliding mode function, the state of charge Lyapunov function is determined.

[0038] Based on the observed polarization voltage error, the sliding mode function of polarization voltage is determined, and based on the sliding mode function of polarization voltage, the Lyapunov function of polarization voltage is determined.

[0039] Based on the terminal voltage Lyapunov function, the state of charge Lyapunov function, and the polarization voltage Lyapunov function, a first quantitative relationship is determined between the state of charge observation error and a preset first equivalent control quantity in the adaptive double power sliding mode observer, and a second quantitative relationship is determined between the polarization voltage observation error and a preset second equivalent control quantity in the adaptive double power sliding mode observer.

[0040] Based on the first quantitative relationship, the battery charge state adaptive double power sliding membrane observer is updated, and based on the second quantitative relationship, the polarization voltage adaptive double power sliding membrane observer is updated.

[0041] In one possible implementation, the adaptive double-power sliding mode observer includes an end voltage adaptive double-power sliding mode observer, a battery charge state adaptive double-power sliding mode observer, and a polarization voltage adaptive double-power sliding mode observer.

[0042] The terminal voltage adaptive double power sliding mode observer is as follows:

[0043] In the formula, k 1,1 and k 1,2 These are the switching gains of the sliding mode observer, all of which are positive. These are terminal voltage observations. Let V1 be the sliding mode function of the terminal voltage, V1 be the first equivalent control variable of the designed adaptive double-power sliding mode observer, and sgn(·) be the coincidence function. C represents the rate of change of the observed terminal voltage over time. p For polarization capacitors, R p For polarization resistance, Q n Let κ be the nominal capacity of the battery, R0 be the derivative of the open-circuit voltage, I be the charging and discharging current, and α be the parameter in the power term of the adaptive double power-law approach, where 0 < α < 1.

[0044] The battery charge state adaptive double-power sliding membrane observer is as follows:

[0045] In the formula, V2 is the observed value of the state of charge, and k is the second equivalent control variable of the designed adaptive double power sliding mode observer. 2,1 and k 2,2 These are the switching gains of the sliding mode observer, all of which are positive. The rate of change of the observed state of charge over time. These are observed values ​​for polarization voltage. This is the first quantitative relationship;

[0046] The polarization voltage adaptive double power sliding membrane observer is as follows:

[0047] In the formula, k 3,1 and k 3,2 V1 represents the switching gain of the sliding mode observer, all of which are positive. V2 represents the third equivalent control variable of the designed adaptive double-power sliding mode observer. These are polarization voltage observations. The rate of change of the observed polarization voltage over time. This is the second quantitative relationship.

[0048] In one possible implementation, after obtaining the state variable estimates, the following is also included:

[0049] The forward Euler method is used to update the differential of the state of charge, the differential of the polarization voltage state, and the differential of the terminal voltage, resulting in updated differentials of the state of charge, the polarization voltage state, and the terminal voltage. Based on these updated differentials, the adaptive double-power sliding mode observer is discretized to obtain a discretized adaptive double-power sliding mode observer.

[0050] Based on the discretized adaptive double power sliding mode observer, the state of charge, polarization voltage, and terminal voltage are updated to obtain the updated state of charge, updated polarization voltage, and updated terminal voltage.

[0051] In one possible implementation, based on the Thevenin equivalent circuit model, the formula for the external characteristic behavior of the lithium battery during charging and discharging is:

[0052] Among them, U t For terminal voltage, U oc U is the open-circuit voltage, I(t) is the charging / discharging current, and U is the charging / discharging current. p Polarization voltage, C p For battery polarization capacitor, R p The polarization resistor is SOC, which stands for State of Charge. Polarization voltage U p The differential form of U is the rate of change of polarization voltage with time. oc (SOC(t)) is the open-circuit voltage.

[0053] In one possible implementation, the polarization voltage differential equation of the lithium battery is:

[0054] Where Δf3 represents the uncertainty caused by the unknown nonlinear polarization voltage term. R is the differential form of the battery polarization voltage. p For polarization resistance, C p For polarization capacitors, U p Let I(t) be the polarization voltage, I(t) be the charging / discharging current, and ΔC be the polarization voltage. P For additional polarization capacitors.

[0055] In one possible implementation, the terminal voltage differential equation is expressed as:

[0056] Where Δf1 represents the uncertainty caused by the unknown nonlinear term terminal voltage. This is the differential form of the terminal voltage. This is the differential form of the open-circuit voltage. This is the differential form of the battery polarization voltage. This is the differential form of the charging and discharging current.

[0057] In one possible implementation, the multiple states of charge refer to the states of charge at different charging stages.

[0058] In one possible implementation, the real-time operating data includes current, voltage, and temperature.

[0059] This application also provides a battery state of charge estimation device, including: a Thevenin equivalent circuit state space model construction module, a nonlinear relationship curve determination module, an online parameter identification module, and a state of charge estimation module;

[0060] The Thevenin equivalent circuit state space model construction module is used to construct the Thevenin equivalent circuit state space model of lithium battery based on the Thevenin equivalent circuit model.

[0061] The nonlinear relationship curve determination module is used to fit the state of charge and open-circuit voltage of the lithium battery based on a preset high-order polynomial, and determine the nonlinear relationship curve between the state of charge and the open-circuit voltage.

[0062] The online parameter identification module is used to collect real-time operating condition data of the lithium battery, and based on the real-time operating condition data, to perform online parameter identification on the state space model of the Thevenin equivalent circuit using the extended Kalman filter algorithm to obtain estimated values ​​of state variables.

[0063] The state of charge estimation module is used to construct an adaptive double power sliding membrane observer. The nonlinear relationship curve and the estimated value of the state variable are input into the adaptive double power sliding membrane observer so that the adaptive double power sliding membrane observer can calculate the estimated value of the lithium battery state of charge in real time.

[0064] In one possible implementation, the Thevenin equivalent circuit state space model construction module is used to construct a Thevenin equivalent circuit state space model of a lithium battery based on the Thevenin equivalent circuit model, specifically including:

[0065] Based on the Thevenin equivalent circuit model, the state-of-charge equation of the lithium battery is determined.

[0066] Based on the Thevenin equivalent circuit model, the polarization voltage differential equation of the lithium battery is determined.

[0067] Based on the Thevenin equivalent circuit model, the terminal voltage equation of the lithium battery is determined, and the terminal voltage equation is converted into a terminal voltage differential equation.

[0068] Based on the state equation of charge, the differential equation of polarization voltage, and the differential equation of terminal voltage, the Thevenin equivalent circuit state-space model of the lithium battery is determined.

[0069] The Thevenin equivalent circuit state-space model is shown below:

[0070] In the formula, U t For terminal voltage, U oc U is the open-circuit voltage, I(t) is the charging / discharging current, and U is the charging / discharging current. p Polarization voltage, C p For polarization capacitor, R p Q is the polarization resistor, SOC is the state of charge, and Q is the polarization resistor. n Let κ be the nominal capacitance of the battery, R0 be the derivative of the open-circuit voltage, Δf1 be the uncertainty caused by the unknown nonlinear term terminal voltage, Δf2 be the uncertainty caused by the unknown nonlinear term, where the nonlinear term represents the nominal capacitance deviation, temperature coefficient, and unknown uncertain disturbance, and Δf3 be the uncertainty caused by the unknown nonlinear polarization voltage term. This is the differential form of the battery terminal voltage. This is the differential form of the battery's state of charge. This is the differential form of the battery polarization voltage.

[0071] In one possible implementation, the nonlinear relationship curve determination module is used to fit the state of charge and open-circuit voltage of the lithium battery based on a preset high-order polynomial, and determine the nonlinear relationship curve between the state of charge and the open-circuit voltage, specifically including:

[0072] Obtain multiple states of charge of the lithium battery and the open-circuit voltage corresponding to each state of charge;

[0073] Based on a pre-defined high-order polynomial, an expression for the relationship between state of charge and open-circuit voltage is constructed.

[0074] Substitute the multiple states of charge and the open-circuit voltage into the state-of-charge-open-circuit voltage relationship expression, and perform fitting processing on the state-of-charge-open-circuit voltage relationship expression based on the fitting algorithm to obtain the nonlinear relationship curve between the multiple states of charge and the open-circuit voltage;

[0075] The nonlinear relationship curve is shown below: U oc (SOC)=a0+a1SOC+a2SOC 2 +…+a 11 SOC 11 +a 12 SOC 12 ;

[0076] In the formula, a i i = 0, 1, 2, ..., 11, 12 are the fitting coefficients, and SOC is the battery state of charge. 2 SOC is the square of the battery's state of charge. 11 SOC is the 11th power of the battery's state of charge. 12 It represents the 12th power of the battery's state of charge.

[0077] In one possible implementation, the online parameter identification module is used to perform online parameter identification on the Thevenin equivalent circuit state-space model based on the real-time operating data using an extended Kalman filter algorithm to obtain estimated values ​​of state variables, specifically including:

[0078] Select the state variables to be identified, and establish the online parameter identification state space equation based on the state variables and the real-time operating data;

[0079] The state-space equations of the parameters are linearized online to obtain the state transition matrix and the system output matrix.

[0080] Set initial filtering conditions, calculate initial estimates of the state variables based on the initial filtering conditions, and calculate the initial error covariance matrix based on the initial filtering conditions;

[0081] The initial estimate of the state variable is updated based on the state transition matrix to obtain the prior estimate of the state variable, and the initial error covariance matrix of the state variable is updated based on the state transition matrix to obtain the error covariance matrix.

[0082] Calculate the gain matrix based on the system output matrix, calculate the posterior estimate of the state variable based on the gain matrix, and update the error covariance matrix based on the gain matrix;

[0083] Based on the posterior estimate of the state variable, the estimated value of the state variable is determined.

