CN106802396A - A kind of diagnostic method of battery internal short-circuit - Google Patents

Abstract

The present invention relates to a kind of diagnostic method of battery internal short-circuit, comprise the following steps：1) the state-of-charge difference of all battery cells of internal battery pack is obtained；2) the state-of-charge difference according to battery cell in battery pack calculates the difference electricity 3 of each battery cell) using the rate of change L of linear regression acquisition difference electricity, that is, obtain average drain currents of the battery cell in time of measuring section；4) the average terminal voltage value according to battery pack in average drain currents and time of measuring section obtains the near short circuit resistance of each battery cell in battery pack；5) by the near short circuit resistance of each battery cell respectively with setting short-circuit resistance threshold value compared with, if near short circuit resistance is more than short-circuit resistance threshold value, then judge that the battery cell is normal monomer, if near short circuit resistance is less than or equal to short-circuit resistance threshold value, judge that the battery cell is short-circuit monomer.Compared with prior art, the present invention has the advantages that diagnosis is quick, accurately recognizes.

Description

Method for diagnosing short circuit in battery

Technical Field

The invention relates to the technical field of battery fault diagnosis, in particular to a method for diagnosing a short circuit in a battery.

Background

The occurrence of internal short circuit of the battery mainly has two main reasons, one is because of the existence of hidden troubles such as dust, burrs of raw materials such as a current collector and the like in the production process of the battery; the other is the internal short circuit caused by the complicated using environment of the battery, especially the power battery, such as the environment with high temperature, low temperature or mechanical vibration, the battery is overcharged and overdischarged, and lithium dendrite may occur during the high current operation, so that the diaphragm is punctured to cause the internal short circuit of the battery.

The battery takes place the internal short circuit and can cause the inside return circuit that becomes of battery, consumes the electric quantity of this battery constantly, causes the inside nonconformity of group battery, seriously influences dynamic property, the durability that the group battery used, can produce a large amount of heats when serious, and then makes the battery overheated, takes place the thermal runaway, has influenced the security that the group battery used greatly.

Generally, a vehicle battery pack is formed by connecting hundreds of battery monomers in series and parallel, once thermal runaway is caused by internal short circuit of one monomer, thermal runaway of the whole battery pack can be caused, and at present, no good control method exists. The safety of the battery is important and one of the most important links in the industry at present.

The internal short circuit of the battery cell is not easy to be found in the initial stage, and if the internal short circuit cannot be found in time, the thermal runaway of the battery is likely to be caused after the battery cell is continuously used. On the contrary, if the battery cell in which the internal short circuit occurs can be diagnosed at the initial stage of the internal short circuit, the reliability of the use of the battery can be greatly improved.

The current patents relate to methods for diagnosing the short circuit in the battery, which mainly adopt the method of calculating the voltage difference between the battery monomer and the average voltage of the battery pack and the number of times that the battery monomer is balanced to judge, can only qualitatively detect the battery with the internal short circuit, and can often generate the condition of misjudgment when some are influenced by factors such as the looseness of a battery link bolt and the like.

Disclosure of Invention

The present invention is directed to overcoming the above-mentioned drawbacks of the prior art and providing a method for diagnosing a short circuit in a battery, which is fast and accurately identified.

The purpose of the invention can be realized by the following technical scheme:

a method for diagnosing the internal short circuit of a battery is used for obtaining the internal short circuit resistance value of a short circuit battery monomer in a battery pack, and comprises the following steps:

1) acquiring the charge state difference of each battery monomer in the battery pack;

2) calculating the difference electric quantity of each single battery according to the charge state difference of the single batteries in the battery pack

3) Obtaining the change rate L of the difference electric quantity by linear regression to obtain the measuring time of the battery monomerAverage leakage current I in a segment_deplete；

4) According to the average leakage current I_depleteMeasuring the average terminal voltage value of the battery pack in the time section to obtain the approximate short circuit resistance value of each battery monomer in the battery pack;

5) comparing the approximate short-circuit resistance value of each single battery with a set short-circuit resistance value threshold, if the approximate short-circuit resistance value is larger than the short-circuit resistance value threshold, judging that the single battery is a normal single battery, and if the approximate short-circuit resistance value is smaller than or equal to the short-circuit resistance value threshold, judging that the single battery is a short-circuit single battery.

