A lithium-ion battery state-of-charge estimation method and system

Abstract

The application discloses a lithium ion battery energy state estimation method and system, and belongs to the field of lithium ion battery energy state estimation. The method comprises the following steps: a second-order RC-PNGV equivalent circuit model is constructed, and voltage and current data of a lithium ion battery are input into the second-order RC-PNGV equivalent circuit model; an improved forgetting factor recursive least square method is used for online parameter identification, and battery model parameters are obtained; the battery model parameters are input into a BP neural network, and a preliminary energy state estimation value is output; and the preliminary energy state estimation value is input into a multi-innovation gain optimization Kalman filter for noise filtering, so that a final energy state estimation result is obtained. The application has high precision and robustness in battery residual energy state estimation under various complex working conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of lithium-ion battery energy state estimation, and in particular relates to a lithium-ion battery energy state estimation method and system. Background Art

[0002] With the rapid adoption of electric vehicles, lithium-ion batteries have become the primary power source for modern transportation. Their performance directly determines vehicle range and safety. State of Energy (SOE) is a key metric for assessing a battery's remaining available energy, representing the ratio of the battery's current energy to its rated capacity. Accurate SOE estimation helps improve battery efficiency, extend battery life, and enhance vehicle reliability. However, its accuracy is challenged by factors such as battery nonlinearity, ambient temperature variations, and inconsistent charge and discharge rates.

[0003] Existing SOE estimation methods include power integration method, model-based method and data-driven method. First, the power integration method calculates the remaining energy by real-time integration of the battery terminal voltage and current under the premise of knowing the initial SOE value. This method is simple to calculate, but is affected by the initial value error, sensor accuracy and battery aging. Long-term integration causes the error to continue to increase, making it difficult to meet high-precision requirements. Second, the model-based method is to establish a battery equivalent circuit model (such as the Thevenin model and the PNGV model) and combine it with a state observer (such as the extended Kalman filter EKF and the unscented Kalman filter UKF) for dynamic estimation. This type of method uses the physical characteristics of the battery to model and is robust to measurement noise. However, this method relies on accurate battery model parameters, and traditional parameter identification algorithms (such as the fixed forgetting factor FFRLS) cannot dynamically track parameter drift caused by temperature changes and charge and discharge rate fluctuations, resulting in model mismatch. Third, the data-driven method uses machine learning algorithms (such as BP neural networks and long short-term memory networks (LSTM)) to learn the mapping relationship between parameters such as voltage and current and SOE, avoiding complex mechanism modeling and adapting to nonlinear systems. However, this method is sensitive to noise and has a delayed dynamic response, and the estimation error increases significantly when the current fluctuates violently. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention proposes a lithium-ion battery energy state estimation method and system to solve the problems existing in the above-mentioned prior art.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a method for estimating the energy state of a lithium-ion battery, comprising:

[0006] Construct a second-order RC-PNGV equivalent circuit model and input the voltage and current data of the lithium-ion battery into the second-order RC-PNGV equivalent circuit model;

[0007] The improved forgetting factor recursive least squares method is used for online parameter identification to obtain battery model parameters;

[0008] Inputting the battery model parameters into a BP neural network and outputting a preliminary energy state estimation value;

[0009] The preliminary energy state estimation value is input into the innovation gain optimized Kalman filter for noise filtering to obtain the final energy state estimation result.

[0010] Preferably, the second-order RC-PNGV equivalent circuit model includes an open-circuit voltage source, a polarization resistor, a polarization capacitor, and an equivalent capacitor representing a current accumulation effect.

[0011] Preferably, the process of performing online parameter identification using the improved forgetting factor recursive least squares method includes:

[0012] Assign an independent adaptive forgetting factor to each parameter to be estimated;

[0013] Decouple the covariance matrix and recursive gain matrix in the forgetting factor recursive least squares method;

[0014] Each forgetting factor is dynamically adjusted according to the current fluctuation index and the prediction error index.

[0015] Preferably, the adaptive forgetting factor formula is:

[0016] ;

[0017] in, and is the maximum and minimum value of the i-th forgetting factor, is the forgetting factor of the i-th parameter channel at time k, and its value range is is the sensitivity coefficient, The current fluctuation index quantifies the intensity of current fluctuation. The larger the value, the more severe the load change. is the forecast error index, which is expressed by and The ratio of quantifies the degree of model mismatch, and Joint decision The value of , M is the length of the moving interval, is the average value of the input current in the moving range, is the current measurement value at the nth moment, is the historical maximum current value, is the difference between the model-predicted value and the actual measured value of the battery terminal voltage, is the error threshold.

[0018] Preferably, the formula of the recursive gain matrix is:

[0019] ;

[0020] in, is the gain matrix, is the definition of the decoupled diagonal covariance matrix, is the definition of the forgetting factor diagonal matrix, is a 5-dimensional regression vector, yes is the transposed vector;

[0021] , , , , , , is defined as follows:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] in, is the covariance of the i-th parameter at time k-1, is the forgetting factor of the i-th parameter at time k-1, each element represents the characteristic variable related to the i-th parameter to be estimated, is the battery terminal voltage value actually output by the system, is the regression vector, is the set of characteristic variables, is the voltage value at the previous moment, is the voltage value at the first two moments, Current value at the current moment, is the current value at the previous moment, is the current value at the first two moments, Corresponding regression vector The first element of , Corresponding regression vector The second element , Similarly, is the parameter vector to be estimated, Corresponding respectively The weight coefficient of .

[0028] Preferably, the input parameters of the BP neural network include voltage, time-varying current, resistance and capacitance; and the output parameter is a preliminary energy state estimation value.

[0029] Preferably, the filtering process of the multi-innovation gain optimized Kalman filter includes:

[0030] Constructing a multi-innovation vector of length j, wherein the multi-innovation vector includes a sequence of historical terminal voltage measurement values;

[0031] Expanding a state gain matrix according to the multiple innovation vectors;

[0032] Assigning weight factors to gains at different moments, wherein the weight factors decrease over time;

[0033] Optimize the filter gain matrix by a constant gain factor.

