CN115856681A

CN115856681A - Battery SOC estimation method based on EKF adaptive temperature regulation

Info

Publication number: CN115856681A
Application number: CN202211653572.0A
Authority: CN
Inventors: 邵海涵; 巫火桂; 徐振华
Original assignee: Dongguan Zhenhua New Energy Technology Co ltd
Current assignee: Dongguan Zhenhua New Energy Technology Co ltd
Priority date: 2022-12-21
Filing date: 2022-12-21
Publication date: 2023-03-28

Abstract

The invention relates to the technical field of battery SOC estimation, and discloses a battery SOC estimation method based on EKF adaptive temperature regulation, which is characterized in that an adaptive temperature regulation model function is added on the basis of an EKF Kalman filtering algorithm, so that the dynamic estimation of the battery SOC under different temperature conditions is ensured, and the error precision of the battery under different temperature conditions is improved; the traditional EKF does not consider the influence of temperature on battery capacity, ohmic internal resistance, polarization resistance and polarization capacitance, and has limitation on the estimation precision of battery SOC under different temperature conditions; the battery SOC estimation method based on EKF adaptive temperature regulation has the advantages of being suitable for dynamic estimation of battery SOC of different chemical systems, achieving rapid convergence of battery SOC error accuracy and the like.

Description

Battery SOC estimation method based on EKF adaptive temperature regulation

Technical Field

The invention relates to the technical field of battery SOC estimation, in particular to a battery SOC estimation method based on EKF adaptive temperature regulation.

Background

With the breakthrough and the great development of the lithium battery technology in China in recent years, the lithium battery is widely applied to the fields of electric automobiles, electric tools, energy storage systems and the like, and the BMS (battery management system) is used as a core component of the lithium battery, not only implements a safe and reliable protection function on the charging and discharging process of the lithium battery, but also needs to accurately estimate the SOC (state of charge) of the lithium battery, and provides accurate and reliable battery residual capacity for users.

The lithium battery has very complicated internal chemical components, so that the state of charge of the lithium battery cannot be directly measured, and the state of charge of the lithium battery can be estimated according to equivalent circuit characteristics of the lithium battery, such as electrical characteristic curves or calculation formulas of internal resistance, open-circuit voltage, current, temperature and the like of the lithium battery.

At present, the mainstream battery SOC estimation methods commonly used in the industry include: the ampere-hour integration method, the open-circuit voltage look-up table method, the kalman filter method (EKF), the neural network method, etc. can effectively estimate the SOC of the battery, but each has advantages and disadvantages.

An ampere-hour integration method: the SOC of the battery is calculated by collecting the current, time and temperature of the battery, integrating the time and the current and combining compensation coefficients such as temperature, current multiplying power and battery aging. The method has the advantages of simple algorithm, easy realization and poor user experience, and has the defects that the measurement error and the calculation error exist, the accumulated error of the battery SOC estimation is gradually increased after long-time operation, the estimation precision of the battery SOC is influenced, and the accumulated error is usually corrected by combining with open-circuit voltage, but the correction operation can cause the battery SOC jump.

Open circuit voltage lookup: under the condition that the battery is fully kept still, the open-circuit voltage (OCV) of the battery is measured, the relation curve of the open-circuit voltage corresponding to the temperature and the SOC of the battery is searched, and the SOC of the battery is obtained.

Kalman filtering method: and taking a state space model and an observation model of the noise and the signal as algorithm models, and updating the estimation of the state variable by using an observation value at the current moment and an estimation value at the previous moment during measurement by using a least square method. The essence of prediction of the battery SOC by the Kalman filtering method is an ampere-hour integration method, and meanwhile, a measured voltage value is used for correcting a priori estimation value. The method has the advantages that the method is suitable for the processor to carry out recursive operation on the estimation result, so that the battery SOC estimation error can be rapidly converged, and the method is suitable for the battery SOC estimation of various chemical systems.

