CN107957560A

CN107957560A - A kind of lithium ion battery SOC algorithm for estimating based on equivalent circuit

Info

Publication number: CN107957560A
Application number: CN201711376573.4A
Authority: CN
Inventors: 方彦彦; 唐玲; 云凤玲; 栗敬敬; 崔义; 王琳舒; 黄倩
Original assignee: China Automotive Battery Research Institute Co Ltd
Current assignee: China Automotive Battery Research Institute Co Ltd
Priority date: 2017-12-19
Filing date: 2017-12-19
Publication date: 2018-04-24
Anticipated expiration: 2037-12-19
Also published as: CN107957560B

Abstract

The present invention provides a kind of lithium ion battery SOC algorithm for estimating based on equivalent circuit, including step:S1, at different temperature, obtains open-circuit voltage U_OCVWith the relation of SOC and temperature T, S2, establish equivalent-circuit model, obtains model parameter and the relation of SOC and temperature T, and S3, calculate SOC value under Current Temperatures T and time t, including simplifies voltage characteristic equation, and voltage characteristic equation is solved.The SOC methods of estimation of lithium ion battery provided by the invention, principle is simple, and estimated accuracy is high, is no more than 1% to the SOC estimated accuracies maximum deviation of lithium ion battery.

Description

A kind of lithium ion battery SOC algorithm for estimating based on equivalent circuit

Technical field

The invention belongs to detection field, and in particular to a kind of evaluation method of charge states of lithium ion battery.

Background technology

In recent years, global automobile quantity drastically rises, also increasing to the demand of the energy, while dirty caused by environment Dye is also more serious.New-energy automobile, especially electric automobile have become the developing direction of future automobile, but its development speed is still Restricted by power battery and its application technology.How to extend battery service life, improve battery energy efficiency and can It is that electric vehicle industrialization must solve the problems, such as by property, therefore study battery management technique there is very great meaning.

Power battery charged state (State of Charge) abbreviation SOC.The remaining capacity of lithium ion battery is that battery exists One of most important performance parameter in operational process, the estimation of remaining capacity is a very important link.For electric car For, the SOC of battery is estimated exactly, can not only improve cruising ability, can also extend battery life, improves security.

The content of the invention

For shortcoming existing for this area, the invention discloses a kind of lithium ion battery SOC based on equivalent circuit Algorithm for estimating, to estimate the SOC of battery exactly.

Realize that above-mentioned purpose technical solution of the present invention is：

A kind of lithium ion battery SOC algorithm for estimating based on equivalent circuit, including step:

S1, at different temperature, obtains open-circuit voltage U_OCVWith the relation of SOC and temperature T,

S2, establish equivalent-circuit model, obtains the relation of the model parameter and the SOC and temperature T, and the step is specific For

S21, establish three rank equivalent-circuit models, and the Ohmic resistance R of series connection is included in equivalent circuit₀With three RC units, Each RC units are made of resistance and capacitance in parallel；Determine the equivalent circuit terminal voltage U and open-circuit voltage U_OCVCharacteristic close System；

Ohmic internal resistance R in S22, the acquisition equivalent-circuit model₀With the relation of SOC and temperature T：Determine pulsed discharge Terminate the voltage characteristic of moment.

S222, obtain ohmic internal resistance R under temperature T₀With the relation of SOC

S223, obtain ohmic internal resistance R at other temperature₀With the relation of SOC

RC cell parameters R in S23, the acquisition equivalent-circuit model₁, C₁, R₂, C₂, R₃, C₃With the pass of SOC and temperature T System；

S231, the voltage U (t) for measuring the equivalent circuit after pulsed discharge terminates moment；

S232, obtain RC cell parameters R at identical temperature₁, C₁, R₂, C₂, R₃, C₃With the relation of SOC.

S233, the relation for obtaining parallel connection RC cell parameters R1, C1, R2, C2, R3, C3 and SOC at other temperature.

SOC value under the time t of S3, estimation Current Temperatures T and battery operation, including S31, simplified voltage characteristic equation, S32, solve voltage characteristic equation.

Wherein, in step S1, open-circuit voltage U under series of temperature T is obtained_OCVWith the relation of SOC, the temperature range of T for- 10~50 DEG C, SOC is at least nine value in the range of 0.1~0.9.