[0034] Preferably, the constant gain factor is dynamically adjusted according to the battery status.

[0035] In a second aspect, the present invention provides a lithium-ion battery energy state estimation system, comprising:

[0036] A model building module is used to build a second-order RC-PNGV equivalent circuit model, and input the voltage and current data of the lithium-ion battery into the second-order RC-PNGV equivalent circuit model;

[0037] Parameter identification module, used to perform online parameter identification using improved forgetting factor recursive least squares method to obtain battery model parameters;

[0038] An output module, configured to input the battery model parameters into a BP neural network and output a preliminary energy state estimation value;

[0039] The filtering module is used to input the preliminary energy state estimation value into the most innovative gain optimized Kalman filter for noise filtering to obtain the final energy state estimation result.

[0040] Compared with the prior art, the present invention has the following advantages and technical effects:

[0041] The present invention provides a lithium-ion battery energy state estimation method, comprising: first, constructing a second-order RC-PNGV equivalent circuit model, and inputting voltage and current data of the lithium-ion battery into the second-order RC-PNGV equivalent circuit model; second, using an improved forgetting factor recursive least squares method to perform online parameter identification to obtain battery model parameters; third, inputting the battery model parameters into a BP neural network to output a preliminary energy state estimation value; finally, inputting the preliminary energy state estimation value into a multi-innovation gain optimized Kalman filter for noise filtering to obtain a final energy state estimation result.

[0042] The present invention dynamically optimizes battery model parameters by improving the forgetting factor recursive least squares method, significantly reducing modeling errors caused by factors such as temperature changes and current fluctuations. At the same time, an independent adaptive forgetting factor is assigned to each parameter, quickly tracking parameter changes when the current suddenly changes, and suppressing noise interference in static conditions.

[0043] The present invention combines the nonlinear mapping capability of the BP neural network with the noise suppression characteristics of the multi-innovation gain optimized Kalman filter to reduce the SOE estimation error; the multi-innovation gain optimized Kalman filter attenuates the influence of historical data through a weight factor, and dynamically adjusts the filter response speed in combination with a constant gain factor, effectively responding to different states such as battery charging and discharging / stationary. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0045] Figure 1 Schematic diagram of a second-order RC equivalent circuit model according to an embodiment of the present invention.

[0046] Figure 2 Schematic diagram of the BP neural network model according to an embodiment of the present invention.

[0047] Figure 3 This is a flowchart of estimating SOE based on the BP-MIGKF model method according to an embodiment of the present invention.

[0048] Figure 4 Figure 3 is a schematic diagram comparing the output voltages of a 2-RC-PNGV model and a 2-RC model under the Hybrid Pulse Power Characterization (HPPC) test of an embodiment of the present invention. Figures (a-1) and (a-2) are partial enlarged views of (a-1), and (a-5) are voltage error comparison views.

[0049] Figure 5The output voltage estimation results at 25°C under the HPPC test of an embodiment of the present invention are shown; wherein (a-1) is a voltage comparison diagram, (a-2), (a-3) and (a-4) are partial enlarged diagrams of (a-1), and (a-5) is a voltage error comparison diagram.

[0050] Figure 6 Figure 2 shows the output voltage estimation results at 25°C under dynamic stress test (DST) conditions in an embodiment of the present invention. (b-1) is a voltage comparison diagram, (b-2), (b-3), and (b-4) are magnified views of a portion of (b-1), and (b-5) is a voltage error comparison diagram.

[0051] Figure 7 Figure 2 shows the output voltage estimation results at 25°C under the Beijing Bus Dynamic Street Test (BBDST) conditions of an embodiment of the present invention. (c-1) is a voltage comparison diagram, (c-2), (c-3), and (c-4) are partial enlarged diagrams of (c-1), and (c-5) is a voltage error comparison diagram.

[0052] Figure 8 1 is a schematic diagram comparing the output voltage error at 25°C under different conditions in an embodiment of the present invention, and is a schematic diagram comparing the MAX, MAE, RMSE, and MAPE estimation results under different conditions, respectively.

[0053] Figure 9 Schematic diagram of the output voltage estimation results at 15°C under HPPC according to an embodiment of the present invention; wherein (a-1) is a voltage comparison diagram, (a-2), (a-3) and (a-4) are partial enlarged diagrams of (a-1), and (a-5) is a voltage error comparison diagram.

[0054] Figure 10 Schematic diagram of the 15°C output voltage estimation results under DST conditions of an embodiment of the present invention; wherein, (b-1) is a voltage comparison diagram, (b-2), (b-3) and (b-4) are partial enlarged diagrams of (b-1), and (b-5) is a voltage error comparison diagram.

[0055] Figure 11 Schematic diagram of the output voltage estimation results at 15°C under BBDST conditions of an embodiment of the present invention; wherein, (c-1) is a voltage comparison diagram, (c-2), (c-3) and (c-4) are partial enlarged diagrams of (c-1), and (c-5) is a voltage error comparison diagram.

[0056] Figure 12 1 is a schematic diagram comparing the output voltage error at 15°C under different conditions in an embodiment of the present invention, and is a schematic diagram comparing the MAX, MAE, RMSE, and MAPE estimation results under different conditions, respectively.

[0057] Figure 13 Fig. 3 is a schematic diagram of SOE estimation results of a training set at 25°C under HPPC condition according to an embodiment of the present application; wherein (a-1) is a voltage comparison diagram, (a-2), (a-3) and (a-4) are partial enlarged diagrams in (a-1).

[0058] Figure 14 Fig. 4 is a schematic diagram of SOE estimation results of a test set at 25°C under HPPC condition according to an embodiment of the present application; wherein (b-1) is a voltage comparison diagram, (b-2), (b-3) and (b-4) are partial enlarged diagrams in (b-1), (c-1) is a voltage error comparison diagram, (c-2), (c-3) and (c-4) are partial enlarged diagrams in (c-1).

[0059] Figure 15 Fig. 5 is a schematic diagram of SOE estimation results of a training set at 25°C under DST condition according to an embodiment of the present application; wherein (a-1) is a voltage comparison diagram, (a-2), (a-3) and (a-4) are partial enlarged diagrams in (a-1).