A neural network method: a large amount of measurement data such as voltage and current and battery SOC data are used as training samples, training and modification are repeatedly carried out through forward propagation of input information and backward propagation of error transmission in the learning process of the neural network, and when the predicted battery SOC reaches the error range of the design requirement, a new data is input to obtain a predicted value of the battery SOC. The method has the advantages that a specific battery model does not need to be established, the state of charge of the battery can be estimated at any time only by proper data samples and a more accurate neural network mode, the method is suitable for batteries of various chemical systems, and the defects that more sample data are required, and the estimation accuracy of the SOC of the battery is influenced by the data accuracy, the quantity and different training methods are overcome.

Disclosure of Invention

The invention aims to provide a battery SOC estimation method based on EKF adaptive temperature regulation, and aims to solve the problem that in the prior art, the accuracy error of battery SOC estimation is large.

The invention is realized in the way, 1, the battery SOC estimation method based on EKF self-adaptive temperature regulation is characterized by comprising the following steps:

1) Performing battery modeling by adopting a dual-polarized equivalent circuit model;

2) Carrying out parameter identification on the battery model to obtain parameter tables under different battery SOC states and different temperature states;

3) According to the established battery model, establishing a state equation and an observation equation of the battery as follows:

the state equation is as follows:

wherein Upa (k) and Upc (k) are k times R _pa C _pa 、R _pc C _pc A parallel network voltage; upa (k-1) and Upc (k-1) are at time R of k-1 _pa C _pa 、R _pc C _pc A parallel network voltage; SOC (k) is the remaining capacity of the battery at the time k; SOC (k-1) is the battery residual capacity at the moment of k-1; i (k) is the battery current at the moment k; rpa and Rpc are polarization resistances; cpa and Cpc are polarization capacitors; delta t is a current sampling period; qi is the battery capacity at the current (temperature T);

the observation equation: u (k) = Uoc (SOC (k)) -Upa (k) -Upc (k) -I (k) × R0

Wherein U (k) is the battery terminal voltage at the moment k; uoc (SOC (k)) is the battery OCV open circuit voltage at time k; upa (k) is a k-time battery model R _pa C _pa A parallel network voltage; upc (k) is a battery model R at the k moment _pc C _pc A parallel network voltage; i (k) is the battery current at the moment k; r0 is ohmic internal resistance; uoc (SOC (k)) is a non-linear function and is derivable for SOC (k); from the Taylor expansion:

equivalently replacing the state equation and the observation equation according to the EKF equation set to obtain the following calculation formula;

prior state vector

State transition matrix

/>

Control matrix

Input variable U _k ＝I(k)

Observation matrix

The KEF state equation and the space equation of the battery model are as follows:

wherein, the first and the second end of the pipe are connected with each other,

for a priori evaluation of the moment K>

Deducing an observation value for the time K>

The SOC estimation value at the moment k is obtained, and R0 is the ohmic internal resistance of the battery;

according to EKF equation system

A posteriori estimation

evaluated for the posterior at time K>

For K time error covariance matrix estimation, K _k For the gain matrix at time K, P _k-1 Is a K-1 time error covariance matrix, Q _k-1 State noise at time K-1, W _k Is the state noise covariance at time K, R _k For observing noise at time K, V _k The noise covariance was observed for time K.

4) Based on a posteriori estimation

The values and the battery temperature, the parameters Rpa, cpa, cpc and R0 are obtained by inquiring the parameter table, and A is updated _k 、B _k (ii) a Posterior evaluation->

The SOC (k) in (1) is the optimal estimation result of the battery SOC.

Further, in the step 1), according to the established battery model, the following formula is obtained:

U _L ＝U _oc -Upa-Upc-I _L *R ₀ +V

wherein R is _pa 、R _pc Polarizing internal resistance of the battery; c _pa 、C _pc Polarizing the capacitor for the battery; r _pa 、C _pa The parallel network shows transient response of terminal voltage when the battery is charged and discharged; r _pc 、C _pc The parallel network shows the influence of concentration polarization and electrochemical polarization inside the battery on terminal voltage; u shape _oc Is the battery Open Circuit Voltage (OCV); r ₀ Ohmic internal resistance; u shape _L Is the battery terminal voltage; i is _L Is the battery current; upa is R _pa 、C _pa Terminal voltage of the parallel network; upc is R _pc 、C _pc Terminal voltage of the parallel network; u shape _oc = f (SOC) is a nonlinear equation representing the relationship between the open circuit voltage and the remaining battery capacity SOC;

is R _pa 、C _pa The parallel network voltage represents the relation between the electric polarization internal resistance transient voltage and time t;

is R _pc 、C _pc The parallel network voltage represents the relation between the concentration polarization internal resistance transient voltage and time t; v is the measurement noise generated by the calculation process.

