Lithium battery charge state estimation method based on grey Kalman filtering model

Abstract

The invention discloses a lithium battery charge state estimation method based on a grey Kalman filtering model. The method specifically comprises the following steps: establishing a recursive relational expression of lithium battery state-of-charge (soc) estimated values at previous and later moments according to a gray GM (1, 1) model; constructing a state space expression according to the recursive relational expression; establishing a grey Kalman filtering model according to the state space expression in combination with the Kalman principle; soc is extracted from a public lithium battery data set of the Wishball University to serve as input of a gray Kalman filtering model, and the state of charge is estimated; and performing precision evaluation on an estimation result. According to the method, the state of charge of the lithium battery is estimated in three different scenes, including different driving cycles, random hybrid driving cycles and different temperatures under the same driving cycle condition; the result shows that the grey Kalman filtering model provided by the invention has a better estimation and prediction effect.

Description

Technical Field

[0001] The content of the present invention belongs to the technical field of lithium batteries, and specifically relates to a method for estimating the state of charge of a lithium battery based on a grey Kalman filter model. Background Art

[0002] With the wide use of electric vehicles and electronic devices, as the main energy supply device for these devices, the performance stability and reliability of lithium batteries are crucial. The state of charge of a lithium battery refers to the ratio of the remaining capacity after the battery has been used for a period of time or left unused for a long time to the capacity in a fully charged state, usually expressed as a percentage. It is a relative quantity, expressed as a percentage, and its value range is 0-100%. When the state of charge is 100%, it means the battery is fully charged, and when the state of charge is equal to 0, it means the battery is completely discharged. The state of charge is an important indicator for evaluating the remaining battery power and is of great significance for ensuring the safe and stable operation of the battery. The state of charge is one of the key elements of the battery management system. The state of charge can indicate the remaining power in the battery that can provide range for the vehicle. Accurately estimating the state of charge can not only provide information on the current and remaining performance of the lithium battery, but also ensure the safe and reliable operation of electric vehicles.

[0003] Methods for estimating the state of charge (SOC) of lithium batteries include: methods based on characterization parameters, ampere-hour integration method, model-based methods, and data-driven methods, etc. In the methods based on characterization parameters, the characterization parameters can include the current remaining capacity, impedance spectrum, open-circuit voltage, etc. These parameters can reflect the internal state of the battery from different dimensions, thus providing a rich information basis for the accurate estimation of SOC. The characterization method based on parameters needs to establish an offline relationship between the characterization parameters and the state of charge. The ampere-hour integration method is a very classic method for estimating the state of charge. There are certain defects in the use of the ampere-hour integration method. For example, it is difficult to obtain the exact initial value of SOC. To overcome this inherent defect of the ampere-hour integration method, the strategy usually adopted by researchers is to combine the ampere-hour integration method with other more accurate SOC estimation methods. For example, the open-circuit voltage OCV is used to determine the initial state of charge SOC, and then the ampere-hour integration method is used to calculate the subsequent SOC trajectory. Model-based methods mainly rely on accurate models and efficient state estimation algorithms to complete the accurate estimation of SOC. The performance of this method is jointly determined by the effectiveness of the model and the state estimation algorithm. Among them, the Kalman filter class of algorithms is one of the most commonly used methods in SOC estimation. The data-driven method is a method based on data analysis and mining. This method estimates SOC by collecting data such as the voltage and current of the battery and using a data model. Intelligent algorithms such as neural networks and support vector machines are commonly used methods in data-driven models. The advantages of these data-driven methods are that they can monitor the state of charge of the battery in real time and do not require knowledge of the internal structure and chemical reaction mechanism of the battery. At the same time, this method can also evaluate and predict the health state of the battery, which helps to detect and handle battery failures in a timely manner. However, the data-driven method also has some limitations. First of all, this method requires a large amount of historical data for training and learning, and for some new batteries or batteries under different usage scenarios, the model may need to be retrained. Secondly, the selection of the data model and the setting of parameters will also affect the accuracy and reliability of the estimation results, and fine adjustment and optimization are required.