Further, the relation of open-circuit voltage UOCV and SOC under temperature T are expressed with five rank multinomials：

U_OCV=a₀+a₁SOC+a₂SOC²+a₃SOC³+a₄SOC⁴+a₅SOC⁵

Wherein Uocv represents battery open circuit voltage, and a0~a5 is multinomial coefficient, and is constant, and SOC is the charged of battery State.

Alternatively, T one group of U of acquisition per 4-8 DEG C when less than 10 DEG C_OCVWith the relation of SOC, every 8-12 when T is more than 10 DEG C DEG C obtain one group of U_OCVWith the relation of SOC.

Wherein, the step S21 is：

For three rank equivalent-circuit models, the characteristic equation of battery model is established：

Wherein, U₀For the ohmic internal resistance R₀The voltage at both ends, U₁~U₃For the voltage at three RC units both ends, I is Electric current；

Solution formula (1), the expression formula that can obtain equivalent circuit terminal voltage are：

Wherein, U₁(0)、U₂(0) and U₃(0) when being respectively that pulsed discharge (HPPC) timing starts, three RC units both ends Voltage initial value.

In step S22, pulsed discharge (HPPC) is existing for existing test method, pulse discharge time, electric current etc. Specification (such as according to Freedom battery testings handbook).

According to the structure of Fig. 2, pulsed discharge terminates moment, and the change of voltage is entirely by ohmic internal resistance R₀Produce. Therefore, ohmic internal resistance R₀Obtained using following formula：

In formula, U_LThe voltage jump terminated for pulsed discharge, I are impulse discharge current value.

Wherein, the step S22 is：

According to the voltage response curves that under temperature T, HPPC of the battery under different SOC is tested, calculated using formula (4) Obtain the ohmic internal resistance R under different SOC₀And R₀- SOC curves.The SOC value is at least nine numerical value in the range of 0.1~0.9. To R at this temperature₀- SOC curves carry out multinomial fitting, and the fitting of a polynomial formula is：

R₀=b₀+b₁SOC+b₂SOC²+b₃SOC³+b₄SOC⁴+b₅SOC⁵

Wherein R₀Represent ohmic internal resistance, b₀~b₅For multinomial coefficient, and it is constant, SOC is the state-of-charge of battery.

Pulsed discharge terminates moment, electric current zero, and circuit structure shown in Fig. 2 is zero input response, its voltage characteristic equation For：

Further, the step S231 is specially：

From the circuit structure of Fig. 2, after pulsed discharge terminates moment, the voltage vanishing at ohmic internal resistance both ends, but three The voltage at a RC units both ends will not vanishing.Therefore formula (3) is changed into：

In principle, using the nonlinear fitting instrument of mathematical software, directly voltage response curves can be intended according to formula (4) Close, obtain the parameter value of three RC units.But due in formula (4) there are exponential function, and the number of the capacitance in Fig. 2 structures Value kF from tens to hundreds of is differed, and therefore, is directly fitted using formula (5), it is difficult to fit procedure is controlled, simultaneously because intending Close parameter and be in denominator position, each interative computation, can introduce truncated error.Obtained result stability is poor.So will Formula (5) can be written as：

Wherein, c₁~c₃And d₁~d₃For with the relevant constant of RC cell parameters.

Wherein, the voltage characteristic equation after pulsed discharge being terminated moment in step S231 is determined as

Wherein, t_sIt is the time stood after pulsed discharge, c₁~c₃And d₁~d₃For with the relevant constant of RC cell parameters.

HPPC experiments include first carrying out pulsed discharge to battery, then stand.t_sTime zero when being end-of-pulsing, i.e. arteries and veins Time after impulse electricity.

Wherein, step S232 is：

According to the voltage response curves that under temperature T, battery is stood after the HPPC test of pulse electric discharge under different SOC, adopt The c under different SOC is obtained by nonlinear fitting with (6) formula₁~c₃And d₁~d₃Value.The SOC value is in the range of 0.1~0.9 At least nine numerical value, the RC cell parameters values under different SOC are calculated further according to following formula：

According to Ri the and Ci values under obtained different SOC, to R₁- SOC, R₂- SOC, R₃- SOC, C₁- SOC, C₂- SOC and C₃- The parameter list of SOC carries out cubic spline interpolation, obtains encrypted R₁- SOC, R₂- SOC, R₃- SOC, C₁- SOC, C₂- SOC and C₃- The parameter list of SOC.

