CN107367692A - A kind of least square method lithium battery model parameter identification method with forgetting factor - Google Patents
A kind of least square method lithium battery model parameter identification method with forgetting factor Download PDFInfo
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- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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Abstract
The invention discloses a kind of least square method lithium battery model parameter identification method with forgetting factor, including Step 1: establish Order RC equivalent-circuit model；Step 2: carry out the difference equation that bilinear transformation draws the input of equivalent-circuit model system and system output；Step 3: establish band forgetting factorLeast square method of recursion；Step 4: establish coefficient equation；Step 5: the parameter of collection battery；Step 6: pick out the parameter of equivalent-circuit model.The present invention carries out Identifying Dynamical Parameters using OCV SOC functional relations and with forgetting factor least squares algorithm to Order RC equivalent-circuit model, forgetting factor is introduced in conventional least square method of recursion, alleviate the problem of legacy data is superimposed in computing recursive process, overcome " data saturation " phenomenon.
Description
Technical field
The present invention relates to field of batteries, more particularly to a kind of least square method lithium battery model parameter with forgetting factor is distinguished
Knowledge method.
Background technology
The internal chemical reaction of lithium ion battery charge and discharge process is complex, therefore this process is time-varying and non-linear
, thus the parameter that model is obtained by theory analysis is highly difficult.Although have at present using offline exponentially fitted method
Model parameter has been picked out, but due to the time variation of battery system, with factors such as battery SOC, ambient temperature, cycle-indexes
Change, its model parameter can also have greatly changed, therefore in order to improve SOC estimated accuracy, the adaptation of strengthening system
Ability is, it is necessary to battery model on-line parameter identification and make real-time amendment.Parameter Estimation is in situation known to model structure
Under, a kind of mathematical method of model parameter is determined by the data of collection.By building the model structure of lithium ion battery, knot
Lithium ion battery OCV-SOC relation curves are closed, method the most frequently used at present is least squares identification theory, can using the theory
Recognized with the Order RC equivalent circuit model parameter to battery.
Least square method of recursion is a kind of discrimination method for being readily appreciated that and grasping, and implements also fairly simple, big portion
In the case of point, least square method of recursion can provide the parameter identification result with accurate statistics characteristic.Simply in parameter identification
In, least square method of recursion is the algorithm for having infinite memory length, and for battery system, least square method is in recursive operation mistake
Legacy data is more and more in journey, can cause the characteristic for the reaction new data that recursion result can not be well.
The content of the invention
It is an object of the invention to provide a kind of least square method lithium battery model parameter identification method with forgetting factor,
In most cases, least square method of recursion can provide the parameter identification result with accurate statistics characteristic, simply in parameter
In identification, least square method of recursion is the algorithm for having infinite memory length, and for battery system, least square method is transported in recursion
Legacy data is more and more during calculation, can cause the characteristic for the reaction new data that recursion result can not be well, and introduce forget because
Son can effectively overcome " data saturation " phenomenon.
To achieve the above object, technical scheme provided by the invention is：A kind of least square method lithium electricity with forgetting factor
Pool model parameter identification method, comprises the following steps：
Step 1, establishes Order RC equivalent-circuit model, and the expression formula of the equivalent-circuit model is
By being to the Laplace's equation that equivalent-circuit model is obtained after expression formula progress discretization
Step 2, bilinear transformation is carried out to the equivalent-circuit model Laplace's equation of step 1, draws equivalent circuit
Model system inputs is with the difference equation of system output
Wherein I (k) inputs for system, and y (k) exports for system,
θ=[a1 a2 a3 a4 a5], a2, a3, a4, a5 are corresponding constant coefficient；
Step 3, establish the least square method of recursion with forgetting factor λ
Wherein It is observation at this moment
Size, observation actual as system y (k+1), y (k+1) withJust it is prediction error after subtracting each other, typically
Can be arbitrary value, P (0)=α I, α, which tries one's best, to be taken greatly, and I is unit battle array；
Step 4, establish coefficient equation
Wherein T is the sampling period；
Step 5, gather the parameter of battery, with sampling period T come gather the terminal voltage V (k) of battery, end electric current I (k), end
Voltage V (k-1), end electric current I (k-1), battery charge state SOC (k-1) and terminal voltage V (k-2), end electric current I (k-2)；Calculate
Voc(k)-V (k), to obtain the input Φ (k) in identification process, system output y (k).
