A battery capacity online estimation method based on extended Kalman filter

Abstract

The application relates to the technical field of battery management systems, in particular to a battery capacity online estimation method based on an extended Kalman filter, which mainly comprises the following steps: determining system state variables and system observation variables; establishing a system state equation and a system observation equation; establishing a recursive model for battery capacity estimation according to the extended Kalman filter algorithm; and estimating the battery capacity according to the recursive model after initial information is determined. The application has low error sensitivity to charging and discharging capacity and SOC, can realize online estimation of the battery capacity in the actual use process of the battery, and can break the dependence on the initial capacity of the battery after a certain number of iterations.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of battery management system, and particularly relates to a battery capacity online estimation method based on extended Kalman filter. BACKGROUND

[0002] Batteries have been widely used in transportation, industry, medical treatment, power storage and many other fields. Battery capacity is an important indicator to measure the performance of a battery, which represents the ability of the battery to store electric charge. Different degrees of capacity attenuation will occur in various batteries during use. The capacity attenuation of the battery is not only related to external factors such as storage conditions, charging and discharging conditions, maintenance conditions, but also affected by internal factors such as positive and negative electrode materials and electrolyte quality. This leads to the nonlinearity of the capacity attenuation of the battery during use. The extended Kalman filter converts the nonlinear system into an approximate linear system by using the first-order Taylor expansion, but since the extended Kalman filter is a recursive estimation algorithm, the initial value provides a starting point for subsequent iterative calculations. If the initial value is greatly deviated, the estimated value will also be greatly affected in the subsequent iteration process.

[0003] At present, the battery capacity can be measured by external equipment, estimated by charging and discharging curve characteristics, or calculated by small current full discharge. Among them, the method of measuring battery capacity by using external equipment is not universally applicable to the already installed and used batteries; the charging and discharging curve characteristics of the battery need to be extracted through a large number of long-term experiments, and some types of batteries may not have good consistency and cannot accurately estimate the battery capacity through the charging and discharging curve characteristics; the small current full discharge method for determining the battery capacity is not affected by the installation and use conditions of the battery, but it will cause irreversible damage to some batteries. The ratio of the change amount of the battery storage electric quantity to the change amount of the SOC (State of Charge) during the battery charging and discharging process can reflect the battery capacity, but since there are measurement errors and calculation errors in the charging and discharging electric quantity and the SOC, the battery capacity cannot be directly obtained by this method.

[0004] The above various methods all have certain problems. Therefore, it has positive significance for the use and maintenance of the battery to study a battery capacity online estimation method based on extended Kalman filter with low error and reliable and practical. SUMMARY

[0005] The present application discloses a battery capacity online estimation method based on extended Kalman filter to improve the convenience of battery capacity estimation and reduce the influence on the electrical device.

[0006] To achieve the above object, the technical scheme adopted by the present application is as follows: a battery capacity online estimation method based on extended Kalman filter, comprising the following steps:

[0007] determining system state variables and system observation variables;

[0008] establishing system state equations and system observation equations;

[0009] establishing a recursive model for battery capacity estimation according to the extended Kalman filter algorithm;

[0010] estimating the battery capacity according to the recursive model after determining the initial information.

[0011] The system state variables are battery capacities, and the system observation variables are the battery charge and discharge process power change values and corresponding SOC change amounts.

[0012] The system state equation is as follows:

[0013] X k =f(X k-1 )+ω k-1

[0014] wherein the system state variable X k is the battery capacity of the kth iteration, ω k-1 is the process noise of the k-1th iteration, and since the battery capacity loss of adjacent two iterations can be ignored, the system state function f(X k-1 )=X k-1 .