[0060] Figure 16 Fig. 6 is a schematic diagram of SOE estimation results of a test set at 25°C under DST condition according to an embodiment of the present application; wherein (b-1) is a voltage comparison diagram, (b-2), (b-3) and (b-4) are partial enlarged diagrams in (b-1), (c-1) is a voltage error comparison diagram, (c-2), (c-3) and (c-4) are partial enlarged diagrams in (c-1).

[0061] Figure 17 Fig. 7 is a schematic diagram of SOE estimation results of a training set at 25°C under BBDST condition according to an embodiment of the present application; wherein (d-1) is a voltage comparison diagram, (d-2), (d-3) and (d-4) are partial enlarged diagrams in (d-1).

[0062] Figure 18 Fig. 8 is a schematic diagram of SOE estimation results of a test set at 25°C under BBDST condition according to an embodiment of the present application; wherein (e-1) is a voltage comparison diagram, (e-2), (e-3) and (e-4) are partial enlarged diagrams in (e-1), (f-1) is a voltage error comparison diagram. DETAILED DESCRIPTION

[0063] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0064] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0065] Example 1

[0066] like Figure 3 As shown, this embodiment provides a lithium-ion battery energy state estimation method, including:

[0067] S1. Construct a second-order RC-PNGV equivalent circuit model and input the voltage and current data of the lithium-ion battery into the second-order RC-PNGV equivalent circuit model;

[0068] Furthermore, the second-order RC-PNGV equivalent circuit model includes an open-circuit voltage source, a polarization resistor, a polarization capacitor, and an equivalent capacitor representing a current accumulation effect.

[0069] Specifically, in order to obtain the current state of charge of the battery conveniently and accurately, it is necessary to select a suitable battery model. Commonly used equivalent circuit models include the Rint model, the Thevenin model, the PNGV (Partnership for a New Generation of Vehicles) model and the second-order equivalent model. The PNGV model has higher expressive power than the Thevenin model, and the change of OCV can be better described. After considering the polarization effect and ohmic internal resistance of the battery, the model will obtain higher accuracy. Compared with the first-order model, the second-order model can more accurately predict the response time and change rate of the battery. However, the accuracy of models above the second order has not been significantly improved, and the computational complexity will also be greatly increased. Therefore, this embodiment adopts a second-order RC-PNGV model that combines the PNGV model and the second-order RC (Remote Control) model. The model adds an equivalent capacitor that can change with the integral of the open-circuit load current of the battery. The two RCs in series correspond to the two electrodes on the impedance spectrum of the lithium-ion battery, showing the polarization phenomenon of the lithium-ion battery. The equivalent circuit model of the second-order RC-PNGV is as follows Figure 1 shown.

[0070] exist Figure 1 middle, Represents an ideal voltage source, used to simulate the circuit voltage of the voltage; It represents the loop voltage fluctuation caused by the cumulative effect of current; and It indicates the loop voltage fluctuation caused by the cumulative effect of current; and Together they constitute the loop voltage Description of changes; is the ohmic resistance, and is the polarization resistance, and A group of polarized capacitors. and The time constant of the other group is relatively large, simulating a slow and stable voltage change process; and The time constant is relatively small, simulating the rapid change in voltage. According to Kirchhowski's law, the voltage and current expressions of the equivalent circuit can be obtained as shown in Equation (1). The expression for calculating SOE using the power integration method is shown in Equation (2).

[0071] (1)

[0072] (2)

[0073] In formula (1), is the terminal voltage of the battery when connected to the load, For load The voltage across the terminals, For load The voltage across the terminals, for and of current.

[0074] In formula (2), is the initial value of SOE, is the rated capacity of the battery, is the coulombic efficiency of the battery.

[0075] For the selected 2RC-PNGV equivalent model, select As a state variable, after discretizing formula (1) and formula (2) of SOE, its state space equation can be shown as formula (3):

[0076] (3)

[0077] In formula (3), these two equations are the state equation and observation equation of the battery model, respectively, where: is the SOE at time k, is the SOE at time k+1, Represents the voltage drop during the dynamic process inside the battery at time k, corresponding to two RC respectively. It represents the voltage drop at time k+1. is the sampling time interval, is the terminal voltage of the battery at time k, is the observation error, is the terminal voltage of the battery at time k+1, is the open circuit voltage at time k+1, are measurement errors.

[0078] S2. Use the improved forgetting factor recursive least squares method to perform online parameter identification and obtain battery model parameters;

[0079] The recursive least squares (RLS) method is a model parameter estimation method based on filtering theory. Due to its simplicity, high parameter identification accuracy, and minimal computational effort, it has been widely used in parameter identification. This algorithm treats the parameter identification problem of a battery under operating conditions as a dynamic system modeling process, where the current I serves as the system input and the voltage U serves as the system output. By modeling the battery as a single-input, single-output system, the coefficients of the difference equation are determined, and a recursive method is used to estimate the model parameters in real time. The basic principle is shown in Equation (4).

[0080] (4)

[0081] In formula (4), is the regression vector, a set of characteristic variables consisting of historical voltage and current data. is the parameter vector to be estimated, which represents the weight coefficient of each feature in the regression vector.

[0082] is the actual output value of the system, that is, the battery terminal voltage, and its specific definition is shown in formula (5):

[0083] (5)

[0084] In formula (5), is the voltage value at the previous moment, is the voltage value at the first two moments, Current value at the current moment, is the current value at the previous moment, is the current value at the first two moments. Corresponding respectively The weight coefficient reflects the impact of each historical data on the current voltage.

[0085] The parameter identification method based on the RLS algorithm is shown in formula (6):

[0086] (6)

[0087] In formula (6), is the gain matrix, is the covariance matrix at the previous moment, is the covariance matrix at the current moment, represents the estimation error, is the actual output value of the system, yes The transposed vector of is the parameter vector to be estimated at the previous moment.