Wherein, for the step S233 specifically, changing temperature T, repetition S232, obtains encrypted R at other temperature₁- SOC, R₂- SOC, R₃- SOC, C₁- SOC, C₂- SOC and C_3-The parameter list of SOC, establishes R₁、R₂、R₃、C₁、C₂And C₃With SOC and temperature Two-dimensional parameter network

Further, mathematical software is not used directly in the SOC value under calculating Current Temperatures T and time t in step S32 Solving Nonlinear Equation instrument solve the obtained nonlinearity equation of equivalent-circuit model, and by the way of program is write Solve, including：

I) SOC initial values are set as 0.9, calculate the terminal voltage value U of battery；

Ii the relative deviation of battery terminal voltage the value U* and U under current t) are calculated

Δ=| U-U* |/U；

Iii) if Δ >=0.001, make SOC value reduce 0.001, repeat i)~ii)；If Δ<0.001, then export this SOC Value, is the SOC value under Current Temperatures T and time t.

Due to having been obtained for formula (2) U_ocv、R₀、R₁、R₂、R₃、C₁、C₂And C₃Value under different SOC and temperature T, because This, step S31 is：

The expression formula of equivalent circuit terminal voltage is written as：

For Current Temperatures T and time t, then the U (t), U in formula (8)₁(0)、U₂(0) and U₃(0) and I is known quantity, And U_ocv、R₀、R₁、R₂、R₃、C₁、C₂And C₃Only related to SOC, then formula (8) can be write

Formula (9) is solved, you can obtain the SOC value under Current Temperatures T and time t.

The beneficial effects of the present invention are：

The present invention provides a kind of SOC methods of estimation of lithium ion battery.The principle of this method is simple, and estimated accuracy is high.Tool Body includes：

1st, SOC methods of estimation provided by the invention are no more than 1% to the SOC estimated accuracies maximum deviation of lithium ion battery.

2nd, SOC methods of estimation provided by the invention carry out nonlinear fitting in the RC cell parameters to equivalent-circuit model When, the parametric form of fitting is changed, the stability and speed of fitting can be effectively improved.

3rd, SOC methods of estimation provided by the invention obtain equivalent-circuit model RC cell parameters and SOC relation when, Polynomial fitting method is not used, and parameter list is established using Technique of Cubic Spline Interpolation, can effectively avoid fitting of a polynomial The deviation brought.

4th, the present invention provides SOC methods of estimation when solving equivalent circuit voltage characteristic equation, and direct solution is not non-linear Equation, is solved using the method for writing program, effectively improves solving precision, reduced and solve the time.

Brief description of the drawings

Fig. 1 is the flow chart of the method for estimation of the battery SOC of the invention based on equivalent circuit；

Fig. 2 is the circuit structure of equivalent circuit；

Fig. 3 solves the flow chart of formula (9) by the way of program is write.

Fig. 4 is the open-circuit voltage that fitting obtains and the relation of SOC.

Fig. 5 is the ohmic internal resistance that fitting obtains and the relation of SOC.

Fig. 6 to Figure 11 is respectively the parameter list of R1-SOC, R2-SOC, R3-SOC, C1-SOC, C2-SOC and C3-SOC.

Figure 12 contrasts for obtained SOC estimation and experiment value,

The deviation situation of Figure 13 estimation results.

Embodiment

Illustrate the present invention below by most preferred embodiment.Those skilled in the art institute it should be understood that, embodiment is only used for Illustrate rather than for limiting the scope of the invention.

In embodiment, unless otherwise instructed, means used are the means of this area routine.

Embodiment 1

The present embodiment combines the battery that a positive electrode is ternary material, exemplified by T=25 DEG C, using estimated below side Method, estimates its SOC.

Detailed process comprises the following steps：

S1, obtain the open-circuit voltage U_OCVWith the relation of the SOC and temperature T

Open-circuit voltage U of the battery obtained according to constant-current discharge at 25 DEG C of temperature under different SOC_ocv, the SOC value is At least nine numerical value in the range of 0.1~0.9.To the U at 25 DEG C_ocv- SOC curves carry out multinomial and intend fitting.

