Battery SOC and SOP estimation method and system based on fractional-order model

Abstract

The present disclosure relates to the related technical field of battery parameter estimation, and provides a battery SOC and state of power (SOP) estimation method and system based on a fractional-order model. The method comprises: establishing a fractional-order model of a battery to obtain a state equation and an output equation of a battery model; using a genetic algorithm-based parameter identification method to identify battery parameters in the model; using a fractional integral to calculate the charging and discharging process of the battery, and using an improved unscented Kalman filter method to estimate the SOC of the battery; and establishing a continuous SOP estimation model under a multi-constraint condition to estimate the SOP. The present disclosure achieves cooperative estimation of the SOC and the SOP, introduces a fractional calculus to establish a more accurate battery model, uses a fractional-order control theory to improve the estimation precision of the SOC and the SOP, and can better optimize the usage and control strategy of the battery, thereby prolonging the service life of the battery, and improving the energy utilization efficiency of the system.

Description

Battery SOC and SOP estimation method and system based on fractional-order model

[0001] The present invention claims priority to the Chinese patent application filed with the Patent Office of China on December 7, 2023, with application number 202311686407.X and invention name “Battery SOC and SOP Estimation Method and System Based on Fractional Order Model”, the entire contents of which are incorporated by reference into the present invention. Technical Field

[0002] The present disclosure relates to the technical field related to battery parameter estimation, and more specifically, to a battery SOC and SOP estimation method and system based on a fractional-order model. Background Art

[0003] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0004] SOC (State of Charge) and SOP (State of Power) are two key parameters in the battery management system. They have a significant impact on the performance and life of the battery. Among them, SOC can reflect the remaining battery life, allowing the system to load a matching control algorithm to extend the battery life, thereby effectively improving the overall performance and reliability of electric vehicles. SOP can provide data support for the vehicle's main control system to achieve vehicle power distribution, energy optimization, and extend the service life of the battery pack, making the control of the vehicle's main control system more accurate and scientific. Therefore, how to optimize and improve the estimation accuracy of SOC and SOP is crucial to improving the core competitiveness of the battery management system's performance and expanding its scope of industrial application.

[0005] The inventors discovered that most current SOC and SOP estimation methods use integer-order models. Real-world applications and extensive experimental results show that the more RC links an integer-order circuit model has, the more accurate the model output. However, this increases the model complexity, requiring the processor to identify more model parameters. This makes model parameter identification difficult, leading to an exponential increase in processor computing resources and ultimately causing delayed model output, making it unsuitable for practical applications.

[0006] Summary of the Invention

[0007] In order to solve the above problems, the present disclosure proposes a battery SOC and SOP estimation method and system based on a fractional-order model. This technical solution introduces fractional-order calculus to establish a more accurate battery model, adopts a SOC and SOP collaborative estimation method, and uses a fractional-order control algorithm to improve the estimation accuracy of SOC and SOP. This solution can accurately estimate SOC and SOP parameters, save processor computing resources, and provide protection for the system to optimize the use and control strategy of batteries, thereby extending the service life of the battery and improving the energy utilization efficiency of the system.

[0008] In order to achieve the above objectives, the present disclosure adopts the following technical solutions:

[0009] One or more embodiments provide a battery SOC and SOP estimation method based on a fractional-order model, comprising the following steps:

[0010] Establish a fractional-order model of the battery and obtain the state equation and output equation of the battery model;

[0011] For the fractional-order model of the battery, the genetic algorithm parameter identification method is used to identify the battery parameters in the model;

[0012] The battery charge and discharge process is calculated using fractional-order integration, and the battery SOC is estimated using the improved unscented Kalman filter method.

[0013] Based on the battery SOC, a continuous peak power estimation model under multi-constraint conditions is established with reference to the current and voltage parameters of the battery itself, and the peak current is estimated to obtain the estimated value of the peak power.

[0014] One or more embodiments provide a battery SOC and SOP estimation system based on a fractional-order model, including the following:

[0015] A fractional-order model building module is configured to build a fractional-order model of the battery and obtain a state equation and an output equation of the battery model;

[0016] A parameter identification module is configured to identify each battery parameter in the fractional-order model of the battery using a genetic algorithm parameter identification method;

[0017] The SOC estimation module is configured to calculate the battery charge and discharge process using fractional-order integration and estimate the battery SOC using an improved unscented Kalman filter method;

[0018] The SOP estimation module is configured to establish a continuous peak power estimation model under multiple constraints based on the battery SOC and with reference to the current and voltage parameters of the battery itself, estimate the peak current, and then obtain an estimated value of the peak power.