[0084] In one possible implementation, the state-of-charge estimation module is used to construct an adaptive double-power sliding membrane observer, specifically including:

[0085] An adaptive double-power sliding mode observer is constructed, and a switching gain is set for the adaptive double-power sliding mode observer. The adaptive double-power sliding mode observer includes an end voltage adaptive double-power sliding mode observer, a battery charge state adaptive double-power sliding mode observer, and a polarization voltage adaptive double-power sliding mode observer.

[0086] Set the terminal voltage observation error, state of charge observation error, and polarization voltage observation error;

[0087] Based on the terminal voltage observation error, the terminal voltage sliding mode function is determined, and based on the terminal voltage sliding mode function, the terminal voltage Lyapunov function is determined.

[0088] Based on the state of charge observation error, the state of charge sliding mode function is determined, and based on the state of charge sliding mode function, the state of charge Lyapunov function is determined.

[0089] Based on the observed polarization voltage error, the sliding mode function of polarization voltage is determined, and based on the sliding mode function of polarization voltage, the Lyapunov function of polarization voltage is determined.

[0090] Based on the terminal voltage Lyapunov function, the state of charge Lyapunov function, and the polarization voltage Lyapunov function, a first quantitative relationship is determined between the state of charge observation error and a preset first equivalent control quantity in the adaptive double power sliding mode observer, and a second quantitative relationship is determined between the polarization voltage observation error and a preset second equivalent control quantity in the adaptive double power sliding mode observer.

[0091] Based on the first quantitative relationship, the battery charge state adaptive double power sliding membrane observer is updated, and based on the second quantitative relationship, the polarization voltage adaptive double power sliding membrane observer is updated.

[0092] In one possible implementation, the adaptive double-power sliding mode observer includes an end voltage adaptive double-power sliding mode observer, a battery charge state adaptive double-power sliding mode observer, and a polarization voltage adaptive double-power sliding mode observer.

[0093] The terminal voltage adaptive double power sliding mode observer is as follows:

[0094] In the formula, k 1,1 and k 1,2 These are the switching gains of the sliding mode observer, all of which are positive. These are terminal voltage observations. Let V1 be the sliding mode function of the terminal voltage, V1 be the first equivalent control variable of the designed adaptive double-power sliding mode observer, and sgn(·) be the coincidence function. C represents the rate of change of the observed terminal voltage over time. p For polarization capacitors, R p For polarization resistance, Q n Let κ be the nominal capacity of the battery, R0 be the derivative of the open-circuit voltage, I be the charging and discharging current, and α be the parameter in the power term of the adaptive double power-law approach, where 0 < α < 1.

[0095] The battery charge state adaptive double-power sliding membrane observer is as follows:

[0096] In the formula, V2 is the observed value of the state of charge, and k is the second equivalent control variable of the designed adaptive double power sliding mode observer. 2,1 and k 2,2 These are the switching gains of the sliding mode observer, all of which are positive. The rate of change of the observed state of charge over time. These are polarization voltage observations. This is the first quantitative relationship;

[0097] The polarization voltage adaptive double power sliding membrane observer is as follows:

[0098] In the formula, k 3,1 and k 3,2 V1 represents the switching gain of the sliding mode observer, all of which are positive. V2 represents the third equivalent control variable of the designed adaptive double-power sliding mode observer. These are polarization voltage observations. The rate of change of the observed polarization voltage over time. This is the second quantitative relationship.

[0099] In one possible implementation, the state-of-charge estimation module, after obtaining the estimated values ​​of the state variables, further includes:

[0100] The forward Euler method is used to update the differential of the state of charge, the differential of the polarization voltage state, and the differential of the terminal voltage, resulting in updated differentials of the state of charge, the polarization voltage state, and the terminal voltage. Based on these updated differentials, the adaptive double-power sliding mode observer is discretized to obtain a discretized adaptive double-power sliding mode observer.

[0101] Based on the discretized adaptive double power sliding mode observer, the state of charge, polarization voltage, and terminal voltage are updated to obtain the updated state of charge, updated polarization voltage, and updated terminal voltage.

[0102] This application also provides a terminal device, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor executes the computer program to implement the battery state-of-charge estimation method as described in any of the preceding claims.

[0103] This application also provides a computer-readable storage medium including a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to perform a battery state-of-charge estimation method as described in any of the preceding claims.

[0104] This application provides a method, apparatus, device, and storage medium for estimating the state of charge of a battery, which, compared with the prior art, has the following advantages:

[0105] By employing the Thevenin equivalent circuit model, a Thevenin equivalent circuit state-space model of the lithium battery is constructed, which reduces the hardware computing power requirements in subsequent state-of-charge (SOC) evaluation. Simultaneously, by fitting the nonlinear relationship curve between the SOC and open-circuit voltage of the lithium battery using a high-order polynomial, it better adapts to the different operating characteristics and environmental conditions of various lithium batteries, ensuring that the fitted curve maintains high accuracy under different conditions and improving the system's robustness. Furthermore, considering that the characteristic parameters of lithium batteries change with time, temperature, load, and other factors, an extended Kalman filter algorithm is used to apply the Thevenin equivalent circuit state-space model. Online parameter identification using an effective circuit state-space model can more accurately reflect the actual state of the lithium battery and improve the estimation accuracy of the lithium battery's state of charge (SOC). Finally, based on the strong robustness of the sliding mode observer and its insensitivity to external disturbances and parameter perturbations, an adaptive double-power sliding mode observer is constructed. The nonlinear relationship curve and the estimated state variables are input into the adaptive double-power sliding mode observer to calculate the lithium battery SOC estimate in real time. This effectively suppresses the influence of external disturbances and system noise on the SOC estimate, thereby improving the accuracy of the lithium battery system's SOC estimation. Attached Figure Description

[0106] Figure 1 is a schematic flowchart of an embodiment of a battery state-of-charge estimation method provided in this application;

[0107] Figure 2 is a schematic diagram of an embodiment of a battery state-of-charge estimation device provided in this application;

[0108] Figure 3 is a schematic diagram of the structure of a Thevenin equivalent circuit model according to an embodiment of this application;

[0109] Figure 4 is a schematic diagram comparing the observations under different initial charge states of an embodiment provided in this application;

[0110] Figure 5 is a schematic diagram comparing the observation errors under different initial charge states of an embodiment provided in this application;

[0111] Figure 6 is a schematic diagram comparing the terminal voltage tracking under different initial charge states of an embodiment provided in this application;

[0112] Figure 7 is a schematic diagram comparing the state of charge observation with observation noise according to an embodiment provided in this application;

[0113] Figure 8 is a comparative schematic diagram of the state of charge observation error with observation noise in one embodiment of the present application;

[0114] Figure 9 is a schematic diagram comparing the voltage tracking performance of the charged state with observation noise according to an embodiment provided in this application. Detailed Implementation

[0115] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0116] Example 1, referring to Figure 1, Figure 1 is a flowchart illustrating an embodiment of a battery state-of-charge estimation method provided in this application. As shown in Figure 1, the method includes steps 101-104, as detailed below:

[0117] Step 101: Based on the Thevenin equivalent circuit model, construct the Thevenin equivalent circuit state space model of the lithium battery.

[0118] In one embodiment, the equivalent circuit model is typically used to simplify a complex lithium battery system into an equivalent circuit, using components such as resistors, capacitors, and inductors to represent the characteristics of the lithium battery. The equivalent circuit model typically includes parameters such as the battery's open-circuit voltage and internal resistance, which can help predict the voltage and current response of the lithium battery under different operating conditions. Compared with using electrochemical mechanism models to study the internal dynamics of lithium-ion batteries, it can reduce the requirements for hardware computing power and is more suitable for application in power battery management systems. Based on this, in this embodiment, considering the trade-off between model accuracy and computing cost, the Thevenin equivalent circuit model is used to characterize the lithium battery.

[0119] In one embodiment, the Thevenin equivalent circuit model includes an ideal voltage source, namely the open-circuit voltage U. oc (SOC(t)), Ohmic internal resistance R0, terminal voltage U t The nominal capacity Q of the RC network and battery n The RC network is used to describe the polarization characteristics of the battery, including the capacitance C. p and diffusion resistance R p Among them, capacitor C p U reflects the transient response during battery charging and discharging. p Indicates capacitance C pThe voltage across the circuit is called the polarization voltage; as shown in Figure 3, which is a schematic diagram of the Thevenin equivalent circuit model.

[0120] In one embodiment, based on the Thevenin equivalent circuit model, the external characteristic behavior of a lithium battery during charging and discharging can be described as follows:

[0121] In the formula, U t For terminal voltage, U oc U is the open-circuit voltage, I(t) is the charging / discharging current, and U is the charging / discharging current. p Polarization voltage, C p For battery polarization capacitor, R p The polarization resistor is SOC, which stands for State of Charge. Polarization voltage U p The differential form of U is the rate of change of polarization voltage with time. oc (SOC(t)) is the open-circuit voltage.

[0122] In one embodiment, when constructing the Thevenin equivalent circuit state-space model of a lithium battery based on the Thevenin equivalent circuit model, the following steps are taken: the state-of-charge equation of the lithium battery is determined based on the Thevenin equivalent circuit model; the polarization voltage differential equation of the lithium battery is determined based on the Thevenin equivalent circuit model; the terminal voltage equation of the lithium battery is determined based on the Thevenin equivalent circuit model, and the terminal voltage equation is converted into a terminal voltage differential equation; the state-of-charge equation, the polarization voltage differential equation, and the terminal voltage differential equation are used to determine the Thevenin equivalent circuit state-space model of the lithium battery.

[0123] Specifically, the state of charge (SOC) can be defined as the ratio of the battery's remaining capacity to its nominal capacity. Since the capacity value changes under actual operating conditions due to factors such as temperature (T), SOC level, and battery aging, the state of charge equation for a lithium battery is:

[0124] In the formula, SOC0 is the initial state of charge, I(t) is the charging / discharging current (positive for discharging, negative for charging), η is the charging / discharging efficiency, and Q is the discharge efficiency. n This refers to the nominal capacity of the battery.