The step 1) specifically comprises the following steps:

11) the method comprises the steps that the overall characteristics of an average battery model equivalent battery pack are adopted, the current value of the battery pack and the average voltage value of the battery pack are used as input values, and the average charge state of the battery pack is estimated in a high-frequency mode according to an extended Kalman filter EKF algorithm;

12) the method comprises the steps of adopting a difference battery model to be equivalent to the difference between the characteristics of single batteries in a battery pack and the overall characteristics of the battery pack, taking a current value I of the battery pack, the difference value between the terminal voltage of the single batteries and the average terminal voltage of the battery pack and the average charge state value estimated by the average battery model as input values, and estimating the charge state difference of each single battery in a low-frequency mode according to an extended Kalman filter EKF algorithm.

In the step 2), the calculation formula of the difference electric quantity is as follows:

ΔC_k＝C·ΔSOC_k

wherein C is the current capacity of a single battery in the battery pack, delta SOC_kIs the differential state of charge, Δ C, between the cell SOC at time k and the average SOC of the battery pack_kThe difference electric quantity between the single battery electric quantity and the average electric quantity of the battery pack at the moment k is taken as the electric quantity.

In the step 3), the calculation formula of the change rate L of the difference electric quantity is as follows:

wherein, is_(n)Is the value of the linear regression line at the post-cut-off point within the measurement time interval, Δ C₍₁₎Is the value of the linear regression line at the starting point in the measurement time interval, t_(n)To measure the end point of a time interval, t₍₁₎Is the starting point of the measurement time interval.

In the step 4), the calculation formula of the internal short circuit resistance value of the short circuit battery monomer in the battery pack is as follows:

wherein R is_ISCInternal short circuit resistance value, U, of a short circuit cell in a battery pack_meanTo measure the average terminal voltage value of the battery during the time interval,the terminal voltage value of the ith battery pack collected in the measurement time interval is measured, and n is the total terminal voltage value of the battery pack collected in the measurement time interval.

In the step 5), the set short-circuit resistance threshold is 200 Ω.

In the step 11), the average battery model is a second-order RC model.

The expression of the average battery model is as follows:

U_mean＝U_oc(SOC_mean)-IR₀-U_D-U_T

wherein, U_meanTo average terminal voltage of the cell model, U_ocVoltage source, SOC, being a model of an average battery_meanIs the average state of charge of the battery, I is the battery current value, R₀Is internal resistance, U_DFor distributing voltage, U, for active polarisation of internal resistance_TAnd voltage distribution for concentration polarization internal resistance.

In the step 12), the differential battery model is a Rint model

The expression of the differential battery model is as follows:

wherein,in order to differentiate the terminal voltage values of the batteries,to be at SOC_meanOpen circuit voltage U of nearby i-th single battery and average battery_ocDifference, Δ SOCⁱIs the average state of charge SOC of the ith single battery and the battery pack_meanI is the battery current value, Δ RⁱThe difference internal resistance of the ith single battery and the average internal resistance of the battery pack.

Compared with the prior art, the invention has the following advantages:

firstly, the diagnosis is rapid: the method can quantitatively diagnose the single battery with the internal short circuit in the battery pack on line with a small calculated amount under the condition of limited hardware, obtain the approximate short circuit resistance value of the single internal short circuit battery in the battery pack, quantitatively predict in advance when the internal short circuit sign is small, reduce the probability of thermal runaway of the battery and improve the service performance of the battery pack.

Secondly, accurately identifying: the method adopts an average battery model and a difference battery model, and combines an extended Kalman filtering EKF algorithm to realize the identification of the state of charge difference of each battery monomer in the battery pack, thereby realizing the diagnosis of the internal short circuit fault of the battery pack and improving the dynamic property, the safety and the durability of the battery pack.

Drawings

FIG. 1 is a flow chart of the method of the present invention.

FIG. 2 is a diagram of an average cell model according to an embodiment of the present invention.

Fig. 3 is a diagram of a differential cell model according to an embodiment of the invention.

Detailed Description

The invention is described in detail below with reference to the figures and specific embodiments.

Examples

The method identifies the difference of the SOC of the battery monomer in the battery pack by combining the EKF with the frequency division model, diagnoses the approximate short-circuit resistance value of the internal short-circuit battery monomer by utilizing the differential SOC delta SOC obtained by the method, and can diagnose the approximate short-circuit resistance value of the internal short-circuit battery monomer in the battery pack in an online quantitative manner with lower calculated amount. The short circuit occurs in the battery cell, the internal part of the battery cell can form a loop, the electric quantity of the battery cell is continuously consumed, and the charge state difference delta SOC of the battery cell tends to increase continuously.