[0019] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps in the above-mentioned battery SOC and SOP estimation method based on the fractional-order model are completed.

[0020] A computer-readable storage medium is characterized in that it is used to store computer instructions, and when the computer instructions are executed by a processor, the steps in the above-mentioned battery SOC and SOP estimation method based on the fractional-order model are completed.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] In the present disclosure, by introducing the concept of fractional order calculus, a more accurate battery model can be established, and fractional order control theory, SOC and SOP joint estimation and other strategies are utilized to improve SOC and SOP estimation accuracy, which is conducive to better optimizing battery use and control strategy, effectively extending battery life and improving the energy efficiency of battery. At the same time, for the problems such as large accuracy error between each parameter in the identification result, the present disclosure also creatively discloses a kind of improved unscented Kalman filtering algorithm, and further improves the estimation accuracy of SOC and SOP in combination with the fractional order battery model. The SOC estimation method of the lithium battery disclosed in the present disclosure effectively reduces its initial error, and the error influence of SOC on the SOP estimation process is also reduced to a minimum, effectively enhancing the robustness of the SOP estimation algorithm, and ensuring the accuracy of lithium battery SOC and SOP estimation.

[0023] The disclosed technical solution can be used for both new energy vehicles and electric bicycles. It overcomes the accuracy and real-time limitations of traditional methods. By leveraging a fractional-order battery model and advanced algorithms, it achieves a more accurate and real-time estimation of the battery's state of charge, providing a better driving experience for new energy vehicle drivers.

[0024] The advantages of the present disclosure and additional advantages will be described in detail in the following specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings, which constitute a part of the present disclosure, are used to provide a further understanding of the present disclosure. The exemplary embodiments of the present disclosure and their descriptions are only used to explain the present disclosure and do not constitute a limitation of the present disclosure.

[0026] FIG1 is an overall flow chart of the SOC and SOP estimation method of Example 1 of the present disclosure;

[0027] FIG2 is a fractional-order equivalent circuit model of a lithium battery according to Example 1 of the present disclosure;

[0028] FIG3 is a schematic diagram of the SOC estimation process flow of Example 1 of the present disclosure;

[0029] FIG4 is a comparison of SOC measurement values ​​under DST conditions and estimated values ​​by other algorithms in a verification experiment of Example 1 of the present disclosure;

[0030] FIG5 is a comparison diagram of SOC estimation result errors of four algorithms under DST conditions in the verification experiment of Example 1 of the present disclosure;

[0031] FIG6 is a comparison diagram of terminal voltage estimation values ​​of four algorithms under DST conditions in the verification experiment of Example 1 of the present disclosure;

[0032] FIG7 is a comparison diagram of terminal voltage errors of four algorithms under DST conditions in the verification experiment of Example 1 of the present disclosure. DETAILED DESCRIPTION

[0033] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0034] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present disclosure belongs.

[0035] It should be noted that the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof. It should be noted that, in the absence of conflict, the various embodiments in the present disclosure and the features in the embodiments can be combined with each other. The embodiments will be described in detail below with reference to the accompanying drawings.

[0036] Example 1

[0037] In the technical solutions disclosed in one or more embodiments, as shown in FIG1 to FIG7 , a battery SOC and SOP estimation method based on a fractional-order model includes the following steps:

[0038] Step 1: Establish a fractional-order model of the battery to obtain the state equation and output equation of the battery model;

[0039] Step 2: For the fractional-order model of the battery, a genetic algorithm parameter identification method is used to identify the battery parameters in the model;

[0040] Step 3: Use fractional-order integration to calculate the battery charge and discharge process, and use the improved unscented Kalman filter method to estimate the battery SOC value;

[0041] Step 4: Based on the battery SOC value, a peak power estimation model under multiple constraints is established with reference to the battery current and voltage parameters to estimate the peak current and thereby obtain an estimated value of the peak power.

[0042] In this embodiment, this implementation adopts fractional-order calculus to establish a more accurate battery fractional-order model compared to the existing technology to improve the estimation accuracy of SOC and SOP; by accurately estimating SOC and SOP, it is beneficial to better optimize the control strategy to further extend the battery life and improve the battery energy utilization efficiency in the system.