[0125] The state-of-charge equation of a lithium battery can be converted into the corresponding state-of-charge equation, which can be expressed as:

[0126] In the formula, Let Q be the differential form of the battery's state of charge, where η is the charge / discharge efficiency, and Q is the discharge efficiency. nLet I(t) be the nominal capacitance of the battery, I(t) be the charging / discharging current, and Δf2 be the uncertainty caused by an unknown nonlinear term, where the nonlinear term represents the nominal capacitance deviation, temperature coefficient, and unknown uncertain disturbance. Q n U is the nominal capacity of the battery. t U is the battery terminal voltage. p Q is the polarization voltage. n R0 is the nominal capacity of the battery, and U is the internal resistance in ohms. oc (SOC(t)) is the open-circuit voltage.

[0127] Specifically, the differential equation for the polarization voltage of a lithium battery caused by current can be expressed as:

[0128] In the formula, Δf3 represents the uncertainty caused by the unknown nonlinear polarization voltage term. R is the differential form of the battery polarization voltage. p For polarization resistance, C p For polarization capacitors, U p Let I(t) be the polarization voltage, I(t) be the charging / discharging current, and ΔC be the polarization voltage. P For additional polarization capacitors.

[0129] Specifically, in the Thevenin equivalent circuit model, according to Kirchhoff's voltage theorem, the terminal voltage equation of a lithium battery is: U t (t)=U oc (SOC(t))-U p (t)-I(t)R0;

[0130] In the formula, U t (t) represents the terminal voltage.

[0131] From the operating characteristics of the RC circuit, it can be seen that when the sampling time is sufficiently short, the change in terminal voltage caused by the current can be ignored, i.e., dI / dt≈0. Therefore, the differential equation of the terminal voltage is expressed as:

[0132] In the formula, Δf1 represents the uncertainty caused by the unknown nonlinear term terminal voltage. This is the differential form of the terminal voltage. This is the differential form of the open-circuit voltage. This is the differential form of the battery polarization voltage. This is the differential form of the charging and discharging current.

[0133] In one embodiment, the Thevenin equivalent circuit state-space model is as follows:

[0134] In the formula, U t For terminal voltage, Uoc I is the open-circuit voltage, I is the total current, and U is the open-circuit voltage. p Polarization voltage, C p For polarization capacitor, R p Q is the polarization resistor, SOC is the state of charge, and Q is the polarization resistor. n Let κ be the nominal capacitance of the battery, R0 be the derivative of the open-circuit voltage, Δf1 be the uncertainty caused by the unknown nonlinear term terminal voltage, Δf2 be the uncertainty caused by the unknown nonlinear term, where the nonlinear term represents the nominal capacitance deviation, temperature coefficient, and unknown uncertain disturbance, and Δf3 be the uncertainty caused by the unknown nonlinear polarization voltage term. This is the differential form of the terminal voltage. This is the differential form of the battery's state of charge. This is the differential form of the battery polarization voltage.

[0135] In one embodiment, after obtaining the Thevenin equivalent circuit state-space model, by letting and The Thevenin equivalent circuit state-space model can be represented as a lumped parameter model, which simplifies the Thevenin equivalent circuit state-space model, makes the parameters more physically meaningful and interpretable, and facilitates subsequent online parameter identification.

[0136] Specifically, the lumped parameter model is represented as follows:

[0137] In practice, modeling errors and measurement noise are difficult to completely avoid during battery system modeling. In the model, parameters Δf1, Δf2, and Δf3 are closely related to modeling errors and disturbances; modeling errors are typically caused by the battery open-circuit voltage U. oc The nonlinear relationship between the battery and the state of charge (SOC), or the circuit parameters in the equivalent circuit model, are caused by changes in battery operating conditions. Therefore, in order to more accurately describe the dynamic characteristics of the lithium battery system, this embodiment uses parameters Δf1, Δf2, and Δf3 to represent the bounded uncertainty caused by modeling errors and measurement noise, thereby compensating for model errors and further improving the simulation accuracy of the model.

[0138] In one embodiment, the Thevenin equivalent circuit state-space model is further converted into a Thevenin equivalent circuit model state-space equation matrix, wherein the Thevenin equivalent circuit model state-space equation matrix is ​​as follows:

[0139] In the formula, state variable x1 is the terminal voltage, state variable x2 is the state of charge, and state variable x3 is the polarization voltage.

[0140] Based on the state-space equation matrix of the Thevenin equivalent circuit model, the dynamic state equation of the lithium battery can be expressed as:

[0141] In the formula, A is the system matrix, B is the system input matrix, C is the system output matrix, d is the system modeling uncertainty and disturbance coefficient, x represents the state variable, and y represents the system output.

[0142] By transforming the state-space equation matrix form of the Thevenin equivalent circuit model, we can further analyze the dynamic characteristics and behavior of the circuit. The state-space equation matrix form can represent the system as a set of differential equations, which can better understand the interaction between the system's state variables and how the system evolves over time. It can also explore the dynamic characteristics of the circuit more deeply and provide a more specific mathematical foundation for subsequent control and analysis work.

[0143] In one embodiment, the observability of a linear system can be determined by matrix O. M The observability construction yields:

[0144] O M =[C CA CA] 2 ] T ;

[0145] In the formula, A and C = [1 0 0] are the system state matrix and output matrix, respectively.

[0146] Under any operating conditions, the observability matrix of the system is always full rank. Therefore, all states modeled are observable. Thus, the state of charge (SOC) of the battery based on this state equation is observable. The observability of a system refers to the property that the state of the system can be inferred or determined through the output of the system. In control theory, the observability of a system means that any initial state of the system can be uniquely determined by the output of the system in a finite time.

[0147] Step 102: Based on a preset high-order polynomial, fit the state of charge and open-circuit voltage of the lithium battery to determine the nonlinear relationship curve between the state of charge and the open-circuit voltage.

[0148] In one embodiment, multiple states of charge (SOCs) of the lithium battery and the open-circuit voltage corresponding to each SOC are obtained; a SOC-open-circuit voltage relationship expression is constructed based on a preset high-order polynomial; the multiple SOCs and the open-circuit voltage are substituted into the SOC-open-circuit voltage relationship expression, and the SOC-open-circuit voltage relationship expression is fitted based on a fitting algorithm to obtain a nonlinear relationship curve between the multiple SOCs and the open-circuit voltage.

[0149] Specifically, the multiple states of charge refer to the states of charge at different charging stages.

[0150] Specifically, regarding the open-circuit voltage U of a lithium battery oc Due to the nonlinear characteristics of the battery, a 12th-order polynomial function was selected as the preset higher-order polynomial to fit the experimental data of multiple states of charge of the battery and the open-circuit voltage corresponding to each state of charge. The fitting results are continuous and differentiable.

[0151] Specifically, the nonlinear relationship curve is shown below: U oc (SOC)=a0+a1SOC+a2SOC 2 +...+a 11 SOC 11 +a 12 SOC 12 ;

[0152] In the formula, a i i = 0, 1, 2, ..., 11, 12 are the fitting coefficients, and SOC is the battery state of charge. 2 SOC is the square of the battery's state of charge. 11 SOC is the 11th power of the battery's state of charge. 12 It represents the 12th power of the battery's state of charge.

[0153] In one embodiment, based on the nonlinear relationship curve, the derivative expression of the open-circuit voltage over the entire state of charge (SOC) range of the lithium battery is as follows:

[0154]

[0155] In the formula, It is the differential form of the nonlinear relationship curve;

[0156] Furthermore, based on the derivative expression of the open-circuit voltage, further differentiation yields:

[0157] In the formula, κ is the derivative of the open-circuit voltage.

[0158] Step 103: Collect real-time operating condition data of the lithium battery. Based on the real-time operating condition data, use the extended Kalman filter algorithm to perform online parameter identification on the state space model of the Thevenin equivalent circuit to obtain estimated values ​​of state variables.

[0159] In one embodiment, the real-time operating data includes current and voltage.

[0160] Specifically, the current of the lithium battery is collected through a current sensor; the voltage of the lithium battery is collected through a voltage sensor.

[0161] Preferably, the real-time operating data also includes temperature; the temperature of the lithium battery is collected by a temperature sensor.

[0162] In one embodiment, a state variable to be identified is selected, and a state-space equation for online parameter identification is established based on the state variable and the real-time operating data.

[0163] Specifically, the selected state variables to be identified are:

[0164] Specifically, the parameters are used to identify the state-space equations online, as shown below:

[0165] In the formula, U t,k Let I be the terminal voltage obtained by sampling at time k. k-1 The total operating current obtained by sampling at time k-1 is... C is the shunt on the polarization resistor obtained by sampling at time k. p,k R is the polarization capacitance obtained by sampling at time k. p,k R is the battery polarization resistance obtained by sampling at time k. 0,k R is the battery internal resistance obtained by sampling at time k, and Ts is the simulation step size. 0,k-1 R is the ohmic internal resistance of the battery obtained by sampling at time k-1. p,k-1 C is the battery polarization resistance obtained by sampling at time k-1. p,k-1 f(x) is the polarization capacitance obtained by sampling at time k-1. k-1 ,u k-1 ) is the state transition equation, g(x) k-1 ,u k-1 ) is the observation equation, u k-1 x represents the terminal voltage obtained by sampling at time k. k-1 The state variables are obtained by sampling at time k-1.

[0166] Preferably, the simulation step size Ts is set to 0.1s.

[0167] In one embodiment, the state-space equations of the online identification of the parameters are linearized to obtain the state transition matrix and the system output matrix.

[0168] Specifically, the state transition matrix is ​​as follows:

[0169] In the formula, Let be the state transition matrix.

[0170] Specifically, the system output matrix is ​​as follows:

[0171] In the formula, This is the system output matrix.

