A Nonlinear Modeling Method for Lithium-Ion Batteries Based on Hammerstein-CARMA

Abstract

The present invention provides a non - linear modeling method for lithium - ion batteries based on Hammerstein - CARMA, belonging to the technical field of lithium - ion batteries, and solving the technical problem of low accuracy of traditional equivalent circuit models of lithium - ion batteries. The technical solution is as follows: It includes the following steps: Step 1) Measure the load current and terminal voltage data of the battery through intermittent constant - current discharge to determine the OCV - SOC relationship; Step 2) Establish a non - linear model of lithium - ion batteries based on Hammerstein - CARMA; Step 3) Construct the algorithm flow of COA; Step 4) Introduce various improvement measures on the basis of COA to construct ICOA; Step 5) Use ICOA to identify model parameters and predict the terminal voltage of lithium - ion batteries. The beneficial effects of the present invention are: The present invention uses the improved coyote optimization algorithm for parameter identification, with high identification accuracy and fast convergence speed.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium-ion batteries, and in particular to a non-linear modeling method for lithium-ion batteries based on Hammerstein-CARMA. Background Art

[0002] With the continuous innovation of industrial technologies, energy consumption has been increasing, and resource shortage has become an increasingly serious problem. In recent years, the new energy industry has been emerging continuously, and electric vehicles, as a typical representative, have become a popular field. Electric vehicle enterprises led by NIO and XPeng in China have been growing continuously, and with the strong support of the country, they have gradually influenced domestic vehicle manufacturing enterprises to develop towards new energy and pollution-free directions.

[0003] Lithium-ion batteries are currently widely used to provide power for electric vehicles. They are controlled by a Battery Management System (BMS) to achieve optimal efficiency. The State of Charge (SOC) of a lithium-ion battery is an important parameter in the BMS, which can provide a basis for the control strategy of the vehicle battery pack. High-precision SOC estimation results can effectively ensure the safe and reliable operation of the BMS. Establishing an accurate battery model is an important prerequisite for accurate SOC estimation. The equivalent circuit model of a lithium-ion battery is a linear dynamic model. However, in the actual application process, the model output is affected by external noise, and there are also certain measurement errors in the input current, making the battery model exhibit non-linearity, which to a certain extent affects the parameter identification effect. In the field of system identification, the research on non-linear models is quite extensive, and using the block structure model in the field of system identification to replace the battery model is a new research field. How to associate the battery model with the non-linear block structure model through analysis and derivation is an important issue.

[0004] How to solve the above technical problems is the subject faced by the present invention. Summary of the Invention

[0005] The object of the present invention is to provide a non - linear modeling method for lithium - ion batteries based on Hammerstein - CARMA. In the actual application process, the output of the battery model is affected by external noise, and there are also certain measurement errors in the input current, making the battery model show a kind of non - linearity, which to a certain extent affects the parameter identification effect. Considering the above factors, the Hammerstein controlled autoregressive moving average model (Hammerstein - CARMA) is introduced. This model has colored noise in the external input, and the model input shows non - linearity. Hammerstein - CARMA is a non - linear model that has been studied in depth and is in line with the lithium - ion battery model in actual situations. The present invention introduces this model structure into lithium - ion batteries, uses swarm intelligence optimization algorithms to identify the parameters of the established non - linear lithium - ion battery model, and uses a variety of working conditions to verify the accuracy of the model. The results show that the non - linear lithium - ion battery model based on Hammerstein - CARMA has higher accuracy, and the predicted terminal voltage error value is significantly lower than that of the conventional equivalent circuit model.

