CN104267354A - Peak power prediction method for power battery - Google Patents

Peak power prediction method for power battery Download PDF

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CN104267354A
CN104267354A CN201410592570.4A CN201410592570A CN104267354A CN 104267354 A CN104267354 A CN 104267354A CN 201410592570 A CN201410592570 A CN 201410592570A CN 104267354 A CN104267354 A CN 104267354A
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battery
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fractional order
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CN104267354B (en
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朱春波
李晓宇
魏国
裴磊
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Harbin Institute of Technology
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Harbin Institute of Technology
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Abstract

The invention discloses a peak power prediction method for a power battery, relates to a peak power prediction technology for the power battery, and aims to improve the peak power prediction accuracy for the power battery. The method disclosed by the invention comprises the following two parts: A, parameter online estimation based on a simplified electrochemical impedance spectrum equivalent circuit model and fractional order combined kalman filtering; B, a battery peak power prediction method based on decomposition of zero-state response and zero-input response. According to the invention, the simplified impedance spectrum model comprising a fractional order component is selected as a reference model for the battery peak power prediction, so that the peak power prediction method based on the model not only can accurately predict short-time peak output power of the battery, but also can accurately predict the peak power output capacity of the battery within a longer time period. The peak power prediction method is suitable for online peak power prediction of an electric car.

Description

A kind of peak power Forecasting Methodology of electrokinetic cell
Technical field
The present invention relates to the peak power forecasting techniques of electrokinetic cell.
Background technology
The content of the Forecasting Methodology of batteiy peak power disclosed in domestic patent is less, has the method that some electrokinetic cell peak powers are predicted in paper periodical both domestic and external.
These methods mostly adopt the single order RC equivalent-circuit model of battery, using the restrictive condition that SOC, terminal voltage, electric current are predicted as peak power, early stage power forecasting method adopts the prediction of off-line battery model supplemental characteristic complete battery pair output/feedback peak power, but battery is along with change that the is aging or environment such as temperature, operating mode, model parameter also can change thereupon, therefore, the power estimation method reliability based on off-line model supplemental characteristic is poor;
In the up-to-date paper delivered, battery model supplemental characteristic is obtained online by method for parameter estimation, effectively can improve the accuracy of estimation, but due to the error of single order RC model self comparatively large, it is effective that power prediction can only be confined in the shorter time.
In order to reduce state equation for discretization error during power prediction, less time discretization interval (as get the time interval be 1s or 0.1s) is adopted in paper, by the method for recurrence calculation, obtain battery the peak power predicted value at 10s place or predicted value at 60s place after current time, the shortcoming of this method there is a large amount of recurrence calculation, poor real.This method also cannot be improved the power caused due to model oneself error and estimates inaccurate problem in addition.
Summary of the invention
The present invention is the peak power forecasting reliability in order to improve electrokinetic cell, reduces calculated amount, thus provides a kind of peak power Forecasting Methodology of electrokinetic cell.
A peak power Forecasting Methodology for electrokinetic cell, it is realized by following steps:
The step of steps A, battery model parameter On-line Estimation, is specially:
Steps A 1, when to secondary cell modeling, due to electric automobile operating condition frequency characteristic, the impedance operator of the medium frequency therefore in battery electrochemical impedance spectrum model can be reduced to purely resistive element R by the purely resistive element R commonly used and normal phase element Q parallel circuit and describe, the battery electrochemical impedance spectrum equivalent-circuit model after being simplified;
Electrochemical impedance spectroscopy equivalent-circuit model after this simplification comprises open-circuit voltage OCV e, ohmic internal resistance R owith weber impedance Z w;
Electrochemical impedance spectroscopy equivalent-circuit model after steps A 2, the simplification that obtains according to steps A 1 sets up state equation needed for fractional order Kalman filter and observation equation, is specially:
Get the total current I flowing through secondary cell ldischarge time be on the occasion of, data sampling period is 1s;
Δ r = d r dt r , r > 0
Wherein △ rfor differentiating operator, r is differential order, when r is decimal, and △ rrepresent fractional order differential operator, when r is integer, △ rfor integer differentiating operator;
Get fractional order element Z wbe both end voltage be U wquantity of state, have:
Δ 0.5 U W = 1 W I L = X W I L
For battery model parameter, diffusion parameter X w, open-circuit voltage OCV ewith ohmic internal resistance R oalong with the change of battery charge state (SOC) is slowly, therefore:
Δ 1 X W ≈ 0 Δ 1 OCV e ≈ 0 Δ 1 R o ≈ 0
Above-mentioned four equations are rewritten as matrix form, obtain the state equation of fractional order Kalman integrated filter:
Δ 0.5 1 1 1 U W X W OCV e R o = 0 I L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U W X W OCV e R o ;
Get U lfor the observed quantity of system, then have:
U L=OCV e-I LR o-U W
I lrepresent and the total current flowing through battery;
Get:
x = U W X W OCV e R o , N = 0.5 1 1 1 , y=U L
Obtain the observation equation of fractional order Kalman integrated filter:
Δ N x = 0 I L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x y = - 1 0 1 - I L x
After this equation discretize, have:
Δ N x k = 0 I L , k - 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x k - 1 + w y k = - 1 0 1 - I L , k x k + v
Wherein, w, v represent state-noise and the observation noise of system respectively;
Define (being also called the definition of Gr ü nwald-Letnikov fractional order differential) according to the progression of fractional order differential:
Δ N x k + 1 = Σ j = 0 k ( - 1 ) j N j x k - j
Wherein,
N j = diag [ 0.5 j 1 j 1 j 1 j ] ,
r j = 1 forj = 0 r ( r - 1 ) . . . ( r - j + 1 ) / j ! forj > 0 ,
Separately get: γ j = N j , The discretize recursion expression-form of Fractional Differential Equation is obtained by above formula:
Definition:
A k - 1 = ∂ f ( x k - 1 , I L , k - 1 ) ∂ x k - 1 | x k - 1 = x ^ k - 1 + = 0 I L , k - 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ,
C k = ∂ g ( x k , I L , k ) ∂ x k | x k = x ^ k - = - 1 0 1 - I L , k
According to the progression definition of fractional order differential, wherein: calculated amount the increase along with the time is constantly increased, this situation is not suitable for engineer applied, for this reason, above formula is rewritten as form below:
Σ j = 1 k ( - 1 ) j γ j x k + 1 - j = Σ j = 1 L ( - 1 ) j γ j x k + 1 - j , k ≤ 64 , L = k k > 64 , L = 64
Steps A 3, the state equation needed for fractional order Kalman filter utilizing steps A 2 to build and observation equation, carry out time renewal and measurement updaue to state, parameter and covariance matrix according to fractional order federated Kalman filtering algorithm:
Be specially:
Initialization:
x ^ 0 = E [ x ] , P 0 + = E [ ( x - x ^ 0 ) ( x - x ^ 0 ) T ]
Wherein, E [x] represents the mathematical expectation of x, is experience preset value when method calculates, represent the estimated value of x at initial time (k=0), represent the estimated value of x at the noise covariance of initial time (k=0);
The time of state, parameter and covariance matrix upgrades:
x ^ k - = f ( x ^ k - 1 + , I L , k - 1 )
P k - = ( A k - 1 + γ 1 ) P k - 1 + ( A k - 1 + γ 1 ) T + Q + Σ j = 2 L γ j P k - j + γ j T
Wherein, Q knoise w kcovariance, for k moment state and model parameter x kpredicted value, for k-1 moment state and model parameter x k-1modified value, for the noise covariance matrix P of k moment x kpredicted value, for the noise covariance matrix P of k-1 moment x k-1modified value;
The measurement updaue of state, parameter and covariance matrix:
L k = P k - ( C k ) T [ C k P k - ( C k ) T + R k ] - 1
x ^ k + = x ^ k - + L k x [ y k - g ( x ^ k - , I L , k ) ]
P k + = ( I - L k C k ) P k -
Wherein, R knoise v kcovariance, L kit is k moment Kalman filter gain size;
The terminal voltage U of steps A 4, collection battery lwith the total current I flowing through secondary cell l, the state equation needed for fractional order Kalman filter after the electrochemical impedance spectroscopy equivalent-circuit model after the simplification utilizing steps A 1 to obtain and steps A 3 upgrade and observation equation, obtain open-circuit voltage OCV e, ohmic internal resistance R o, diffusion parameter X westimated value, by obtain open-circuit voltage OCV e, ohmic internal resistance R o, diffusion parameter X westimated value as the estimated result of battery, the secondary cell completed based on fractional order federated Kalman filtering simplifies impedance spectrum model parameter On-line Estimation;
Step B, the battery model parameter On-line Estimation result obtained according to steps A, carry out the step of power prediction:
The weber impedance Z of step B1, derivation fractional order element wwhether be linear time invariant element:
If the both end voltage U of fractional order element winitial value be 0, when applying amplitude is I lstep current excitation time, the both end voltage U of fractional order element wvoltage responsive situation after Ns is calculated as follows, and N is positive number:
If the open-circuit voltage OCV of battery model e, ohmic internal resistance R o, diffusion parameter X win power prediction process, numerical values recited is constant;
Then U wvoltage responsive when k=1s is:
U ^ W , 1 = X ^ W , 0 I L - ( - 1 ) 1 0.5 1 U W , 0
Wherein, symbol ^ represents predicted value;
U wvoltage responsive when k>=2 is:
U ^ W , k + 1 = X ^ W , 0 I L - Σ j = 1 L ( - 1 ) j 0.5 j U ^ W , k + 1 - j + w
Calculate:
U ^ W , 1 = X ^ W I L
U ^ W , 2 = X ^ W , 0 I L - ( ( - 1 ) 1 0.5 1 U ^ W , 1 + ( - 1 ) 2 0.5 2 U W , 0 )
After calculating:
U ^ W , 2 = 1.5 X ^ W , 0 I L
Recursion obtains the voltage responsive at 10s and 60s place and is thus:
U ^ W , 10 = 3.524 X ^ W , 0 I L
U ^ W , 60 = 8.722 X ^ W , 0 I L
Thus, as battery model parameter X wconstant or when slowly changing, output valve U wwith I lfor linear relationship, infer fractional order element Z wfor linear time invariant element;
Then, the power forecasting method of fractional order element is:
In order to predict the voltage responsive of fractional order element at k+ Δ Ts place this voltage responsive is divided into zero state response and zero input response
U ^ W , k + ΔT = U ^ W , k + ΔT zs + U ^ W , k + ΔT zi
Wherein zero state response is:
U ^ W , k + ΔT zs = a X ^ W , k I max
For the k+10s moment, a=3.524; For the k+60s moment, a=8.722;
Zero input response determined by the data before the k moment, get length L=60 time memory of fractional order differential;
The zero input response in k+1 moment is:
U ^ W , k + 1 zi = - Σ j = 1 L ( - 1 ) j 0.5 j U ^ W , k + 1 - j zi
Recursion can obtain the input voltage response of k+ Δ T moment fractional order element place zero thus:
U ^ W , k + ΔT zi = Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j
Wherein, battery model fractional order element Z wthe estimated value of two ends terminal voltage between (k+1-L) ~ k moment, when the prediction k+10 moment, b=α, α are one group of constant coefficient matrix;
When the prediction k+60 moment, b=β, β are other one group of constant coefficient matrix;
Thus, can obtain battery constant-current discharge electric current is I maxtime battery in the terminal voltage predicted value in k+ Δ T moment:
U ^ L , k + 10 = OCV ^ e , k + ΔT + I L R ^ o + U ^ W , k + ΔT zi + U ^ W , k + ΔT zs ;
The method of electric discharge peak value power prediction is:
If battery charge state (SoC or SOC) is the restrictive condition of battery limit duty, SoC minbe the minimum value that battery discharge stops state-of-charge, then obtain maximum discharge current value now:
I max , SoC = ( So C k - SoC min ) × Capacity ΔT
Capacity is battery capacity value, and unit is ampere * hour (Ah), SoC kfor the battery charge state in k moment, SoC minfor the minimum state-of-charge that battery discharge limits, the minimum state-of-charge adopted as certain power battery for hybrid electric vehicle is SoC min=30%;
If battery terminal voltage U lfor the restrictive condition of battery limit duty, if now with maximum discharge current I maxto battery discharge, battery model parameter OCV ein the predicted value in k+ △ T moment be:
OCV ^ e , k + ΔT = OCV ^ e , k + I max × OCV k + ΔT , I max - OCV k I max lim
In above formula, for the battery model parameter OCV calculated by fractional order federated Kalman filtering algorithm ein the estimated value in k moment, for OCV ein the predicted value in k+ △ T moment; I maxbeing in terminal voltage as maximum discharge current value during battery limit duty restrictive condition, is value to be solved, it is the maximum discharge current of battery; OCV kbe the battery open circuit voltage values in the k moment, can be calculated by OCV (SoC) pre-defined function and obtain, it has been generally acknowledged that OCV and SoC has clear and definite corresponding relation; The funtcional relationship of the pre-defined function of OCV and SoC can be obtained by handbook of batteries or test; for battery is in the k+ △ T moment, assuming that with battery open circuit voltage values corresponding during constant-current discharge, can be calculated by OCV (SoC) pre-defined function equally and obtain; Due in most cases, the change of OCV is all less and slowly, therefore can think open circuit voltage variations amount within the △ T period and discharge current linear;
And then calculate, suppose that battery is I at discharge current maxtime, the estimated value U of battery terminal voltage l, k+ △ T:
U L , k + ΔT = OCV ^ e , k + I max OCV ( SoC k - I max lim × ΔT Capacity ) - OCV ( SoC k ) I max lim - I max R ^ o - a I max X ^ W , k - Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j
Wherein, the estimated value of terminal voltage be k moment open-circuit voltage estimated value, open circuit voltage variations value, ohmic internal resistance voltage difference, fractional order element Z in the △ T period wzero state response magnitude of voltage, zero input response magnitude of voltage sum;