[0088] On the basis of the traditional RLS algorithm, the forgetting factor recursive least squares (FFRLS) method introduces the forgetting factor , which is applied as a weight coefficient to the observation data matrix and the system output vector, as shown in Equation (7). Whenever new observation data is obtained, the algorithm dynamically adjusts the weight ratio of new and old data through exponential weighting and updates the model parameters accordingly. As observation data continues to accumulate, the FFRLS algorithm can respond more quickly to changes in input variables, thereby achieving better parameter identification results in a dynamic environment.

[0089] (7)

[0090] During actual battery operation, model parameters fluctuate due to the influence of SOE and input current changes. Due to the inconsistency of the actual change rates of the estimated parameters, the traditional FFRLS algorithm is prone to large identification errors when processing battery systems. For FFRLS algorithm systems, large identification errors will be generated. The solution is to decouple the covariance and gain matrix in the FFRLS algorithm and calculate the error according to the coefficients to be estimated. The characteristic of is that it configures the corresponding forgetting factor, so as to independently correct each coefficient to be estimated and avoid mutual interference between coefficients with different change rates. On the other hand, the forgetting factor in the FFRLS algorithm The value of will have a great impact on the result of parameter identification. It is generally expressed as When the value is small, the algorithm is more sensitive to the change of input current. When the current changes drastically, it can track the change of model parameters in time, but the identification result is easily affected by noise and causes fluctuations. When the forgetting factor is large, the algorithm is more stable. However, due to the high influence of old data, the tracking effect of the algorithm is poor when the input current changes drastically. Therefore, a fixed forgetting factor is difficult to adapt to changes in external working conditions, resulting in a decrease in the accuracy of model parameter identification. Therefore, the forgetting factor value should be adaptive.

[0091] The improved adaptive forgetting factor recursive least squares (IMAFFRLS) parameter identification algorithm based on improved forgetting factors is employed. First, a multi-forgetting factor configuration strategy is employed to assign a separate forgetting factor to each parameter to be estimated, achieving differentiated tracking capabilities for different parameters and effectively addressing the limitation of traditional algorithms that treat all parameters in a "one-size-fits-all" manner. Second, an innovative matrix decoupling mechanism is designed to decompose the covariance matrix and gain matrix according to the parameter dimensions, avoiding the error propagation problem caused by matrix coupling in traditional algorithms. Finally, a dynamic adjustment mechanism is introduced to enable each forgetting factor to automatically adjust based on operating conditions such as input current fluctuations and terminal voltage prediction errors. When the system is stable, the forgetting factor is increased to enhance interference resistance, while when the operating conditions suddenly change, the forgetting factor is reduced to improve tracking speed, thus achieving an optimal balance between identification accuracy and dynamic response speed.

[0092] The covariance matrix and gain matrix in the FFRLS algorithm are decoupled, and the recursive expression of the decoupled algorithm is shown in formula (8):

[0093] (8)

[0094] in, is the gain matrix, is the decoupled diagonal covariance matrix, is the forgetting factor diagonal matrix, is a 5-dimensional regression vector (column vector), is the parameter vector to be estimated at the previous moment, is the parameter vector to be estimated at the current moment; is the covariance of the i-th parameter at the previous moment, is the covariance of the i-th parameter at the current moment; represents the estimation error, is the output variable.

[0095] The definition of is as shown in formula (9), The definition of is as shown in formula (10), is the forgetting factor of the i-th parameter at the previous moment. The definition of is as shown in formula (11), Corresponding regression vector The first element of , Corresponding regression vector The second element , Similarly, each element Represents the characteristic variable related to the i-th parameter to be estimated. They are respectively The forgetting factor.

[0096] (9)

[0097] (10)

[0098] (11)

[0099] In order to optimize the algorithm's adaptability to the changing external environment, this embodiment proposes an improved adaptive forgetting factor adjustment strategy, which normalizes the current fluctuation index and the forecast error index The core of the algorithm is to design an adaptive mechanism based on dual-index feedback. When the two indicators are small, the forgetting factor of each channel is Approaching the maximum value , enhance the algorithm's anti-interference ability; when the current fluctuates violently or the error increases, Automatically approach the minimum value This dynamic adjustment mechanism enables the algorithm to maintain high-precision estimation in steady state while quickly responding to sudden changes in working conditions.

[0100] (12)

[0101] In formula (12), and is the maximum and minimum value of the i-th forgetting factor, is the forgetting factor of the i-th parameter channel at time k, and its value range is is the sensitivity coefficient, It is the current fluctuation index, which quantifies the intensity of current fluctuation. The larger the value, the more severe the load change. is the forecast error index, which is expressed by the error With threshold The ratio of quantifies the degree of model mismatch. and Joint decision value. is the length of the moving interval, is the average value of the input current in the moving range, is the current measurement value at the nth moment, This is the maximum current value in history. is the battery terminal voltage observation error (i.e. the difference between the predicted value and the actual value). The maximum value of each forgetting factor are all set to 0.99, and the minimum It is 0.94.

[0102] S3, inputting the battery model parameters into a BP neural network and outputting a preliminary energy state estimation value;

[0103] Specifically, the training process and hyperparameter selection of the BP neural network to estimate the SOE. The BP network is one of the most common neural network models with a feedforward structure and is trained through an error backpropagation mechanism. The network consists of an input layer, a hidden layer, and an output layer. Its main features are the forward propagation of signals and the backpropagation of errors. The hidden layer is responsible for handling nonlinear problems, and its configuration should be adjusted according to the complexity of the problem. The input data signal is first passed into the neural network through the input layer, and after step-by-step calculations in the hidden layer, the result is finally produced in the output layer. If the result of the output layer does not match the expected value, the second step of the backpropagation process is entered. In order to ensure that the predicted output is always close to the expected value, the weights and thresholds are adaptively adjusted according to the prediction error.