[0043] Step 1: Establish a fractional order model;

[0044] A fractional-order model is constructed based on the second-order RC model, as shown in Figure 2. The fractional-order model constructed in this embodiment includes three parts: Based on the ohmic internal resistance R0 of the battery, the ohmic polarization characteristics of the battery are described; the first constant phase element CPE1 and the first resistor R1 are used to form a fractional-order link to describe the charge transfer process and double layer effect in the electrochemical process of the battery; the second constant phase element CPE2 and the second resistor R2 are used to form a fractional-order link to describe the transport reaction behavior of the electrolyte and solid phase interface in the electrochemical process of the battery.

[0045] Unlike the prior art, this embodiment establishes a fractional-order lithium battery model by directly discretizing the fractional-order calculus equation. This is more compatible with the improved unscented Kalman filter algorithm and improves the processor's calculation speed and estimation accuracy. The model formula and specific derivation process are as follows:

[0046] In the above formula, represents the continuous integral differential operator, where a and t are the upper and lower limits of the integral respectively, r is the fractional order of each link; h is the sampling time length, i is the Newton coefficient, t is the independent variable of the function, and f(t) is the dependent variable of the function;

[0047] In Figure 2, the impedance expressions of the two constant phase elements CPE1 and CPE2 are as shown in formula (3):

[0048] Among them, C CPE1 Represents the electrochemical polarization capacitance, C CPE2 represents the concentration difference diffusion capacitance, n1 and n2 are the orders of polarization capacitance and diffusion capacitance respectively; j is a complex number, and w is the angular frequency.

[0049] Combining the fractional order model and Thevenin theorem, we can get:

[0050] The measurement equation is: U0=U OCV -UR -U1-U2 (5)

[0051] Among them, Uocv represents the open circuit voltage of the power supply, U R , U1, and U2 represent the three loop terminal voltages of capacitors R, R1, and R2 respectively.

[0052] According to the above formula, the state space equation of the continuous fractional order model can be obtained as follows:

[0053] By discretizing equation (6), we can obtain a fractional-order model, including the state equation and the output equation, as shown in the following equation:

[0054] Among them, x k is the state variable at time k, y k is the observed variable at time k, u k is the input quantity at time k, C is the output matrix at time k, w k 、v k is the process noise and observation noise of the system at time k, T s n is the sampling time, L m is the memory length.

[0055] In the state equation, matrices A, B and Newton's least binomial coefficient γ i They are respectively Equation (8), Equation (9) and Equation (10), where n1 and n2 are the orders of the two constant phase elements;

[0056] Where Δt is the independent variable of the function, C1 and C2 represent the parameters of the fractional-order element, η k-1 is the coulombic efficiency of battery charge and discharge, Q N is the process noise covariance.

[0057] The integer-order lithium battery model cannot describe the charge transfer reaction between the electrolyte and the solid phase interface layer and the double-layer effect electrochemical process, which will cause the estimated SOC and SOP of the lithium battery to deviate significantly from the actual value after multiple operating cycles. Therefore, this embodiment improves the second-order RC model into a fractional-order model with a more comprehensive description mechanism, which can more accurately describe the dynamic behavior inside the battery and ensure the accuracy of the SOC and SOP estimation after multiple operating cycles of the lithium battery.

[0058] In step 2, based on the constructed fractional-order model, a genetic algorithm is further used to identify parameters. The parameters to be identified are R0, R1, R2, C1, C2 and the fractional orders n1 and n2 of the two capacitors. The specific steps are as follows:

[0059] (1) Initialization: Randomly generate multiple individuals to form a population. Each parameter to be identified encodes a chromosome, and the solution of the battery parameter is used as an individual.

[0060] First, a population of individuals is randomly generated, each representing a solution. The individuals are then binary-coded, with each code forming a chromosome. Each chromosome is divided into seven parts, representing the seven parameters to be identified.

[0061] (2) exchanging gene fragments among individuals in the population;

[0062] According to the set mating probability, the "father generation" and "mother generation" are selected from the population for "hybridization", that is, the gene fragments of the encoded genes are exchanged;

[0063] (3) mutations are made at random positions in the new individuals that exchange gene fragments;

[0064] Gene mutation is performed according to the set mutation probability: two new individuals will be generated after "hybridization", and the new individuals will mutate at random gene sites.

[0065] (4) Decode the mutated individuals and calculate their fitness values;

[0066] Decode the mutated individuals, convert the binary of the gene fragment into decimal, and substitute the decoded individuals into the fitness function until an individual meets the requirements of the fitness function, and then stop evolving. The fitness function is as follows:

[0067] Among them, Y e (j) is the predicted value obtained by the genetic algorithm, Y(j) is the actual value of the measurement, and J(i) is the sum of the squares of the differences between the two.

