CN109031142A - A kind of secondary cell model and method for estimating state based on piecewise linear interpolation - Google Patents

Abstract

The invention belongs to the field of battery state estimation, and in particular relates to a secondary battery model and state estimation method based on piecewise linear interpolation. The present invention obtains a secondary battery model based on piecewise linear interpolation by applying piecewise linear interpolation to the secondary battery model, and uses the secondary battery model based on piecewise linear interpolation in the state filter to improve the state of the secondary battery The accuracy of the estimation can reduce the calculation amount and overfitting of the state estimation of the secondary battery.

Description

A secondary battery model and state estimation method based on piecewise linear interpolation

technical field

The invention belongs to the field of battery state estimation, and in particular relates to a secondary battery model and state estimation method based on piecewise linear interpolation.

Background technique

In the application of the secondary battery, it is necessary to estimate the state of the battery such as SOC (state of charge) and capacity fading. Existing technologies often use state filters such as EKF (Extended Kalman Filter) when estimating the state of the battery. In the process of applying the state filter, it is necessary to provide a system model of the battery to estimate the state of the battery through the external physical quantities of the battery such as current and voltage.

In the current technology, the battery models used by the state filter can be divided into four types: empirical model, data-driven model, equivalent circuit model, and electrochemical model.

The empirical model is based on the empirical analysis of the use data of the secondary battery, the relationship between statistical data, and the calculation of the battery parameters; the advantage is that it is simple to implement, the amount of calculation is small, but the accuracy is insufficient.

The equivalent circuit model is based on the equivalent circuit of the battery, and the calculation of the battery parameters is realized by means of circuit analysis; the advantage is that it is simple to implement, the amount of calculation is small, but the accuracy is insufficient.

The electrochemical model is based on the specific structure of the secondary battery, and establishes a model for the internal reaction of the secondary battery through the electrochemical relationship to calculate the parameters of the battery. The advantage is that it has high precision, but the model is complex and the amount of calculation is large.

The data-driven model is based on the usage data of the secondary battery. The relationship between the data is calculated by mathematical methods to calculate the parameters of the battery. Low problem, and the problem of overfitting, and overfitting will reduce the accuracy of the model.

Contents of the invention

In view of the above existing problems or deficiencies, in order to solve the problems of high calculation amount, low model accuracy and model overfitting of the secondary battery model when the state filter uses a data-driven model, the present invention provides a piecewise linear based Interpolated secondary battery model and state estimation method.

A secondary battery model based on piecewise linear interpolation, including a state transition model and an output model.

The specific form of the state transition model is:

Among them, k is the ordinal number of the sampling point, p and q are the order of the model, i _k represents the battery current of the sampling point k, Represents the theoretical dynamic voltage of the battery at sampling point k. The formulas of a _u and b _u are as follows:

in Represents the battery SOC at sampling point k, Y ₁ ,..., Y _r and Piecewise linear interpolation of node coordinates for a _u . r and m are the order of piecewise linear interpolation of a _u . v'=v _y,ku , w'=w _y,ku . v _{y, ku} stands for The serial number of the interval in the interval (-∞, Y ₂ ), [Y ₂ , Y ₃ ], ..., [Y _r-1 , ∞) satisfies It is located in the v _{y, kuth} interval among the above intervals. w _{y, ku} stands for in interval The sequence number of the interval in which satisfies It is located in the w _{y, k-u+1th} interval in the above interval.

Among them, I ₁ ,..., I _s and Piecewise linear interpolation of node coordinates for b _u . s and n are the order of piecewise linear interpolation of b _u . v'=v _i,ku , w'=w _i,ku . v _{i, ku} represents the serial number of the interval where i _ku is located in the interval (-∞, I ₂ ), [I ₂ , I ₃ ), ..., [I _s-1 , ∞), satisfying that i _ku is located in the vth interval in the above interval _{i, ku} intervals. w _{i, ku} stands for in interval The sequence number of the interval in which satisfies It is located in the w _i,k-u+ 1th interval among the above intervals.