[0104] Data-driven methods have significant advantages over model-based methods in SOE estimation, especially in terms of self-learning ability and adaptability. Through algorithms such as neural networks, the complex relationship between SOE and measured variables such as current and voltage can be automatically learned from a large amount of historical data without relying on precise battery model formulas. This not only reduces the complexity of modeling, but also enhances the flexibility and responsiveness of modeling under different working environments and conditions, supports real-time updates and automatically adapts to fluctuations in battery status. In contrast, model-based methods usually rely on precise battery model formulas to estimate SOE. These formulas are computationally intensive and difficult to cover all actual situations, especially in the case of battery aging, temperature changes or load fluctuations. The model accuracy will drop significantly. In addition, there is an error accumulation problem when using the power integration method for SOE estimation, and in long-term use, the battery discharge curve is difficult to accurately describe by simple integration. Given these characteristics, BP neural network has become an effective method to solve this problem.

[0105] In this embodiment, time-varying current, voltage, resistance and capacitance are selected as input parameters. These parameters are monitored under specific operating temperatures and conditions, and the output of the battery test is SOE. The resistance and capacitance of the battery are important parameters that reflect the internal characteristics of the battery, which directly affect the dynamic behavior of the battery and the change in SOE. By obtaining these internal parameters through parameter identification, the actual performance of the battery under different working conditions can be more accurately reflected, avoiding relying solely on simple inputs of voltage and current. The changes in resistance and capacitance are closely related to factors such as battery health, temperature, and load. Using them as input parameters helps the BP neural network to more comprehensively understand the working environment and status of the battery, thereby capturing more complex nonlinear relationships. In addition, resistance and capacitance are key parameters in the internal resistance model and equivalent circuit model of the battery, which can more realistically reflect the intrinsic characteristics of the battery. Therefore, the BP neural network can learn richer information during the training process, enhance the prediction ability of SOE, and improve the accuracy and stability of the estimation.

[0106] Figure 2 This BP neural network model for SOE estimation visually demonstrates the logical relationship between the input layer, hidden layer, and output layer. Input layer parameters include factors that influence the accuracy of SOE estimation, such as voltage, current, resistance, and capacitance. The number of hidden layer nodes can be adjusted based on the complexity of the problem being processed and the number of input parameters. The output of the output layer is the neural network's predicted SOE.

[0107] S4. Input the preliminary energy state estimation value into a multi-innovation gain optimized Kalman filter for noise filtering to obtain a final energy state estimation result.

[0108] Specifically, the BP model itself has certain limitations. When faced with battery data that is noisy or undergoes drastic dynamic changes, the error in its estimation results will increase significantly, making it difficult to guarantee estimation accuracy. Kalman filtering, as a classic state estimation method, has demonstrated unique advantages in improving the accuracy of SOE estimation. In particular, when battery data is affected by noise and uncertainty factors, Kalman filtering can effectively reduce the estimation error by dynamically adjusting the system state. Based on this, the SOE results estimated by the BP model are input into an improved Kalman filtering method—Multi-information Gain Optimization Kalman Filter (MIGKF)—to achieve more accurate SOE estimation.

[0109] The traditional Extended Kalman Filter (EKF) relies only on a single error to update the state variable when applied to nonlinear systems. Although this method can achieve state estimation to a certain extent, its approximation of nonlinear systems is not accurate enough, which can easily lead to insufficient estimation accuracy under complex working conditions. To overcome this shortcoming, a multi-information combined with Kalman filtering method is adopted to improve the estimation accuracy. Although the use of the multi-information method will increase the amount of calculation, considering that the improvement of estimation accuracy is more important, the computational cost can be appropriately increased. Multi-information vector As shown in formula (13).

[0110] (13)

[0111] in, is the length of the extended innovation, is the terminal voltage measurement value at the ki-th moment, is the measurement residual at the ki-th moment, is the observation matrix, is the predicted value of the state at time ki based on the information at time ki-1.

[0112] The corresponding state gain matrix To expand, It is composed of the gains of the current and past j-1 steps, is the gain at the ki-th moment. The matrix is ​​shown in formula (14).

[0113] (14)

[0114] When new and old information are introduced as corrections to the posterior estimate of the current state matrix, the interference caused by the old data will accumulate over time due to measurement errors in the output voltage and current. In addition, the impact of the new measurement data should be greater than that of the old data. If the impact of the new and old measurement data is equal, interference may also accumulate. In this case, by assigning different weight factors to different new information, the correction effect of the old data can be reduced. Therefore, the posterior update of the time state matrix is ​​shown in Equation (15).

[0115] (15)

[0116] In formula (15), It is based on the prior state prediction at time k-1. By assigning different weight factors to the gains at different times, the gains at each moment can be weighed, thereby correcting and suppressing the accumulated interference. . The value is 1 to ensure that the current gain has a greater weight, and p is an adjustable coefficient.

[0117] When the battery system state changes suddenly, it may face the challenge of not being able to track the real state of the system in time. To solve this problem, a constant gain factor is introduced. Optimize the filter gain matrix. By adjusting The value of can flexibly adjust the gain matrix according to the change of the system state, ensuring that the filtering algorithm can respond quickly when the system state changes suddenly, and timely and accurately track the real state of the system, thereby optimizing the final SOE estimation result. The improved gain is shown in Equation (16). The improved state gain matrix is ​​shown in (17). The improved state matrix is ​​shown in Equation (18).

[0118] (16)

[0119] (17)

[0120] (18)

[0121] In formula (16), is the covariance matrix of state prediction, is the observation matrix, is the measurement noise covariance matrix. In formula (17), is the improved gain, is the improved gain at the ki-th moment.

[0122] Gain Factor It should be adjusted according to the actual situation to ensure that it is applicable to different battery states. When the battery is at rest, the SOE value remains unchanged. At this time, the polarization effect has the greatest impact on the voltage, and the change of the polarization effect is more complex. The polarization effect is caused by the chemical reaction and ion migration process inside the battery, which will have a continuous impact on the voltage over time. Therefore, when the battery is at rest, using the EKF algorithm to estimate the SOE is likely to lead to increased errors. It is usually a positive value less than 1. During the charging and discharging process of the battery, due to the dynamic behavior of the battery and the energy conversion process, This is because the battery's electrochemical reaction changes rapidly during charging and discharging, and the battery's voltage and current fluctuate greatly, so a larger To compensate for these changes and ensure the accuracy of SOE estimation. The value of is typically between 1 and 2, which helps improve the response speed and accuracy of battery state estimation. A larger gain factor is used to account for the rapid changes in voltage and current that may occur during battery charging and discharging, and to reduce estimation errors caused by battery nonlinearity. By appropriately adjusting the gain factor, you can effectively balance battery state estimation accuracy with system response speed, better adapting to dynamic battery changes.