[0068] (5) Using elite selection based on fitness value, select individuals for the next iteration;

[0069] According to the roulette principle, find the probability P of each individual being selected i , the formula is as follows:

[0070] In the above formula, J i is the fitness value of the i-th individual, N is the number of individuals in the population, f i Represents the adaptive function value of each individual.

[0071] (6) Update the mating probability and mutation probability, and perform the next iterative calculation until the set number of iterations is reached, and output the optimal individual, which is the battery parameter value.

[0072] In step 2 of this embodiment, a genetic algorithm is further used to perform parameter identification based on the fractional-order circuit model. Compared with the parameter identification method in the prior art, the genetic algorithm in this technical solution is more accurate in identifying the parameters in the equivalent circuit model, further improving the estimation accuracy of the lithium battery terminal voltage, and better improving the battery performance, which is very suitable for application in battery management systems.

[0073] In step 3, the battery charge and discharge process is calculated using fractional-order integration, and the battery SOC is estimated using an improved unscented Kalman filter method.

[0074] This embodiment addresses the problem of inaccurate battery SOC estimation in the unscented Kalman filter (UKF) under complex working conditions and noise uncertainty, and improves the UKF algorithm. Specifically, the UKF algorithm is improved by continuously updating the noise covariance and measurement covariance of the system using the measured value, model estimated value and residual weighted value of the sigma point of each state, thereby realizing adaptive update and feedback of the noise and improving the accuracy of the algorithm.

[0075] The derivation steps of the improved UKF algorithm are as follows:

[0076] Noise Adaptation:

[0077] Where μ k and y k is the output residual of the measurement sigma estimate, represents the posterior state estimate at time k, is a nonlinear function, Kk is the Kalman gain, ω k The covariance with mean 0, represents the observed variable at time k, L is the dimension of the input variable, i is the Newton coefficient, represents the covariance weight.

[0078] Get a set of sigma point estimates:

[0079] Where n represents the state dimension; λ represents the scale scaling parameter, λ = α 2 (n+κ)-n, κ represents another proportional factor, which is usually 0 or 3-n; represents the i-th column of the square root of the covariance matrix.

[0080] Through formula (16), process noise and measurement noise can be updated in real time and then improved by combining with the UKF algorithm.

[0081] The SOC calculation process is shown in Figure 3. After the battery parameters obtained in step 2 are used, the improved UKF algorithm is used to estimate the SOC value in combination with the experimental data. The calculation process using the improved UKF algorithm includes the following steps:

[0082] The first step is to initialize the filter;

[0083] in, is the initial value, P0 is the estimated variance;

[0084] The second step is to perform state prediction and obtain Sigma points through untraceable transformation;

[0085] The third step is to calculate the predicted value of the state variable and the covariance matrix of the state variable;

[0086] Where, P x,k / k-1 is the a priori estimate of the covariance. Q k is the process noise. represents the mean weight of the sampling points, represents the covariance weight; is the mean of the Gaussian distribution on the i-th column, represents the state prediction at time k-1 for time k, It represents the state prediction of time k at time k-1 on the i-th column, Indicates The state prediction at time k at time k-1 in the symmetric dimension.

[0087] The fourth step is to calculate the observation quantity and sum the weighted observation quantity;

[0088] Where, represents the observed quantity; u k Represents the original state quantity;

[0089] The fifth step is to calculate the observation variance matrix and the covariance between the state variables and the observations;

[0090] Where R k is the measurement noise. yy,k represents the observation variance matrix, P xy,k represents the covariance between the state variable and the observation, represents the observation value at time k at time k-1 on the i-th column, Represents the observation value at time k-1.

[0091] Step 6: Calculate the Kalman gain coefficient; K k =P xy,k / P yy,k

[0092] Step 7: Update the state variables and calculate the error covariance.

[0093] Where, is the optimal estimate of the state, P x,k / k is the covariance estimate.

[0094] In this embodiment, multiple simulation experiments were conducted using battery testing equipment to verify the obtained fractional-order model. Multiple OCV-SOC charge (discharge) experiments were conducted, and the experimental data were averaged to obtain OCV-SOC data. The OCV-SOC relationship was obtained through function fitting.

[0095] Furthermore, in addition to the parameters mentioned above, the open circuit voltage is also identified. In this solution, the open circuit voltage of the lithium battery is obtained by using the SOC relationship curve provided by the battery manufacturer and adding the fitting formula determined by experiment. The experimental test process used can be as follows:

[0096] (1) The lithium battery is discharged at a constant current of 1C until the terminal voltage of the lithium battery drops to the minimum cut-off voltage. The lithium battery is left to stand for 1 hour.