[0172] In one embodiment, an initial state x0, a state error covariance P0, and a system noise variance matrix Q are defined. k The observation noise variance matrix R k The initial filtering conditions are set based on the initial state and the state error covariance, wherein the initial filtering conditions include initial filtering conditions for state variables and initial filtering conditions for the state error covariance matrix.

[0173] Specifically, the initial conditions for filtering the state variables are as follows:

[0174] In the formula, x0 represents the initial state of the system, and E[x0] represents the expected value after estimating or predicting the initial state of the system. This is the estimated system state at the initial moment.

[0175] Specifically, the initial conditions for filtering the state variables are as follows:

[0176] In the formula, P0 is the state error covariance, and var(x0) is the variance of the initial state of the system.

[0177] In one embodiment, the collected real-time operating condition data is substituted into the initial conditions for filtering the state variables to calculate the initial estimated value of the state variables; the collected real-time operating condition data is substituted into the initial conditions for filtering the state variables to calculate the initial error covariance matrix.

[0178] In one embodiment, the initial estimate of the state variable is updated according to the state transition matrix to obtain the prior estimate of the state variable.

[0179] Specifically, setting state variables The estimated time update formula substitutes the state transition matrix into the state variables. The prior estimates of the state variables are obtained from the estimated time update formula.

[0180] Specifically, the state variable Estimated time update formula:

[0181] In the formula, Let k be the estimated value of the state variable at time k, i.e., the prior estimate. Let A be the estimated value of the state variable at time k-1. k-1 Let be the state transition matrix.

[0182] In one embodiment, the initial error covariance matrix of the state variables is updated based on the state transition matrix to obtain the error covariance matrix.

[0183] Specifically, a time update formula for the error covariance is set, the state transition matrix is ​​substituted into the time update formula for the error covariance, and the initial error covariance matrix of the state variable is updated to obtain the error covariance matrix.

[0184] Specifically, the time update formula for the error covariance is as follows:

[0185] In the formula, P k / k-1 This is the estimated value of the error covariance at time k-1. Q is an estimate of the state transition matrix. k Let P be the process noise covariance matrix. k-1 / k-1 Let be the actual value of the error covariance at time k-1. This is the transpose of the estimated value of the state transition matrix.

[0186] In one embodiment, a gain matrix is ​​calculated based on the system output matrix, and a posterior estimate of the state variable is calculated based on the gain matrix.

[0187] Specifically, the Extend-Kalman gain matrix update formula is set, and the system output matrix and the error covariance matrix are input into the Extend-Kalman gain matrix update formula to obtain the gain matrix.

[0188] Specifically, setting state variables The estimated measurement update formula substitutes the prior estimate of the state variable and the gain matrix into the state variable. The estimated measurement update formula yields the posterior estimate of the state variable.

[0189] Specifically, set the Extend-Kalman gain matrix update formula:

[0190] In the formula, K k Let be the gain matrix at time k. Let be the transpose of the estimated value of the measurement matrix at time k. Let R be the measurement matrix at time k. k To observe the noise covariance matrix.

[0191] Specifically, setting state variables Estimated measurement update formula:

[0192] In the formula, y kThe terminal voltage U obtained by sampling at time k t value.

[0193] In one embodiment, the error covariance matrix is ​​updated based on the gain matrix.

[0194] Specifically, a measurement update formula for the error covariance is set, and the gain matrix is ​​input into the measurement update formula for the error covariance to obtain the updated error covariance matrix.

[0195] Specifically, set the measurement update formula for the error covariance:

[0196] In the formula, P k / k Let be the estimated value of the error covariance at time k.

[0197] In one embodiment, the estimated value of the state variable is determined based on the posterior estimate of the state variable.

[0198] In this embodiment, the process of using the extended Kalman filter algorithm to perform online parameter identification of the state-space model of the Thevenin equivalent circuit and obtain state variable estimates is illustrated by the following example:

[0199] The Kalman filter performs two estimations in each time period: a prior estimate based on time updates and a posterior estimate based on measurement updates. This is achieved by setting the initial state x0, the state error covariance P0, and the system noise variance matrix Q. k and the observation noise variance matrix R k The initial filtering conditions are determined; after acquiring real-time operating data of the lithium battery, the current and voltage are used as inputs to calculate and set the initial filtering conditions and state variables in sequence. Estimated time update formula, error covariance time update formula, Extend-Kalman gain matrix update formula, state variables In the estimated measurement update formula and the error covariance measurement update formula, and within each time period, for the state variables... Estimated time update formula and state variables The estimated measurement update formula and the error covariance measurement update formula are iteratively calculated. During this process, the estimated values ​​of the state variables can be obtained in real time as the simulation progresses. It includes the ohmic internal resistance R0 and the capacitance C p and diffusion resistance R p The value of is obtained from the above three parameters.

[0200] In one embodiment, the initial state x0 is set as follows: due to the initial state This mainly includes the shunt of the battery polarization internal resistance, ohmic internal resistance, polarization internal resistance, and polarization capacitor. These parameters should be set according to the actual battery pack model, and only parameters within the specified order of magnitude are required.

[0201] In one embodiment, the state error covariance P0 is set as follows: the initial value of the state error covariance P0 represents the confidence level of the current predicted state. The smaller P0 is, the higher the confidence level of the current predicted state. This value determines the initial convergence speed. Generally, a small value is set at the beginning in order to obtain a faster convergence speed.

[0202] In one embodiment, for the system noise variance matrix Q k Setting: System noise variance matrix Q k A smaller value indicates a higher degree of confidence in the model's predictions; however, a value that is too small can lead to divergence. The system noise variance matrix Q... k The larger the value, the lower the confidence level in the predicted value, and the higher the confidence level in the measured value.

[0203] In one embodiment, for the observation noise variance matrix R k Setting: Observation noise variance matrix R k If the value is too large, the Kalman filter response will slow down because it has less confidence in the value of new measurements; the observation noise variance matrix R k A smaller value indicates faster system convergence, but an excessively small value can lead to oscillations; the observation noise variance matrix R k Approximately normal distribution, according to the 3σ principle, take (3σ) of the normal distribution. 2 As the observation noise variance matrix R k The initial value.

[0204] During simulation and debugging, the system noise variance matrix Q can be set first. k Adjusting from small to large, the observation noise variance matrix R k Adjust from large to small; first fix one value and adjust another, observe the convergence speed and waveform output, and finally obtain an empirical value, thus achieving the purpose of parameter identification.

[0205] Step 104: Construct an adaptive double-power sliding membrane observer, inputting the nonlinear relationship curve and the estimated state variable into the adaptive double-power sliding membrane observer so that the adaptive double-power sliding membrane observer can calculate the estimated state of charge of the lithium battery in real time.

[0206] In one embodiment, the adaptive double-power sliding mode observer is designed with a double-power approach law, which can achieve fast and stable estimation and convergence control of the system state error. This design enables the state variables to converge to the true value quickly during the estimation process, which can improve the real-time performance and response speed of the state of charge estimation.

[0207] In one embodiment, the adaptive double power approach law divides the approaching motion into two stages with the sliding mode variable s=1. In the first stage, the sliding mode variable s converges from any position to s=1, and in the second stage, the sliding mode variable s converges from s=1 to s=0. The convergence speed of these two stages is accelerated by the adaptive double power approach law function composed of the two parts, thereby achieving rapid adjustment of the sliding mode variable and global fast convergence performance.

[0208] Furthermore, based on the aforementioned adaptive double power-law approach, the change process of the battery state of charge can be divided into two stages: the first stage is to allow the state of charge to gradually converge from any position to a specific value, and the second stage is to allow the state of charge to further converge from this specific value to another target value.

[0209] Specifically, the adaptive double-power approach rate function, consisting of two parts, includes a power term based on the state variable -k1|s|. 1+α sgn(s) and the power term -k2|s| 1-α sgn(s); where the expression for the adaptive double-power approach function is as follows:

[0210] In the formula, parameters k1>0, k2>0, 0<α<1 and c=1, s is the designed linear sliding diaphragm variable, which is linearly related to the tracking error e, and sgn(·) is the coincidence function, which outputs 1 when the input is greater than 0 and -1 when the input is less than 0.

[0211] Specifically, in the initial stage, when the system state is far from the sliding surface (s=0), its approaching motion is in the first stage, within the range |s|>>1. The term amplifies the error, accelerates the convergence speed, and plays a dominant role in the convergence of the sliding mode variable; when the system state is close to the sliding surface (s=0), its approach motion is in the second stage, within the range |s|<1. The term amplifies the error, accelerates the convergence speed, and plays a dominant role in the convergence of sliding mode variables. This will give the double power-law a certain advantage, thus obtaining a faster convergence rate at different stages, thereby verifying that the double power-law has better global fast convergence performance.

[0212] Specifically, by introducing the power term |s| 1+α and |s| 1-α This causes the sliding mode observer to switch gain k. i The adaptive adjustment (i=1,2) not only shortens the convergence time but also ensures that the sliding mode variable s has a very small convergence velocity when it reaches the vicinity of the sliding mode plane (s=0), effectively reducing the chattering effect of the sliding mode observer; when the system is in a stable state, the system is in the sliding mode, with s=0 and This indicates that when the sliding mode variable reaches the sliding surface, the approach velocity decreases to zero, achieving a smooth transition, effectively eliminating the chattering of the observed signal, effectively controlling the tracking error to converge to zero, and achieving accurate estimation of the internal state of the system.

[0213] In one embodiment, stability refers to whether a system can remain near a certain equilibrium state without diverging when subjected to external disturbances or changes in initial conditions. In sliding mode control, stability means that, for an adaptive double power approach function, the system state s can converge to the equilibrium point in a finite time under its influence, ensuring that the system behavior is controllable and stable.

[0214] Specifically, based on the Lyapunov stability theory, the Lyapunov function is defined as follows:

[0215] In the formula, V is the constructed Lyapunov function, and s is the constructed sliding mode function.