The fitting polynomial formulas is：

U_OCV=a₀+a₁SOC+a₂SOC²+a₃SOC³+a₄SOC⁴+a₅SOC⁵

Wherein U_ocvRepresent battery open circuit voltage, a₀~a₅For multinomial coefficient, and it is constant, SOC is the charged shape of battery State.

Fig. 4 is fitting as a result, obtained open-circuit voltage and the relation of SOC are：

U_OCV=3.3233+0.02455SOC-8.9131 × 10^-4SOC²

+1.6196×10^-5SOC³-1.2246×10^-7SOC⁴+3.3391×10^-10SOC⁵

S2, establish equivalent-circuit model, obtains the relation of the model parameter and the SOC and temperature T, which includes Following sub-step：

S21, establish three rank equivalent-circuit models, specifies the battery terminal voltage U and open-circuit voltage U_OCVCharacteristic relation.

For circuit diagram shown in Fig. 2, the characteristic equation of battery model is established：

U₀=IR₀

U=U_ocv-U₀-U₁-U₂-U₃

Wherein, U₀For the ohmic internal resistance R₀The voltage at both ends, U₁~U₃For the voltage at three RC units both ends, I is electricity Stream.

Solution formula (1), the expression formula that can obtain terminal voltage are：

Wherein, U₁(0)、U₂(0) and U₃(0) when being respectively that timing starts, the voltage initial value at three RC units both ends.

Ohmic internal resistance R in S22, the acquisition equivalent-circuit model₀With the relation of SOC and temperature T.

S221, determine that pulsed discharge terminates the voltage characteristic of moment.

Wherein, U_LThe voltage jump terminated for pulsed discharge, I are impulse discharge current value.

S222, obtain ohmic internal resistance R at certain identical temperature₀With the relation of SOC

According to the voltage response curves that at 25 DEG C of temperature, HPPC of the battery under different SOC is tested, using S221 institutes The ohmic internal resistance R under different SOC is calculated in the method for stating₀And R₀- SOC curves.The SOC value is 0.1,0.2,0.3,0.4, 0.5,0.6,0.7,0.8 with 0.9.To the R at 25 DEG C₀- SOC curves carry out following fitting of a polynomial：

R₀=b₀+b₁SOC+b₂SOC²+b₃SOC³+b₄SOC⁴+b₅SOC⁵

Fig. 5 is fitting result, and obtained ohmic internal resistance and the relation of SOC is：

R₀=2.5800-0.03058SOC-4.5770 × 10^-4SOC²

+1.6125×10^-6SOC³-8.6662×10^-8SOC⁴+5.0321×10^-10SOC⁵

RC cell parameters R in parallel in S23, the acquisition equivalent-circuit model₁, C₁, R₂, C₂, R₃, C₃With SOC and temperature T Relation.Include following sub-step：

S231, determine pulsed discharge terminate moment after voltage characteristic.

In principle, using the nonlinear fitting instrument of mathematical software, directly voltage response curves can be intended according to formula (4) Close, obtain the parameter value of three RC units.But due in formula (4) there are exponential function, and the number of the capacitance in Fig. 2 structures Value kF from tens to hundreds of is differed, simultaneously because fitting parameter is in denominator position, each interative computation, can introduce and block mistake Difference.Therefore, directly it is fitted using formula (5), it is difficult to fit procedure is controlled, obtained result stability is poor.So will Formula (5) is written as：

S232, obtain parallel connection RC cell parameters R at certain identical temperature₁, C₁, R₂, C₂, R₃, C₃With the relation of SOC.

According to the voltage response curves that at 25 DEG C of temperature, battery is stood after the HPPC experiment impulse electricities under different SOC, base The c under different SOC is obtained by nonlinear fitting in formula (6)₁~c₃And d₁~d₃Value.