[0097] (2) The lithium battery is charged at a constant current of 1C for 6 minutes and then left to stand for 1 hour. After standing, the SOC corresponding to the terminal voltage of the lithium battery is about 10%;

[0098] (3) Repeat step (2) eight times to obtain the corresponding open circuit voltage values ​​of the lithium battery at 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90% SOC respectively.

[0099] (4) The lithium battery is charged at a constant current of 1C until the terminal voltage reaches the maximum cut-off voltage, then the battery is switched to constant voltage mode. At this point, trickle charging begins and the charging is stopped when the current decreases to 0.05C. The battery is then left to stand for 1 hour. The terminal voltage at this point is the open circuit voltage when the SOC is 100%.

[0100] (5) The lithium battery is discharged at a constant current of 1C for 6 minutes, and then left to stand for 1 hour. The terminal voltage of the lithium battery after standing is the open circuit voltage corresponding to the SOC of 90%;

[0101] (6) Repeat step (5) eight times to obtain the corresponding open circuit voltage values ​​of the lithium battery at 80%, 70%, 60%, 50%, 40%, 30%, 20%, and 10% SOC respectively.

[0102] (7) The lithium battery is discharged at a constant current of 0.02C until the terminal voltage of the lithium battery drops to the minimum cut-off voltage and then left to stand for 1 hour. The terminal voltage of the lithium battery after standing is the open circuit voltage value when the SOC is 0%.

[0103] This embodiment uses a polynomial function to fit OCV and SOC. As the power increases, the degree of fitting also increases. The formula is as follows: OCV (SOC) = a1 × SOC 7 +a2×SOC 6 +a3×SOC 5 +a4×SOC 4 + a5×SOC 3 +a6×SOC 2 +a7×SOC+a8

[0104] By combining the identification parameters, state equations, output equations, OCV-SOC relationship and complex dynamic stress test conditions (DST), SOC can be estimated. Experimental results show that the improved UKF algorithm shows extremely high estimation accuracy and robustness.

[0105] In step 4, the sustained peak power estimation model is the SOP estimation model, and the construction process is as follows:

[0106] Step 41: Determine a battery voltage calculation model based on the fractional-order equivalent circuit model and the identified SOC value;

[0107] Step 42: Determine a load current calculation formula at a certain time point based on the voltage calculation model, and obtain a peak current calculation formula under the peak voltage constraint;

[0108] Step 43: Assuming that the peak current in the set time period remains constant, a peak charge and discharge current calculation formula in the set time period is obtained based on the battery voltage calculation model and the peak current calculation formula;

[0109] The set time period can be set to be within the range from time point k to time point k+L;

[0110] Step 44: Based on the SOC constraint, the peak charge current and peak discharge current constraints, and the OCV constraint, and according to the peak charge and discharge current calculation formula within the set time period, a continuous peak charge and discharge current formula under multiple constraint conditions is determined, and then a continuous peak power estimation formula under multiple constraint conditions is obtained, that is, a continuous peak power estimation model is obtained.

[0111] The various constraints for calculating continuous peak charge and discharge current and continuous peak power include:

[0112] SOC constraint: The SOC value is within the battery SOC value limit range, and the current constraint for the next cycle is based on the current SOC value;

[0113] Peak charge current and peak discharge current constraints: The peak charge and discharge current of the battery cell itself is within the current limit of the battery cell itself;

[0114] OCV constraint: The actual terminal voltage of the battery must be between the upper and lower peak values ​​of the open circuit voltage to maintain the battery in a comfortable operating state.

[0115] Based on the fractional-order equivalent circuit model, the lithium-ion battery voltage calculation model can be obtained as follows:

[0116] Among them, U L,k+1 represents the terminal voltage in the fractional-order equivalent circuit model, I L,k+1 is the operating current in the fractional-order equivalent circuit model, U CPE2,k+1 They are respectively represented as the terminal voltages at both ends of R1 and R2, L is the terminal voltage indicator symbol for distinguishing the open circuit voltage, and the subscript k+1 represents the k+1 moment.

[0117] Based on the superposition principle, the and U CPE2,k+1 It can be expressed like this:

[0118] Among them, τ1 and τ2 are U CPE2,k+1 time constant.

[0119] And, for U in formula (17) oc (SOC k+1 ) Perform a first-order Taylor expansion at time point k, and we get:

[0120] Among them, Q n is the rated capacity of the battery.