[0004] Among these four types of methods, the model-based method is superior to other methods in terms of accuracy and robustness. The performance of the model-based estimation method is jointly determined by the model and the state estimation algorithm. The Kalman filter class of algorithms is one of the most commonly used algorithms in battery SOC estimation. The present invention borrows the advantages of two models. Generally, the Kalman filter algorithm is used in combination with an empirical model. It can be found through derivation that the GM(1,1) model and the single-exponential model in the lithium battery empirical model can be transformed. However, the unique cumulative operator of the grey model can reflect the cumulative process of lithium battery degradation, which is an advantage compared to the empirical model. By establishing a recurrence relationship through the time response formula of the grey model, the state equation and the observation equation are constructed, and the Kalman filter algorithm is skillfully combined to form a grey Kalman filter model for SOC estimation. Summary of the Invention

[0005] To solve the problem of insufficient accuracy in estimating the state of charge (SOC) of lithium batteries based on the empirical model fusion Kalman filter algorithm, the present invention proposes a method for estimating the SOC of lithium batteries based on a grey Kalman filter model (GKFM). According to the data characteristics extracted from the University of Wisconsin lithium battery dataset, it shows an approximately linear downward trend. By combining the advantages of the grey GM(1,1) model and the Kalman filter, the SOC is continuously predicted and updated, so as to more accurately estimate the SOC value of the lithium battery.

[0006] To achieve the above technical objectives, the present invention provides the following technical solutions:

[0007] A method for estimating the state of charge of a lithium battery based on a grey Kalman filter model, which specifically includes the following steps:

[0008] S1. According to the single-exponential model in the lithium battery empirical model, derive the basic form of the grey GM(1,1) model; and establish a recurrence relation between two adjacent time instants based on the time response formula of the grey GM(1,1) model.

[0009] S2. Build a state space model according to the recurrence relation between two adjacent time instants.

[0010] S3. Combine the state space model built in step S2 with the Kalman theory to obtain a grey Kalman filter model for estimating the state of charge of the lithium battery.

[0011] S4. Extract the state of charge soc of the lithium battery from the public dataset, and estimate soc through the grey Kalman filter model established in step S3.

[0012] S5. Evaluate the accuracy of the estimation result of soc.

[0013] Further, step S1 specifically includes:

[0014] S11. Obtain the single-exponential model in the lithium battery empirical model, and the formula is expressed as:

[0015]

[0016] Among them, y is the output item of the lithium battery empirical model, n represents the nth data, e represents the natural constant, and a1, a2, and a3 are the parameters of the single-exponential model.

[0017] S12. Take the first derivative of y with respect to n, concretize y as the state of charge soc of the lithium battery, and perform a first-order accumulation on the soc sequence to obtain the basic form of the whitening differential equation of GM(1,1), and the formula expression is:

[0018]

[0019] Among them, a = -a2, b = -a2a3; soc (1) soc(k) is the state of charge data of the lithium battery at the k-th moment (0) The first-order cumulative form of (k), that is:

[0020]

[0021] S13. Then, discretize the basic form of the whiting differential equation of GM(1,1) to obtain:

[0022] soc (0) (k) + az (1) (k) = b;

[0023] Among them,

[0024] S14. Use the least squares method to estimate the parameters a and b, and the formula is expressed as:

[0025]

[0026] Among them, Represents the estimated values of the parameters a and b trained from the first n data;

[0027] S15. Substitute Back into the basic form of the whiting differential equation of GM(1,1) to obtain the time response formula of GM(1,1), and the formula is expressed as:

[0028]

[0029] According to the basic definition of the cumulative reduction of the gray GM(1,1) model, the cumulative reduction value can be obtained, that is, the estimated value of soc at the k-th moment The formula is expressed as:

[0030]

[0031] Among them, Are the first-order cumulative forms of the estimated values of soc at the k-th moment and the k-1-th moment respectively;

[0032] Finally, the recurrence relationship between the estimated values of soc at two consecutive moments is established as:

[0033]

[0034] Furthermore, in step S2, the established state space model includes a state equation and an observation equation, and the formula expressions of the state equation and the observation equation are specifically:

[0035] State equation:

[0036] Observation equation:

[0037] Wherein, is the observation estimated value; ω k and υ k are the noises of the state equation and the observation equation respectively. ω k obeys the normal distribution with a mean of 0 and a variance of Q, and υ k obeys the normal distribution with a mean of 0 and a variance of R; the state equation is obtained according to the recurrence relation, and the observation equation is the output of the state equation considering external noise.