[0015] The system observation equation is as follows:

[0016] Z k =h(X k )+θ k

[0017] wherein the system observation variable Z k of the kth iteration is a column vector containing ΔSOC k and ΔQ k , i.e. Z k =[ΔSOC k , ΔQ k ] T , ΔQ k is the power change value of the kth iteration, ΔSOC k is the SOC change amount of the kth iteration, θ k is the system observation noise of the kth iteration, and the system observation function

[0018] The establishment of the recursive model for battery capacity estimation comprises the following steps:

[0019] The predicted system state is calculated by obtaining the current predicted system state based on the estimated system state value at the previous moment, as shown in the following formula:

[0020]

[0021] in, This is the system state estimate for the (k-1)th iteration. For based on The system state prediction values ​​obtained after k iterations;

[0022] The predicted value of the system state covariance matrix is ​​calculated based on the estimated value of the system state covariance matrix at the previous time step, the covariance matrix of the system process noise, and the system state function. The formula is as follows:

[0023]

[0024] Among them, P k-1 This is the estimated value of the system state covariance matrix for the (k-1)th iteration. For P-based k-1 The predicted values ​​of the system state covariance matrix obtained after k iterations are: A is the Jacobian matrix of the system state function f(·) with respect to the system state variables, W is the Jacobian matrix of the system state function f(·) with respect to the process noise, and Q is the covariance matrix of the system process noise.

[0025] The Kalman gain is calculated based on the predicted value of the current system state covariance matrix, the covariance matrix of the system observation noise, and the system observation function. The formula is shown below:

[0026]

[0027] Among them, K k Let be the Kalman gain after k iterations, V be the Jacobian matrix of the system observation function h(·) with respect to the system state noise, R be the covariance matrix of the system observation noise, and H be the Jacobian matrix of the system observation function h(·) with respect to the system state variables. H will change with the changes in the system observations.

[0028] Update the system state estimate by calculating the optimal estimate of the current system state based on the current system state prediction, system observation variables, Kalman gain, and system observation function, as shown in the following formula:

[0029]

[0030] updating the system state covariance matrix estimation value; calculating the system state covariance matrix estimation value according to the current system state covariance matrix prediction value, the Kalman gain and the system observation function, and the formula is as follows:

[0031]

[0032] Wherein, I is the unit matrix of the same order as H.

[0033] The initial information includes: the initial state variable X0 of the system, i.e. the initial capacity of the battery, the initial system state covariance matrix O0, the covariance matrix Q of the system process noise and the covariance matrix R of the system observation noise.

[0034] The beneficial effects of the present application are: (1) the battery capacity online estimation can be realized in the actual use process of the battery; (2) after a certain number of iterations, the dependence on the initial capacity of the battery can be eliminated; (3) the error sensitivity of the charging and discharging capacity and the SOC is low. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 It is the flow chart of the battery capacity online estimation of the present application.

[0036] Figure 2 It is the comparison chart of the estimated capacity and the calibrated capacity of the first embodiment of the present application.

[0037] Figure 3 It is the comparison chart of the estimated capacity and the calibrated capacity of the second embodiment of the present application. DETAILED DESCRIPTION

[0038] The specific embodiments of the present application will be described in detail below. The present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present application, therefore the present application is not limited by the disclosed specific embodiments.

[0039] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terms used only for describing specific embodiments, not for limiting the present application.

[0040] First embodiment:

[0041] The rated capacity of the lithium cobalt oxide battery is 1.5 Ah, and the positive and negative electrode materials are lithium cobalt oxide and artificial graphite respectively. The battery is cycled with a depth of about 20% at a rate of 2C, i.e. 0.3 Ah of electric quantity is cycled at a current of 3 A, and the capacity of the battery is calibrated by full charging and discharging at a small current at the beginning of the cycle and after a period of time. The charging quantity and SOC change from the beginning of charging to the end of charging, and the discharging quantity and SOC change from the beginning of discharging to the end of discharging during the cycle charging and discharging process are used as system observation variables, and the battery capacity during the cycle charging and discharging process is estimated by using the application. As shown in Figure 1 The specific steps of the method of the application are as follows:

[0042] Step one, determine the system state variables and system observation variables.

[0043] The battery capacity is used as the state variable of the system, and the charging quantity and SOC change from the beginning of charging to the end of charging, and the discharging quantity and SOC change from the beginning of discharging to the end of discharging during the cycle charging and discharging process are used as the observation variables of the system.

[0044] Step two, establish the system state equation and the system observation equation.