[0006] The present invention is realized by the following measures: A non - linear modeling method for lithium - ion batteries based on Hammerstein - CARMA, which specifically includes the following steps:

[0007] Step 1) Measure the load current and terminal voltage data of the battery through intermittent constant - current discharge to determine the OCV - SOC relationship;

[0008] Step 2) Establish a non - linear lithium - ion battery model based on Hammerstein - CARMA;

[0009] Step 3) Construct the algorithm flow of COA;

[0010] Step 4) Introduce a variety of improvement measures on the basis of COA to construct ICOA;

[0011] Step 5) Use ICOA to identify the model parameters and predict the terminal voltage under a variety of working conditions;

[0012] As a further optimization scheme of the non - linear modeling method for lithium - ion batteries based on Hammerstein - CARMA of the present invention, the specific content of the said step 2) is as follows:

[0013] The second - order RC model represents the electrochemical polarization effect and concentration - difference polarization effect of lithium batteries through two parallel RC links. Its structure is relatively simple, parameter identification is easy to achieve, and the accuracy can basically meet the needs of research.

[0014] There are two parallel RC links in the second - order Thevenin model, R 1 and C1 represents the electrochemical polarization effect, R 2 and C 2 represent the concentration difference polarization effect. U oc and U correspond to the open-circuit voltage and terminal voltage of the battery, and C 1 and C 2 The voltages across both ends are represented by U 1 and U 2 respectively, and R 0 is the ohmic internal resistance. According to Kirchhoff's law, a battery equivalent circuit model is established:

[0015]

[0016] Using the bilinear transformation s = 2(1 - z -1 ) / T(1 + z -1 )(where T is the sampling period), mapping the above formula from the s-plane to the z-plane, we can obtain:

[0017]

[0018]

[0019] where: τ 1 = R 1 C 1 , τ 2 = R 2 C 2 , a = R 0 , b = τ 1 τ 2 , c = τ 1 + τ 2 , d = R 0 + R 1 + R 2 , e = R 0 (τ 1 + τ 2 ) + R 1 τ 1 + R 2 τ 2 .

[0020] Discretizing the above formula, we can obtain the difference equation:

[0021]

[0022] In the actual identification process, there are certain external disturbances in the output of the battery model, and there are measurement errors in the input current, making the output of the model show a certain non-linearity. These two situations affect the parameter identification effect. To address this problem, this paper integrates the external disturbance and the measurement error of the input into the second-order RC model, and constructs a lithium-ion battery model with a Hammerstein-CARMA structure.

[0023] The external disturbance of the battery model is w(z), and the output terminal voltage is y(z), satisfying y(z) = U - U oc . The model input I(z) is the theoretical value of the input to the battery model. Usually, there are measurement errors in it, and in the lithium-ion battery model based on the Hammerstein-CARMA structure, it can be expressed as:

[0024]

[0025] where is the non-linear current input value with measurement errors, and γ 1 , γ 2 are error coefficients.

[0026] Assume that the external disturbance w(z) of the system has a rational spectral density, the pole polynomial of the disturbance channel is the same as that of the process channel, and the zero polynomial has the same order as the pole polynomial, that is:

[0027]

[0028] Thus, the expression for the output of the battery model terminal voltage can be obtained:

[0029]

[0030] Assume b 0 = 1, let n a = 3, n b = 2, n d = 2, and the lithium-ion battery model based on Hammerstein-CARMA can be obtained:

[0031]

[0032] where y(z) is the battery terminal voltage value, is the input current after considering measurement noise.

[0033] Define the parameter vector η and the information vector

[0034] η = [a 1 , a 2 , b 1 , b 2 , γ 1, γ 2 , d 1 , d 2 T ∈ R n (9)

[0035]

[0036] can be integrated into an identification model:

[0037]

[0038] Furthermore, an algorithm can be used for identification.

[0039] As a further optimization scheme of a nonlinear modeling method for lithium-ion batteries based on Hammerstein-CARMA of the present invention, step 3) specifically includes the following contents:

[0040] The Coyote Optimization Algorithm (COA) is an intelligent bionic optimization algorithm with a unique structure. It can improve the convergence speed while ensuring the interaction between populations, thereby enhancing population diversity and having excellent identification effects. Its core idea is to regard the parameters to be estimated as the social states of coyote individuals. Based on social adaptability, the newly born coyotes and the oldest coyotes are selected for survival of the fittest, and issues such as the inheritance, mutation of the newly born coyotes, and the expulsion and acceptance of the coyote population are considered. Finally, the optimal coyote is obtained. The pseudo-code of the algorithm is as follows:

[0041]

[0042]

[0043] As a further optimization scheme of a nonlinear modeling method for lithium-ion batteries based on Hammerstein-CARMA of the present invention, step 4) specifically includes the following steps:

[0044] Step 4-1): Chaos is a common nonlinear phenomenon. In swarm intelligence optimization algorithms, the randomness, ergodicity, and regularity of chaotic variables can be used for optimization, so as to maintain population diversity and enhance global search ability. Compared with the common Logistic mapping, the Tent mapping has better ergodic uniformity and faster convergence speed. The present invention introduces this mapping into COA. The expression is as follows:

[0045]

[0046] z is a chaotic sequence. The conventional Tent mapping sequence has small cycles and unstable periodic points, so a random variable is introduced for improvement. The improved expression is as follows:

[0047] ​

[0048] where r t is a random number in the range of (0, 1), and NT is the number of elements in the Tent chaos sequence.

[0049] After generating the chaos sequence, map it to the solution space:

[0050]

[0051] lb j and ub j are the upper and lower bounds during the initialization of the coyote individuals.

[0052] Step 4-2) The mechanism of within-group influence and individual update in the coyote optimization algorithm is as follows:

[0053]

[0054]

[0055]

[0056] r 1 and r 2 are random numbers between 0 and 1, η 1 is the selected coyote and the difference from the best coyote alpha p in the group, η 2 is the difference between another selected coyote and the cultural trend cult p in the group. The growth of coyotes within the group is affected by the best wolf alpha p and the cultural trend cult in the group.

[0057] Due to the randomness of the grouping of the coyote population, the quality of the best wolf and the cultural trend in the group may not meet the algorithm requirements, and the phenomenon of insufficient guiding force may occur, which may cause the algorithm to fall into a local optimum. On this basis, considering the guiding role of the best coyote beta in the population, a new way of coyote growth is constructed, and the best coyote in the group, the best coyote in the population, and two randomly selected coyotes are jointly used as the influencing factors for coyotes within the group. At the same time, in order to make the algorithm more effectively approach the optimal solution, an adaptive operator is introduced into the influencing factors r 1 and r 2 to unify the influencing factors, and the improvement method is as follows:

[0058]

[0059]

[0060] η 3 = beta - alpha p (20)

[0061]

[0062] wherein:

[0063]

[0064] r = r 0 ×2 α (23)

[0065] τ 1 and τ 2 represent the influence weights on the p - th group's optimal wolf alpha p and the population - optimal wolf beta, η 3 is the difference between the population - optimal coyote and the within - group optimal coyote. r 0 is the initial influence factor, G is the maximum number of iterations, and k is the current number of iterations. In the original coyote algorithm, r 1 and r 2 are random numbers within 0 to 1, and there is a certain degree of uncertainty and randomness during the within - group coyote influence process. By introducing an adaptive operator and determining the value of the initial influence factor, the uncertainty and randomness can be effectively offset. During the iterative process of the entire algorithm, the adaptive operator changes periodically with the increase in the number of iterations, so that the influence factor is within a reasonable range and the optimal value is searched for during the entire operation process, thereby accelerating the convergence speed.

[0066] During the entire algorithm process, the within - group coyotes are all influenced by the randomly selected coyote within the group, the within - group optimal coyote, and the global optimal coyote, effectively improving the population diversity, making the algorithm less likely to fall into local optimality during the convergence process and having a faster convergence speed.

[0067] Through the above improvements, an improved coyote optimization algorithm (ICOA) is proposed.