[0216] Specifically, by using the double power reaching law function and differentiating it with respect to time, we can obtain:

[0217] In the formula, V is the constructed Lyapunov function, Let be the differential form of the Lyapunov function, s be the constructed sliding mode function, and α, k1, and k2 be the parameters to be designed. α, k1, and k2 are empirical values ​​obtained through simulation experiments and obtained by trial and error. Let sgn(·) be the differential form of the sliding mode function, and let sgn(·) be the coincidence function.

[0218] Specifically, based on Lyapunov stability theory, a Lyapunov function V is introduced to describe the stability of the system, and the derivative of the Lyapunov function V... The rate of change of the system state is represented by... The sign of the system can be used to determine whether it is converging toward the equilibrium point; for any time point, there exists when When the system state converges to the equilibrium point in a finite time, it proves that the adaptive double-power sliding mode approach law satisfies the system stability condition; that is... When t→∞, s=0 satisfies the stability condition, and the closed-loop system is asymptotically stable. When t→∞, s=0. If used for a sliding mode observer, it means that the observation error of the system converges to zero, the observed value can reflect the dynamic changes of the true value, and in different convergence stages, its convergence speed depends on the sliding mode switching coefficients k1 and k2.

[0219] In one embodiment, an adaptive double-power sliding mode observer is constructed, and a switching gain is set for the adaptive double-power sliding mode observer. The adaptive double-power sliding mode observer includes an end voltage adaptive double-power sliding mode observer, a battery charge state adaptive double-power sliding mode observer, and a polarization voltage adaptive double-power sliding mode observer.

[0220] Specifically, regarding the terminal voltage U t The terminal voltage adaptive double power sliding mode observer is as follows:

[0221] In the formula, k 1,1 and k 1,2 These are the switching gains of the sliding mode observer, all of which are positive. Terminal voltage U t The observed values, Let V1 be the linear sliding mode function of the terminal voltage, V1 be the first equivalent control quantity of the designed adaptive double power sliding mode observer, and sgn(·) be the coincidence function. It is the differential form of the nonlinear relationship curve.

[0222] Specifically, for the State of Charge (SOC), the battery charge state adaptive double-power sliding membrane observer is as follows: V2 = -k 2,1 |s SOC | 1+α sgn(s SOC )-k 2,2 |s SOC | 1-α sgn(s SOC );

[0223] In the formula, In the state of charge The estimated value, V2 is the second equivalent control variable of the designed adaptive double power sliding mode observer, k 2,1 and k 2,2 These are the switching gains of the sliding mode observer, all of which are positive values, s SOC This is the sliding mode function for the charged state.

[0224] Specifically, regarding the polarization voltage U P The polarization voltage adaptive double power sliding film observer is as follows:

[0225] In the formula, k 3,1 and k 3,2 V1 represents the switching gain of the sliding mode observer, all of which are positive. V2 represents the third equivalent control variable of the designed adaptive double-power sliding mode observer. Polarization voltage U P Estimated value Let be the sliding mode function of the polarization voltage. This is the polarization voltage sliding mode function.

[0226] In one embodiment, terminal voltage observation error, state of charge observation error, and polarization voltage observation error are set; based on the terminal voltage observation error, a terminal voltage sliding mode function is determined, and based on the terminal voltage sliding mode function, a terminal voltage Lyapunov function is determined; based on the state of charge observation error, a state of charge sliding mode function is determined, and based on the state of charge sliding mode function, a state of charge Lyapunov function is determined; based on the polarization voltage observation error, a polarization voltage sliding mode function is determined, and based on the polarization voltage sliding mode function, a polarization voltage Lyapunov function is determined.

[0227] Specifically, the terminal voltage observation error is defined as... At this point, the linear sliding mode function of the terminal voltage is taken. for:

[0228] Specifically, the state of charge observation error is defined as... At this point, the linear sliding mode function s of the charged state is taken. SOC for:

[0229] Specifically, the polarization voltage observation error is defined as... At this point, the linear sliding mode function of the polarization voltage is taken. for:

[0230] Specifically, based on the terminal voltage observation error, the state of charge observation error, and the polarization voltage observation error, a dynamic equation for the lithium battery system error is constructed, as shown below:

[0231] In the formula, This is the differential form of the terminal voltage observation error. This is the differential form of the state-of-charge observation error. This is the differential form of the polarization voltage observation error.

[0232] By definition The dynamic equation for the lithium battery system error is transformed into:

[0233] Specifically, when the dynamic equation of the lithium battery system error converges to zero, that is, when the error between the estimated value and the true value of the adaptive double power sliding diaphragm observer approaches zero, the estimated value will track the dynamic change process of the true value; that is, the estimated value can reflect the change of the true value.

[0234] However, in lithium battery systems, the terminal voltage can be directly measured by sensors, while the battery's state of charge (SOC) and internal resistance cannot be directly measured and must be estimated indirectly. Since SOC and internal resistance cannot be directly measured, their errors cannot be directly obtained. However, there is a quantitative relationship between the SOC observation error, polarization voltage observation error, and terminal voltage observation error, and this relationship is crucial for effective feedback in the battery model. Therefore, to verify the stability of the sliding mode observer and obtain the quantitative relationship between the SOC observation error, polarization voltage observation error, and terminal voltage observation error, Lyapunov stability theory can be used. By applying this theory, the stability of the adaptive double-power sliding mode observer can be proven. That is, when the dynamic error system converges to zero, the adaptive double-power sliding mode observer can accurately estimate the quantitative relationship between the SOC observation error, polarization voltage observation error, and terminal voltage observation error, thereby achieving effective control and monitoring of the battery system.

[0235] Specifically, based on the aforementioned terminal voltage sliding mode function, the terminal voltage Lyapunov function for determining the terminal voltage observation error is as follows:

[0236] In the formula, For terminal voltage observation error, Let Lyapunov be the terminal voltage function.

[0237] Specifically, based on the state-of-charge sliding mode function, the Lyapunov function of the state-of-charge observation error is determined:

[0238] In the formula, Let e ​​be the Lyapunov function of the charged state. SOC Error in state of charge observation.

[0239] Specifically, based on the polarization voltage sliding mode function, the polarization voltage Lyapunov function for the polarization voltage observation error is determined:

[0240] In the formula, Let Lyapunov be the polarization voltage function. This represents the observation error of the polarization voltage.

[0241] In one embodiment, based on the terminal voltage Lyapunov function, the state of charge Lyapunov function, and the polarization voltage Lyapunov function, a first quantitative relationship is determined between the state of charge observation error and a preset first equivalent control quantity in the adaptive double power sliding mode observer, and a second quantitative relationship is determined between the polarization voltage observation error and a preset second equivalent control quantity in the adaptive double power sliding mode observer.

[0242] Specifically, after obtaining the Lyapunov function of the terminal voltage, in order to ensure the accuracy of the terminal voltage observation error... Convergence requires that the time derivative of the Lyapunov function of the terminal voltage be guaranteed. Negative constant, thus satisfying the terminal voltage observation error Time derivative of the Lyapunov function with respect to the terminal voltage The signs are always opposite:

[0243] In the formula, This is the differential form of the Lyapunov function of the terminal voltage.

[0244] Specifically, when the selected At that time, it can be guaranteed Sliding mode variables within a finite time The voltage converges asymptotically to zero, at which point the terminal voltage observation error... and Converging to zero means the system is in an ideal sliding mode. At this point, sliding motion will be induced to ensure... Furthermore, the influence of the bounded uncertainty term Δf1 is compensated; when the above conditions are met, based on the concept of equivalent control and the terminal voltage dynamic error system, the unmeasurable open-circuit voltage error can be represented. Relationship with the first equivalent control quantity V1:

[0245] In the formula, This represents the open-circuit voltage observation error.

[0246] Due to U oc There is a strict correspondence between it and SOC. and The relationship can be expressed by the first-order differential of a polynomial. To more accurately describe the continuous-time open-circuit voltage U... oc The relationship between the difference and the SOC difference can be expressed by the first-order differential of the polynomial, ultimately yielding the unmeasurable e. SOC The representation of this is used as the first quantitative relationship between the state of charge observation error and the preset first equivalent control quantity in the adaptive double-power sliding mode observer. The first quantitative relationship is as follows:

[0247] In the formula, e SOC κ represents the observation error of the nuclear power state of the battery, and κ is the derivative of the open-circuit voltage.

[0248] In one embodiment, after obtaining the Lyapunov function of the state of charge, in order to ensure the observation error of the state of charge e SOC Convergence requires guaranteeing the time derivative of the Lyapunov function in its charged state. Negative definite, thus satisfying e SOC and The signs are always opposite:

[0249] Specifically, when the selected At that time, it can be guaranteed Sliding mode variable s within a finite time SOC It asymptotically converges to zero; at this point... and Converging to zero means the system is in an ideal sliding mode. At this point, sliding motion will be induced to ensure... Furthermore, the influence of the bounded uncertainty term Δf2 is compensated; when the above conditions are met, based on the concept of equivalent control and the dynamic error system of the state of charge, the polarization voltage observation error can be obtained. The relationship between the equivalent control quantity V2 and the polarization voltage observation error is used as the second quantitative relationship between the second equivalent control quantity preset in the adaptive double power sliding mode observer. The second quantitative relationship is as follows:

[0250] In the formula, This represents the observation error of the polarization voltage.

[0251] Specifically, after obtaining the polarization voltage Lyapunov function, in order to ensure the accuracy of polarization voltage observation errors... Convergence requires that the time derivative of its polarization voltage Lyapunov function be guaranteed. Negative definite, thus satisfying the condition. and The signs are always opposite:

[0252] Specifically, when the selected V3 > max(|Δf3| - V3), it can be guaranteed that Sliding mode variable within a finite time It asymptotically converges to zero, at which point and When the polarization voltage converges to zero, i.e., the ideal sliding mode is reached, the sliding motion will be induced to ensure... Furthermore, the effect of the bounded uncertainty term Δf3 is compensated.