[0121] The first-order residual term ΔU in formula (20) oc (SOC k )≈0, then formula (17) can be approximately equivalent to:

[0122] Further expanding equation (21), we get the new terminal voltage equation:

[0123] Therefore, the load current calculation formula at a certain time point k+1 can be expressed as follows:

[0124] In order to extend the service life of the battery, it should be ensured that the battery operates within the appropriate voltage range. Therefore, the terminal voltage U L,k Meet U L,min ≤U L,k ≤U L,max Among them, U L,max is the peak charging voltage at that moment, U L,min is the peak discharge voltage at that moment. From this, we can see that the peak current under the peak voltage constraint can be expressed as:

[0125] in, is the maximum discharge current in one cycle; It is the maximum charging current in one cycle.

[0126] The maximum charge current and maximum discharge current calculated by equations (24) and (25) are both peak currents within a single cycle. However, during the actual operation of an electric vehicle, the battery may be in a special state for a considerable period of time, and the peak current over a long period of time cannot be calculated using these two equations. Therefore, this embodiment develops a method for calculating the continuous peak current over a long period of time.

[0127] It is stipulated that the peak current from time point k to time point k+L remains unchanged, that is, I k =I k+1 =I k+2 =…=I k+L According to formula (18), the voltage of ZARC1 element at time point k+L can be obtained: Its terminal voltage is shown in formula (26).

[0128] The same method can be used to obtain the ZARC2 element voltage at time point k+L. Its terminal voltage is shown in formula (27).

[0129] U oc (SOC k+L ) is expanded at time point k, we can get formula (28):

[0130] After the continuous current acts for L×Δt time, the terminal voltage U L,k+L It can be expressed as:

[0131] In order to make the formula more intuitive, the above formula (29) is further rewritten as follows:

[0132] Therefore, the current at any time point k+L is expressed by equation (31):

[0133] Combined with what has been said before, the actual terminal voltage of the battery should be between the upper and lower peak values ​​to maintain the battery in a comfortable working state. The peak charge and discharge current calculation formula from time point k to time point k+L is:

[0134] in, It is the maximum discharge current within the time range L×Δt; It is the maximum charging current within the time range L×Δt.

[0135] In order to avoid serious damage to the battery pack, the battery SOC should always be kept within a reasonable operating range, and the SOC at any k moment should meet the SOC min ≤SOC k ≤SOC max It is known that the ampere-hour measurement method calculates the battery's SOC through current, so the peak charge and discharge current in a cycle can be obtained in reverse through the following formula:

[0136] in, Indicates that the current SOC state limits the peak discharge current in the next cycle. Indicates that the current SOC state limits the peak charging current in the next cycle. Then for the peak charging current in the next L×Δt time range and peak discharge current They can be expressed by the following formulas:

[0137] Also consider: I chg and I dis , the continuous peak charge and discharge current under multiple constraints is obtained as follows:

[0138] Among them, I dis,L is the maximum discharge current within the next L×Δt time range; I chg,L is the maximum charging current in the next L×Δt time range. Combining formula (21), the continuous peak charge and discharge power estimation model of the battery in the next L×Δt time range can be obtained as:

[0139] Among them, P maxis the maximum discharge power in the user manual of the battery cell; P min is the minimum charging power in the battery cell manual. Substituting equation (29) into equations (40) and (41), we get:

[0140] in, and The peak discharge power and peak charging power are respectively estimated by using a continuous peak power estimation method under multiple constraints to estimate the battery peak power within the next L×Δt time range.

[0141] In this embodiment, SOC estimation is achieved by combining SOC with multiple constraints. A continuous peak power estimation model under multiple constraints is established with reference to the battery's current and voltage parameters, achieving a precise SOP estimate. Experiments have shown that the resulting SOP value is more accurate. Compared to existing SOP accuracy, this solution can better improve the effectiveness and reliability of batteries and is very suitable for use in lithium battery management systems.

[0142] In order to verify the accuracy and stability of the fractional-improved UKF algorithm (ie, the method of this embodiment), the following test was performed: This embodiment adopts a dynamic stress test condition (DST), and the initial value of SOC is set to 80% in this experimental condition.

[0143] Under DST conditions, the accuracy of the fractional-order-improved UKF was verified by comparing the estimation results of the existing methods 2RC-UKF, 2RC-improved UKF, fractional-order-UKF, and fractional-order-improved UKF. RC refers to the second-order model, and fractional-order refers to the fractional-order model. Among them, UKF is the unscented Kalman filter.

[0144] Figure 4 shows the SOC estimation results of the four algorithms, Figure 5 shows the SOC estimation error, Figure 6 shows the terminal voltage estimation value, and Figure 7 shows the terminal voltage estimation error.