[0068] As a further optimization scheme of a Hammerstein - CARMA - based non - linear lithium - ion battery modeling method of the present invention, step 5) specifically includes the following steps:

[0069] Segment the intermittent constant - current discharge condition measured in step 1), and each segment experiences rest, pulse discharge, and then rest. Use the algorithm for segment - by - segment identification. Taking the constant - current discharge process with an initial SOC = 0.72 as an example, use ICOA for parameter identification. The algorithm population size is set to 100, the number of groups is 5, and the number of coyote individuals in each group is 20. Use the sum of the squared errors between the experimentally measured terminal voltage and the actual terminal voltage to establish the fitness function f(x):

[0070]

[0071] where y(k) is the measured voltage, is the predicted voltage. Through piecewise identification, the model parameters of the lithium-ion battery corresponding to different initial SOCs can be obtained. By fitting SOC and the parameters, the variation curve of the parameters with respect to SOC can be obtained.

[0072] The obtained parameters are combined with the actual data to predict the terminal voltage, and the accuracy of the model under intermittent constant current discharge experiments is verified.

[0073] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0074] (1) The present invention establishes a second-order RC model of a lithium-ion battery according to Kirchhoff's law, conducts intermittent constant current discharge experiments, and fits the OCV-SOC relationship.

[0075] (2) In the actual identification process, it is considered that there are certain external disturbances in the terminal voltage output of the battery model and measurement errors in the input current, which affect the identification effect of the model parameters. The present invention integrates the external disturbance and the measurement noise of the input into the second-order RC model, and constructs a lithium-ion battery model with a Hammerstein-CARMA structure, effectively improving the identification accuracy of the model. The terminal voltage prediction error is significantly lower than the prediction error under the second-order RC model structure.

[0076] (3) In the process of model parameter identification, the present invention uses a swarm intelligence optimization algorithm for piecewise identification. To ensure the superiority of the algorithm in terms of accuracy and convergence speed, the present invention improves on the original COA. The chaotic Tent map is introduced, the guiding role of the population-optimal wolf is considered, a new way of coyote growth is constructed, and at the same time, an adaptive operator is introduced into the influencing factors to unify each influencing factor. In the whole algorithm process, the coyotes within the group are all affected by the coyotes randomly selected within the group, the optimal coyote within the group, and the global optimal coyote, effectively improving the population diversity, making the algorithm not easily fall into local optimum during the convergence process and having a faster convergence speed. At the same time, the Tent chaos is used to generate an initial population with uniform distribution, which can not only retain the randomness of the initialized individuals but also improve the population diversity, thereby improving the convergence speed of the algorithm. Description of the Drawings

[0077] The drawings are used to provide further understanding of the present invention, and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention, and do not constitute a limitation to the present invention.

[0078] Figure 1 is the OCV-SOC fitting curve of the present invention.

[0079] Figure 2 This is the second-order RC model diagram of the lithium-ion battery of the present invention.

[0080] Figure 3 This is the structural diagram of the Hammerstein-CARMA model of the present invention.

[0081] Figure 4 This is the structural diagram of the non-linear model of the lithium-ion battery based on Hammerstein-CARMA of the present invention.

[0082] Figure 5 This is the curve diagram of the change of the fitness function during the ICOA, COA and PSO iteration processes of the present invention.

[0083] Figure 6 This is the curve diagram of the terminal voltage prediction of two models under the intermittent constant current discharge condition of the present invention.

[0084] Figure 7 This is the curve diagram of the terminal voltage prediction error of two models under the intermittent constant current discharge condition of the present invention Detailed implementation manners

[0085] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0086] The present invention takes the Panasonic lithium-ion battery NCR-18650B as the research object. The rated voltage of the battery is 3.7V and the capacity is 3400mAh. The battery is charged in a constant current charging mode (0.5C) until the cut-off voltage is reached. After standing for a period of time, the battery reaches a fully charged state.

[0087] See Figures 1 to 7 , the present invention provides a non-linear modeling method for lithium-ion batteries based on Hammerstein-CARMA. The method includes the following steps:

[0088] Step 1) Conduct an intermittent constant current discharge experiment on at room temperature. The discharge rate is 1C and the current is 3400mA. After multiple discharges, the battery reaches the cut-off voltage, and the time length is 21211S. Select multiple groups of voltages after the battery discharges and stands still as the open circuit voltage, and perform polynomial fitting with the corresponding SOC to determine the OCV-SOC coefficient:

[0089]

[0090] The OCV-SOC fitting curve is as Figure 1 shown.