[0253] In one embodiment, the battery charge state adaptive double power sliding membrane observer is updated based on the first quantitative relationship, and the polarization voltage adaptive double power sliding membrane observer is updated based on the second quantitative relationship.

[0254] Specifically, the updated adaptive double-power sliding mode observer is represented as follows:

[0255] In the formula, k 1,1 and k 1,2 These are the switching gains of the sliding mode observer, all of which are positive. These are terminal voltage observations. Let V1 be the sliding mode function of the terminal voltage, V1 be the first equivalent control variable of the designed adaptive double-power sliding mode observer, and sgn(·) be the coincidence function. C represents the rate of change of the observed terminal voltage over time. p For polarization capacitors, R p For polarization resistance, Q n Let κ be the nominal capacity of the battery, R0 be the derivative of the open-circuit voltage, I be the charging and discharging current, and α be the parameter in the power term of the adaptive double power-law approach, where 0 < α < 1. V2 is the observed value of the state of charge, and k is the second equivalent control variable of the designed adaptive double power sliding mode observer. 2,1 and k 2,2 These are the switching gains of the sliding mode observer, all of which are positive. The rate of change of the observed state of charge over time. These are polarization voltage observations. This is the first quantitative relationship; k 3,1 and k 3,2 V1 represents the switching gain of the sliding mode observer, all of which are positive. V2 represents the third equivalent control variable of the designed adaptive double-power sliding mode observer. These are polarization voltage observations. The rate of change of the observed polarization voltage over time. This is the second quantitative relationship.

[0256] Specifically, based on the stability of the designed adaptive double-power sliding mode observer, the nonlinear relationship curve and the estimated value of the state variable are input into the adaptive double-power sliding mode observer to calculate the estimated value of the lithium battery state of charge in real time, which can ensure that the internal state variables of the lithium battery system can be estimated accurately.

[0257] In one embodiment, since many systems in actual control systems are continuous, while digital computing devices such as hardware boards perform calculations in a discrete manner, the battery management system needs to discretize the continuous system model when performing calculations on the hardware board, that is, to convert the continuous state-space mathematical model into an equivalent discrete state-space mathematical model.

[0258] The Euler method is a common numerical integration method. Due to its simple structure, low computational cost, and ease of numerical solution on hardware boards, this embodiment adopts the explicit Euler method, namely the forward Euler method, to discretize the adaptive double power sliding mode observer for the sum and state of charge estimation of lithium batteries.

[0259] In one embodiment, the forward Euler method is used to update the differential of the state of charge, the differential of the polarization voltage state, and the differential of the terminal voltage, resulting in updated differentials of the state of charge, the polarization voltage state, and the terminal voltage. Based on these updated differentials, the adaptive double-power sliding mode observer is discretized to obtain a discretized adaptive double-power sliding mode observer. Based on this discretized adaptive double-power sliding mode observer, the state of charge, the polarization voltage, and the terminal voltage are updated to obtain updated differentials of the state of charge, the polarization voltage, and the terminal voltage.

[0260] Specifically, at any given moment in the time domain, the differential components of the terminal voltage, state of charge, and polarization voltage state variables are known, i.e. and Using the forward difference method to replace its differential value, and taking the step size Ts as a constant, the approximate discretization equation corresponding to the adaptive double power sliding mode observer is:

[0261] In the formula, This is the estimated value of the voltage state variable at time k+1. This is the estimated value of the voltage state variable at time k.

[0262] Specifically, the discrete form of the adaptive double-power sliding mode observer for battery state of charge estimation is obtained based on the approximate discretization equation, i.e., the discretized adaptive double-power sliding mode observer, as shown below:

[0263] In the formula, U t,k+1 SOC k+1 and U p,k+1 These are the final discretized estimates of the battery terminal voltage, state of charge, and polarization voltage at time k+1, respectively.

[0264] Specifically, the local truncation error is proportional to the step size. When the step size is small enough, the error caused by numerical calculation can be ignored.

[0265] Preferably, the battery state-of-charge estimation method provided in this embodiment is suitable for estimating the state-of-charge value of NMC-based batteries, because the U of NMC-based batteries... OC The relationship between it and its SOC is unique; however, for LFP-based batteries, due to U OCThe curve has two plateau periods and a lag effect, making it difficult to obtain U. OC The differential value between SOC and the value of the state of charge. This drawback can be addressed by coordinating charging and discharging U. OC Piecewise linearization is used to overcome this, which is the direction for later optimization.

[0266] In one embodiment, the adaptive double-power sliding mode observer in the battery state-of-charge estimation method provided in this embodiment is verified by algorithm.

[0267] 1. Considering the initial SOC error, the state of charge estimation results are compared in Figures 4 and 5. Figure 4 shows a comparison of observations under different initial SOC states, and Figure 5 shows a comparison of observation errors under different initial SOC states. It can be seen that the proposed adaptive double-power sliding mode observer algorithm can converge to the target value under different initial error conditions, and the smaller the initial error, the faster the convergence speed. Even with an initial SOC error of 80%, the adaptive double-power sliding mode observer algorithm can quickly converge to within the critical error range of 3% within 425 seconds. The terminal voltage tracking is shown in Figure 6; Figure 6 is a comparison of terminal voltage tracking under different initial SOC states.

[0268] 2. In the battery management system of lithium batteries, due to limitations in sensor accuracy and electromagnetic interference, it is difficult for the online system to obtain accurate voltage and current values. To evaluate the robustness of the adaptive double-power sliding mode observer algorithm to the error of the current measurement signal, random normal distribution noise is added to the measured voltage and current signals, 5mV Gaussian noise is added to the voltage measurement, and 1mA Gaussian noise is added to the current measurement. The initial state of charge (SOC) error is defined as 20%. The predicted SOC and battery terminal voltage results are shown in Figures 7, 8, and 9. Figure 7 is a comparison of SOC observations with and without observation noise, Figure 8 is a comparison of SOC observation errors with and without observation noise, and Figure 9 is a comparison of SOC terminal voltage tracking with and without observation noise. It can be seen that the SOC and terminal voltage of the lithium battery can converge to the true values, proving that the designed sliding mode observer has a certain anti-interference capability.

[0269] Example 2, referring to Figure 2, is a structural schematic diagram of an embodiment of a battery state-of-charge estimation device provided in this application. As shown in Figure 2, the device includes a Thevenin equivalent circuit state-space model construction module 201, a nonlinear relationship curve determination module 202, an online parameter identification module 203, and a state-of-charge estimation module 204, as detailed below:

[0270] The Thevenin equivalent circuit state space model construction module 201 is used to construct the Thevenin equivalent circuit state space model of the lithium battery based on the Thevenin equivalent circuit model.

[0271] The nonlinear relationship curve determination module 202 is used to fit the state of charge and open-circuit voltage of the lithium battery based on a preset high-order polynomial, and determine the nonlinear relationship curve between the state of charge and the open-circuit voltage.

[0272] The online parameter identification module 203 is used to collect real-time operating condition data of the lithium battery, and based on the real-time operating condition data, to perform online parameter identification on the state space model of the Thevenin equivalent circuit using the extended Kalman filter algorithm to obtain estimated values ​​of state variables.

[0273] The state of charge estimation module 204 is used to construct an adaptive double power sliding membrane observer, inputting the nonlinear relationship curve and the estimated value of the state variable into the adaptive double power sliding membrane observer so that the adaptive double power sliding membrane observer can calculate the estimated value of the lithium battery state of charge in real time.

[0274] In one embodiment, the Thevenin equivalent circuit state-space model construction module 201 is used to construct a Thevenin equivalent circuit state-space model of a lithium battery based on the Thevenin equivalent circuit model. Specifically, it includes: determining the state-of-charge equation of the lithium battery based on the Thevenin equivalent circuit model; determining the polarization voltage differential equation of the lithium battery based on the Thevenin equivalent circuit model; determining the terminal voltage equation of the lithium battery based on the Thevenin equivalent circuit model, and converting the terminal voltage equation into a terminal voltage differential equation; and determining the Thevenin equivalent circuit state-space model of the lithium battery based on the state-of-charge equation, the polarization voltage differential equation, and the terminal voltage differential equation.

[0275] In one embodiment, the Thevenin equivalent circuit state-space model is as follows:

[0276] In the formula, U t For terminal voltage, U oc U is the open-circuit voltage, I(t) is the charging / discharging current, and U is the charging / discharging current. p Polarization voltage, C p For polarization capacitor, R p Q is the polarization resistor, SOC is the state of charge, and Q is the polarization resistor. n Let κ be the nominal capacitance of the battery, R0 be the derivative of the open-circuit voltage, Δf1 be the uncertainty caused by the unknown nonlinear term terminal voltage, Δf2 be the uncertainty caused by the unknown nonlinear term, where the nonlinear term represents the nominal capacitance deviation, temperature coefficient, and unknown uncertain disturbance, and Δf3 be the uncertainty caused by the unknown nonlinear polarization voltage term. This is the differential form of the battery terminal voltage. This is the differential form of the battery's state of charge. This is the differential form of the battery polarization voltage.

[0277] In one embodiment, the nonlinear relationship curve determination module 202 is used to fit the state of charge and open-circuit voltage of the lithium battery based on a preset high-order polynomial to determine the nonlinear relationship curve between the state of charge and the open-circuit voltage. Specifically, this includes: acquiring multiple states of charge of the lithium battery and the open-circuit voltage corresponding to each state of charge; constructing a state of charge-open-circuit voltage relationship expression based on the preset high-order polynomial; substituting the multiple states of charge and the open-circuit voltage into the state of charge-open-circuit voltage relationship expression; and performing fitting processing on the state of charge-open-circuit voltage relationship expression based on a fitting algorithm to obtain the nonlinear relationship curve between the multiple states of charge and the open-circuit voltage.