Further, in the step 1), according to a ampere-hour integral principle of the battery charge, the following formula is obtained:

wherein, SOC (t 0) is the battery residual capacity at the last time t 0; eta is the coulombic efficiency coefficient, which is defined as

Qn is the rated capacity of the battery; qi is the actual total capacity of the battery at the present current i, based on>

Is the integral of the current and the time difference t-t0 from time t0 to t.

Further, in the step 2), HPPC testing is performed on the battery by using a battery detection device, so as to obtain a relationship among the direct current resistance of the battery, the SOC of the battery, the charge and discharge performance of the battery, and the impulse current response.

Further, in the step 2), during the HPPC test of the battery, a plurality of test points are set in an interval in which the specified pulse test battery SOC point starts from 90% to 10%, the interval is 10%, and the battery SOC point starts from 10% to 0.

In step 2), eight test points are set in the interval from 10% to 0 of the SOC point of the battery in the HPPC test of the battery, wherein the eight test points are respectively 0%, 2.5%, 5%, 7.5%, 92.5%, 95%, 97.5% and 100%.

Further, in the step 2), the obtained parameters include ohmic internal resistances R0, upa, upc, RC time constants, uoc, upa, upc, time constant τ 1, and time constants τ 2, rpa, cpa, rpc, and Cpc.

Further, in the step 3), the state equation and the observation equation are transformed into a matrix equation as follows:

and equivalently replacing the matrix equation with the calculation formula.

Compared with the prior art, the battery SOC estimation method based on EKF adaptive temperature regulation increases the function of an adaptive temperature regulation model on the basis of EKF (extended Kalman Filter algorithm), ensures that the battery realizes dynamic estimation on the battery SOC under different temperature conditions, and improves the error accuracy of the battery under different temperature conditions.

Drawings

FIG. 1 is a schematic diagram of a dual-polarized equivalent circuit model provided by the present invention;

FIG. 2 is a diagram of operating condition data for HPPC testing of a battery provided by the present invention;

FIG. 3 is a graph of a test of pulse power at 95% SOC of a battery according to the present invention;

FIG. 4 is a SOC-OCV polynomial fit curve of a battery provided by the present invention at 25 ℃;

FIG. 5 is a graph illustrating the estimation of battery SOC according to the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.

The following describes the implementation of the present invention in detail with reference to specific embodiments.

The same or similar reference numerals in the drawings of the present embodiment correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by the terms "upper", "lower", "left", "right", etc. based on the orientation or positional relationship shown in the drawings, it is only for convenience of describing the present invention and simplifying the description, but it is not intended to indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and are not to be construed as limiting the present patent, and the specific meaning of the terms may be understood by those skilled in the art according to specific circumstances.

The battery SOC estimation method based on EKF adaptive temperature regulation comprises the following steps:

1) Performing battery modeling by adopting a dual-polarization equivalent circuit model;

the state equation is as follows:

prior state vector

/>

State transition matrix

Control matrix

Input variable U _k ＝I(k)

Observation matrix

for a priori evaluation of the moment K>

Deducing an observation value for the time K>

R0 is the ohmic internal resistance of the battery and is the SOC estimated value at the moment k;

according to EKF equation set derivation

Posterior estimation

evaluation of posterior for K time>

For K time error covariance matrix estimation, K _k For the gain matrix at time K, P _k-1 Is a K-1 time error covariance matrix, Q _k-1 State noise at time K-1, W _k Is the state noise covariance at time K, R _k For observing noise at time K, V _k The noise covariance is observed for time K.