Release thus, when with terminal voltage U lduring constraint condition as the extreme working position of battery, the maximum operating currenbt of battery is:
I max , U L = U min lim - OCV ^ e , k + Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j OCV ( SoC k - I max lim × ΔT Capacity ) - OCV ( SoC k ) I max lim - R ^ o - X ^ W , k
The k+ Δ T moment, when reaching crest discharge power, considers above-mentioned restrictive condition, and maximum discharge current value is:
I max = min ( I max , SoC , I max , U L , I max lim )
The crest discharge power in k+ Δ T moment is:
P ^ peak , k + ΔT dis = I max OCV ^ e , k + I max OCV ( SoC k - I max lim × ΔT Capacity ) - OCV ( SoC k ) I max lim - I max R ^ o - a I max X ^ W , k - Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j
The Forecasting Methodology of the feedback current peak power of battery and the Forecasting Methodology of above-mentioned discharge power be in like manner:
If I lfor on the occasion of;
If SoC is the restrictive condition of battery limit duty, SoC maxbe the maximum SOC of battery, then obtain minimum feedback current value now:
I min , SoC = ( SoC k - SoC max ) × Capacity ΔT
If U lfor the restrictive condition of battery limit duty, then obtain minimum feedback current value now:
I min , U L = U max lim - OCV ^ e , k + Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j OCV ( SoC k - I min lim × ΔT Capacity ) - OCV ( SoC k ) I min lim - R ^ o - X ^ W , k
The k+ Δ T moment, when reaching peak value feedback power, considers above-mentioned restrictive condition, and minimum feedback current value is:
I min = max ( I min , SoC , I min , U L , I min lim )
Thus, the peak power of battery current feedback is obtained:
P ^ peak , k + ΔT cha = I min OCV ^ e , k + I min OCV ( SoC k - I min lim × ΔT Capacity ) - OCV ( SoC k ) I min lim - I min R ^ o - a I min X ^ W , k - Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j
Complete the peak power prediction of electrokinetic cell.
In steps A, because the battery model that uses in method is based on the electrochemical impedance spectroscopy test data of battery, battery model parameter has clear and definite physical significance, ohmic internal resistance R ophysical significance be:
R o≈R Ω+R SEI+R ct
Wherein, R Ωfor high frequency ohmage, R sEIfor SEI membrane impedance, R ctfor Charge-transfer resistance;
In addition, weber impedance is defined by following formula:
Z W = 1 W ( jw ) 0.5
Wherein, W is ionic diffusion coefficient, for the ease of impedance parameter On-line Estimation, gets:
X W = 1 W
Obtain:
Z W = X W ( jw ) 0.5 .
Beneficial effect of the present invention:
1, the present invention has selected the reference model that the simplification impedance spectrum model comprising fractional order element is predicted as battery peak power, because fractional order element has the memory characteristic of long period, therefore the electrokinetic cell peak power Forecasting Methodology based on this model that the present invention proposes not only can predict the maximum output in short-term of battery accurately, also can the peak power fan-out capability of Accurate Prediction battery in long period section.
2, method of the present invention is under multiple electric automobile operating condition, can keep good peak power predictive ability, and the adaptability for working condition of the inventive method is better than the online power prediction algorithm of tradition based on single order RC model.
3, the method that the method adopts zero state response and zero input response to decompose predicts the voltage responsive situation in k+10 moment and k+60 moment, eliminate k ~ k+10, state recursion link between k ~ k+60, greatly reduce the calculated amount of peak power prediction, be applicable to the online peak power prediction of electric automobile.
Accompanying drawing explanation
Fig. 1 is the battery impedance spectroscopy equivalent-circuit model simplified;
Fig. 2 is the current value emulation schematic diagram that electrokinetic cell battery collects when analog operation operating mode is run;
This simulated condition is made up of, for the reliability of verification method the United States Federal's city operating mode (FUDS operating mode) and discharge and recharge pulse operation.
Fig. 3 is that battery terminal voltage predicts the outcome and the comparison diagram of surveying terminal voltage;
Wherein UL is battery actual measurement terminal voltage, ULd10 is the terminal voltage predicted value that hypothesis battery reaches when discharging peak value duty in 10s, ULd60 is the terminal voltage predicted value of hypothesis battery when reaching electric discharge peak value duty in 60s, and ULr60 is the terminal voltage predicted value of hypothesis battery when reaching energy feedback peak value duty in 10s.Contrast can find, respectively at 10s discharge pulse operating mode and 60s discharge pulse operating mode place and UL closely, deducibility thus, the inventive method has good battery discharge characteristic predictive ability to ULd10 and ULd60.
Fig. 4 is 10s electric discharge peak power and the 60s electric discharge peak value power prediction value of battery.