[0091] Step 2) Establish a nonlinear model of lithium-ion battery based on Hammerstein-CARMA;

[0092] Step 3) Construct the algorithm flow of COA;

[0093] Step 4) Introduce a variety of improvement measures on the basis of COA to construct ICOA;

[0094] Step 5) Use ICOA to identify model parameters and predict the terminal voltage under various working conditions;

[0095] As a nonlinear modeling method of lithium-ion battery based on Hammerstein-CARMA of the present invention, the specific steps of the said step 2) are as follows:

[0096] The second-order RC model represents the electrochemical polarization effect and concentration difference polarization effect of the lithium battery through two parallel RC links. The structure is relatively simple, the parameter identification is easy to achieve, and the accuracy can basically meet the research needs.

[0097] There are two parallel RC links in the second-order Thevenin model. R 1 and C 1 represent the electrochemical polarization effect, and R 2 and C 2 represent the concentration difference polarization effect. U oc and U correspond to the open-circuit voltage and terminal voltage of the battery. The voltages at both ends of C 1 and C 2 are represented by U 1 and U 2 respectively, and R 0 is the ohmic internal resistance. The structure diagram is as Figure 2 shown. Establish the battery equivalent circuit model according to Kirchhoff's law:

[0098]

[0099] Adopt the bilinear transformation s = 2(1 - z -1 ) / T(1 + z -1 )(T is the sampling period), map the above formula from the s-plane to the z-plane, and the following can be obtained:

[0100]

[0101]

[0102] Where: τ 1 = R 1 C 1 , τ 2 = R 2 C 2 , a = R 0, b = τ 1 τ 2 , c = τ 1 +τ 2 , d = R 0 +R 1 +R 2 , e = R 0 (τ 1 +τ 2 )+R 1 τ 1 +R 2 τ 2 。

[0103] Discretizing the above equation, the difference equation can be obtained:

[0104]

[0105] In the actual identification process, there are certain external disturbances in the output of the battery model, and there are measurement errors in the input current, making the output of the model show a certain degree of non-linearity. These two situations affect the parameter identification effect. To address this problem, this paper integrates the external disturbance and the measurement error of the input into the second-order RC model, and constructs a lithium-ion battery model with a Hammerstein-CARMA structure. The structure diagram of the Hammerstein-CARMA model is as shown in Figure 3 shown, and the structure diagram of the non-linear model of the lithium-ion battery after construction is as shown in Figure 4 shown.

[0106] The external disturbance of the battery model is w(z), and the output terminal voltage is y(z), satisfying y(z) = U - U oc . The model input I(z) is the theoretical value of the input of the battery model. Usually, there are measurement errors in it, and in the lithium-ion battery model based on the Hammerstein-CARMA structure, it can be expressed as:

[0107]

[0108] where is the non-linear current input value with measurement errors, and γ 1 , γ 2 are error coefficients.

[0109] Assume that the external disturbance w(z) of the system has a rational spectral density, the pole polynomial of the disturbance channel is the same as that of the process channel, and the zero polynomial has the same order as the pole polynomial, that is:

[0110]

[0111] Thus, the expression for the output of the terminal voltage of the battery model can be obtained:

[0112]

[0113] Assume b 0 = 1, let n a = 3, n b = 2, n d = 2, the lithium-ion battery model based on Hammerstein-CARMA can be obtained:

[0114]

[0115] where y(z) is the battery terminal voltage value, is the input current after considering the measurement noise.

[0116] Define the parameter vector η and the information vector

[0117] η = [a 1 , a 2 , b 1 , b 2 , γ 1 , γ 2 , d 1 , d 2 T ∈R n (10)

[0118]

[0119] can be integrated into an identification model:

[0120]

[0121] Furthermore, the algorithm can be used for identification.