In the above formula, a _{u, v, w} , b _{u, v, w} are piecewise linear interpolation node values, where for a _{u, v, w} , the subscript range is 1≤u≤p, 1≤v≤ r, 0≤w≤m; for b _{u, v, w} , the subscript ranges are 0≤u≤q, 1≤v≤s, 0≤w≤n.

The specific form of the output model is:

Among them, y _{term, k} represents the battery voltage at sampling point k, y _{oc, k} represents the battery open circuit voltage at sampling point k, and ∈ _k represents the measurement noise at sampling point k.

The state estimation method of the secondary battery model based on piecewise linear interpolation, the specific steps are as follows:

Step S1, initialize the secondary battery model based on piecewise linear interpolation, and then initialize the prior state vector and the prior state error covariance matrix.

Step S2, measure the battery voltage to obtain the measured value of the battery voltage; according to the measured value of the battery voltage, the initialized prior state vector and the initialized prior state error covariance matrix, for the secondary battery model based on piecewise linear interpolation, through the EKF Obtain the posterior state vector and the posterior state error covariance matrix;

Then, the expected estimate of battery SOC, the variance estimate of battery SOC, the expected estimate of capacity decay, and the variance estimate of capacity decay are obtained through the posterior state vector and the posterior state error covariance matrix;

Step S3, according to the a priori state vector and the a priori state error covariance matrix obtained in step S2, obtain the a priori state vector and a priori state error covariance matrix of the next sampling point through EKF;

Step S4, loop steps S2-S3, use the prior state vector and prior state error covariance matrix of the next sampling point obtained in step S3 as the initialized prior state vector and initialized priori of step S2 in the next cycle The state error covariance matrix starts to be executed cyclically until the state estimation of the secondary battery is completed.

Further, in step S1, by performing a working condition test on the battery, and measuring the battery current, battery voltage, and time in the working condition test, the secondary battery model based on piecewise linear interpolation is initialized by the Levenberg-Marquardt gradient descent method.

Further, in step S1, the components of the prior state vector include battery SOC, capacity decay and piecewise linear interpolation node values.

The present invention obtains a secondary battery model based on piecewise linear interpolation by applying piecewise linear interpolation to the secondary battery model, and uses the secondary battery model based on piecewise linear interpolation in the state filter to improve the state of the secondary battery The accuracy of the estimation can reduce the calculation amount and overfitting of the state estimation of the secondary battery.

Description of drawings

Fig. 1 is the overall flowchart of the present invention;

Fig. 2 is the battery voltage measurement value obtained in the embodiment, the battery voltage estimated value, and the comparison of the battery voltage estimated value when the secondary battery model based on piecewise linear interpolation according to the present invention is not used;

Fig. 3 is the expected estimate of battery SOC obtained by the integration of ampere hours, the expected estimate of battery SOC obtained by EKF, and the expected estimate of battery SOC obtained by EKF when the secondary battery model based on piecewise linear interpolation according to the present invention is not used in the embodiment. Compare;

Fig. 4 is the comparison of the time used for the model operation obtained in the embodiment and the time used for the model operation when the secondary battery model based on piecewise linear interpolation according to the present invention is not used;

Fig. 5 is a comparison of changes in the battery state estimation process between b ₀ in the model obtained in the embodiment and the equivalent value when the secondary battery model based on piecewise linear interpolation according to the present invention is not used. (a) is the result before the change when the secondary battery model based on piecewise linear interpolation according to the present invention is not used, and (b) is the result after the change when the secondary battery model based on piecewise linear interpolation according to the present invention is not used Result, (c) is the result before changing when using the secondary battery model based on piecewise linear interpolation of the present invention, and (d) is the result after changing when using the secondary battery model based on piecewise linear interpolation of the present invention result. In the figure, the circle represents the working point of the battery, and its color from black to white represents different time points from before the change to after the change.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the accompanying drawings and implementation examples.