Wherein Upa (k) and Upc (k) are k times R _pa C _pa 、R _pc C _pc A parallel network voltage; upa (k-1) and Upc (k-1) are at the time R of k-1 _pa C _pa 、R _pc C _pc A parallel network voltage; SOC (k) is the remaining capacity of the battery at the time k; SOC (k-1) is the battery residual capacity at the moment of k-1; i (k) is the battery current at the moment k; rpa and Rpc are polarization resistances; cpa and Cpc are polarization capacitors; delta t is a current sampling period; qi is the battery capacity at the current (temperature T);

the observation equation: u (k) = Uoc (SOC (k)) -Upa (k) -Upc (k) -I (k) × R0

Wherein U (k) is the battery terminal voltage at the moment k; UOC (SOC (k)) The OCV open-circuit voltage of the battery at the moment k; upa (k) is a k-time battery model R _pa C _pa A parallel network voltage; upc (k) is a battery model R at the k moment _pc C _pc A parallel network voltage; i (k) is the battery current at the moment k; r0 is ohmic internal resistance; uoc (SOC (k)) is a non-linear function and is derivable for SOC (k); based on Taylor expansion, we can:

wherein the content of the first and second substances,

for a priori evaluation of the instant K>

Is an estimated value of SOC at the moment k;

4) According to a posteriori estimation

The SOC (k) in (1) is the optimal estimation result of the battery SOC.

According to the battery SOC estimation method based on EKF adaptive temperature regulation, the adaptive temperature regulation model function is added on the basis of EKF (extended Kalman Filter algorithm), dynamic estimation of the battery SOC is guaranteed under different temperature conditions, and the error accuracy of the battery under different temperature conditions is improved.

The traditional EKF does not consider the influence of temperature on battery capacity, ohmic internal resistance, polarization resistance and polarization capacitance, and has limitation on the estimation precision of the battery SOC under different temperature conditions.

The battery SOC estimation method based on EKF adaptive temperature regulation has the following advantages:

1) The method is suitable for dynamic estimation of the SOC of the batteries of different chemical systems;

2) The rapid convergence of the SOC error precision of the battery is realized;

3) And automatically selecting battery model identification parameters of different temperature areas to estimate and correct the SOC of the battery.

In this embodiment, the selected cell model is SW18650-26HPA lithium iron phosphate cell, the cell capacity is 3.5Ah, and since the accuracy of the battery model determines the estimation accuracy of the SOC, the selection of the battery equivalent circuit model is particularly important, and the currently commonly used battery equivalent circuit models include: the method comprises the steps of selecting a pure resistance equivalent circuit model, a Thevenin equivalent circuit model (a first-order circuit model), a dual-polarization equivalent circuit model (a second-order circuit model) and a fractional order model, wherein the selection of the models needs to comprehensively consider factors such as model precision, calculation complexity and practicability, the polarization characteristic of a battery can be simulated by the Thevenin equivalent circuit model under normal conditions, however, the internal concentration polarization and the electrochemical polarization of the battery have large influence on the charging and discharging efficiency of the battery, the early-stage and later-stage simulation errors of the Thevenin equivalent circuit on the battery are large, an RC network needs to be added on the basis of the Thevenin equivalent circuit model to represent the influence of the internal concentration polarization and the electrochemical polarization of the battery on open-circuit voltage, and the model is the Thevenin equivalent circuit model.

In this embodiment, referring to fig. 1, a dual-polarization equivalent circuit model is used for battery modeling, so that all polarization characteristics of a battery can be accurately described, the model is high in precision, and the structure is simple compared with a model of three or more orders and is easy to calculate.

In step 1), according to the established battery model, obtaining the following formula:

U _L ＝U _oc -Upa-Upc-I _L *R ₀ +V

In the step 1), according to the ampere-hour integral principle of the battery charge, the following formula is obtained:

Is the integral of the current and the time difference t-t0 from time t0 to time t.