[0278] In one embodiment, the nonlinear relationship curve is as follows: U oc (SOC)=a0+a1SOC+a2SOC 2 +…+a 11 SOC 11 +a 12 SOC 12 ;

[0279] In the formula, a i i = 0, 1, 2, ..., 11, 12 are the fitting coefficients, and SOC is the battery state of charge. 2 SOC is the square of the battery's state of charge. 11 SOC is the 11th power of the battery's state of charge. 12 It represents the 12th power of the battery's state of charge.

[0280] In one embodiment, the online parameter identification module 203 is used to perform online parameter identification on the Thevenin equivalent circuit state space model based on the real-time operating data using the extended Kalman filter algorithm to obtain state variable estimates. Specifically, this includes: selecting state variables to be identified; establishing an online parameter identification state space equation based on the state variables and the real-time operating data; linearizing the online parameter identification state space equation to obtain a state transition matrix and a system output matrix; setting initial filtering conditions; calculating initial state variable estimates based on the initial filtering conditions; calculating an initial error covariance matrix based on the initial filtering conditions; updating the initial state variable estimates according to the state transition matrix to obtain prior estimates of the state variables; updating the initial error covariance matrix based on the state transition matrix to obtain an error covariance matrix; calculating a gain matrix based on the system output matrix; calculating a posterior estimate of the state variables based on the gain matrix; updating the error covariance matrix based on the gain matrix; and determining the state variable estimates based on the posterior estimates of the state variables.

[0281] In one embodiment, the state of charge estimation module 204 is used to construct an adaptive double-power sliding mode observer, specifically including: constructing an adaptive double-power sliding mode observer and setting a switching gain for the adaptive double-power sliding mode observer, wherein the adaptive double-power sliding mode observer includes a terminal voltage adaptive double-power sliding mode observer, a battery charge state adaptive double-power sliding mode observer, and a polarization voltage adaptive double-power sliding mode observer; setting terminal voltage observation error, state of charge observation error, and polarization voltage observation error; determining a terminal voltage sliding mode function based on the terminal voltage observation error, and determining a terminal voltage Lyapunov function based on the terminal voltage sliding mode function; determining a state of charge sliding mode function based on the state of charge observation error, and determining a state of charge Lyapunov function based on the state of charge sliding mode function. Lyapunov function; based on the polarization voltage observation error, determine the polarization voltage sliding mode function, and based on the polarization voltage sliding mode function, determine the polarization voltage Lyapunov function; based on the terminal voltage Lyapunov function, the state of charge Lyapunov function, and the polarization voltage Lyapunov function, determine a first quantitative relationship between the state of charge observation error and a preset first equivalent control quantity in the adaptive double power sliding mode observer, and a second quantitative relationship between the polarization voltage observation error and a preset second equivalent control quantity in the adaptive double power sliding mode observer; based on the first quantitative relationship, update the battery charge state adaptive double power sliding mode observer, and based on the second quantitative relationship, update the polarization voltage adaptive double power sliding mode observer.

[0282] In one embodiment, the adaptive double-power sliding mode observer includes an end voltage adaptive double-power sliding mode observer, a battery charge state adaptive double-power sliding mode observer, and a polarization voltage adaptive double-power sliding mode observer.

[0283] In one embodiment, the terminal voltage adaptive double power sliding mode observer is as follows:

[0284] In the formula, k 1,1 and k 1,2 These are the switching gains of the sliding mode observer, all of which are positive. These are terminal voltage observations. Let V1 be the sliding mode function of the terminal voltage, V1 be the first equivalent control variable of the designed adaptive double-power sliding mode observer, and sgn(·) be the coincidence function. C represents the rate of change of the observed terminal voltage over time. p For polarization capacitors, R p For polarization resistance, Q n Let κ be the nominal capacity of the battery, R0 be the derivative of the open-circuit voltage, I be the charging and discharging current, and α be the parameter in the power term of the adaptive double power-law approach, where 0 < α < 1.

[0285] In one embodiment, the battery charge state adaptive double-power sliding membrane observer is as follows:

[0286] In the formula, V2 is the observed value of the state of charge, and k is the second equivalent control variable of the designed adaptive double power sliding mode observer. 2,1 and k 2,2 These are the switching gains of the sliding mode observer, all of which are positive. The rate of change of the observed state of charge over time. These are polarization voltage observations. This is the first quantitative relationship.

[0287] In one embodiment, the polarization voltage adaptive double power sliding film observer is as follows:

[0288] In the formula, k 3,1 and k 3,2 V1 represents the switching gain of the sliding mode observer, all of which are positive. V2 represents the third equivalent control variable of the designed adaptive double-power sliding mode observer. These are polarization voltage observations. The rate of change of the observed polarization voltage over time. This is the second quantitative relationship.

[0289] In one embodiment, the state of charge estimation module 204, after obtaining the estimated values ​​of the state variables, further includes: updating the differential of the state of charge, the differential of the polarization voltage state, and the differential of the terminal voltage using the forward Euler method to obtain updated differentials of the state of charge, the polarization voltage state, and the terminal voltage; discretizing the adaptive double-power sliding mode observer based on the updated differentials of the state of charge, the updated polarization voltage state, and the updated terminal voltage to obtain a discretized adaptive double-power sliding mode observer; and updating the state of charge, the polarization voltage, and the terminal voltage based on the discretized adaptive double-power sliding mode observer to obtain updated differentials of the state of charge, the updated polarization voltage, and the updated terminal voltage.

[0290] In another embodiment, the above-mentioned battery state-of-charge estimation device includes: a processor, wherein the processor is used to execute the above-mentioned program modules stored in memory, including: a Thevenin equivalent circuit state-space model construction module 201, a nonlinear relationship curve determination module 202, a parameter online identification module 203, and a state-of-charge estimation module 204.

[0291] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the device described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0292] It should be noted that the above-described embodiment of the battery state-of-charge estimation device is merely illustrative. The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0293] Based on the above-described embodiments of the battery state of charge estimation method, another embodiment of this application provides a battery state of charge estimation terminal device. The battery state of charge estimation terminal device includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the battery state of charge estimation method of any embodiment of this application.

[0294] For example, in this embodiment, the computer program can be divided into one or more modules, which are stored in the memory and executed by the processor to complete this application. The one or more modules can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in the battery state-of-charge estimation terminal device.

[0295] The battery state-of-charge estimation terminal device can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The battery state-of-charge estimation terminal device may include, but is not limited to, a processor and memory.

[0296] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. This processor is the control center of the battery's state-of-charge estimation terminal device, connecting all parts of the terminal device via various interfaces and lines.

[0297] The memory can be used to store the computer programs and / or modules. The processor, by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory, realizes various functions of the battery state-of-charge estimation terminal device. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, applications required for at least one function, etc.; the data storage area may store data created based on the use of the mobile phone, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0298] Based on the above embodiments of the battery state-of-charge estimation method, another embodiment of this application provides a storage medium, the storage medium including a stored computer program, wherein, when the computer program is running, the device where the storage medium is located controls the execution of the battery state-of-charge estimation method of any embodiment of this application.

[0299] In this embodiment, the storage medium is a computer-readable storage medium, and the computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable medium can include any entity or device capable of carrying the computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0300] In summary, this application provides a method, apparatus, device, and storage medium for estimating the state of charge (SOC) of a battery. It constructs a Thevenin equivalent circuit state-space model of a lithium battery using a Thevenin equivalent circuit model. Based on a pre-defined high-order polynomial, it fits the SOC and open-circuit voltage of the lithium battery to determine the nonlinear relationship curve between them. It collects real-time operating data of the lithium battery and, based on this data, uses an extended Kalman filter algorithm to perform online parameter identification on the Thevenin equivalent circuit state-space model, obtaining estimated values ​​of the state variables. It constructs an adaptive double-power sliding window observer, inputting the nonlinear relationship curve and the estimated values ​​of the state variables into the observer, enabling the observer to calculate the estimated SOC of the lithium battery in real time. Compared with existing technologies, the technical solution of this application can improve the accuracy of lithium battery SOC estimation.

[0301] The above description is only a preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and substitutions can be made without departing from the technical principles of this application, and these improvements and substitutions should also be considered within the scope of protection of this application.

Claims

1. A method for estimating the state of charge (SOC) of a battery, wherein, include: Based on the Thevenin equivalent circuit model, a Thevenin equivalent circuit state-space model of lithium battery is constructed. Based on a preset high-order polynomial, the state of charge and open-circuit voltage of the lithium battery are fitted to determine the nonlinear relationship curve between the state of charge and the open-circuit voltage. Real-time operating condition data of the lithium battery is collected. Based on the real-time operating condition data, the parameters of the Thevenin equivalent circuit state space model are identified online using the extended Kalman filter algorithm to obtain estimated values ​​of state variables. An adaptive double-power sliding membrane observer is constructed, and the nonlinear relationship curve and the estimated value of the state variable are input into the adaptive double-power sliding membrane observer so that the adaptive double-power sliding membrane observer can calculate the estimated value of the state of charge of the lithium battery in real time.

2. The method for estimating the state of charge of a battery as described in claim 1, wherein, Based on the Thevenin equivalent circuit model, a Thevenin equivalent circuit state-space model of a lithium battery is constructed, specifically including: Based on the Thevenin equivalent circuit model, the state-of-charge equation of the lithium battery is determined. Based on the Thevenin equivalent circuit model, the polarization voltage differential equation of the lithium battery is determined. Based on the Thevenin equivalent circuit model, the terminal voltage equation of the lithium battery is determined, and the terminal voltage equation is converted into a terminal voltage differential equation. Based on the state equation of charge, the differential equation of polarization voltage, and the differential equation of terminal voltage, the Thevenin equivalent circuit state-space model of the lithium battery is determined. The Thevenin equivalent circuit state-space model is shown below: In the formula, U t For terminal voltage, U oc U is the open-circuit voltage, I(t) is the charging / discharging current, and U is the charging / discharging current. p Polarization voltage, C p For polarization capacitor, R p Q is the polarization resistor, SOC is the state of charge, and Q is the polarization resistor. n Let κ be the nominal capacitance of the battery, R0 be the derivative of the open-circuit voltage, Δf1 be the uncertainty caused by the unknown nonlinear term terminal voltage, Δf2 be the uncertainty caused by the unknown nonlinear term, where the nonlinear term represents the nominal capacitance deviation, temperature coefficient, and unknown uncertain disturbance, and Δf3 be the uncertainty caused by the unknown nonlinear polarization voltage term. This is the differential form of the battery terminal voltage. This is the differential form of the battery's state of charge. This is the differential form of the battery polarization voltage.