As shown in Figure 4, the inventive method has electric discharge peak value power prediction ability preferably.
Embodiment
The peak power Forecasting Methodology of embodiment one, a kind of electrokinetic cell,
The invention discloses a kind of peak estimation method of electrokinetic cell, the method comprises two parts: the battery peak power Forecasting Methodology that A decomposes based on zero state response and zero input response based on the electrochemical impedance spectroscopy equivalent-circuit model simplified and the parameter On-line Estimation of fractional order federated Kalman filtering, B.
Being specially of the method: the power of battery Forecasting Methodology of decomposing based on the electrochemical impedance spectroscopy equivalent-circuit model simplified, fractional order federated Kalman filtering, zero state response and zero input response.It is realized by following steps:
Step one, electrochemical impedance spectroscopy test result according to battery, due in impedance spectrum, doing further simplification by electrochemical impedance spectroscopy equivalent-circuit model, the electrochemical impedance spectroscopy equivalent-circuit model after being simplified, as shown in Figure 1, and U tand I lrepresent the terminal voltage of battery respectively and flow through the total current of battery.
The impedance spectrum equivalent-circuit model of this simplification comprises OCV e, R oand Z wthree elements.
Wherein, OCV efor compound open-circuit voltage, main reflection battery open circuit voltage characteristic, because equivalent-circuit model simplifies many processes of cell dynamics process, and have ignored each dynamic (dynamical) boundary condition of battery charge and discharge process, therefore due to the error of this battery model itself, OCV ebe the approximate value of OCV, numerically mainly contain other chemical reaction potential values such as the ion diffuse polarization potential of OCV and small part.
OCV e≈OCV
R ofor compound ohmic internal resistance, this parameter mainly reflects the medium-high frequency ohm impedance characteristic (frequency is greater than 0.5Hz) of battery electrochemical impedance spectrum, and this parameter numerically approximates high frequency ohmage (R Ω), SEI membrane impedance (R sEI), Charge-transfer resistance (R ct) impedance sum.
R o≈R Ω+R SEI+R ct
Z wbe used to the weber impedance (Warburg) of the ion diffuse polarization characteristic describing battery, U wfor the voltage at weber impedance two ends.Natural many phenomenons meet fractional order characteristic, and the ion diffuse characteristic process of battery charge and discharge process is especially true.From the electrochemical impedance spectroscopy of battery be Qwest figure, ion diffuse process meets fractional order differential characteristic, and this characteristic commonly uses fractional order physical component---weber impedance represents.Weber impedance is defined by following formula:
Z W = 1 W ( jw ) 0.5
Wherein, W is ionic diffusion coefficient, for the ease of impedance parameter On-line Estimation, gets: obtain:
Z W = X W ( jw ) 0.5
The feature of this impedance spectrum equivalent-circuit model is a simplified high frequency (frequency is greater than 1kHz) in Conventional impedance spectrum equivalent-circuit model and intermediate frequency impedance, and (frequency is greater than 0.5Hz, and be less than 1kHz), from the associated description of test figure and other paper, above-mentioned simplification impedance spectrum model can effectively reduce model parameter quantity, is suitable for the On-line Estimation of model parameter.
Step 2: set up state equation needed for fractional order Kalman filter and observation equation according to above-mentioned equivalent-circuit model:
Based on quantity of state and the parameter value of fractional order Kalman integrated filter estimating circuit, concrete method is as follows.
First, I is got ldischarge time be on the occasion of, data sampling period is 1s.
1, row write state equation and the observation equation of fractional order Kalman integrated filter:
Δ r = d r dt r , r > 0
Wherein: △ rfor differentiating operator, r is differential order, when r is decimal, and △ rrepresent fractional order differential operator, when r is integer, △ rfor integer differentiating operator.
Get fractional order element Z wboth end voltage U wfor quantity of state, have:
Δ 0.5 U W = 1 W I L = X W I L
For parameter X w, OCV e, R oalong with the change of battery charge state (SoC) is slowly, therefore:
Δ 1 X W ≈ 0 Δ 1 OCV e ≈ 0 Δ 1 R o ≈ 0
Above-mentioned four equations are rewritten as matrix form, have:
Δ 0.5 1 1 1 U W X W OCV e R o = 0 I L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U W X W OCV e R o
Get U lfor the observed quantity of system, then have:
U L=OCV e-I LR o-U W
Get:
x = U W X W OCV e R o , N = 0.5 1 1 1 , y=U L
Then have:
Δ N x = 0 I L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x y = - 1 0 1 - I L x
After above-mentioned equation discretize, have:
Δ N x k = 0 I L , k - 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x k - 1 + w y k = - 1 0 1 - I L , k x k + v
Wherein, w, v represent state-noise and the observation noise of system respectively, usually, can suppose that both are independent noise.