The flow of diagnosing the internal short circuit of the battery cell of the invention is shown in fig. 1, and specifically comprises the following steps:

s1, identifying the difference of the SOC of the battery monomer in the battery pack by using the working data of the battery pack measured by the sensor, combining the basic battery parameters of the battery pack, the frequency division model including an average battery model and a difference battery model, and the extended Kalman filter EKF;

step S1 specifically includes the following steps:

1) collecting battery pack working data by using a current sensor, a voltage sensor and a temperature sensor;

2) the second-order RC model shown in FIG. 2 is used as the overall characteristic of the equivalent battery pack of the average battery model, wherein the battery pack formed by connecting single batteries in series is regarded as a large battery, and the current value I of the battery pack measured by a current sensor and the average voltage value U 'measured by a voltage sensor are used'_meanAs an input value, and combined with an EKF algorithm, to estimate the average state of charge (SOC) of the battery pack in a high frequency manner_meanAnd then the SOC is measured_meanThe estimation result is output to a controller, and the controller controls charging and discharging of the battery pack.

In FIG. 2, R₀Represents the internal resistance of the battery; r connected together in parallel_DC_DAnd R_TC_TRespectively representing the active polarization internal resistance and the concentration polarization internal resistance of the battery pack; u shape_DAnd U_TAre respectively R in the model_DC_DAnd R_TC_TThe distribution voltage of (1); u shape_ocVoltage source for the average cell model, representing the open circuit voltage of the cell, U at equilibrium_ocAnd state of charge SOC of the battery pack_meanThere is a one-to-one correspondence; u shape_meanThe terminal voltage of the average battery model. I is the current of the battery pack, since the identified battery pack is formed by connecting a plurality of single batteries in series, the currents passing through the battery pack and all the single batteries are equal and are measured by the current sensor.

The second-order RC model in the step 2) has the following parameter relation:

U_mean＝U_oc(SOC_mean)-IR₀-U_D-U_T(1)

therein, SOC_meanIndicating average state of charge of the battery, i.e. tablesDisplaying the average SOC of all single batteries in the battery pack; u shape_ocRepresenting the open circuit voltage of the battery, U in equilibrium_ocValue and SOC of_meanThe values of (a) have a one-to-one correspondence; i is the current magnitude of the battery pack, the battery pack of the scheme is formed by connecting a plurality of single batteries in series, and the currents passing through the battery pack and all the single batteries are equal; r₀Expressing the ohmic internal resistance of the battery pack; u shape_DAnd U_TA distribution voltage representing polarization internal resistance of the battery pack. U shape_meanIs the terminal voltage of the average cell model, theoretically the terminal voltage of all the cells in the battery packAverage value U '(measured by a voltage sensor)'_meanEqual (generally, errors exist, because in the prior engineering practical application, in order to reduce the calculation amount, a simpler equivalent circuit model is adopted, the real characteristics of the battery can not be completely simulated, and only an approximate equivalent model is adopted), U'_meanAs shown in formula (2):

in the formula,representing the terminal voltage of the ith single battery, and N represents the number of single batteries in the battery pack.

The EKF algorithm, the state equation and the output equation are respectively expressed as (3) and (4):

x_k+1＝f(x_k,u_k)+w_k(3)

y_k＝g(x_k,u_k)+v_k(4)

wherein, f (x)_k,u_k) Is a function of state, g (x)_k,u_k) As a measurement function, x_kIs a state vector, u_kTo be transportedIn value, u in step S2_kValue of battery current, y, measured for current sensor_kAs an output value, i.e., a model estimation value, y in step S2_kFor the model output voltage, w_k，v_kIs a process noise with a mean value of 0 and random variance, which together determine the value of Kalman gain in the EKF algorithm, where w_k，v_kVariance of (d) is taken as Var (w)_k)＝1e-8，Var(v_k) 0.01^ 2. The two variances represent the influence degree of external turbulence or parameter errors (including model and system parameter errors) on the output results of the model and the system, the smaller the value of the variance is, the higher the reliability of the corresponding value is, and the larger the two parameter values are, the larger the distortion degree of the corresponding output result is. Therefore, Var (w) is generally used_k) The larger, the Var (v)_k) The smaller the interference degree of the input value is, the larger the interference degree of the input value is, the smaller the interference degree of the output comparison value of the system is, the more reliable the comparison value is, the more credible the system is about the actually measured comparison parameter value, and the larger the corresponding Kalman gain value is. In turn, Var (w)_k) The smaller, the Var (v)_k) The larger the input value, the more reliable the system is to believe that the measured parameters estimated by the model are also smaller in the corresponding kalman gain values. General prophase estimation is given as Var (w)_k) Larger, Var (v)_k) Smaller so that the estimated value converges as quickly as possible.