[0123] In this embodiment, the entire SOE estimation process consists of three modules: IMAFFRLS online parameter identification module, BP neural network state estimation module and MIGKF correction module. These three modules work together to form a complete battery state estimation system. The latter two modules constitute the BP-MIGKF method and are the core of SOE estimation. The overall flow chart is as follows: Figure 2 As shown in the figure. First, a second-order RC-PNGV equivalent circuit model is constructed, and the voltage and current data of the lithium-ion battery are input into the second-order RC-PNGV equivalent circuit model. Second, the IMAFFRLS algorithm is used for online parameter identification to obtain the battery model parameters. Third, the battery model parameters are input into the BP neural network, which outputs a preliminary SOE estimate. Finally, the preliminary estimated SOE is passed to the MIGKF method to filter the noise in the output estimate and obtain the final SOE estimate.

[0124] Experimental example:

[0125] (1) Experimental platform construction:

[0126] This experiment requires experimental data, which is collected using a battery test bench. A temperature test chamber is used to control the experimental temperature of the lithium-ion battery. The charge and discharge tester measures parameters such as current and voltage, and connects to a host computer via TCP / IP to record the data in real time. The experimental conditions are set at a room temperature of 25°C. The constant temperature chamber is set at 19.11°C and then slowly raised to and maintained at 25°C. The equipment is validated under HPPC, DST, and BBDST operating conditions.

[0127] (2) Model comparison experiment:

[0128] This example uses HPPC operating data to verify the accuracy of the model and compares the improvement in modeling accuracy between the proposed second-order RC-PNGV equivalent circuit model and the traditional second-order RC model. Figure 4Results show that the output voltage error of the second-order RC-PNGV model is significantly lower than that of the traditional second-order RC model, and the error curve fluctuates less. The maximum error of the latter is 0.058V, while that of the former is only 0.041V. This demonstrates that the second-order RC-PNGV model offers superior performance in terms of accuracy and stability, effectively reducing the impact of model errors during the charge and discharge processes. Therefore, the second-order RC-PNGV model provides a more accurate and reliable solution for battery modeling, making it particularly suitable for high-precision battery management systems.

[0129] (3) Parameter identification of lithium-ion batteries under different temperatures and working conditions:

[0130] To verify the tracking ability of the parameter identification algorithm, the OCV-SOE function was applied to the FFRLS and IMAFFRLS algorithms to obtain simulated voltage values. The simulated voltage values ​​were then compared with the experimentally measured voltage values ​​to verify the performance of the parameter identification algorithm. Figure 5 、 Figure 6 、 Figure 7 The simulation voltage results of FFRLS and IMAFFRLS algorithms are compared under 25℃ HPPC, DST, and BBDST conditions respectively.

[0131] Depend on Figure 5 (a-1) Figure 6 (b-1) and Figure 7 As can be seen from (c-1) in the figure, the IMAFFRLS algorithm can well follow the reference voltage curve under different working conditions at a temperature of 25°C. Especially at the moment of voltage mutation, its tracking ability is significantly better than that of the FFRLS algorithm. Figure 5 (a-5) Figure 6 (b-5) and Figure 7 As can be seen from (c-5) in the figure, the overall error curve of the IMAFFRLS algorithm fluctuates less during the entire process and is closer to 0. In particular, the error curve of the IMAFFRLS algorithm fluctuates less than that of the FFRLS algorithm at the beginning and end of the experiment.

[0132] The evaluation indicators of the experimental results are expressed as maximum error (MAX), mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE). Equation (19) is the calculation formula for each evaluation indicator.

[0133] (19)

[0134] from Figure 8Analysis shows that at 25°C, the IMAFFRLS algorithm's MAX is less than 6%, a significant improvement over the FFRLS algorithm. At 25°C, the IMAFFRLS algorithm's MAE, RMSE, and MAPE remain superior, all remaining within 2%. In summary, the IMAFFRLS algorithm exhibits strong convergence and tracking performance at 25°C, demonstrating high robustness and accuracy.

[0135] The traditional RLS algorithm performs poorly when the temperature changes. The main reason is that the battery parameters fluctuate with temperature, and the RLS algorithm with a fixed forgetting factor has difficulty tracking these changes efficiently. This leads to errors in SOE estimation, power management deviations, and a decline in battery performance and life. In contrast, IMAFFRLS uses an adaptive forgetting factor that can dynamically adjust the update rate, thereby achieving more accurate battery modeling. To evaluate the feasibility of the IMAFFRLS algorithm, this example conducted experiments using data sets at different temperatures (15°C). Figure 9 (a-1) Figure 10 (b-1) and Figure 11 (c-1) shows the comparison of simulated voltage results of FFRLS and IMAFFRLS algorithms under HPPC, DST and BBDST conditions at 15°C.

[0136] Depend on Figure 9 (a-5) in Figure 10 (b-5) in Figure 11 From (c-5) in , we can see that the IMAFFRLS algorithm has better tracking ability and convergence at 15℃, and the overall error is smaller, while the FFRLS algorithm has poor tracking effect in the middle and late stages. Figure 12 Further analysis shows that the MAX of the IMAFFRLS algorithm is kept within 7%, and the MAE, RMSE and MAPE are kept within 2%. Compared with the FFRLS algorithm, it shows excellent performance at a temperature of 15°C.