[0038] Furthermore, step S3 specifically includes:

[0039] S31. Prediction stage; first, use the estimated value of the state of charge at time k to obtain the estimated value of the state of charge at time k + 1, and the formula is expressed as:

[0040]

[0041] Wherein, A k is the state transition matrix,

[0042] Then, according to the error covariance matrix P k at time k, obtain the estimated value of the error variance matrix at time k + 1 The formula is expressed as:

[0043]

[0044] Next, calculate the Kalman gain coefficient K k+1 , and the formula is expressed as:

[0045]

[0046] S32. Update stage; first, correct through the difference between the observed state of charge y k+1 of the lithium battery at time k + 1 and the estimated value in the prediction stage, combined with the Kalman gain coefficient K k+1 , and the formula is expressed as:

[0047]

[0048] Wherein, x k+1 is the state of charge of the lithium battery at time k + 1;

[0049] Then, update and correct the error covariance matrix at time k + 1 to complete the construction of the grey Kalman model; the formula is expressed as:

[0050]

[0051] At this time, the gray Kalman filter model is constructed.

[0052] Furthermore, in step S4, the state of charge of the lithium battery is estimated based on the publicly available lithium battery dataset of the University of Wisconsin. Specifically:

[0053] S41. According to the ampere-hour integration method, the soc under a single driving cycle, the soc under multiple driving cycles with multiple intersections, and the soc under the same driving cycle but different temperatures are respectively extracted from the publicly available lithium battery dataset of the University of Wisconsin;

[0054] S42. Preprocess the extracted soc data to more effectively estimate the state of charge of the lithium battery;

[0055] S43. Input the obtained true soc values into the gray Kalman filter model constructed in step S3 to estimate the state of charge of the lithium battery from multiple dimensions.

[0056] More specifically, the preprocessing in step S42 is specifically as follows:

[0057] Discard the SOC values of the lithium batteries with the remaining power below 30% in the lithium battery dataset, extract data at the node of the fixed time interval t to estimate the lithium battery SOC; use the soc data with 70% of the data length for model parameter training, and the remaining 30% of the training length is used to obtain the estimation result.

[0058] Furthermore, in step S5, the accuracy evaluation of the soc estimation result is achieved by calculating the mean absolute percentage error MAPE and the root mean square error RMSE between the true value and the estimated value. The formula is expressed as:

[0059]

[0060] Among them, soc (0) (i), Are respectively the true value and the estimated value of the state of charge of the lithium battery at the i-th moment.

[0061] Based on the above technical solutions, the present invention has at least the following beneficial effects:

[0062] (1) Strong adaptability to multiple scenarios: By combining the gray GM(1,1) model and the Kalman filter, the constructed gray Kalman filter model can effectively cope with complex dynamic environments, and shows stable SOC estimation performance under different driving cycles (including random hybrid driving cycles) and different temperature conditions under the same driving cycle, significantly improving the environmental adaptability and robustness of the model.

[0063] (2) High dynamic estimation accuracy: The grey model is good at dealing with small sample and uncertain data, capturing the system change trend by establishing a recursive relationship of SOC; the Kalman filter dynamically corrects the prediction error, and the combination of the two achieves more accurate real-time state estimation, especially maintaining high accuracy under dynamic working conditions.

[0064] (3) Algorithm lightweight and practicality: Compared with traditional complex models, the grey Kalman filter model has a simple structure and high computational efficiency, and is suitable for resource-constrained scenarios such as in-vehicle battery management systems. At the same time, it is verified through public data sets, confirming its practical application value.

[0065] In summary, through model fusion innovation, this method solves the problems of insufficient accuracy and poor adaptability faced by traditional single methods in dynamic environments, providing an efficient and reliable technical means for lithium battery SOC estimation. Description of the Drawings

[0066] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for description in the embodiments will be briefly introduced below.