Obtaining the parameter matrix by adopting a first-order Taylor formula to linearize the formulas (3) and (4)

State vector x in EKF algorithm_kCan be expressed as:

x_k＝[SOC_mean,k,U_D,k,U_T,k]^T(7)

therein, SOC_mean,kRepresenting the average state of charge of the battery pack at the moment of the k node; u shape_D,kAnd U_T,kAnd the distribution voltage represents the polarization internal resistance of the battery pack at the moment of the k node.

g(x_k,u_k)＝U_oc(SOC_mean,k)-I_kR₀-U_D,k-U_T,k(9)

In the formula, f (x)_k,u_k) Is a function of the state of the average cell; g (x)_k,u_k) A measurement function for an average battery, i.e., an average battery model estimated terminal voltage value of the average battery; and delta t is sampling time, and 1s is taken, namely the frequency of estimating the average SOC of the battery pack by the average battery model is 1 HZ. Tau is_D，τ_TRespectively representing the active polarization internal resistance R of the battery_DC_DSum concentration polarization internal resistance R_TC_T；SOC_mean,kThe average state of charge of the battery pack at the k-node moment is the average SOC of all single batteries in the battery pack; u shape_D,kAnd U_T,kDistributing voltage for polarization internal resistance of the battery pack at the k-node moment; i is_kThe current value measured by the current sensor at the k node moment is obtained; u shape_oc(SOC_mean,k) Representing the open-circuit voltage of the battery at the time of the k node, η being the coulombic efficiency, taking 1 when discharging and less than 1 when charging, here taking 0.99, R₀Is the average internal resistance of the cell.

F (x) in the formula (8)_k,u_k) G (x) in (9)_k,u_k) For state vector x_kPartial differentiation is carried out and respectively takenAndthe parameter matrix for obtaining the average cell model is:

3) using the Rint model shown in fig. 3 as a differential battery model to equate the difference between the characteristics of the single battery in the battery pack and the overall characteristics of the battery pack, using the current value I of the battery pack measured by the current sensor, and the difference between the average voltage value and the single voltage measured by the voltage sensorAs shown in equation (13), and average state of charge SOC estimated by the average battery model_meanThe value is used as an input value and is combined with an EKF algorithm to estimate the SOC of the single battery in a low-frequency modeⁱAnd average state of charge SOC of battery pack_meanDifference Δ SOC therebetweenⁱAnd estimating the delta SOC of the difference battery modelⁱThe value is output to the controller.

In the Rint model of step S3, the relationship between the parameters is:

ΔSOCⁱrepresenting the average state of charge SOC of the ith single battery and the battery pack_meanA difference of (a);is represented at SOC_meanOpen circuit voltage U of nearby i-th single battery and average battery_ocThe difference is that, in the equilibrium state,value of and Δ SOCⁱHas a value ofA one-to-one correspondence relationship; Δ RⁱThe differential internal resistance of the ith single battery and the average internal resistance of the battery pack is represented;to differentiate the terminal voltage of the battery, theoretically with that of the ith cellAverage terminal voltage U with battery pack_meanDifference of (2)Equality (usually, there is an error because the difference of the polarization internal resistances is not considered in the difference model, and the difference of the polarization internal resistances is considered to greatly increase the complexity of the calculation, and the applied model is an approximate difference battery model), as shown in equation (13):

the EKF algorithm of the step 3), the state equation and the output equation are shown as the formula (3) and the formula (4).

The state vector in the EKF algorithm of step 3) can be expressed as:

showing the battery SOC and the average state of charge SOC of the battery pack of the ith monomer at the moment of k node_meanThe difference in (a).

In the formula,is a state function of the difference cell;a terminal voltage of the difference battery estimated for a measurement function of the difference battery, i.e., a difference battery model;representing the average state of charge SOC at equilibrium_meanNear the i-th cell open circuit voltage and the average cell pack open circuit voltage U_oc(SOC_mean) A difference of (a); Δ RⁱThe differential internal resistance of the ith single battery and the average internal resistance of the battery pack is represented; i is_kThe current value measured by the current sensor at the k node moment is obtained.