Step 6, θ (0), P (0) and forgetting factor λ are initialized, the parameter and step gathered according to step 5
Three least square method of recursion obtains the θ values of step 2, and θ values are substituted into the coefficient equation and then obtain the left side in coefficient equation
Coefficient, that is, pick out the parameter of equivalent-circuit model.
Preferably, the sampling period T=1s of the step 4, SOC (0)=90%.
Preferably, the θ (0) in the step 6 is arbitrary value, P (0)=α I, α=5000, λ=0.96.
Beneficial effect of the present invention is using OCV-SOC functional relations and with forgetting factor least squares algorithm to Order RC etc.
Imitate circuit model and carry out Identifying Dynamical Parameters, introduce forgetting factor in conventional least square method of recursion, alleviate and passed in computing
The problem of legacy data is superimposed during pushing away, overcomes " data saturation " phenomenon.
Brief description of the drawings
Fig. 1 is the Order RC model of lithium battery.
Fig. 2 is different multiplying constant current intermittent discharge OCV-SOC curves.
Embodiment
1 embodiment of the invention is introduced to accompanying drawing 2 referring to the drawings.
A kind of least square method lithium battery model parameter identification method with forgetting factor, comprises the following steps：
Step 1, establishes Order RC equivalent-circuit model, and the expression formula of the equivalent-circuit model is
It is discrete to (1) formula by the Laplace's equation to obtaining equivalent-circuit model after expression formula progress discretization
Change, solving state equation is：
Wherein：
Battery model Laplace's equation such as following formula can be obtained by formula (2) (3).
Step 2, bilinear transformation progress discretization is carried out to the equivalent-circuit model Laplace's equation (6) of step 1,
OrderThe transmission function of discretization can be obtained：
Show that equivalent-circuit model system inputs and the difference equation of system output is
Wherein I (k) inputs for system, and y (k) exports for system,
θ=[a1 a2 a3 a4 a5], a2, a3, a4, a5 are corresponding constant coefficient；
Step 3, the least square method of recursion with forgetting factor λ is established,
If k moment sensor samples error is e (k), then：
WillN-dimensional is expanded to, k=1,2 ... N+n, n=2, following formula can be obtained：
Take functional J (θ)：
Because principle of least square method is J (θ) is taken minimum value, institute is in the hope of J (θ) extreme value, order：
It can obtain：
Recursive operation is carried out to the process of above-mentioned (9)-(13), that is, obtains formula (14),
It is the reference value estimated by last moment system,It is the big of observation at this moment
Small, actual as system y (k+1) observation, withJust it is prediction error after subtracting each other, by prediction error with increasing
Beneficial item K (k+1) is multiplied, and is the correction of predicted value this moment, finally obtains this moment optimal estimationSymbol must be provided
Conjunction conditionWith P (0), gain term K (k+1) could be obtained, and then starts least square method, typicallyCan be any
Value, P (0)=α I, α, which tries one's best, to be taken greatly, and I is unit battle array.
Least square method of recursion is the algorithm for having infinite memory length, and for battery system, least square method is in recursion
The more and more characteristics that can cause reaction new data that recursion result can not be well of legacy data in calculating process, to avoid above-mentioned feelings
Condition, forgetting factor λ, 0 ＜ λ ＜ 1 are introduced, i.e.,：
P-1(k+1)=λ P-1(k)+Φ(k+1)ΦT(k+1) (16)；
So even if (N+1) is very big, P (N+1) also tends not to 0, effectively overcomes " data saturation " phenomenon.Band is forgotten
The step of factor least-squares algorithm is：
It is common least square method as λ=1, the smaller ability of tracking of λ is stronger, but fluctuates also bigger, typically takes 0.95<
λ<1。
Step 4, coefficient equation is established, according to the sampled measurements information of system, sampling period T=1s, SOC (0)=
90%.The structure and unknown parameter of battery eliminator model are estimated, is made：Formula (18) is substituted into (7)
Formula, it can obtain：
It can be obtained by the coefficient correspondent equal of (6) (19)：
Wherein T is the sampling period, and the coefficient on the right of this formula can be obtained by least square method of recursion, and the left side is model
Unknown parameter.
Step 5, gather the parameter of battery, with sampling period T come gather the terminal voltage V (k) of battery, end electric current I (k), end
Voltage V (k-1), end electric current I (k-1), battery charge state SOC (k-1) and terminal voltage V (k-2), end electric current I (k-2)；Calculate
Voc(k)-V (k), to obtain the input Φ (k) in identification process, system output y (k).