[0067] Figure 1 It is the flowchart for constructing the grey Kalman filter model of the present invention;

[0068] Figure 2 It is the SOC estimated value under the US06 driving cycle;

[0069] Figure 3 It is the SOC estimated value under different driving cycles;

[0070] Figure 4 It is the SOC estimated value under a random mixed driving cycle;

[0071] Figure 5 It is the SOC estimated value at different temperatures;

[0072] Figure 6 It is the overall flowchart of the method proposed by the present invention. Detailed Embodiments

[0073] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0074] Although the steps in the present invention are arranged with reference numerals, they are not used to limit the order of the steps. Unless the order of the steps is clearly stated or the execution of a certain step requires other steps as a basis, the relative order of the steps can be adjusted. It can be understood that the term "and / or" used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

[0075] For the state of charge estimation, the prior art directly using an empirical model for estimation cannot achieve ideal accuracy; while in the present invention, through derivation and analysis, it is found that there are similarities between the grey model and the lithium battery empirical model, and the grey accumulation operator can effectively reflect the cumulative usage trend of the state of charge. Therefore, the present invention designs a grey Kalman filter model according to the actual problem to solve the state of charge estimation problem of lithium batteries, and proposes a method for estimating the state of charge of lithium batteries based on the grey Kalman filter model, as Figure 6 shown, which specifically includes the following steps:

[0076] S1. According to the single-exponential model in the lithium battery empirical model, derive the basic form of the grey GM(1,1) model; and establish a recurrence relation between two adjacent moments (i.e., two adjacent terms) based on the time response formula of the grey GM(1,1) model;

[0077] As a preferred embodiment, as Figure 1 shown, step S1 specifically includes:

[0078] S11. Obtain the single-exponential model in the lithium battery empirical model, which is expressed by the formula:

[0079]

[0080] where y is the output term of the lithium battery empirical model, n represents the nth data, e represents the natural constant, and a1, a2, and a3 are the parameters of the single-exponential model;

[0081] S12. Take the first derivative of y with respect to n, specify y as the state of charge soc of the lithium battery, and perform a first-order accumulation on the soc sequence to obtain the basic form of the white differential equation of GM(1,1), which is expressed by the formula:

[0082]

[0083] where a = -a2, b = -a2a3; soc (1) (k) is the first-order accumulation form of the state of charge data soc (0) (k) at the kth moment, that is:

[0084]

[0085] S13. Then, discretize the basic form of the whitenization differential equation of GM(1,1) to obtain:

[0086] soc (0) (k)+az (1) (k) = b;

[0087] Where,

[0088] S14. Estimate the parameters a and b using the least squares method, and the formula is expressed as:

[0089]

[0090] Where, represent the estimated values of the parameters a and b trained from the first n data;

[0091] S15. Substitute back into the basic form of the whitenization differential equation of GM(1,1) to obtain the time response formula of GM(1,1), which is expressed as:

[0092]

[0093] According to the basic definition of the cumulative reduction restoration of the gray GM(1,1) model, the cumulative reduction restoration value can be obtained, that is, the estimated value of soc at the k-th moment The formula is expressed as:

[0094]

[0095] Where, are the first-order cumulative forms of the estimated values of soc at the k-th moment and the k-1-th moment respectively;

[0096] Finally, the recurrence relation between the estimated values of soc at two consecutive moments is established as:

[0097]

[0098] S2. Build a state space model according to the recurrence relation between two consecutive moments;

[0099] In this embodiment, the gray model is combined with the Kalman theory. Therefore, referring to the Kalman filter model, the built state space model includes a state equation and an observation equation. The specific formulas of the state equation and the observation equation are expressed as:

[0100] State equation:

[0101] Observation equation:

[0102] Where, is the observed estimate; ω k and υ k are the noises of the state equation and the observation equation respectively. ω k obeys a normal distribution with a mean of 0 and a variance of Q, and υ k obeys a normal distribution with a mean of 0 and a variance of R; the state equation is obtained according to the recurrence relation, and the observation equation is the output of the state equation considering external noise.

[0103] S3. Combine the state space model established in step S2 with the Kalman theory to obtain a grey Kalman filter model for estimating the state of charge of a lithium battery;

[0104] As a preferred embodiment, as Figure 1 shown, step S3 specifically includes:

[0105] S31. Prediction stage; first, use the estimated value of the state of charge at time k to obtain the estimated value of the state of charge at time k + 1. The formula is expressed as:

[0106]

[0107] where A k is the state transition matrix,

[0108] Then, according to the error covariance matrix P k at time k, obtain the estimated value of the error variance matrix at time k + 1 The formula is expressed as:

[0109]

[0110] Next, calculate the Kalman gain coefficient K k+1 , and the formula is expressed as:

[0111]

[0112] S32. Update stage; first, correct by the difference between the observed state of charge y k+1 of the lithium battery at time k + 1 and the estimated value in the prediction stage, combined with the Kalman gain coefficient K k+1 . The formula is expressed as:

[0113]

[0114] where x k+1 is the state of charge of the lithium battery at time k + 1;

[0115] Then, update and correct the error covariance matrix at time k + 1 to complete the construction of the grey Kalman model; the formula is expressed as:

[0116]

[0117] At this time, the grey Kalman filter model is constructed.