Define according to Gr ü nwald-Letnikov fractional order differential:
Δ N x k + 1 = Σ j = 0 k ( - 1 ) j N j x k - j
Wherein:
N j = diag [ 0.5 j 1 j 1 j 1 j ] ,
r j = 1 forj = 0 r ( r - 1 ) . . . ( r - j + 1 ) / j ! forj > 0 ,
Separately get:
γ j = N j
Arrive the discretize recursion expression-form of Fractional Differential Equation can be obtained fom the above equation:
Definition:
A k - 1 = ∂ f ( x k - 1 , I L , k - 1 ) ∂ x k - 1 | x k - 1 = x ^ k - 1 + = 0 I L , k - 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ,
C k = ∂ g ( x k , I L , k ) ∂ x k | x k = x ^ k - = - 1 0 1 - I L , k
According to Gr ü nwald-Letnikov fractional order differential definition, wherein calculated amount the increase along with the time is constantly increased, this situation is not suitable for engineer applied, for this reason, above formula is rewritten as form below:
Σ j = 1 k ( - 1 ) j γ j x k + 1 - j = Σ j = 1 L ( - 1 ) j γ j x k + 1 - j , k ≤ 64 , L = k k > 64 , L = 64
Step 2, utilize fractional order Kalman integrated filter estimated state and parameter value
Initialization:
x ^ 0 = E [ x ] , P 0 + = E [ ( x - x ^ 0 ) ( x - x ^ 0 ) T ]
Wherein, E [x] represents the mathematical expectation of x, is experience preset value when method calculates, represent the estimated value of x at initial time (k=0), represent the estimated value of x at the noise covariance of initial time (k=0).
The time of state, parameter and covariance matrix upgrades:
x ^ k - = f ( x ^ k - 1 + , I L , k - 1 )
P k - = ( A k - 1 + γ 1 ) P k - 1 + ( A k - 1 + γ 1 ) T + Q + Σ j = 2 L γ j P k - j + γ j T
Wherein, Q knoise w kcovariance, for k moment state and model parameter x kpredicted value, for k-1 moment state and model parameter x k-1modified value, for the noise covariance matrix P of k moment x kpredicted value, for the noise covariance matrix P of k-1 moment x k-1modified value.
The measurement updaue of state, parameter and covariance matrix:
L k = P k - ( C k ) T [ C k P k - ( C k ) T + R k ] - 1
x ^ k + = x ^ k - + L k x [ y k - g ( x ^ k - , I L , k ) ]
P k + = ( I - L k C k ) P k -
Wherein, R knoise v kcovariance, L kit is k moment Kalman filter gain size.
Power prediction part:
The basic thought of power prediction:
In use, the size of output power value is determined by load characteristic electrokinetic cell.Different loadtypes, load operating mode all can cause the power of battery to export the difference of situation.The object of maximum output prediction is reliably protecting battery system while, dopes the maximum power output ability of battery in certain moment, to have given play to the maximum performance of battery.The prerequisite of peak power prediction protects battery system reliably, prevents its super-charge super-discharge.
Key point has two: the constraint condition of cell operating status and the reference operating mode of power prediction;
The limiting constraint of cell operating status: the instruction manual of reference battery, the main constraints of cell operating status has: maximum charging current, maximum discharge current, charge cutoff voltage, discharge cut-off voltage, SoC operation interval etc.Obtaining current, voltage, SoC are as constraint condition in the present invention.
The reference operating mode of power prediction: if prediction battery is at the power output capacity in k+ Δ T moment, need to know the battery applying working condition between k ~ k+ Δ T, but this operating mode is unknown.Conventional standard charged/discharged operating mode has: constant current, constant voltage, constant power load operating mode.Wherein, solve the calculated amount of battery peak power based on constant current operating mode minimum and the power output capacity of battery can be reflected, therefore get constant current operating mode and can effectively prevent from over-charging of battery from crossing as the work operating mode between k ~ k+ Δ T putting.
The Z of 1, derivation fractional order element wwhether be linear time invariant element:
Suppose U winitial value be 0, when applying amplitude is I lstep current excitation time, the voltage responsive situation of Uw after Ns is calculated as follows:
Suppose battery model parameter OCV e, R o, X win power prediction process, numerical values recited is constant.