In this embodiment, in step 2), HPPC testing is performed on the battery by using the battery detection device, so as to obtain a relationship between the dc resistance of the battery, the SOC of the battery, the charge/discharge performance of the battery, and the pulse current response. In this embodiment, in the step 2), the obtained parameters include direct current internal resistances R0, upa, upc, RC time constants, uoc, upa, upc, time constant τ 1, time constants τ 2, rpa, cpa, rpc, and Cpc. In the step 2), in the HPPC test of the battery, a plurality of test points are set in the interval of a specified pulse test battery SOC point starting from 90% to 10% and a middle interval of 10%, and the battery SOC point starting from 10% to 0.

In the step 2), in the HPPC test of the battery, eight test points are set in the interval from 10% of the SOC point of the battery to 0, wherein the eight test points are respectively 0%, 2.5%, 5%, 7.5%, 92.5%, 95%, 97.5% and 100%.

The HPPC test is used for embodying the pulse charging and discharging performance characteristics of the power battery, the battery detection equipment is used for carrying out the HPPC test, the direct current internal resistance (including ohmic resistance and polarization resistance) of the battery to be tested can be obtained, and meanwhile, the relation between the SOC of the battery and the charging and discharging performance and the pulse current response of the battery can also be obtained.

The pulse test SOC point specified by the common HPPC test method is from 90% to 10% and 10% in the middle, and 9 points in total, while 0% -10% and 90% -100% for the battery are just the most significant intervals of polarization, and once the data of the part is lost, the model precision is greatly influenced, so that the HPPC test in the embodiment adds 8 test points: 0%, 2.5%, 5%, 7.5%, 92.5%, 95%, 97.5%, 100%. The measured condition data is shown in fig. 2, and then, the pulse power test curve at each SOC point of the battery needs to be analyzed, for example, the pulse power test curve for 95% of the SOC of the battery is analyzed as follows, and is shown in fig. 3.

1) 10S discharge pulse (interval U1-U4): when the cell is subjected to a 10 second discharge pulse, the cell voltage drops rapidly from U1 to U2 due to the polarization phenomenon, and it is believed that this voltage drop is primarily a function of ohmic polarization. The U2 to U3 portions can be considered as voltage drops generated by electrochemical polarization and concentration polarization together during the sustained discharge. When the discharge current disappears, the cell voltage snaps back from U3 to U4, again believed to be due to the disappearance of ohmic polarization.

2) 40S shelf (U4-U5 interval): this interval, which may be considered a zero input response, may be fitted to the second order RC parameter through this segment of the curve, which is later expanded specifically.

3) 10S charging pulse (U5-U8 interval): the same thing as discharging. According to calculation, ohmic internal resistance and RC parameters of the battery in the discharging direction and the charging direction are found to be different to a certain extent under the same SOC state, parameters of the charging and discharging direction can be respectively calculated from the viewpoint of improving model precision, and then parameter switching is carried out according to actual current conditions during application.

4) 40S shelf (U8-U9 interval): the same thing as discharging.

Referring to fig. 3, the dc internal resistance in the discharging direction may be:

it can also be:

considering that the test has errors, the average of the two can be taken. The same principle is also used for calculating the direct current internal resistance in the charging direction. A40 second hold between U4-U5 interval, may be answered with the formula of zero input response>

Fitting is performed, where τ 1= rpa × cpa, τ2= rpc cpc; uoc, upa, upc, time constant τ 1 and time constant τ 2 were obtained by MATLABCurveFittingTool. Rpa and Rpc can be obtained according to the current and voltage at the U3 time Cpa and Cpc, and Cpa and Cpc can be obtained through a time constant.

Finally, parameter tables under different battery SOC states can be obtained. The following table 1 shows the state of the battery at 25 ℃, and the battery is required to be respectively placed in incubators of-35 degrees, -20 degrees, 0 degrees and 45 degrees, and the battery parameters are identified according to the experimental method.

TABLE Battery parameters at 125 deg.C

/>

In step 3), the state equation and the observation equation are transformed into a matrix equation as follows:

and equivalently replacing the matrix equation with the calculation formula.

In this example, the Uoc (SOC (k)) is a curve obtained by polynomial fitting of SOC to OCV of the battery, and is a graph obtained by polynomial fitting of OCV to SOC of the battery at 25 ℃.