[0118] S4. Extract the state of charge (SOC) of the lithium battery from the public dataset, and estimate the SOC through the grey Kalman filter model established in step S3.

[0119] In this embodiment, the state of charge of the lithium battery is estimated based on the public lithium battery dataset of the University of Wisconsin. Specifically:

[0120] S41. According to the ampere-hour integration method, extract the SOC under a single driving cycle, the SOC under multiple intersections of multiple driving cycles, and the SOC at different temperatures under the same driving cycle condition from the public lithium battery dataset of the University of Wisconsin respectively.

[0121] S42. Preprocess the extracted SOC data to more effectively estimate the state of charge of the lithium battery.

[0122] For lithium batteries, it is better to charge when the battery power remains about 15% to 30%. Because the full charge process and the complete discharge process of the battery belong to a cycle period, and 15% to 30% is the best charging period for lithium batteries. It is not possible to charge when the battery is overly discharged, nor is it appropriate to charge when the battery still has a lot of power. Any of these operations will make the lithium battery less durable and even gradually unable to charge, and then the battery has to be replaced. Under this premise, the present invention preprocesses the data, discards the SOC values of the lithium batteries with a remaining power of less than 30% in the lithium battery dataset, extracts data at 1-minute intervals to estimate the lithium battery SOC; uses 70% of the data length of the SOC data for model parameter training, and the remaining 30% of the training length is used to obtain the estimation result.

[0123] S43. Input the obtained true SOC value into the grey Kalman filter model constructed in step S3 to estimate the state of charge of the lithium battery from multiple dimensions.

[0124] In this embodiment, based on the public dataset of the University of Wisconsin, the SOC is estimated under various lithium battery charge and discharge scenarios, including comparative experiments under different driving cycles at 25°C, comparative experiments under random mixed driving cycles, and experimental comparisons of the state of charge at different temperatures under the same driving cycle.

[0125] S5. Evaluate the accuracy of the estimation result of the SOC.

[0126] As a preferred embodiment, in step S5, the accuracy of the estimated result of the SOC is evaluated by calculating the mean absolute percentage error MAPE and the root mean square error RMSE between the true value and the estimated value, and the formula is expressed as:

[0127]

[0128] where SOC (0) (i), are respectively the true value and the estimated value of the state of charge of the lithium battery at the i-th moment.

[0129] The superiority of the method proposed in this aspect is shown below during actual experiments.

[0130] This embodiment discusses the estimation of the state of charge of the lithium battery from four dimensions;

[0131] Firstly, the estimation of the state of charge of the lithium battery under different driving cycles is carried out. These driving cycles include US06, HWFET, UDDS, and LA92. Secondly, the estimation of the state of charge of the lithium battery under the condition of a random hybrid driving cycle is carried out, which includes four cycles. Cycles 1 to 4 are randomly mixed by US06, HWFET, UDDS, and LA92. Thirdly, considering the changes caused by the influence of temperature on the lithium battery, in order to ensure the stability of the model, the state of charge values at different temperatures are estimated from the same driving cycle. Finally, the gray Kalman filter model designed by the present invention is also compared with other model algorithms to illustrate the superiority of the model.