U wvoltage responsive when k=1s is:
U ^ W , 1 = X ^ W , 0 I L - ( - 1 ) 1 0.5 1 U W , 0
U wvoltage responsive when k>=2 is:
U ^ W , k + 1 = X ^ W , 0 I L - Σ j = 1 L ( - 1 ) j 0.5 j U ^ W , k + 1 - j + w
Calculate:
U ^ W , 1 = X ^ W I L
U ^ W , 2 = X ^ W , 0 I L - ( ( - 1 ) 1 0.5 1 U ^ W , 1 + ( - 1 ) 2 0.5 2 U W , 0 )
Can obtain after calculating:
U ^ W , 2 = 1.5 X ^ W , 0 I L
Recursion obtains the voltage responsive at 10s and 60s place and is thus:
U ^ W , 10 = 3.524 X ^ W , 0 I L
U ^ W , 60 = 8.722 X ^ W , 0 I L
Be easy to thus infer Z welement is linear time invariant element.
Power prediction:
Due to Z welement is linear time invariant element, and the response of element under current excitation can be decomposed according to the superposition theorem of circuit.In order to predict Z win the voltage responsive at k+ Δ Ts place, be divided into zero state response and zero input response:
U ^ W , k + ΔT = U ^ W , k + ΔT zs + U ^ W , k + ΔT zi
Wherein:
Wherein zero state response is:
U ^ W , k + ΔT zs = a X ^ W , k I max
For the k+10s moment, a=3.524; For the k+60s moment, a=8.722.
Zero input response determined by the data before the k moment, get length L=60 time memory of fractional order differential.
The zero input response in k+1 moment is:
U ^ W , k + 1 zi = - Σ j = 1 L ( - 1 ) j 0.5 j U ^ W , k + 1 - j zi
Recursion can obtain the k+ Δ T moment and locate battery model element Z thus wlocate zero input voltage response:
U ^ W , k + ΔT zi = Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j
Wherein, when the k+10 moment, b=α, α are constant coefficient matrix.
When the k+60 moment, b=β, β are constant coefficient matrix.
Thus, can obtain battery constant-current discharge electric current is I maxtime battery in the voltage prediction value in k+ Δ T moment.
U ^ L , k + 10 = OCV ^ e , k + ΔT + I L R ^ o + U ^ W , k + ΔT zi + U ^ W , k + ΔT zs ;
Peak power for energy type electrokinetic cell is predicted, gets SoC bound, bound cut-off voltage, maximum charging and discharging currents as the extreme working position of battery.
When wherein, when any one parameter value preferentially reaches its restrained boundary, think battery this parameter for this reason numerical value be issued to extreme working position, the input/output performance number now calculated is the peak power predicted value in k+ Δ T moment.
The step of peak power prediction is as follows:
Electric discharge peak value power prediction:
If SoC is the restrictive condition of battery limit duty, then:
I max , SoC = ( So C k - SoC min ) × Capacity ΔT
If U lfor the restrictive condition of battery limit duty, then:
OCV ^ e , k + ΔT = OCV ^ e , k + I max × OCV k + ΔT , I max - OCV k I max lim
U L , k + ΔT = OCV ^ e , k + I max OCV ( SoC k - I max lim × ΔT Capacity ) - OCV ( SoC k ) I max lim - I max R ^ o - a I max X ^ W , k - Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j
Release thus, as terminal voltage U tduring constraint condition as the extreme working position of battery, working current is:
I max , U L = U min lim - OCV ^ e , k + Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j OCV ( SoC k - I max lim × ΔT Capacity ) - OCV ( SoC k ) I max lim - R ^ o - X ^ W , k
The k+ Δ T moment, when reaching crest discharge power, discharge current value was:
I max = min ( I max , SoC , I max , U L , I max lim )
The crest discharge power in k+ Δ T moment is:
P ^ peak , k + ΔT dis = I max OCV ^ e , k + I max OCV ( SoC k - I max lim × ΔT Capacity ) - OCV ( SoC k ) I max lim - I max R ^ o - a I max X ^ W , k - Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j
Similar with electric discharge peak value power method, the feedback current peak power of battery can be calculated:
Now I lfor on the occasion of.
If SoC is the restrictive condition of battery limit duty, then:
I min , SoC = ( SoC k - SoC max ) × Capacity ΔT
If U lfor the restrictive condition of battery limit duty, then:
I min , U L = U max lim - OCV ^ e , k + Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j OCV ( SoC k - I min lim × ΔT Capacity ) - OCV ( SoC k ) I min lim - R ^ o - X ^ W , k
The k+ Δ T moment, when reaching peak value feedback power, feedback current value was:
I min = max ( I min , SoC , I min , U L , I min lim )
Thus, the peak power of battery current feedback is obtained:
P ^ peak , k + ΔT cha = I min OCV ^ e , k + I min OCV ( SoC k - I min lim × ΔT Capacity ) - OCV ( SoC k ) I min lim - I min R ^ o - a I min X ^ W , k - Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j
It can thus be appreciated that if battery runs with constant current mode in k to k+ Δ T time, then the electric discharge peak power in k+ Δ T moment, current feedback peak power are predicted by above formula respectively and are obtained.