The SOC value is 0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8 and 0.9.It is calculated not further according to following formula With the RC cell parameters values under SOC.The expression formula is：

According to the R under step difference SOC obtained above₁~R₃And C₁~C₃Value, to R₁- SOC, R₂- SOC, R₃- SOC, C₁- SOC, C₂- SOC and C_3-The parameter list of SOC carries out cubic spline interpolation, obtains encrypted R₁- SOC, R₂- SOC, R₃- SOC, C₁- SOC, C₂- SOC and C_3-The parameter list of SOC.

Parameter the result is shown in Fig. 6~11.

SOC value under S3, estimation Current Temperatures T and time t

The step includes following sub-step：

S31, simplify voltage characteristic equation

Due to having been obtained for formula (2) U_ocv、R₀、R₁、R₂、R₃、C₁、C₂And C₃Value under different SOC and temperature T, because This, formula (2) can be rewritten as：

Formula (9) is solved, you can obtain the SOC value under the time t of Current Temperatures T and battery operation.

S32, solve voltage characteristic equation

Formula (9) is a nonlinearity equation, is directly asked using the Solving Nonlinear Equation instrument of mathematical software Solution, can not obtain stable solving result, and it is longer to solve the time.There is bound in itself in view of SOC value, therefore using volume The mode of program writing solves formula (9), and specific flow is as shown in Figure 3.

I) SOC initial values are set as 0.9, the terminal voltage value U of battery is calculated according to formula (9)；

Ii) the relative deviation of battery terminal voltage the value U* and U under current t

Δ=| U-U* |/U；

Iii) if Δ >=0.001.Then make SOC value reduce 0.001, repeat i)~ii).If Δ<0.001, then export this SOC Value, is the SOC value under Current Temperatures T and time t.

Specific programming demonstration is following (only to list the program for solving nonlinear equation, each parameter and SOC in unlisted formula The program of relation)：

The overall process that this method is estimated from parameter acquiring to SOC is described in detail in the present embodiment.In practical applications, for Identical battery, the expression formula of all parameter acquisition procedure, that is, S1 and S2 and estimation procedure, which simplify process S31, only to be needed to hold Row once, obtains corresponding parameter value.Carry out only needing specifically to perform S32 steps during SOC estimations.

Implementation result：

Figure 12 is shown in the contrast of obtained SOC estimation and experiment value, and experiment test (experiment) and in advance is seen from figure Survey result (prediction) substantially completely to overlap, deviation situation is shown in Figure 13.Positive and negative maximum deviation is each about 0.6%.

Embodiment 2

Using the method with 1 system of embodiment, the temperature of other values is set, T obtains one group for every 5 DEG C when less than 10 DEG C U_OCVWith the relation of SOC, one group of U of every 10 DEG C of acquisitions when T is more than 10 DEG C_OCVWith the relation of SOC.

Obtained SOC estimation is contrasted with experiment value, its maximum deviation is no more than 1%.

More than embodiment be only the preferred embodiment of the present invention is described, not to the scope of the present invention into Row limits, on the premise of design spirit of the present invention is not departed from, technical side of this area ordinary skill technical staff to the present invention The all variations and modifications that case is made, should all fall into the protection domain that claims of the present invention determines.

Claims

1. a kind of lithium ion battery SOC algorithm for estimating based on equivalent circuit, it is characterised in that including step:

S2, establish equivalent-circuit model, obtains model parameter and the relation of SOC and temperature T, which is specially

S21, establish three rank equivalent-circuit models, and the Ohmic resistance R of series connection is included in equivalent circuit₀With three RC units, each RC Unit is made of resistance and capacitance in parallel, determines the equivalent circuit terminal voltage U and open-circuit voltage U_OCVCharacteristic relation；

Ohmic internal resistance R in S22, the acquisition equivalent-circuit model₀With the relation of SOC and temperature T：Determine that pulsed discharge terminates The voltage characteristic of moment, obtains ohmic internal resistance R under temperature T₀With the relation of SOC；

RC cell parameters R in S23, the acquisition equivalent-circuit model₁, C₁, R₂, C₂, R₃, C₃With the relation of SOC and temperature T；

S231, the voltage U (ts) for measuring the equivalent circuit after pulsed discharge terminates moment；

S232, obtain RC cell parameters R at identical temperature₁, C₁, R₂, C₂, R₃, C₃With the relation of SOC；

SOC value under the time t of S3, calculating Current Temperatures T and battery operation, including simplify voltage characteristic equation, it is special to voltage Property equation is solved.