[0145] As shown in Figure 4, the improved UKF algorithm converges significantly faster than the UKF algorithm in the initial stages, showing a significant advantage. The fractional-order model also converges faster than the second-order model. At intermediate times, the fractional-improved UKF algorithm's estimates are closest to the measured values, while the 2RC-UKF algorithm's estimates deviate the most from the measured values. At later times, the fractional-improved UKF and fractional-UKF algorithms achieve better estimation results. Figure 5 shows that the mean absolute error and root mean square error (RMS) of the SOC estimation for the 2RC-UKF algorithm are 2.37% and 1.57%, respectively; for the 2RC-improved UKF algorithm, they are 1.73% and 1.15%, for the fractional-UKF algorithm, 0.44% and 0.58%, and for the fractional-improved UKF, 0.30% and 0.22%. The fractional-improved UKF algorithm exhibits excellent convergence performance, with extremely low mean absolute error and root mean square error, making it an excellent estimate.

[0146] Figure 6 shows that under DST conditions, the voltage estimated by the fractional-order-improved UKF algorithm is closest to the measured value, followed by the fractional-order-UKF algorithm. Figure 7 shows that the mean absolute error and root mean square error of the terminal voltage estimation using the 2RC-UKF algorithm are 1.17% and 1.45%, respectively; the 2RC-improved UKF algorithm is 1.05% and 0.90%, the fractional-order-UKF algorithm is 0.73% and 0.693%, and the fractional-order-improved UKF is 0.64% and 0.54%. This indicates that the fractional-order-improved UKF algorithm has the smallest terminal voltage estimation error.

[0147] Experiments and simulations show that the fractional-order model is significantly more accurate than the second-order model, while the improved UKF algorithm performs even better, far surpassing the UKF algorithm. The fractional-order-improved UKF algorithm has been verified to demonstrate excellent accuracy and rapid convergence. Testing has also shown that the fractional-order-improved UKF algorithm exhibits outstanding estimation accuracy and robustness.

[0148] Verification has shown that this method demonstrates high accuracy and reliability in SOC and SOP estimation. Experimental results demonstrate that fractional-order models offer high accuracy and reliability in SOC and SOP estimation. Compared to existing methods, fractional-order model-based methods better adapt to the nonlinear characteristics and uncertainties of batteries, improving estimation accuracy and stability, making them well-suited for applications in the control and management of electric vehicles and renewable energy systems.

[0149] Example 2

[0150] Based on Example 1, this embodiment provides a battery SOC and SOP estimation system based on a fractional-order model, including:

[0151] A fractional-order model building module is configured to build a fractional-order model of the battery and obtain a state equation and an output equation of the battery model;

[0152] A parameter identification module is configured to identify each battery parameter in the fractional-order model of the battery using a genetic algorithm parameter identification method;

[0153] The SOC estimation module is configured to calculate the battery charge and discharge process using fractional-order integration and estimate the battery SOC using an improved unscented Kalman filter method;

[0154] The SOP estimation module is configured to establish a continuous peak power estimation model under multiple constraints based on the battery SOC and with reference to the current and voltage parameters of the battery itself, estimate the peak current, and then obtain an estimated value of the peak power.

[0155] It should be noted here that the various modules in this embodiment correspond one-to-one to the various steps in Example 1, and the specific implementation processes are the same, which will not be repeated here.

[0156] Example 3

[0157] Based on Example 1, this embodiment provides an electronic device, characterized in that it includes a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are executed by the processor, the steps in the battery SOC and SOP estimation method based on the fractional-order model described in Example 1 are completed.

[0158] Example 4

[0159] Based on Example 1, this embodiment provides a computer-readable storage medium, characterized in that it is used to store computer instructions. When the computer instructions are executed by a processor, the steps in the battery SOC and SOP estimation method based on the fractional-order model described in Example 1 are completed.

[0160] The foregoing description is merely a preferred embodiment of the present disclosure and is not intended to limit the present disclosure. Those skilled in the art will readily appreciate that various modifications and variations are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present disclosure shall be included within the scope of protection of the present disclosure.

[0161] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Those skilled in the art should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. Battery SOC and SOP estimation method based on fractional-order model, Characterized in that, It includes the following steps: Establish a fractional-order model of the battery to obtain the state equation and output equation of the battery model; For the fractional-order model of the battery, use the genetic algorithm parameter identification method to identify each battery parameter in the model; Use fractional-order integration to calculate the charge and discharge process of the battery, and use the improved unscented Kalman filter method to estimate the SOC of the battery; Based on the battery SOC, establish a continuous peak power estimation model under multiple constraint conditions by referring to the current and voltage parameters of the battery itself, estimate the peak current, and then obtain the estimated value of the peak power.