[0137] (4) Performance comparison of BP-MIGKF and other algorithms under HPPC, DST and BBDST working conditions:

[0138] In order to verify the validity and feasibility of the BP-MIGKF estimation model, the experiment was conducted at a temperature of 25℃. , current , after IMAFFRLS algorithm parameter identification , , , , , is the training data of BP neural network, where 70% of the data set is randomly selected as the training set, and the remaining 30% of the data set is used as the test set. The maximum iteration is 700 times, the learning rate is 0.001, the number of hidden layer nodes is set to 8, and the training target error is set to 1 e -9 , according to the use of these parameters, BP training is first performed in the training set by fitting learning , , , , , , and and predict the training result value The learning ability was then verified using the test set. The predicted training and validation sets were then fed into the EKF, MIEKF, and MIGKF methods for iterative denoising and optimization. The power integration method was used to estimate the SOE as a reference. The SOEs estimated by BP, BP-EKF, BP-MIEKF, and BP-MIGKF under HPPC, DST, and BBDST operating conditions were compared to verify the superiority and feasibility of the BP-MIGKF algorithm.

[0139] The estimated results of SOE under HPPC working conditions are as follows: Figure 13 and Figure 14 As shown, Figure 13 (a-1) shows the training set SOE reference value and the estimated value of different algorithms. Figure 14 (b-1) shows the test set SOE reference value and the estimated values ​​of different algorithms. Figure 14 (c-1) in the figure shows the test set SOE estimation error.

[0140] Depend on Figure 14 From (b-1) in the figure, we can see that the estimated curve of the BP-MIGKF algorithm is closest to the reference curve, while the estimated curves of other algorithms have certain differences from the reference curve. Figure 14 As shown in (c-1) in the figure, the BP-MIGKF algorithm exhibits minimal fluctuations and errors, indicating good stability. However, the estimation error increases at the end of the battery's discharge. This is primarily due to a decrease in the accuracy of the battery model parameter identification at the end of discharge. Although IMAFFRLS improves model accuracy slightly, the error remains significant. Secondly, when the SOE falls below 20%, the physical and chemical properties of the lithium-ion battery undergo drastic changes, leading to increased error.

[0141] To better compare the SOE estimation accuracy of the BP, BP-EKF, BP-MIEKF, and BP-MIGEKF algorithms, it is necessary to compare key metrics from the four algorithms' estimation results. The five algorithms were compared using the three evaluation metrics: MAX, MAE, and RMSE. The MAX, MAE, and RMSE on the test set were used to compare because the test set provides a true reflection of the model's generalization and prediction accuracy in real-world applications. Performance metrics on the training set are primarily used for model learning and parameter optimization. While they can reflect a model's ability to fit known data, they cannot assess its adaptability or robustness to new data. Comparing the MAX, MAE, and RMSE on the test set allows for a comprehensive assessment of the model's worst-case stability, overall accuracy, and sensitivity to large errors, thereby more objectively verifying its effectiveness and feasibility.

[0142] Table 1 Comparison of SOE estimation results of HPPC at 25℃

[0143]

[0144] Table 1 shows a comparison of SOE estimation results under HPPC conditions at 25°C. Under HPPC conditions, the BP-MIGKF algorithm achieves a maximum SOE of 2.03%, a MAE of 0.15%, and an RMSE of 0.49%. The proposed algorithm achieves the lowest values ​​for all three performance metrics, demonstrating its stability and superiority. Further testing is required to verify the performance of the BP-MIGKF algorithm under different conditions.

[0145] The estimated results of SOE under DST working conditions are as follows: Figure 15 and Figure 16 As shown in the figure, the estimated results of SOE under BBDST working conditions are as follows: Figure 17 and Figure 18 As shown, Figure 15 (a-1) and Figure 17 (d-1) in the figure shows the SOE reference values ​​of the training set and the estimated values ​​of different algorithms under DST and BBDST conditions, respectively. Figure 16 (b-1) and Figure 18 (e-1) in the figure shows the SOE reference value of the test set under DST and BBDST conditions and the estimated values ​​of different algorithms. Figure 16 (c-1) and Figure 18(f-1) in the figure shows the test set SOE estimation error under DST and BBDST conditions, respectively. The figure shows that the BP network predicts a large fluctuation in the SOE curve and poor convergence, while the BP-EKF, BP-MIEKF, and BP-MIGKF algorithms converge well and have relatively small errors. Comparing the BP-EKF, BP-MIEKF, and BP-MIGKF algorithms, it can be seen that the BP-MIGKF algorithm further reduces the error and tracks the SOE prediction curve better. However, under DST and BBBDST operating conditions, due to the smaller current changes and the inclusion of shorter, smaller pulses in the test, the internal battery characteristics may change more significantly, resulting in more significant error fluctuations. This demonstrates that the method proposed in this embodiment can effectively improve the accuracy and stability of SOE estimation.

[0146] Table 2 Comparison of test set SOE estimation results under DST and BBDST conditions

[0147]

[0148] Table 2 compares the SOE estimation results for the test set under the DST and BBDST conditions. Under the DST condition, the BP-MIGKF algorithm achieves a maximum SOE of 1.97%, a MAE of 0.30%, and an RMSE of 0.82%. Under the BBDST condition, the BP-MIGKF algorithm achieves a maximum SOE of 0.60%, a MAE of 0.11%, and an RMSE of 0.38%. The BP-MIGKF algorithm achieves significantly lower maximum, MAE, and RMSE on the test set under both conditions than other methods, demonstrating its superior prediction accuracy and stability.

[0149] In this embodiment, accurately estimating the SOE of lithium-ion batteries is a critical and challenging step in battery state monitoring. It is directly related to the battery's safety, performance, and lifespan, and is affected by multiple factors such as temperature changes, charge and discharge rates, and battery aging. Therefore, this embodiment provides a high-precision, real-time SOE estimation method. Based on a second-order RC-PNGV equivalent circuit model, it uses the IMAFFRLS algorithm for parameter identification and the BP-MIGKF method to accurately estimate SOE. This technical solution is crucial for improving the reliability of battery management systems.

[0150] This example draws the following conclusions through experimental analysis:

[0151] (1) The second-order RC-PNGV equivalent circuit model outperforms the traditional second-order model and reduces the error from 5.82% to 4.06%, indicating that its accuracy has been improved and the data results are more reliable.