[0132] Firstly, the state of charge of the lithium battery under different driving cycles is estimated, including several typical driving conditions such as US06, HWFET, UDDS, and LA92. Taking US06 as an example for introduction. US06 is an automobile emission test condition formulated by the US Environmental Protection Agency. It is designed according to the actual situation of urban traffic congestion and highway driving, and is used to evaluate the emissions and fuel economy of automobiles under real conditions. When there is urban traffic congestion, it is used to simulate actual driving situations such as parking waiting, traffic light waiting, and sudden acceleration on urban roads. When driving on the highway, the vehicle is required to drive at a relatively high speed within a certain time to examine the fuel economy and emissions of the vehicle when driving at high speed. Figure 2It is the SOC estimation value under US06 conditions. During the process of estimating the state of charge, the value of the grey development coefficient a obtained by parameter estimation is 0.014697, and the MAPE of the estimation result is 4.79%. Generally, when the usage range of MAPE is below 10%, the model is considered available. The estimation result of the present invention is within the error range. The MAPE value not only indicates that the model can well capture the true change trend of SOC, but also means that in practical applications, the model can provide more accurate remaining power information for drivers, which helps to optimize driving strategies, extend the cruising range and reduce the inconvenience caused by insufficient power.

[0133] Figure 3 The (a), (b), (c), and (d) in it are the estimation values under HWFTa, HWFTb, UDDS, and LA92 respectively. The HWFET driving cycle, divided into HWFTa and HWFTb, as an important tool for simulating high-speed driving performance, its core lies in examining the fuel economy and emission performance of the vehicle at high speed and stable speed. In this cycle, the vehicle needs to continuously drive at a preset high speed to test its operating efficiency under long-term and high-load conditions. Through Figure 3 the SOC estimation values of HWFTa and HWFTb in it, it can be clearly seen that under high-speed driving conditions, the decline of the battery SOC is relatively stable, which benefits from the lower energy demand of the vehicle during high-speed cruising. In addition, the grey development coefficients of HWFTa and HWFTb are 0.009486 and 0.009498 respectively, indicating that the model has high accuracy in predicting the SOC change under high-speed conditions. At the same time, their estimation errors are 3.05% and 2.71% respectively, far lower than the acceptable range, further verifying the effectiveness of the model. In contrast, the UDDS driving cycle focuses more on simulating the stop-and-go driving mode in the city, especially frequent acceleration and deceleration situations, and is mainly used to test the fuel economy and performance of the vehicle under urban road conditions. This driving mode poses a higher challenge to the battery management system of electric vehicles because frequent power changes will significantly affect the SOC of the battery. Figure 3 The SOC estimation value of UDDS in it shows that under urban road conditions, the fluctuation of the battery SOC is stronger than that of HWFET. Nevertheless, the model can still accurately capture this change, its grey development coefficient is 0.003104, and the estimation error is 4.61%. Although slightly higher than HWFET, it is still within the acceptable range, indicating that the model also has good adaptability under complex urban driving conditions. The LA92 driving cycle focuses on simulating the driving conditions and characteristics of a specific city or region, such as specific traffic patterns, road conditions, etc. This cycle is of great significance for evaluating the performance of electric vehicles in different regional environments. Figure 3The soc estimation value of LA92 demonstrates the flexibility of the model in dealing with different driving environments. Its grey development coefficient is 0.004811, and the estimation error is 3.89%, which also proves the effectiveness and accuracy of the model.

[0134] Secondly, it is the state of charge estimation of lithium batteries under a random mixed driving cycle. In addition to the state of charge estimation of lithium batteries under a single driving cycle state, during the actual driving process of a vehicle, it is impossible for the entire journey to always be in the same working condition. In order to be closer to the actual vehicle usage situation, the present invention also uses the random mixed driving cycle data in the publicly available dataset of the University of Wisconsin to estimate the state of charge of lithium batteries. The random mixed data includes four groups of data, namely cycle1, cycle2, cycle3, and cycle4. These four groups of data are randomly combined from different situations such as US06, HWFET, UDDS, and LA92. The randomly combined driving cycle can include situations such as driving on highways and waiting in traffic jams in the city, which is more in line with the actual operating state of the vehicle. Therefore, the state of charge estimation of lithium batteries under a random mixed driving cycle can better reflect the performance of the algorithm. The results of the state of charge estimation of lithium batteries under a random mixed driving cycle using the grey Kalman filter model are shown in Figure 4 , Figure 4 . It can be seen from (a), (b), (c), and (d) in

[0135] that the original soc data under the combined driving cycles of cycle1, cycle2, cycle3, and cycle4 begins to show a large fluctuating state compared to the single working condition. Thus, it can be seen that the soc data under the randomly combined driving cycle is indeed closer to the vehicle driving situation. In this fluctuating state, the advantages of the proposed grey Kalman filter model can be more prominent. The errors of the soc estimation values under the random driving cycle are 5.03%, 3.51%, 4.75%, and 5.84% respectively. These MAPE values are all within a reasonable error range. Therefore, from the perspective of soc estimation under a random mixed driving cycle, the performance of the grey Kalman filter model can also be reflected.