[0045] The system state equation is as follows:

[0046] X k =f(X k-1 )+ω k-1

[0047] Wherein, the system state variable X k is the battery capacity of the kth iteration, ω k-1 is the process noise of the k-1th iteration, and f(X k-1 ) represents the state transition function of the system state from the k-1th time to the kth time. In this embodiment, one iteration refers to the process from the beginning of charging to the end of charging or from the beginning of discharging to the end of discharging. Since the loss of battery capacity between adjacent two iterations can be ignored, the system state function f(X k-1 ) = X k-1 .

[0048] The system observation equation is as follows:

[0049] Z k =h(X k )+θ k

[0050] Wherein, the system observation variable Z k of the kth iteration is a column vector containing ΔSOC k and ΔQ k , i.e. Z k = [ΔSOCk , ΔQ k ] T , ΔQ k is the change of SOC in kth iteration, θ k is the change of SOC in kth iteration, θ k is the system observation noise in kth iteration, the system observation function

[0051] Step three, establish the recursive model of battery capacity estimation according to the extended Kalman filter algorithm.

[0052] The recursive model is to calculate iteratively according to the estimation result of the previous moment and the new measurement value between different moments, so as to realize the recursive estimation of the battery capacity.

[0053] Step 3.1, calculate the system state prediction value:

[0054] The current system state prediction value is obtained according to the system state estimation value of the previous moment, and the formula is as follows:

[0055]

[0056] wherein, is the system state estimation value in k-1th iteration, is the kth iteration system state prediction value obtained based on

[0057] Step 3.2, calculate the system state covariance matrix prediction value:

[0058] The current system state covariance matrix prediction value is obtained according to the system state covariance matrix estimation value of the previous moment, the covariance matrix of the system process noise and the system state function, and the formula is as follows:

[0059]

[0060] wherein, P k-1 is the system state covariance matrix estimation value in k-1th iteration, is the kth iteration system state covariance matrix prediction value obtained based on P k-1 , A is the Jacobian matrix of the system state function f(·) with respect to the system state variable, W is the Jacobian matrix of the system state function f(·) with respect to the process noise, and Q is the covariance matrix of the system process noise.

[0061] Step 3.3, calculate the Kalman gain:

[0062] The Kalman gain is calculated according to the current system state covariance matrix prediction value, the covariance matrix of the system observation noise and the system observation function, and the formula is as follows:​

[0063]

[0064] wherein, K k is the Kalman gain of the kth iteration, V is the Jacobian matrix of the system observation function h(·) with respect to the system state noise, R is the covariance matrix of the system observation noise, and H is the Jacobian matrix of the system observation function h(·) with respect to the system state variable. H will change with the change of the system observation variable.

[0065] Step 3.4, update the system state estimation value:

[0066] The optimal estimation value of the current system state is calculated according to the current system state prediction value, the system observation variable, the Kalman gain and the system observation function, and the formula is as follows:

[0067]

[0068] Step 3.5, update the system state covariance matrix estimation value:

[0069] The optimal estimation value of the current system state covariance matrix is calculated according to the current system state covariance matrix prediction value, the Kalman gain and the system observation function, and the formula is as follows:

[0070]

[0071] wherein, I is a unit matrix with the same order as H.

[0072] Step 4, estimate the battery capacity according to the recursive model after determining the initial information.

[0073] Initial information: the initial system state variable X0 of the system is the rated capacity of the battery 1.5 Ah, and the initial system state covariance matrix P0 is 10 -4 ·I1, the covariance matrix of the system process noise Q is 10 -6 ·I1, and the covariance matrix of the system observation noise R is 10 -3 ·I2, wherein I1 and I2 represent 1-order unit matrix and 2-order unit matrix respectively.

[0074] Figure 2 The battery capacity estimated by the method of the present application, the battery rated capacity obtained by the small current full discharge, and the difference between the two are shown. Since the initial system state variable, i.e. the initial capacity of the battery at the beginning of the battery cycle charging and discharging, is greatly different from the rated capacity of the battery, there is a large difference between the battery capacity estimated by the present application and the rated capacity at the beginning of the calculation. However, with the increase of the number of iterations, the difference between the two begins to gradually decrease, and when the number of iterations exceeds 400, the difference between the battery capacity estimated by the present application and the rated capacity is stable within 0.02 Ah.