[0152] (2) To address the multi-parameter identification problem, this example uses the IMAFFRLS algorithm for model parameter identification and compares it with the traditional FFRLS algorithm. The results show that IMAFFRLS can achieve online optimization and parameter estimation with an error below 7%. Therefore, IMAFFRLS achieves high accuracy and low error in battery model identification, and the process is simple and uncomplicated.

[0153] (3) The BP neural network is used to estimate the SOE of lithium-ion batteries, and then the MIGKF algorithm is used to filter the noise in the output estimation. By integrating data-driven and model methods, a more accurate and adaptive correction of the system SOE is achieved, and the error is controlled within 3%.

[0154] Example 2

[0155] Based on the same inventive concept, this embodiment further provides a lithium-ion battery energy state estimation system, comprising:

[0156] A model building module is used to build a second-order RC-PNGV equivalent circuit model, and input the voltage and current data of the lithium-ion battery into the second-order RC-PNGV equivalent circuit model;

[0157] Parameter identification module, used to perform online parameter identification using improved forgetting factor recursive least squares method to obtain battery model parameters;

[0158] An output module, configured to input the battery model parameters into a BP neural network and output a preliminary energy state estimation value;

[0159] The filtering module is used to input the preliminary energy state estimation value into the most innovative gain optimized Kalman filter for noise filtering to obtain the final energy state estimation result.

[0160] The lithium-ion battery energy state estimation system provided by this embodiment has all the advantages of the lithium-ion battery energy state estimation method provided by the first embodiment.

[0161] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for estimating the energy state of a lithium-ion battery, characterized in that: The following steps are involved: Construct a second-order RC-PNGV equivalent circuit model and input the voltage and current data of the lithium-ion battery into the second-order RC-PNGV equivalent circuit model; The improved forgetting factor recursive least squares method is used for online parameter identification to obtain battery model parameters; The process of online parameter identification using the improved forgetting factor recursive least squares method includes: Assign an independent adaptive forgetting factor to each parameter to be estimated; Decouple the covariance matrix and recursive gain matrix in the forgetting factor recursive least squares method; Dynamically adjust each forgetting factor according to the current fluctuation index and prediction error index; The adaptive forgetting factor formula is: ； in, and is the maximum and minimum value of the i-th forgetting factor, is the forgetting factor of the i-th parameter channel at time k, and its value range is is the sensitivity coefficient, The current fluctuation index quantifies the intensity of current fluctuation. The larger the value, the more severe the load change. is the forecast error index, which is expressed by and The ratio of quantifies the degree of model mismatch, and Joint decision The value of , M is the length of the moving interval, is the average value of the input current in the moving range, is the current measurement value at the nth moment, is the historical maximum current value, is the difference between the model-predicted value and the actual measured value of the battery terminal voltage, is the error threshold; Inputting the battery model parameters into a BP neural network and outputting a preliminary energy state estimation value; The preliminary energy state estimation value is input into the innovation gain optimized Kalman filter for noise filtering to obtain the final energy state estimation result.

2. The method according to claim 1, characterized in that The second-order RC-PNGV equivalent circuit model includes an open-circuit voltage source, a polarization resistor, a polarization capacitor, and an equivalent capacitor representing the current accumulation effect.

3. The method according to claim 1, characterized in that The formula of the recursive gain matrix is: ； in, is the gain matrix, is the definition of the decoupled diagonal covariance matrix, is the definition of the forgetting factor diagonal matrix, is a 5-dimensional regression vector, yes is the transposed vector; , , , , , , is defined as follows: ； ； ； ； ； in, is the covariance of the i-th parameter at time k-1, is the forgetting factor of the i-th parameter at time k-1, each element represents the characteristic variable related to the i-th parameter to be estimated, is the battery terminal voltage value actually output by the system, is the regression vector, which is a set of characteristic variables. is the voltage value at the previous moment, is the voltage value at the first two moments, Current value at the current moment, is the current value at the previous moment, is the current value at the first two moments, Corresponding regression vector The first element of , Corresponding regression vector The second element , Similarly, is the parameter vector to be estimated, Corresponding respectively The weight coefficient of .

4. The method according to claim 1, wherein The input parameters of the BP neural network include voltage, time-varying current, resistance and capacitance; the output parameter is a preliminary energy state estimation value.

5. The method according to claim 1, wherein The filtering process of the multi-innovation gain optimized Kalman filter includes: Constructing a multi-innovation vector of length j, wherein the multi-innovation vector includes a sequence of historical terminal voltage measurement values; Expanding a state gain matrix according to the multiple innovation vectors; Assigning weight factors to gains at different moments, wherein the weight factors decrease over time; Optimize the filter gain matrix by a constant gain factor.

6. The method according to claim 5, characterized in that The constant gain factor is dynamically adjusted according to the battery status.

7. A lithium-ion battery energy state estimation system, characterized in that: include: A model building module is used to build a second-order RC-PNGV equivalent circuit model, and input the voltage and current data of the lithium-ion battery into the second-order RC-PNGV equivalent circuit model; Parameter identification module, used to perform online parameter identification using improved forgetting factor recursive least squares method to obtain battery model parameters; The parameter identification module includes: Assign an independent adaptive forgetting factor to each parameter to be estimated; Decouple the covariance matrix and recursive gain matrix in the forgetting factor recursive least squares method; Dynamically adjust each forgetting factor according to the current fluctuation index and prediction error index; The adaptive forgetting factor formula is: ； in, and is the maximum and minimum value of the i-th forgetting factor, is the forgetting factor of the i-th parameter channel at time k, and its value range is is the sensitivity coefficient, The current fluctuation index quantifies the intensity of current fluctuation. The larger the value, the more severe the load change. is the forecast error index, which is expressed by and The ratio of quantifies the degree of model mismatch, and Joint decision The value of , M is the length of the moving interval, is the average value of the input current in the moving range, is the current measurement value at the nth moment, is the historical maximum current value, is the difference between the model-predicted value and the actual measured value of the battery terminal voltage, is the error threshold; An output module, configured to input the battery model parameters into a BP neural network and output a preliminary energy state estimation value; The filtering module is used to input the preliminary energy state estimation value into the most innovative gain optimized Kalman filter for noise filtering to obtain the final energy state estimation result.

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