[0135] Finally, it is the state of charge estimation of lithium batteries at different temperatures under the same driving cycle. Temperature change has a certain impact on the performance of lithium batteries. Therefore, in order to further verify the estimation effect of the proposed model algorithm on the soc of lithium batteries when the temperature changes, this embodiment uses the publicly available lithium battery dataset of the University of Wisconsin for verification. The embodiment uses different temperature changes under the same driving cycle to simulate the estimation accuracy of soc in order to ensure the objectivity and fairness of the comparative experiment. Taking US06 as an example, comparative analysis is carried out at different temperatures respectively, and the comparison results are as shown in Figure 5 shown, Figure 5Among them, (a), (b), (c), and (d) respectively represent four temperature changes of US06 in the publicly available data, which are 10°C, 0°C, -10°C, and -20°C. The grey Kalman filter model is used to estimate the soc at these four temperatures, and the MAPE errors are 3.25%, 2.39%, 3.97%, and 2.77% respectively. From this comparison result, it can be seen that with the change of temperature, the grey Kalman filter model can still effectively estimate the soc value of the lithium battery, further demonstrating the effectiveness of the proposed model.

[0136] Comparison with other algorithms. After completing the soc estimation under different conditions, the grey Kalman filter algorithm GKFM proposed in this invention is compared with other models. Taking US06 as an example, the model comparison results are shown in Table 1. The comparison models include common grey univariate prediction models, such as GM(1,1), adjacent cumulative discrete grey GM(1,1) (ADGM). In addition, it also includes artificial intelligence algorithms, such as support vector machines (SVM), neural network autoregressive model (NNAR), etc. The accuracy measurement criteria of the models are measured by the mean absolute percentage error and the root mean square error respectively. It can be seen from Table 1 that the GKFM model shows that the proposed model is superior to the comparison models from the perspectives of RMSE and MAPE.

[0137] Table 1 Comparison of US06 model errors

[0138]

[0139]

[0140] After comparing the soc values of the US06 driving cycle, the HWFET, UDDS, and LA92 at the same temperature are also subjected to model comparison. The comparison models are the same as those of US06, and the comparison results are shown in Table 2 below:

[0141] Table 2 Comparison of model accuracies under different driving cycles

[0142]

[0143] In the comparison model, GM(1,1) is the first-order accumulated grey GM(1,1) model, and ADGM(1,1) is the adjacent accumulated grey GM(1,1) model; the weight of the accumulation operator in HWFTa, HWFTb, UDDS, and LA92 in this model is 0.1, and the search method is to fit between 0 and 1 with a step size of 0.1 to minimize the fitting error. NNAR and SVM are obtained by directly calling packages in R language. It can be seen from Table 2 that the soc estimation accuracy of the grey Kalman filter model designed by the present invention is the highest. At the same time, SVM has the largest error from both the RMSE and MAPE perspectives. In the grey comparison model, the improved ADGM(1,1) model is superior to the classical GM(1,1) model, and the grey Kalman filter model is superior to the ADGM(1,1) model when estimating the soc of lithium batteries. This also illustrates the pertinence and effectiveness of the improvement of the grey prediction model for the soc estimation of lithium batteries.

[0144] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0145] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for estimating the state of charge of a lithium battery based on a grey Kalman filter model, characterized in that: include: S1. Based on the single exponential model in the lithium battery empirical model, the basic form of the grey GM (1,1) model is derived; And based on the time response of the grey GM (1,1) model, a recursive relationship between the two moments is established; S2, build a state space model based on the recursive relationship between the previous and next moments; S3, combining the state space model constructed in step S2 with the Kalman theory to obtain a grey Kalman filter model for estimating the state of charge of a lithium battery; S4, extracting the state of charge (SOC) of the lithium battery from the public data set, and estimating the SOC through the grey Kalman filter model established in step S3; S5. Evaluate the accuracy of the SOC estimation result.