2. lithium ion battery SOC algorithm for estimating according to claim 1, it is characterised in that in step S1, obtain a series of Open-circuit voltage U under temperature T_OCVWith the relation of SOC, the temperature range of T is -10~50 DEG C, SOC in the range of 0.1~0.9 extremely Few 9 values.

3. lithium ion battery SOC algorithm for estimating according to claim 2, it is characterised in that by open-circuit voltage under temperature T The relation of UOCV and SOC is expressed with five rank multinomials：

U_OCV=a₀+a₁SOC+a₂SOC²+a₃SOC³+a₄SOC⁴+a₅SOC⁵

Wherein Uocv represents battery open circuit voltage, and a0~a5 is multinomial coefficient, and is constant, and SOC is the state-of-charge of battery.

4. lithium ion battery SOC algorithm for estimating according to claim 1, it is characterised in that the step S21 is：

Wherein, U₁(0)、U₂(0) and U₃(0) when being respectively that pulsed discharge timing starts, the voltage initial value at three RC units both ends.

5. lithium ion battery SOC algorithm for estimating according to claim 1, it is characterised in that the step S22 is：

According to the voltage response curves that under temperature T, HPPC of the battery under different SOC is tested, using formula

Wherein, U_LThe voltage jump terminated for pulsed discharge, I are impulse discharge current value,

The ohmic internal resistance R under different SOC is calculated₀And R₀- SOC curves.The SOC value is at least 9 in the range of 0.1~0.9 A numerical value.To R at this temperature₀- SOC curves carry out multinomial fitting, and the fitting of a polynomial formula is：

R₀=b₀+b₁SOC+b₂SOC²+b₃SOC³+b₄SOC⁴+b₅SOC⁵

6. lithium ion battery SOC algorithm for estimating according to claim 1, it is characterised in that put pulse in step S231 Voltage characteristic equation after electricity terminates moment is determined as

Wherein, t_sBe end-of-pulsing electric discharge after time of repose, c₁~c₃And d₁~d₃For with the relevant constant of RC cell parameters.

7. lithium ion battery SOC algorithm for estimating according to claim 6, it is characterised in that step S232 is：

According to the voltage response curves that under temperature T, battery is stood after the HPPC test of pulse electric discharge under different SOC, using (6) Formula obtains the c under different SOC by nonlinear fitting₁~c₃And d₁~d₃Value, the SOC value in the range of 0.1~0.9 extremely Few 9 numerical value, the RC cell parameters values under different SOC are calculated further according to following formula：

According to the R under obtained different SOC_iAnd C_iValue, to R₁- SOC, R₂- SOC, R₃- SOC, C₁- SOC, C₂- SOC and C₃- SOC's Parameter list carries out cubic spline interpolation, obtains encrypted R₁- SOC, R₂- SOC, R₃- SOC, C₁- SOC, C₂- SOC and C₃- SOC's Parameter list.

8. lithium ion battery SOC algorithm for estimating according to claim 1, it is characterised in that

For the step S233 specifically, changing temperature T, repetition S232, obtains encrypted R at other temperature₁- SOC, R₂- SOC, R₃- SOC, C₁- SOC, C₂- SOC and C_3-The parameter list of SOC, establishes R₁、R₂、R₃、C₁、C₂And C₃With SOC and the two-dimensional parameter of temperature Network.

9. lithium ion battery SOC algorithm for estimating according to claim 1, it is characterised in that calculated currently in step S32 Solved during SOC value under temperature T and time t by the way of program is write, including：

Δ=| U-U* |/U；

Iii) if Δ >=0.001, make SOC value reduce 0.001, repeat i)~ii)；If Δ<0.001, then this SOC value is exported, SOC value as under Current Temperatures T and time t.

10. lithium ion battery SOC algorithm for estimating according to claim 4, it is characterised in that in step S31, equivalent circuit The expression formula of terminal voltage is written as：

For temperature T and time t, then the U (t), U in formula (8)₁(0)、U₂(0) and U₃(0) and I is known quantity, and U_ocv、R₀、 R₁、R₂、R₃、C₁、C₂And C₃Only related to SOC, then formula (8) can be write