The following is a polynomial fitted to the OCV-SOC of the cell at different temperatures:

Uoc＝-1.513*e ^-8 *SOC ⁴ +3.73*e ^-6 *SOC ³ -0.0008551*SOC ² +0.03064*SOC+3.188(60℃)

Uoc＝-1.81*e ^-8 *SOC ⁴ +4.838*e ^-6 *SOC ³ -0.0003781*SOC ² +0.01564*SOC+3.345(45℃)

Uoc＝-1.513*e ^-8 *SOC ⁴ +3.73*e ^-6 *SOC ³ -0.0002483*SOC ² +0.009928*SOC+3.45(25℃)

Uoc＝-1.3*e ^-8 *SOC ⁴ +3.11*e ^-6 *SOC ³ -0.0001886*SOC ² +0.007542*SOC+3.472(10℃)

Uoc＝-1.208*e ^-8 *SOC ⁴ +2.819*e ^-6 *SOC ³ -0.0001583*SOC ² +0.006568*SOC+3.482(0℃)

Uoc＝-8.263*e ^-9 *SOC ⁴ +1.898*e ^-6 *SOC3-9.111*e ^-5 *SOC ² +0.005037*SOC+3.509(-10℃)

Uoc＝-5.96*e ^-10 *SOC ⁴ +3.483*e ^-7 *SOC ³ +4.054*e ^-6 *SOC ² +0.003308*SOC+3.516(-20℃)

in this example, KF and EKF derivation was performed as follows

The Kalman filtering is an algorithm for performing optimal estimation on the system state by using a linear system state equation and inputting and outputting observation data through a system, and five formulas of the Kalman filtering are as follows.

The state equation is as follows: x _k ＝A*X _k-1 +B*U _k-1 +W _k-1

X is a state vector, the system state at the moment is presumed according to the system state and the control variable at the previous moment, A is a state transition matrix, B is a control matrix for converting input into state, U is system input, W is system prediction noise and obeys Gaussian distribution, the expected value is 0, and white Gaussian noise W with covariance of Q is obtained _k-1 In the range of N (0, Q).

The observation equation: z _k ＝H*X _k +V _k

Z is an observation vector, generally obtained by measuring vector data by a sensor, H is a conversion matrix for converting a state variable into an observation vector, V is observation noise, obeys Gaussian distribution, and has a period of timeWhite Gaussian noise V with 0 expectation and R covariance _k In the range of N (0, R).

The Kalman filtering algorithm comprises two steps:

1. and (3) prediction: and estimating the system state at the K moment according to the posterior estimation value at the K-1 moment to obtain the prior estimation value at the K moment.

2. Updating: and correcting the prior estimation value in the prediction stage by using the measured value at the moment K to obtain the posterior estimation value at the moment K.

The kalman prediction equation is as follows:

the kalman equation is as follows:

posterior estimates at the K and K-1 times, respectively, kalman filtering results (optimal estimate), ->

For derived a-priori estimates (predictors), P, at instants K _k 、P _k-1 The posteriori estimated covariance (representing) at K, K-1, respectively

Uncertainty in status), ->

Covariance (representing ^ er) estimated a priori for time K>

Uncertainty) of the kalman filter process is a loop iteration process, as can be seen from the above formula.

As Kalman filtering can only be used for processing a linear system, for a nonlinear system, taylor expansion can be performed on a nonlinear function, a high-order item is omitted, only a first-order item of an expansion form is reserved, linearization of the nonlinear function is realized, state estimation and covariance estimation of the system are approximately calculated through a Kalman filtering algorithm, and as a control system is a nonlinear model, a system state equation and an observation equation become.

The state equation is as follows: x _k ＝f(X _k-1 ，U _k-1 ，w _k-1 )

The observation equation: z _k ＝h(X _k ，v _k )

In the above formula, X _k Is a state vector, Z _k For the observation vector, f (), h () are the system nonlinear state function and the measurement function, w, respectively _k-1 And v _k Also non-linear noise, if w is not taken into account _k-1 ，v _k And obtaining a state prediction equation and an observation equation by noise as follows.