As shown in Figure 1, the state estimation method of the secondary battery model based on piecewise linear interpolation can be divided into the following steps:

Step S1, initialize the secondary battery model based on piecewise linear interpolation, and then initialize the prior state vector and the prior state error covariance matrix.

Step S11 , initializing a secondary battery model based on piecewise linear interpolation.

In this embodiment, the battery is subjected to a working condition test, and the battery current, battery voltage, and time in the working condition test are measured, and the secondary battery model based on piecewise linear interpolation is initialized by the Levenberg-Marquardt gradient descent method.

First, test the open circuit voltage of the battery to obtain the open circuit voltage function of the battery. The specific method is as follows:

Fully charge the battery first, and then start measuring time, battery current, and battery voltage. Discharge the battery with a small current (such as 0.1C) until the voltage drops to a low voltage threshold (such as 3V). The battery is then charged with a small current until the voltage rises to a high voltage threshold (eg 4.2V). Roughly estimate the battery SOC during this period by integrating the ampere hour, and the formula is as follows:

Among them, k is the ordinal number of the sampling point, and N _dis is the ordinal number of the sampling point at the end of the discharge. t _k represents the time of sampling point k, i _k represents the battery current of sampling point k, charge is positive, discharge is negative, C _n is the rated capacity, Represents the battery SOC at sampling point k.

The resulting battery SOC and battery voltage during discharge and charge are subjected to piecewise linear interpolation to obtain curves of battery voltage during discharge and charge relative to SOC. The average curve of the measured battery voltage during discharge and charge relative to the battery SOC is obtained to obtain the open circuit voltage function y _oc (z) of the battery.

Next, measure the initial value of the battery voltage y _{term, 0} , and inversely calculate the initial value of the battery SOC according to the battery open circuit voltage function, that is Then, conduct a working condition test on the battery, measure the battery current, battery voltage, and time in the working condition test, and obtain a rough estimate of the battery SOC in the working condition test by integrating the ampere-hour. The formula is as follows:

Among them, C _n is the rated capacity obtained before.

Then, the piecewise linear interpolation node value is used as the parameter for fitting using the Levenberg-Marquardt gradient descent method. The fitting method and formula are as follows:

Take C=[a 1, 1, ₀ ... a _{p, r, m} b 0, 1, ₀ ... b _{q, s, n} ] ^T as the fitting vector, N is the total number of sampling points, and get the initial estimate of the fitting vector C ₀ :

y _k = y _{term, k} - y _{oc, k}

t=max(p,q)+1

Then, the fitted vector is estimated using the Levenberg-marquardt gradient descent method:

Where k>t, Obtained by the state transition model; when k≤t, v'=v _y,ku , w'=w _y,ku .

make ∈=[∈ ₁ ... ∈ _N ] ^T . Starting with l=0, iterate the following formula:

like Then multiply μ by 0.1, add 1 to l, and proceed to the next iteration, otherwise multiply μ by 10, and perform this iteration again. when l reaches an upper limit (such as 1000), or Stop when the lower limit (such as 1×10 ^-6 ) is reached. Let l+1=l _end when stopping, get Finally, the piecewise linear interpolation node value is obtained from each component of C.

Step S12, initializing the prior state vector and the prior state error covariance matrix.

In this embodiment, the components of the prior state vector include battery SOC, capacity decay and piecewise linear interpolation node values.

First, the battery voltage is measured, and the initial value of the battery SOC is obtained by inverting the battery open circuit voltage function Initial value of capacity fade Take 1. The initial value of the piecewise linear interpolation node value is the piecewise linear interpolation node value obtained in step S11. Combine the initial value of the SOC, the initial value of the capacity decay and the initial value of the piecewise linear interpolation node value into a vector to obtain the initial value of the prior state vector

The initial value of the prior state error covariance matrix is obtained empirically. It is specifically obtained through experience and fine-tuning according to the accuracy of the initial state estimation and the requirements for the initial convergence speed of the state estimation. In this embodiment, the initial value of the prior state error covariance matrix is as follows:

where diag represents a diagonal matrix.