3. The method for estimating the state of charge of a battery as described in claim 1, wherein, Based on a preset high-order polynomial, the state of charge (SOC) and open-circuit voltage of the lithium battery are fitted to determine the nonlinear relationship curve between the SOC and the open-circuit voltage, specifically including: Obtain multiple states of charge of the lithium battery and the open-circuit voltage corresponding to each state of charge; Based on a pre-defined high-order polynomial, an expression for the relationship between state of charge and open-circuit voltage is constructed. Substitute the multiple states of charge and the open-circuit voltage into the state-of-charge-open-circuit voltage relationship expression, and perform fitting processing on the state-of-charge-open-circuit voltage relationship expression based on the fitting algorithm to obtain the nonlinear relationship curve between the multiple states of charge and the open-circuit voltage; The nonlinear relationship curve is shown below: The oc (SOC)=a0+a1SOC+a2SOC 2 +…+a 11 SOC 11 +a 12 SOC 12 ; In the formula, a i i = 0, 1, 2, ..., 11, 12 are the fitting coefficients, and SOC is the battery state of charge. 2 SOC is the square of the battery's state of charge. 11 SOC is the 11th power of the battery's state of charge. 12 It represents the 12th power of the battery's state of charge.

4. The method for estimating the state of charge of a battery as described in claim 1, wherein, Based on the real-time operating data, the extended Kalman filter algorithm is used to perform online parameter identification on the state-space model of the Thevenin equivalent circuit to obtain estimated values ​​of state variables, specifically including: Select the state variables to be identified, and establish the online parameter identification state space equation based on the state variables and the real-time operating data; The state-space equations of the parameters are linearized online to obtain the state transition matrix and the system output matrix. Set initial filtering conditions, calculate initial estimates of the state variables based on the initial filtering conditions, and calculate the initial error covariance matrix based on the initial filtering conditions; The initial estimate of the state variable is updated based on the state transition matrix to obtain the prior estimate of the state variable, and the initial error covariance matrix of the state variable is updated based on the state transition matrix to obtain the error covariance matrix. Calculate the gain matrix based on the system output matrix, calculate the posterior estimate of the state variable based on the gain matrix, and update the error covariance matrix based on the gain matrix; Based on the posterior estimate of the state variable, the estimated value of the state variable is determined.

5. The method for estimating the state of charge of a battery as described in claim 1, wherein, The construction of the adaptive double-power sliding membrane observer specifically includes: An adaptive double-power sliding mode observer is constructed, and a switching gain is set for the adaptive double-power sliding mode observer. The adaptive double-power sliding mode observer includes an end voltage adaptive double-power sliding mode observer, a battery charge state adaptive double-power sliding mode observer, and a polarization voltage adaptive double-power sliding mode observer. Set the terminal voltage observation error, state of charge observation error, and polarization voltage observation error; Based on the terminal voltage observation error, the terminal voltage sliding mode function is determined, and based on the terminal voltage sliding mode function, the terminal voltage Lyapunov function is determined. Based on the state of charge observation error, the state of charge sliding mode function is determined, and based on the state of charge sliding mode function, the state of charge Lyapunov function is determined. Based on the observed polarization voltage error, the sliding mode function of polarization voltage is determined, and based on the sliding mode function of polarization voltage, the Lyapunov function of polarization voltage is determined. Based on the terminal voltage Lyapunov function, the state of charge Lyapunov function, and the polarization voltage Lyapunov function, a first quantitative relationship is determined between the state of charge observation error and a preset first equivalent control quantity in the adaptive double power sliding mode observer, and a second quantitative relationship is determined between the polarization voltage observation error and a preset second equivalent control quantity in the adaptive double power sliding mode observer. Based on the first quantitative relationship, the battery charge state adaptive double power sliding membrane observer is updated, and based on the second quantitative relationship, the polarization voltage adaptive double power sliding membrane observer is updated.

6. The method for estimating the state of charge of a battery as described in claim 1, wherein, The adaptive double-power sliding mode observer includes an end voltage adaptive double-power sliding mode observer, a battery charge state adaptive double-power sliding mode observer, and a polarization voltage adaptive double-power sliding mode observer. The terminal voltage adaptive double power sliding mode observer is as follows: In the formula, k 1,1 and k 1,2 These are the switching gains of the sliding mode observer, all of which are positive. These are terminal voltage observations. Let V1 be the sliding mode function of the terminal voltage, V1 be the first equivalent control variable of the designed adaptive double-power sliding mode observer, and sgn(·) be the coincidence function. C represents the rate of change of the observed terminal voltage over time. p For polarization capacitors, R p For polarization resistance, Q n Let κ be the nominal capacity of the battery, R0 be the derivative of the open-circuit voltage, I be the charging and discharging current, and α be the parameter in the power term of the adaptive double power-law approach, where 0 < α < 1. The battery charge state adaptive double-power sliding membrane observer is as follows: In the formula, V2 is the observed value of the state of charge, and k is the second equivalent control variable of the designed adaptive double power sliding mode observer. 2,1 and k 2,2 These are the switching gains of the sliding mode observer, all of which are positive. The rate of change of the observed state of charge over time. These are polarization voltage observations. This is the first quantitative relationship; The polarization voltage adaptive double power sliding membrane observer is as follows: In the formula, k 3,1 and k 3,2 V1 represents the switching gain of the sliding mode observer, all of which are positive. V2 represents the third equivalent control variable of the designed adaptive double-power sliding mode observer. These are polarization voltage observations. The rate of change of the observed polarization voltage over time. This is the second quantitative relationship.

7. The method for estimating the state of charge of a battery as described in claim 1, wherein, After obtaining the estimated values ​​of the state variables, the following is also included: The forward Euler method is used to update the differential of the state of charge, the differential of the polarization voltage state, and the differential of the terminal voltage, resulting in updated differentials of the state of charge, the polarization voltage state, and the terminal voltage. Based on these updated differentials, the adaptive double-power sliding mode observer is discretized to obtain a discretized adaptive double-power sliding mode observer. Based on the discretized adaptive double power sliding mode observer, the state of charge, polarization voltage, and terminal voltage are updated to obtain the updated state of charge, updated polarization voltage, and updated terminal voltage.

8. The method for estimating the state of charge of a battery as described in claim 1, wherein, Based on the Thevenin equivalent circuit model, the formula for the external characteristic behavior of the lithium battery during charging and discharging is as follows: Among them, U t For terminal voltage, U oc U is the open-circuit voltage, I(t) is the charging / discharging current, and U is the charging / discharging current. p Polarization voltage, C p For battery polarization capacitor, R p The polarization resistor is SOC, which stands for State of Charge. Polarization voltage U p The differential form of U is the rate of change of polarization voltage with time. oc (SOC(t)) is the open-circuit voltage.

9. The method for estimating the state of charge of a battery as described in claim 2, wherein, The differential equation for the polarization voltage of the lithium battery is: Where Δf3 represents the uncertainty caused by the unknown nonlinear polarization voltage term. R is the differential form of the battery polarization voltage. p For polarization resistance, C p For polarization capacitors, U p Let I(t) be the polarization voltage, I(t) be the charging / discharging current, and ΔC be the polarization voltage. P For additional polarization capacitors.

10. The method for estimating the state of charge of a battery as described in claim 2, wherein, The differential equation for the terminal voltage is expressed as: Where Δf1 represents the uncertainty caused by the unknown nonlinear term terminal voltage. This is the differential form of the terminal voltage. This is the differential form of the open-circuit voltage. This is the differential form of the battery polarization voltage. This is the differential form of the charging and discharging current.

11. The method for estimating the state of charge of a battery as described in claim 3, wherein, The multiple states of charge refer to the states of charge at different charging stages.

12. The method for estimating the state of charge of a battery as described in claim 4, wherein, The real-time operating data includes current, voltage, and temperature.

13. A battery state-of-charge estimation device, wherein, include: The Thevenin equivalent circuit state-space model construction module, the nonlinear relationship curve determination module, the parameter online identification module, and the state of charge estimation module; The Thevenin equivalent circuit state space model construction module is used to construct the Thevenin equivalent circuit state space model of lithium battery based on the Thevenin equivalent circuit model. The nonlinear relationship curve determination module is used to fit the state of charge and open-circuit voltage of the lithium battery based on a preset high-order polynomial, and determine the nonlinear relationship curve between the state of charge and the open-circuit voltage. The online parameter identification module is used to collect real-time operating condition data of the lithium battery, and based on the real-time operating condition data, to perform online parameter identification on the state space model of the Thevenin equivalent circuit using the extended Kalman filter algorithm to obtain estimated values ​​of state variables. The state of charge estimation module is used to construct an adaptive double power sliding membrane observer. The nonlinear relationship curve and the estimated value of the state variable are input into the adaptive double power sliding membrane observer so that the adaptive double power sliding membrane observer can calculate the estimated value of the lithium battery state of charge in real time.

14. A terminal device, wherein, The device includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor, when executing the computer program, implements the battery state-of-charge estimation method as described in any one of claims 1 to 12.

15. A computer-readable storage medium, wherein, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device on which the computer-readable storage medium is located to perform the battery state-of-charge estimation method as described in any one of claims 1 to 12.

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