F (x) in formula (15)_k) G (x) in (16)_k) For state vector x_kPartial differentiation is carried out and respectively takenAnd

it is noted that at SOC_meanNear Δ SOC- Δ U_ocHas a one-to-one correspondence relationship between them, the formula (A)18) Is shown in SOC_meanNear Δ U_ocThe derivative value for Δ SOC may also be expressed as:

and 3) in the step 3), the frequency of the delta SOC estimated by the differential battery model is 0.01 HZ.

S2, calculating to obtain the difference electric quantity delta C between the electric quantity of the single battery and the average electric quantity of the battery pack by using the estimated value of the difference state of charge delta SOC between the single battery SOC and the average SOC of the battery pack obtained in the step S1 and combining the capacity parameter of the single battery;

in step S2, the calculation formula of the cell differential electric quantity Δ C obtained from the estimated value of the cell differential state of charge Δ SOC is:

ΔC_k＝C·ΔSOC_k

in the formula, C represents the current capacity of the battery cell, i.e., the total electric quantity of the current battery cell when the battery cell is fully charged, and is represented by Ah, and it can be considered that C is consistent with the initial capacity of the battery cell without considering the change of the battery capacity due to factors such as durability and temperature; delta SOC_kRepresenting the difference state of charge between the SOC of the single battery at the k-node moment and the average SOC of the battery pack; delta C_kAnd the difference electric quantity between the single battery electric quantity and the average electric quantity of the battery pack at the moment of the k node is represented.

S3, obtaining the change rate of the delta C by linear regression according to the estimated value of the differential electric quantity delta C of the battery monomer, and obtaining the average leakage current of the differential battery monomer in the period of time;

in step S3, a least square algorithm is used in the calculation method for obtaining the change rate of Δ C by linear regression;

in step S3, the Δ C change rate of the different battery cells and the average leakage current of the battery cells during the period are unified values, and the relationship therebetween is:

l represents the rate of change of Δ C; delta C_(n)Representing the value of the linear regression line at a later cutoff point within the measured time interval; delta C₍₁₎Represents the value of the linear regression line at its real point within the measured time interval; t is t_(n)Representing the end point of the measured time interval; t is t₍₁₎Representing a starting point of the measured time interval; i is_depleteIndicating the leakage current of the differential cell during the measured time period.

S4, diagnosing the approximate short-circuit resistance value of the internal short-circuit battery monomer by using the average leakage current of the different battery monomers and combining the average voltage in the period of time;

estimating the internal short circuit resistance value of the internal short circuit battery cell in the step S4 uses ohm' S law:

R_ISCthe estimated internal short circuit resistance value of the internal short circuit battery monomer; i is_depleteThe leakage current of the differential battery cell in the measured time interval is measured; u shape_meanThe average terminal voltage value of the battery pack in the measured time interval can be expressed as:

the terminal voltage value of the ith battery pack collected by the voltage sensor in the measurement time interval is measured, and n is the terminal voltage value of the battery pack collected by the voltage sensor in the measurement time intervalThe total number of values.

S5, judging whether the approximate short-circuit resistance value of the single battery estimated in the step S4 is larger than the preset short-circuit resistance value, if so, turning to the step S6, otherwise, turning to the step S7;

in this embodiment, the preset value in step S5 may be set to 200 Ω.

S6, judging the battery monomer to be a normal monomer by the battery management system;

and S7, the battery management system judges that the battery cell is an internal short circuit cell.

According to the process, the difference of the SOC of the battery monomer in the battery pack is identified by combining the frequency division model with the EKF, the approximate short-circuit resistance value of the internal short-circuit battery monomer is diagnosed by using the differential SOC delta SOC obtained by the method, the approximate short-circuit resistance value of the internal short-circuit battery monomer in the battery pack can be diagnosed on line and quantitatively with lower calculation amount, the internal short-circuit sign can be diagnosed in tiny hours, a reliable reference basis is provided for battery fault diagnosis, the probability of thermal runaway of the battery is reduced, and the use reliability of the battery pack is improved.