2. The battery SOC and SOP estimation method based on fractional-order model according to claim 1, Characterized in that, The constructed fractional-order model includes the following three parts: Based on the ohmic internal resistance R of the battery 0 , describe the ohmic polarization characteristics of the battery; Use the first constant phase element and the first resistor to form a fractional-order link to describe the charge transfer process and double-layer effect in the battery electrochemical process; Use the fractional-order link composed of the second constant phase element and the second resistor to describe the transport reaction behavior at the electrolyte-solid phase interface in the battery electrochemical process.

3. The battery SOC and SOP estimation method based on fractional-order model according to claim 2, Characterized in that: Adopt the method of directly discretizing the fractional-order calculus equation to establish the fractional-order model of the battery.

4. The battery SOC and SOP estimation method based on fractional-order model according to claim 1, Characterized in that: Based on the constructed fractional-order model, use the genetic algorithm for battery parameter identification. The specific process is as follows: Perform initialization, randomly generate multiple individuals to form a population, encode each parameter to be identified as a chromosome, and use the solution of the battery parameter as an individual; Exchange gene segments of the individuals in the population; Mutate at random positions of the new individuals after exchanging gene segments; Decode the mutated individuals and calculate the fitness value; Adopt elitist selection according to the fitness value to select the individuals for the next iteration; Update the mating probability and mutation probability, perform the next iteration calculation until the set number of iterations is reached, and output the optimal individual, which is the obtained battery parameter value.

5. The battery SOC and SOP estimation method based on fractional-order model according to claim 1, Characterized in that: The algorithm uses the improved unscented Kalman filter, and continuously updates the system noise covariance and measurement covariance by using the measurement value, model estimated value and residual weighted value of sigma points of each state, and performs adaptive update and feedback on the noise.

6. The battery SOC and SOP estimation method based on fractional-order model according to claim 1, Characterized in that: The continuous peak power estimation model is constructed as follows: According to the fractional-order equivalent circuit model and the identified SOC value, determine the battery voltage calculation model; According to the voltage calculation model, determine the load current calculation formula at a certain time point, and obtain the peak current calculation formula under the peak voltage constraint; Assume that the peak current within the set time period remains constant. According to the battery voltage calculation model and the peak current calculation formula, the peak charge and discharge current calculation formula within the set time period is obtained; Based on the SOC constraint, the peak charge current, the peak discharge current constraint, and the OCV constraint, according to the peak charge and discharge current calculation formula within the set time period, the continuous peak charge and discharge current formula under multiple constraints is determined, and then the continuous peak power estimation formula under various constraints is obtained, that is, the continuous peak power estimation model is obtained.

7. The battery SOC and SOP estimation method based on the fractional-order model according to claim 6, characterized in that: The multiple constraints for calculating the continuous peak charge and discharge current and the continuous peak power include: SOC constraint: The SOC value is within the limit range of the battery SOC value, and the current in the next cycle is constrained based on the current SOC value; Peak charge current and peak discharge current constraint: The peak charge and discharge current of the battery cell itself is within the limit value range of the battery cell itself current; OCV constraint: The actual terminal voltage of the battery should be between the upper and lower limit peaks of the open-circuit voltage.

8. A battery SOC and SOP estimation system based on the fractional-order model, characterized in that it includes: A fractional-order model construction module configured to establish a fractional-order model of the battery to obtain the state equation and output equation of the battery model; A parameter identification module configured to use the genetic algorithm parameter identification method to identify each battery parameter in the fractional-order model of the battery; An SOC estimation module configured to use fractional-order integration to calculate the charge and discharge process of the battery and estimate the SOC of the battery by using the improved unscented Kalman filter method; An SOP estimation module configured to establish a continuous peak power estimation model under multiple constraints based on the battery SOC, refer to the current and voltage parameters of the battery itself to estimate the peak current, and then obtain the estimated value of the peak power.

9. An electronic device, characterized in that it includes a memory, a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the steps in the battery SOC and SOP estimation method based on the fractional-order model according to any one of claims 1-7 are completed.

10. A computer-readable storage medium, characterized in that it is used to store computer instructions. When the computer instructions are executed by the processor, the steps in the battery SOC and SOP estimation method based on the fractional-order model according to any one of claims 1-7 are completed.

Images