[0122] As a non-linear modeling method of a lithium-ion battery based on Hammerstein-CARMA of the present invention, step 3) specifically includes the following steps:

[0123] The Coyote Optimization Algorithm (COA) is an intelligent bionic optimization algorithm with a unique structure. It can improve the convergence speed while ensuring the mutual communication between populations, thereby improving population diversity and having excellent identification effects. Its core idea is to regard the parameters to be estimated as the social states of coyote individuals. Based on the social adaptability, the newly born coyotes and the oldest coyotes are selected for survival of the fittest, and issues such as the inheritance, mutation of the newly born coyotes, and the expulsion and acceptance of the coyote population are considered. Finally, the optimal coyote is obtained. The pseudo-code of the algorithm is as follows:

[0124]

[0125] ​As a non-linear modeling method of lithium-ion battery based on Hammerstein-CARMA of the present invention, the step 4) specifically includes the following steps:

[0126] Step 4-1) Chaos is a common non-linear phenomenon. In swarm intelligence optimization algorithms, the randomness, ergodicity and regularity of chaotic variables can be utilized for optimization, so as to maintain population diversity and enhance global search ability. Compared with the common Logistic mapping, Tent mapping has better ergodic uniformity and faster convergence speed. The present invention introduces this mapping into COA. The expression is as follows:

[0127]

[0128] z is a chaotic sequence. The conventional Tent mapping sequence has small periods and unstable periodic points, so a random variable is introduced for improvement. The improved expression is as follows:

[0129]

[0130] In the formula, r t is a random number within the range of (0, 1), and NT is the number of elements in the Tent chaotic sequence.

[0131] After generating the chaotic sequence, map it to the solution space:

[0132]

[0133] lb j and ub j are the upper and lower bounds during the initialization of the coyote individuals.

[0134] Step 4-2) The mechanism of influence within the coyote group and individual update in the coyote optimization algorithm is as follows:

[0135]

[0136]

[0137]

[0138] r 1 、r 2 are random numbers within 0 to 1, η 1 is the selected coyote and the difference between the best coyote alpha p in the group, η 2 is the difference between another selected coyote and the cultural trend cult p in the group. The growth of the coyotes within the group is affected by the best wolf alpha pThe influence of the cultural trend cult.

[0139] Due to the random grouping of the coyote population, the quality of the best wolf within the group and the cultural trend may not meet the algorithm requirements, and there may be a phenomenon of insufficient guiding force, which may cause the algorithm to fall into a local optimum. On this basis, this paper considers the guiding role of the best coyote beta in the population and constructs a new way of coyote growth, taking the best coyote within the group, the best coyote in the population, and two randomly selected coyotes as the influencing factors of the coyotes within the group. At the same time, in order to make the algorithm more effectively approach the optimal solution, an adaptive operator is introduced into the influencing factor r 1 、r 2 to unify each influencing factor. The improvement method is as follows:

[0140]

[0141]

[0142] η 3 = beta - alpha p (21)

[0143]

[0144] Where:

[0145]

[0146] r = r 0 ×2 α (24)

[0147] τ 1 and τ 2 represent the influence weights on the best wolf alpha p in the p-th group and the best wolf beta in the population. η 3 is the difference between the best coyote in the population and the best coyote within the group. r 0 is the initial influencing factor, G is the maximum number of iterations, and k is the current number of iterations. In the original coyote algorithm, r 1 、r 2 are random numbers between 0 and 1, and there is a certain degree of uncertainty and randomness in the influence process within the coyote group. By introducing an adaptive operator and determining the value of the initial influencing factor, the uncertainty and randomness can be effectively offset. During the iterative process of the entire algorithm, the adaptive operator changes periodically with the increase of the number of iterations, so that the influencing factor is within a reasonable range and searches for the optimal value during the entire operation process, thereby accelerating the convergence speed.

[0148] During the entire algorithm process, the coyotes within the group are influenced by randomly selected coyotes within the group, the best coyote within the group, and the global best coyote, effectively improving the population diversity, making it difficult for the algorithm to fall into local optimality during the convergence process, and having a faster convergence speed.

[0149] Through the above improvements, an improved coyote optimization algorithm (ICOA) is proposed.