Claims (10)

1. A method for diagnosing the internal short circuit of a battery is used for obtaining the internal short circuit resistance value of a short circuit battery monomer in a battery pack, and is characterized by comprising the following steps:

1) acquiring the charge state difference of each battery monomer in the battery pack;

2) calculating the difference electric quantity of each single battery according to the charge state difference of the single batteries in the battery pack

3) Obtaining the change rate L of the difference electric quantity by adopting linear regression to obtain the average leakage current I of the battery monomer in the measurement time section_deplete；

4) According to the average leakage current I_depleteMeasuring the average terminal voltage value of the battery pack in the time section to obtain the approximate short circuit resistance value of each battery monomer in the battery pack;

5) comparing the approximate short-circuit resistance value of each single battery with a set short-circuit resistance value threshold, if the approximate short-circuit resistance value is larger than the short-circuit resistance value threshold, judging that the single battery is a normal single battery, and if the approximate short-circuit resistance value is smaller than or equal to the short-circuit resistance value threshold, judging that the single battery is a short-circuit single battery.

2. The method according to claim 1, wherein the step 1) specifically comprises the following steps:

11) the method comprises the steps that the overall characteristics of an average battery model equivalent battery pack are adopted, the current value of the battery pack and the average voltage value of the battery pack are used as input values, and the average charge state of the battery pack is estimated in a high-frequency mode according to an extended Kalman filter EKF algorithm;

12) the method comprises the steps of adopting a difference battery model to be equivalent to the difference between the characteristics of single batteries in a battery pack and the overall characteristics of the battery pack, taking a current value I of the battery pack, the difference value between the terminal voltage of the single batteries and the average terminal voltage of the battery pack and the average charge state value estimated by the average battery model as input values, and estimating the charge state difference of each single battery in a low-frequency mode according to an extended Kalman filter EKF algorithm.

3. The method according to claim 1, wherein the differential charge amount in step 2) is calculated by:

ΔC_k＝C·ΔSOC_k

wherein C is the current capacity of a single battery in the battery pack, delta SOC_kIs the differential state of charge, Δ C, between the cell SOC at time k and the average SOC of the battery pack_kThe difference electric quantity between the single battery electric quantity and the average electric quantity of the battery pack at the moment k is taken as the electric quantity.

4. The method according to claim 1, wherein in the step 3), the variation rate L of the differential charge is calculated as:

$L=\frac{{\mathrm{\ΔC}}_{\left(n\right)}-{\mathrm{\ΔC}}_{\left(1\right)}}{t_{\left(n\right)}-t_{\left(1\right)}}=I_{deplete}$

wherein, is_(n)Is the value of the linear regression line at the post-cut-off point within the measurement time interval, Δ C₍₁₎Is the value of the linear regression line at the starting point in the measurement time interval, t_(n)To measure the end point of a time interval, t₍₁₎Is the starting point of the measurement time interval.

5. The method according to claim 1, wherein in the step 4), the internal short circuit resistance value of the short-circuited battery cell in the battery pack is calculated by the following formula:

$U_{mean}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{U}_{pack}^i$

$R_{ISC}=\frac{U_{mean}}{I_{deplete}}$

wherein R is_ISCInternal short circuit resistance value, U, of a short circuit cell in a battery pack_meanTo measure the average terminal voltage value of the battery during the time interval,the terminal voltage value of the ith battery pack collected in the measurement time interval is measured, and n is the total terminal voltage value of the battery pack collected in the measurement time interval.

6. The method as claimed in claim 1, wherein the threshold value of the short circuit resistance set in step 5) is 200 Ω.

7. The method as claimed in claim 2, wherein in the step 11), the average cell model is a second-order RC model.

8. The method of claim 7, wherein the average cell model is expressed as:

U_mean＝U_oc(SOC_mean)-IR₀-U_D-U_T

wherein, U_meanTo average terminal voltage of the cell model, U_ocVoltage source, SOC, being a model of an average battery_meanIs the average state of charge of the battery, I is the battery current value, R₀Is internal resistance, U_DFor distributing voltage, U, for active polarisation of internal resistance_TAnd voltage distribution for concentration polarization internal resistance.

9. The method as claimed in claim 2, wherein the differential cell model in step 12) is a Rint model

10. The method of claim 9, wherein the differential cell model is expressed as:

${\mathrm{\ΔU}}_B^i={\mathrm{\ΔU}}_{oc}^i\left({\mathrm{\ΔSOC}}^i\right)-{\mathrm{I\ΔR}}^i$

wherein,in order to differentiate the terminal voltage values of the batteries,to be at SOC_meanOpen circuit voltage U of nearby i-th single battery and average battery_ocDifference, Δ SOCⁱIs the average state of charge SOC of the ith single battery and the battery pack_meanI is the battery current value, Δ RⁱThe difference internal resistance of the ith single battery and the average internal resistance of the battery pack.