[0075] The results of this embodiment show the following two points: (1) without full charging or full discharging of the battery, the present application can also realize online estimation of the battery capacity; (2) after a certain number of iterations, the present application method can get rid of the dependence on the initial capacity of the battery.

[0076] Second embodiment:

[0077] In order to understand the influence of the error of the system observation variable on the present application method, three groups of system observation variables with different errors are generated based on the first embodiment, and the present application method is used to estimate the battery capacity according to the system observation variables with errors.

[0078] The specific way of generating three groups of system observation variables with different errors is as follows: first, for the system observation variable Z k = [ΔSOC k , ΔQ k ] T Generate independent random numbers subject to normal distribution, then add random numbers to the system observation variable in the form of relative error. In order to control the error size of the system observation variable, the mean of the normal distribution subject to by the relative error of the three groups of system observation variables is 0, and the standard deviation is 5%, 10% and 15% respectively. In order to exclude the interference of other factors, the initial information used when estimating the battery capacity by using the three groups of system observation data is the same.

[0079] Figure 3 The battery capacity estimated by the present application method for the three groups of system observation variables with different errors and the difference between the two are shown. From Figure 3 It can be seen that the following two points: (1) even if the error of the system observation variable is increased, the present application method can reduce the difference between the estimated capacity and the calibrated capacity caused by the inaccurate initial value after a period of iteration. (2) Although the estimated value of the battery capacity will fluctuate as the error of the system observation variable increases, it will always float around the calibrated value.

[0080] The results of this embodiment show that: (1) even if the error of the system observation variable is increased, the present application can get rid of the dependence on the initial capacity of the battery after a certain number of iterations. (2) The present application has low sensitivity to the error of the charge and discharge quantity and SOC.

Claims

1. An online battery capacity estimation method based on extended Kalman filter, characterized in that, The method comprises the following steps: determining system state variables and system observation variables, the system state variables being battery capacity, and the system observation variables being battery power change values and corresponding SOC change amounts in the charging and discharging process; establishing a system state equation and a system observation equation, the system state equation being as follows: where the system state variable is the battery capacity at the kth iteration, is the process noise at the kth iteration, since the loss of battery capacity between two consecutive iterations is negligible, the system state function ; The system observation equation is as follows: in, System observation variables in the next iteration It contains and The column vector, i.e. , for The change in electricity level in the next iteration for The change in SOC in the next iteration. for System observation noise in the next iteration, system observation function ; establishing a recursive model for battery capacity estimation according to an extended Kalman filtering algorithm, the establishing of the recursive model for battery capacity estimation comprising the following steps: calculating a system state prediction value, the formula being as follows: wherein is the system state estimate of the kth iteration, is based on the system state prediction of the kth iteration; and the system state prediction of the kth iteration. calculating a system state covariance matrix prediction value, the formula being as follows: wherein is a kth iteration system state covariance matrix estimate, is based on obtained a kth iteration system state covariance matrix pre-test, is a system state function a Jacobian matrix with respect to state variables, is a system state function a Jacobian matrix with respect to process noise, is a covariance matrix of system process noise; calculating a Kalman gain, the formula being as follows: wherein is Kalman gain of the next iteration, is a system observation function is a Jacobian matrix with respect to the system state noise, is a covariance matrix of the system observation noise, is a system observation function is a Jacobian matrix with respect to the system state variable, will change with the change of the system observation. updating a system state estimation value, the formula being as follows: wherein is the kth iteration system state prediction value, is the system observation variable, is the kth iteration Kalman gain; is the system observation function; updating a system state covariance matrix estimation value, the formula being as follows: wherein is a system state covariance matrix prediction, is is a Kalman gain of the kth iteration, is a system observation function, is an identity matrix of order equal to is an identity matrix of order equal to determining initial information and estimating battery capacity according to the recursive model.

2. The battery capacity online estimation method based on extended Kalman filter according to claim 1, characterized in that, The initial information includes: system initial state variable i.e. battery initial capacity, initial system state covariance matrix covariance matrix of system process noise and covariance matrix of system observation noise .

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