[0150] As a non-linear modeling method of lithium-ion battery based on Hammerstein-CARMA of the present invention, step 5) specifically includes the following steps:

[0151] Segment the intermittent constant current discharge conditions measured in step 1), and each segment experiences rest, pulse discharge, and then rest. Use the algorithm for segment identification. Taking the constant current discharge process with an initial SOC = 0.72 as an example, use ICOA for parameter identification, set the algorithm population size to 100, the number of groups to 5, and the number of coyote individuals in each group to 20. Use the sum of the squares of the errors between the measured terminal voltage and the actual terminal voltage in the experiment to establish the fitness function f(x):

[0152]

[0153] Where y(k) is the measured voltage, is the predicted voltage. To verify the effectiveness of the algorithm, taking this discharge process as an example, under the same objective function, compare ICOA with COA and PSO, and the results are as Figure 5 shown. On the premise of the same algorithm parameters, while inheriting the characteristic of high identification accuracy of COA, ICOA has a great improvement in the convergence speed, and its accuracy and convergence speed are also significantly better than PSO, a conventional swarm intelligence algorithm. It can be seen that ICOA is effective in the present invention.

[0154] Through segment identification, the lithium-ion battery model parameters corresponding to different initial SOCs can be obtained. By fitting SOC and the parameters, the change curve of the parameters with respect to SOC can be obtained.

[0155] To further verify the accuracy of the non-linear model of the lithium-ion battery based on Hammerstein-CARMA, the obtained parameters are combined with actual data for terminal voltage prediction to verify the model accuracy under intermittent constant current discharge experiments. At the same time, use ICOA to identify the parameters of the second-order RC model of the lithium-ion battery, and use the same method for terminal voltage prediction, and compare with the non-linear model of the lithium-ion battery based on Hammerstein-CARMA established in the present invention. The terminal voltage prediction results and error curves are as Figure 6 、 Figure 7As shown, the results indicate that the Hammerstein-CARMA based non-linear lithium-ion battery model established in the present invention has higher accuracy than the conventional equivalent circuit model.

[0156] In summary, it can be seen that replacing the lithium-ion battery model with the non-linear block structure model of Hammerstein-CARMA has good effects. The model accuracy is higher than that of the conventional equivalent circuit model, which has engineering value.

[0157] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A non-linear modeling method for lithium-ion batteries based on Hammerstein-CARMA, characterized in that, it includes the following steps: Step 1) Measure the load current and terminal voltage data of the battery through intermittent constant current discharge to determine the OCV-SOC relationship; Step 2) Establish a non-linear model of lithium-ion batteries based on Hammerstein-CARMA; The content of the said Step 2) is as follows: There are two parallel RC links in the second-order RC model, where R 1 and C 1 represent the electrochemical polarization effect, and R 2 and C 2 represent the concentration difference polarization effect; U oc and U correspond to the open-circuit voltage and terminal voltage of the battery, and the voltages across C 1 and C 2 are represented by U 1 and U 2 respectively, and R 0 is the ohmic internal resistance; a battery equivalent circuit model is established according to Kirchhoff's law: Using the bilinear transformation s = 2(1 - z -1 ) / T(1 + z -1 ), where T is the sampling period, mapping the above equation from the s-plane to the z-plane, we get: where: τ 1 = R 1 C 1 , τ 2 = R 2 C 2 , a = R 0 , b = τ 1 τ 2 , c = τ 1 + τ 2 , d = R 0 + R 1 + R 2 , e = R 0 (τ 1 + τ 2 ) + R 1 τ 1 + R 2 τ 2 ; a 1 and a 2 are the coefficients of the pole polynomial, d 1 and d 2 are the coefficients of the zero polynomial; Discretize the above formula to obtain a difference equation: Integrate the external disturbance and the input measurement error into the second-order RC model, and construct a lithium-ion battery model with a Hammerstein-CARMA structure; The external disturbance of the battery model is w(z), and the output terminal voltage is y(z), satisfying y(z) = U - U oc , where the model input I(z) is the theoretical value of the input of the battery model and is expressed as follows in the lithium-ion battery model based on the Hammerstein-CARMA structure: where is the non-linear current input value with measurement error, and γ 1 , γ 2 are error coefficients; Assume that the external disturbance w(z) of the system has a rational spectral density, the pole polynomial of the disturbance channel is the same as that of the process channel, and the zero polynomial has the same order as the pole polynomial, that is: Thus, the expression for the terminal voltage output of the battery model is obtained: Assume b 0 = 1, let n a = 2, n b = 2, n d = 2, to obtain a lithium-ion battery model based on Hammerstein-CARMA: where y(z) is the battery terminal voltage value, is the input current after considering the measurement noise; Define the parameter vector η and the information vector η = [a 1 , a 2 , b 1 , b 2 , γ 1 , γ 2 , d 1 , d 2 T ∈R n (9)​ Integrate it into an identification model: Use an algorithm for identification; Step 3) Construct the algorithm flow of COA; Step 4) Introduce a variety of improvement measures on the basis of COA to construct ICOA; Step 5) Use ICOA to identify model parameters and predict the terminal voltage under a variety of working conditions.