2. The method for estimating the state of charge of a lithium battery according to claim 1, characterized in that: Step S1 specifically includes: S11. Obtain a single exponential model in the lithium battery empirical model, the formula is expressed as: Where y is the output item of the lithium battery empirical model, n represents the nth data, e represents the natural constant, and a1, a2, and a3 are the parameters of the single exponential model; S12. Take the first derivative of y with respect to n, visualize y as the state of charge soc of the lithium battery, and perform first-order accumulation on the soc sequence to obtain the basic form of the whitened differential equation of GM(1,1), which is expressed as follows: Among them, a=-a2, b=-a2a3; soc (1) (k) is the lithium battery state of charge data soc at the kth moment (0) The first-order cumulative form of (k), namely: S13. Discretize the basic form of the whitened differential equation of GM(1,1) and obtain: social (0) (k)+az (1) (k)=b; in, S14. The least square method is used to estimate the parameters a and b. The formula is: in, Represents the estimated values ​​of parameters a and b trained with the first n data; S15. Substituting back the basic form of the whitened differential equation of GM(1,1), we get the time response of GM(1,1), which is expressed as: According to the basic definition of the grey GM (1,1) model cumulative reduction, the cumulative reduction value can be obtained, that is, the estimated value of soc at the kth moment: The formula is: in, are the first-order cumulative forms of the soc estimates at the kth moment and the k-1th moment respectively; Finally, the recursive relationship between the estimated values ​​of SOC at the previous and next moments is established as follows:

3. The method for estimating the state of charge of a lithium battery according to claim 2, characterized in that: The state space model constructed in step S2 includes a state equation and an observation equation. The formulas of the state equation and the observation equation are specifically expressed as follows: Equation of state: Observation equation: in, is the observed estimated value; ω k and k are the noises of the state equation and observation equation, ω k It obeys a normal distribution with a mean of 0 and a variance of Q, υ k It obeys a normal distribution with a mean of 0 and a variance of R. The state equation is obtained according to the recursive relationship, and the observation equation is the output of the state equation taking into account external noise.

4. The method for estimating the state of charge of a lithium battery according to claim 3, characterized in that: Step S3 specifically includes: S31, prediction stage: first use the estimated value of the state of charge at time k to obtain the estimated value of the state of charge at time k+1, the formula is expressed as: Among them, A k is the state transfer matrix, Then according to the error covariance matrix P at time k k Get the estimated value of the error variance matrix at time k+1 The formula is: Then calculate the Kalman gain coefficient K at time k+1 k+1 , the formula is: S32, update phase; first, the lithium battery charge state y observed at time k+1 k+1 The difference between the estimated value in the prediction stage and the Kalman gain coefficient K k+1 The correction formula is expressed as: Among them, x k+1 is the state of charge of the lithium battery at time k+1; Then update and correct the error covariance matrix at time k+1 to complete the construction of the grey Kalman model; the formula is expressed as: At this point, the grey Kalman filter model is constructed.

5. The method for estimating the state of charge of a lithium battery according to claim 1, characterized in that: In step S4, the state of charge of the lithium battery is estimated based on the public lithium battery data set of the University of Wisconsin, specifically: S41. Based on the ampere-hour integration method, the SOC under a single driving cycle, the SOC under multiple driving cycles and multiple crossovers, and the SOC under the same driving cycle conditions but at different temperatures are extracted from the public lithium battery data set of the University of Wisconsin. S42, preprocessing the extracted SOC data to more effectively estimate the state of charge of the lithium battery; S43, input the obtained soc true value into the grey Kalman filter model constructed in step S3, and estimate the state of charge of the lithium battery from multiple dimensions.

6. The method for estimating the state of charge of a lithium battery according to claim 5, characterized in that: The preprocessing in step S42 is specifically as follows: The SOC values ​​of lithium batteries with remaining power below 30% in the lithium battery data set are discarded, and data extraction is performed at fixed time intervals t as nodes to estimate the SOC of the lithium battery; 70% of the soc data length is used for model parameter training, and the remaining 30% of the training length is used to obtain the estimation result.

7. The method for estimating the state of charge of a lithium battery according to claim 1, characterized in that: In step S5, the accuracy evaluation of the estimation result of SOC is achieved by calculating the mean absolute percentage error MAPE and the root mean square error RMSE between the true value and the estimated value, and the formula is expressed as: Among them, soc (0) (i) are the true value and estimated value of the lithium battery state of charge at time i respectively.

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