The state prediction equation:

the observation equation:

for an a priori evaluation at time k, ->

Evaluation posterior for time k-1>

An approximation of the observation at time k.

The first order approximation function of the unitary function taylor expansion is:

f(x)≈f(x ₀ )+f′(x ₀ )(x-x ₀ )

can obtain X _k 、Z _k The approximate solution of (c).

In the formula, X _k And Z _k Are the actual state quantity and the observed quantity,

and &>

Is a priori estimate and an observed estimate, is based on the comparison of the measured values>

Is a posteriori estimate.

Although the state equation and the observation equation format of the Kalman filter are satisfied, the matrix A, the matrix H, the matrix W and the matrix V are still the combination of multivariate functions and calculated by partial derivatives.

1) The matrix A is a function f

Partial derivative of a point with respect to X

The matrix H is a function H

Partial derivative of point with respect to X

The matrix W is a function f

Partial derivative of point with respect to W

The matrix V is a function f

Partial derivative of point with respect to V

The state noise ik and the observation noise jk also need to be linearized, so the covariance matrix of the state noise and the observation noise is:

from the above, the system of EKF equations is derived as:

in this embodiment, an implementation process of the battery SOC estimation method based on EKF adaptive temperature adjustment is provided:

1) Initialization

X defining an initial time ₀ Vector, i.e. Upa ₀ 、Upc ₀ And SOC ₀ Initial value of (1), after starting up, the battery is in a standing state, upa ₀ ＝0，Upc ₀ ＝0，SOC ₀ And the last-time stored posterior estimated value is obtained by looking up a table according to the SOC-OCV under the corresponding battery temperature T during the initial use.

Defining the covariance matrix Q of the system noise at the initial moment ₀ ＝0.0000001*diag([2.5,1.5]) Observe the noise covariance matrix R ₀ ＝[0.1]。

Defining an error covariance matrix P at an initial time _3,3 ＝[0]。

Inquiring the SOC according to the battery parameter identification table ₀ And Rpa corresponding to current battery temperature T ₀ ,Cpa ₀ ,Rpc ₀ ,Cpc ₀ ,R0 ₀ Is started.

And defining Qi at the initial moment as the rated capacity of the battery, and inquiring the battery capacity corresponding to the current i and the current battery temperature T in the calculation process.

2) Calculating process

Starting the system, collecting external current U for 1 time at time k =1 and every time delta t _k Terminal voltage Z of battery _k 。

(1) A priori estimation

(2) Error covariance matrix

(3) Calculating a gain matrix

(4) Posterior estimation

(5) Error covariance matrix update

(6) State transition matrix, control matrix update

According to a posteriori estimation

Updating A by looking up the battery parameter identification table to obtain the latest Rpa, cpa, rpc, cpc, R0 values _k 、B _k 。/>

To this end, finishThe EKF estimation process for the battery SOC,

and obtaining the optimal estimation result of the battery state.

Due to the barrel effect of the series-connected battery packs, the discharge capacity of the multi-string battery packs depends on the lowest single battery capacity, and therefore 168 strings of minimum SOC values are selected as the SOC estimation result of the battery packs.

In the embodiment, a 540V/70Ah power battery pack (168 strings/7 parallel) is placed in a 25 ℃ incubator, a high-power charging and discharging experiment cabinet is used for charging and discharging the battery pack according to the requirement of pulse discharging of a test outline, a data recorder is used for monitoring the voltage of 168 strings of single batteries in the test process, working condition data (current, the measured voltage of the 168 strings of single batteries and time) in the charging and discharging test process are led into Matlab, an estimation result is simulated in the Matlab, and referring to the graph shown in FIG. 5, the SOC value of the battery estimated through the algorithm is compared with the SOC calculated by the charging and discharging experiment cabinet (the measurement precision of the charging and discharging experiment cabinet is higher, and the calculated SOC value is considered as a true value).