Step 6, θ (0), P (0) and forgetting factor λ being initialized, θ (0) is arbitrary value, P (0)=α I, α=
5000, λ=0.96.The parameter and the least square method of recursion of step 3 that are gathered according to step 5 obtain the θ values of step 2, will
θ values substitute into the coefficient equation coefficient for then obtaining the left side in coefficient equation, try to achieve R, Rs, Rp, Cp, Cs, that is, pick out equivalent
The parameter of circuit model, and then Mobile state, real-time update can be entered to battery model parameter according to self-defined operating mode.
The present invention is by taking such as Fig. 1 Order RC equivalent-circuit model as an example, while application such as Fig. 2 OCV-SOC curves, normal
Forgetting factor is introduced in least square method of recursion, alleviates the problem of legacy data is superimposed in computing recursive process, overcomes
" data saturation " phenomenon.
Fig. 2 is that the charge-discharge test of ternary lithium ion battery is carried out under 25 degrees Celsius of constant temperatures, is marked respectively
Determine the OCV-SOC curves under the conditions of 0.2C, 0.3C, 0.4C, 0.5C, 0.6C, 0.75C, 1C constant current intermittent discharge.
Setting and operating procedure of the following table for OCV-SOC calibration experiments.
Every group of demarcating steps are as follows：
1. battery is charged by the way of first constant current (0.2C) afterwards constant pressure (blanking voltage 4.25V)；
2. constant current is carried out to battery, constant volume amount (260mAh) is discharged；
3. electric discharge terminates, one hour is stood to treat that polarity effect disappears；
2. 3. 4. repeat step, terminates to battery discharge.
It is described above to be not intended to limit the scope of the present invention, it is all according to the technology of the present invention essence, to the above
Embodiment any modification, equivalent variations and the modification made, in the range of still falling within technical scheme.
Claims (3)
1. a kind of least square method lithium battery model parameter identification method with forgetting factor, it is characterised in that including following step
Suddenly：
Step 1, establishes Order RC equivalent-circuit model, and the expression formula of the equivalent-circuit model is
By being to the Laplace's equation that equivalent-circuit model is obtained after expression formula progress discretization
Step 2, bilinear transformation is carried out to the equivalent-circuit model Laplace's equation of step 1, draws equivalent-circuit model
System inputs is with the difference equation of system output
Y (k)=E (k)-U (k)
=a1y(k-1)+a2y(k-2)+a3I(k)+a4I(k-1)+a5I(k-2)；
Wherein I (k) inputs for system, and y (k) exports for system,
θ[a1 a2 a3 a4 a5], a2, a3, a4, a5 are corresponding constant coefficient；
Step 3, establish the least square method of recursion with forgetting factor λ
WhereinIt is the reference value estimated by last moment system,It is the size of observation at this moment, y
(k+1) observation actual as system, y (k+1) withJust it is prediction error after subtracting each other, typicallyCan be to appoint
Meaning value, P (0)=α I, α, which tries one's best, to be taken greatly, and I is unit battle array；
Step 4, establish coefficient equation
Wherein T is the sampling period；
Step 5, gather the parameter of battery, with sampling period T come gather the terminal voltage V (k) of battery, end electric current I (k), terminal voltage
V (k-1), end electric current I (k-1), battery charge state SOC (k-1) and terminal voltage V (k-2), end electric current I (k-2)；Calculate Voc
(k)-V (k), to obtain the input Φ (k) in identification process, system output y (k).
Step 6, θ (0), P (0) and forgetting factor λ are initialized, the parameter and step 3 gathered according to step 5
Least square method of recursion obtains the θ values of step 2, θ values are substituted into the coefficient equation then obtain the left side in coefficient equation be
Number, that is, pick out the parameter of equivalent-circuit model.
2. a kind of least square method lithium battery model parameter identification method with forgetting factor according to claim 1, its
It is characterised by, the sampling period T=1s of the step 4, SOC (0)=90%.
3. a kind of least square method lithium battery model parameter identification method with forgetting factor according to claim 1, its
It is characterised by, the θ (0) in the step 6 is arbitrary value, P (0)=α I, α=5000, λ=0.96.
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| CN108072847A (en) * | 2018-01-29 | 2018-05-25 | 西南交通大学 | A kind of method of estimation of dynamic lithium battery identification of Model Parameters and remaining capacity |
| CN109633456A (en) * | 2019-01-22 | 2019-04-16 | 武汉大学 | A kind of dynamic lithium battery group SOC estimation method based on segmentation voltage identification method |
| CN109726501A (en) * | 2019-01-11 | 2019-05-07 | 武汉理工大学 | RLS lithium battery model parameter on-line identification method based on variable forgetting factor |
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