Step S2, measure the battery voltage to obtain the measured value of the battery voltage; according to the measured value of the battery voltage, the initialized prior state vector and the initialized prior state error covariance matrix, for the secondary battery model based on piecewise linear interpolation, through the EKF Obtain the posterior state vector and the posterior state error covariance matrix; then obtain the expected estimation of battery SOC, the variance estimation of battery SOC, the expected estimation of capacity decay and the capacity decay through the posterior state vector and posterior state error covariance matrix Variance estimation.

Step S21, measure the battery voltage to obtain the measured value of the battery voltage; according to the measured value of the battery voltage, the initialized prior state vector and the initialized prior state error covariance matrix, for the secondary battery model based on piecewise linear interpolation, through the EKF The posterior state vector and the posterior state error covariance matrix are obtained.

First measure the battery voltage to get the battery voltage measurement. Then, the estimated value of battery voltage is obtained according to the initialized prior state vector and the secondary battery model based on piecewise linear interpolation. A priori state vector with known initialization Will The values of z _k , a _{u, v, w} , b _{u, v, w} are brought into the secondary battery model based on piecewise linear interpolation, and the measurement noise ∈ _k = 0 is used to calculate the battery voltage y _{term, k} , Get battery voltage estimate

When the state transition model is calculated, v _{y, ku} , w _{y, ku} , v _{i, ku} , w _{i, ku} are searched and calculated by dichotomy, which can reduce the amount of calculation required for the formula calculation, thereby reducing the cost of the secondary battery model. purpose of calculation.

Then, according to the measured value of battery voltage, the estimated value of battery voltage, the initialized prior state vector, and the initialized prior state error covariance matrix, for the secondary battery model based on piecewise linear interpolation, the posterior state vector is obtained by EKF Posterior state error covariance matrix

Where ∑ _∈ is the variance of the measurement noise ∈ _k , which is determined according to the model accuracy and measurement accuracy. In this embodiment, 1×10 ^-3 is used.

Step S22, obtaining the expected battery SOC estimate, the variance estimate of the battery SOC, the expected capacity decay estimate, and the capacity decay variance estimate through the posterior state vector and the posterior state error covariance matrix.

posterior state vector middle, For the desired estimate of battery SOC, is the expected estimate of capacity fade. Posterior state error covariance matrix

middle, is the variance estimate of battery SOC, is the variance estimate for capacity decay. Divide the rated capacity C _n by The capacity of the battery after decay can be obtained.

Step S3 , according to the a priori state vector and a priori state error covariance matrix obtained in step S2 , obtain a priori state vector and a priori state error covariance matrix of the next sampling point through EKF.

in, is the state noise covariance matrix, which is determined according to the model accuracy, and is taken in this embodiment as

Step S4, loop steps S2-S3, use the prior state vector and prior state error covariance matrix of the next sampling point obtained in step S3 as the initialized prior state vector and initialized priori of step S2 in the next cycle The state error covariance matrix starts to be executed cyclically until the state estimation of the secondary battery is completed.

FIG. 2 shows that the model of the present invention improves the accuracy of the estimated value of the battery voltage, thereby finally improving the accuracy of the battery state estimation.

FIG. 3 shows that the model and method of the present invention improve the accuracy of the expected estimation of battery SOC.

FIG. 4 shows that the model and method of the present invention reduce the calculation amount of battery state estimation.

Fig. 5 shows that in the process of battery state estimation, the model of the present invention has little change in the models other than the working point, indicating that the model of the present invention can alleviate the over-fitting phenomenon of the model in the process of battery state estimation, so that the final Improve the accuracy of battery state estimation.