Referring to fig. 5, for the SOC values of the charge and discharge aging cabinet and the present algorithm, the estimation error is controlled to be less than 4%, the SOC error is artificially expanded to 40% during initialization, and after multiple iterative updates, the SOC error can be rapidly converged to be within 5%, which indicates that the robustness of the algorithm is good. And setting the temperature box at-20 ℃ and 60 ℃ respectively, and after the battery pack is fully stood, performing the experiment again according to the method, wherein the estimation result is basically consistent with the true value.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims

1. The battery SOC estimation method based on EKF adaptive temperature regulation is characterized by comprising the following steps of:

the state equation is as follows:

wherein Upa (k) and Upc (k) are k times R _pa C _pa 、R _pc C _pc A parallel network voltage; upa (k-1) and Upc (k-1) are at time R of k-1 _pa C _pa 、R _pc C _pc A parallel network voltage; SOC (k) is the battery residual capacity at the moment k; SOC (k-1) is the battery residual capacity at the moment of k-1; i (k) is the battery current at the moment k; rpa and Rpc are polarization resistances; cpa and Cpc are polarization capacitors; delta t is the current sampling period; qi is the battery capacity at the current (temperature T);

the observation equation: u (k) = Uoc (SOC (k)) -Upa (k) -Upc (k) -I (k) × R0

Wherein U (k) is the battery terminal voltage at the moment k; uoc (SOC (k)) is the battery OCV open circuit voltage at time k; upa (k) is a battery model R at the k time _pa C _pa A parallel network voltage; upc (k) is a battery model R at the k moment _pc C _pc A parallel network voltage; i (k) is the battery current at the moment k; r0 is ohmic internal resistance; uoc (SOC (k)) is a non-linear function and is derivable for SOC (k); from the Taylor expansion:

prior state vector

State transition matrix

Control matrix

Input variable U _k ＝I(k)

Observation matrix

wherein the content of the first and second substances,

for a priori evaluation of the moment K>

Deducing an observation value for the time K>

according to an EKF equation system

Posterior estimation

evaluated for the posterior at time K>

4) Based on a posteriori estimation

The SOC (k) in (1) is the optimal estimation result of the battery SOC.

2. The EKF adaptive temperature adjustment-based battery SOC estimation method according to claim 1, wherein in the step 1), based on the established battery model, the following formula is obtained:

U _L ＝U _oc -Upa-Upc-I _L *R ₀ +V

is R _pa 、C _pa The parallel network voltage represents the relation between the transient voltage of the electric polarization internal resistance and time t; />

3. The EKF adaptive temperature adjustment-based battery SOC estimation method according to claim 1, wherein in the step 1), the following formula is obtained according to battery charge ampere-hour integration principle:

4. The EKF adaptive temperature adjustment-based battery SOC estimation method according to any one of claims 1 to 3, wherein in the step 2), HPPC test is performed on the battery by using a battery detection device to obtain the relationship among the DC resistance, the battery SOC, the battery charge-discharge performance and the pulse current response of the battery.

5. The EKF adaptive temperature adjustment-based battery SOC estimation method according to claim 4, wherein in the step 2), during the battery HPPC test, the specified pulse test battery SOC point starts from 90% to 10% and ends with an intermediate interval of 10%, and during the interval that the battery SOC point starts from 10% to 0, a plurality of test points are set.

6. The EKF adaptive temperature adjustment-based battery SOC estimation method according to claim 5, wherein in the step 2), eight test points, which are respectively 0%, 2.5%, 5%, 7.5%, 92.5%, 95%, 97.5%, 100%, are set in the interval from 10% to 0 during the HPPC test of the battery.

7. The EKF adaptive temperature adjustment-based battery SOC estimation method according to any of claims 1 to 3, wherein the parameters obtained in step 2) comprise ohmic internal resistances R0, upa, upc, RC time constants, uoc, upa, upc, time constant τ 1 and time constants τ 2, rpa, cpa, rpc and Cpc.

8. The EKF adaptive temperature adjustment-based battery SOC estimation method according to any of claims 1 to 3, wherein in the step 3), the state equation and the observation equation are transformed into a matrix equation as follows:

and equivalently replacing the matrix equation with the calculation formula.