2. A non-linear modeling method for lithium-ion batteries based on Hammerstein-CARMA according to claim 1, characterized in that, the said Step 4) includes the following steps: Step 4-1) Map and introduce COA, and the expression is as follows: z is a chaotic sequence. The conventional Tent mapping sequence has small periods and unstable periodic points. A random variable is introduced for improvement, and the improved expression is as follows: where r t is a random number in the range of (0, 1), and NT is the number of elements in the Tent chaos sequence; After generating the chaotic sequence, map it to the solution space: lb j and ub j are the upper and lower bounds during the initialization of the coyote individuals; Step 4-2) The mechanism of intra-pack influence and individual update in the coyote optimization algorithm is as follows: r 1 、r 2 are random numbers within 0 to 1, η 1 is the selected coyote and the difference from the optimal coyote alpha within the group, η p Another selected coyote 2 and the difference from the cultural trend cult within the group. The growth of the coyotes within the group is affected by the optimal wolf alpha within the group and the cultural trend cult; p p ​​ A new coyote growth method is constructed, which takes the best coyote within the group, the best coyote in the population, and two randomly selected coyotes as the influencing factors of the coyotes within the group; at the same time, in order to make the algorithm more effectively approach the optimal solution, an adaptive operator is introduced into the influencing factors r 1 、r 2 , and the various influencing factors are unified. The improvement method is as follows: η 3 = beta - alpha p (20) Where: r＝r 0 ×2 α (23) ξ 1 associated with ξ 2 represents the influence weight on the optimal wolf alpha in the p-th group p and the population-optimal wolf beta, η 3 is the difference between the population-optimal coyote and the in-group optimal coyote; r 0 is the initial influence factor, G is the maximum number of iterations, k is the current number of iterations. In the original coyote algorithm, r 1 and r 2 are random numbers within the range of 0 to 1.

3. A non-linear modeling method for lithium-ion batteries based on Hammerstein-CARMA according to claim 1, characterized in that, the said Step 5) includes the following steps: Segment the intermittent constant current discharge conditions measured in Step 1). Each segment experiences standing, pulsed discharge, and then standing again. Use an algorithm for segmental identification. Taking the constant current discharge process with an initial SOC = 0.72 as an example, use ICOA for parameter identification. The algorithm population size is set to 100, the number of groups is 5, and the number of coyote individuals in each group is 20. Establish a fitness function f(x) using the sum of the squares of the errors between the experimentally measured terminal voltage and the actual terminal voltage: where y(k) is the measured voltage, is the predicted voltage. By segmental identification, the lithium-ion battery model parameters corresponding to different initial SOCs are obtained. Through the fitting of SOC and the parameters, the variation curve of the parameters with respect to SOC is obtained; Combine the obtained parameters with the actual data to predict the terminal voltage, and verify the accuracy of the model under intermittent constant current discharge experiments.

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