Claims (4)

1. A secondary battery model based on piecewise linear interpolation, comprising a state transition model and an output model, characterized in that: The specific form of the state transition model is: Among them, k is the ordinal number of the sampling point, p and q are the order of the model, i _k represents the battery current of the sampling point k, Represents the theoretical dynamic voltage of the battery at sampling point k. The formulas of a _u and b _u are as follows: in Represents the battery SOC at sampling point k, Y ₁ ,..., Y _r and Piecewise linear interpolation of node coordinates for a _u . r and m are the order of piecewise linear interpolation of a _u . v'=v _y,ku , w'=w _y,ku . v _{y, ku} stands for The serial number of the interval in the interval (-∞, Y ₂ ), [Y ₂ , Y ₃ ), ..., [Y _r-1 , ∞), satisfying It is located in the v _{y, kuth} interval among the above intervals. w _{y, ku} stands for in interval The sequence number of the interval in which satisfies It is located in the w _{y, ku} +1th interval among the above intervals. Among them, I ₁ ,..., I _s and Piecewise linear interpolation of node coordinates for b _u . s and n are the order of piecewise linear interpolation of b _u . v'=v _i,ku , w'=w _i,ku . v _{i, ku} represents the serial number of the interval where i _ku is located in the interval (-∞, I ₂ ), [I ₂ , I ₃ ), ..., [I _s-1 , ∞), satisfying that i _ku is located in the vth interval in the above interval _{i, ku} intervals. w _{i, ku} stands for in interval The sequence number of the interval in which satisfies It is located in the w _{i, ku} +1th interval among the above intervals. In the above formula, a _{u, v, w} , b _{u, v, w} are piecewise linear interpolation node values, where for a _{u, v, w} , the subscript range is 1≤u≤p, 1≤v≤ r, 0≤w≤m; for b _{u, v, w} , the subscript ranges are 0≤u≤q, 1≤v≤s, 0≤w≤n. The specific form of the output model is: Among them, y _{term, k} represents the battery voltage at sampling point k, y _{oc, k} represents the battery open circuit voltage at sampling point k, and ∈ _k represents the measurement noise at sampling point k. 2. the state estimation method based on the secondary battery model of piecewise linear interpolation as claimed in claim 1, concrete steps are as follows: Step S1, initialize the secondary battery model based on piecewise linear interpolation, and then initialize the prior state vector and the prior state error covariance matrix; the secondary battery model includes a state transition model and an output model; Step S2, measure the battery voltage to obtain the measured value of the battery voltage; according to the measured value of the battery voltage, the initialized prior state vector and the initialized prior state error covariance matrix, for the secondary battery model based on piecewise linear interpolation, through the EKF Obtain the posterior state vector and the posterior state error covariance matrix; Then, the expected estimate of battery SOC, the variance estimate of battery SOC, the expected estimate of capacity decay, and the variance estimate of capacity decay are obtained through the posterior state vector and the posterior state error covariance matrix; Step S3, according to the a priori state vector and the a priori state error covariance matrix obtained in step S2, obtain the a priori state vector and a priori state error covariance matrix of the next sampling point through EKF; Step S4, loop steps S2-S3, use the prior state vector and prior state error covariance matrix of the next sampling point obtained in step S3 as the initialized prior state vector and initialized priori of step S2 in the next cycle The state error covariance matrix starts to be executed cyclically until the state estimation of the secondary battery is completed. 3. The state estimation method of the secondary battery model based on piecewise linear interpolation as claimed in claim 2, characterized in that: in the step S1, by carrying out the working condition test to the battery, and measuring the battery current in the working condition test , battery voltage, time, and initialize the secondary battery model based on piecewise linear interpolation through the Levenberg-Marquardt gradient descent method. 4. The state estimation method of the secondary battery model based on piecewise linear interpolation as claimed in claim 2, characterized in that: in the step S1, the components of the prior state vector include battery SOC, capacity fading and piecewise linear interpolation node value.