If battery operated under other mode of operation, as constant voltage or invariable power pattern, can effectively prevent over-charging of battery from crossing using above-mentioned peak power as the extreme working position of battery and put.

Claims (2)

1. a peak power Forecasting Methodology for electrokinetic cell, is characterized in that: it is realized by following steps:
The step of steps A, battery model parameter On-line Estimation, is specially:
Steps A 1, when to secondary cell modeling, due to electric automobile operating condition frequency characteristic, the impedance operator of the medium frequency therefore in battery electrochemical impedance spectrum model is reduced to purely resistive element R by the purely resistive element R commonly used and normal phase element Q parallel circuit and describes, the battery electrochemical impedance spectrum equivalent-circuit model after being simplified;
Electrochemical impedance spectroscopy equivalent-circuit model after this simplification comprises open-circuit voltage OCV e, ohmic internal resistance R owith weber impedance Z w;
Electrochemical impedance spectroscopy equivalent-circuit model after steps A 2, the simplification that obtains according to steps A 1 sets up state equation needed for fractional order Kalman filter and observation equation, is specially:
Get the total current I flowing through secondary cell ldischarge time be on the occasion of, data sampling period is 1s;
Δ r = d r dt r , r > 0
Wherein △ rfor differentiating operator, r is differential order, when r is decimal, and △ rrepresent fractional order differential operator, when r is integer, △ rfor integer differentiating operator;
Get fractional order element Z wbe both end voltage be U wquantity of state, have:
Δ 0.5 U W = 1 W I L = X W I L
For battery model parameter, diffusion parameter X w, open-circuit voltage OCV ewith ohmic internal resistance R oalong with the change of battery charge state (SOC) is slowly, therefore:
Δ 1 X W ≈ 0 Δ 1 OCV e ≈ 0 Δ 1 R o ≈ 0
Above-mentioned four equations are rewritten as matrix form, obtain the state equation of fractional order Kalman integrated filter:
Δ 0.5 1 1 1 U W X W OCV e R o = 0 I L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U W X W OCV e R o ;
Get U lfor the observed quantity of system, then have:
U L=OCV e-I LR o-U W
I lrepresent and the total current flowing through battery;
Get:
x = U W X W OCV e R o , N = 0.5 1 1 1 , y = U L
Obtain the observation equation of fractional order Kalman integrated filter:
Δ N x = 0 I L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x y = - 1 0 1 - I L x
After this equation discretize, have:
Δ N x k = 0 I L , k - 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x k - 1 + w y k = - 1 0 1 - I L , k x k + v
Wherein, w, v represent state-noise and the observation noise of system respectively;
Define (being also called the definition of Gr ü nwald-Letnikov fractional order differential) according to the progression of fractional order differential:
Δ N x k + 1 = Σ j = 0 k ( - 1 ) j N j x k - j
Wherein,
N j = diag [ 0.5 j 1 j 1 j 1 j ] ,
r j = 1 forj = 0 r ( r - 1 ) . . . ( r - j + 1 ) / j ! forj > 0 ,
Separately get: γ j = N j , The discretize recursion expression-form of Fractional Differential Equation is obtained by above formula:
Definition:
A k - 1 = ∂ f ( x k - 1 , I L , k - 1 ) ∂ x k - 1 | x k - 1 = x ^ k - 1 + = 0 I L , k - 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ,
C k = ∂ g ( x k , I L , k ) ∂ x k | x k = x ^ k - = - 1 0 1 - I L , k
According to the progression definition of fractional order differential, wherein: calculated amount the increase along with the time is constantly increased, this situation is not suitable for engineer applied, for this reason, above formula is rewritten as form below:
Σ j = 1 k ( - 1 ) j γ j x k + 1 - j = Σ j = 1 L ( - 1 ) j γ j x k + 1 - j , k ≤ 64 , L = k k > 64 , L = 64
Steps A 3, the state equation needed for fractional order Kalman filter utilizing steps A 2 to build and observation equation, carry out time renewal and measurement updaue to state, parameter and covariance matrix according to fractional order federated Kalman filtering algorithm:
Be specially:
Initialization:
x ^ 0 = E [ x ] , P 0 + = E [ ( x - x ^ 0 ) ( x - x ^ 0 ) T ]
Wherein, E [x] represents the mathematical expectation of x, is experience preset value when method calculates, represent the estimated value of x at initial time (k=0), represent the estimated value of x at the noise covariance of initial time (k=0);
The time of state, parameter and covariance matrix upgrades:
x ^ k - = f ( x ^ k - 1 + , I L , k - 1 )
P k - = ( A k - 1 + γ 1 ) P k - 1 + ( A k - 1 + γ 1 ) T + Q + Σ j = 2 L γ j P k - j + γ j T
Wherein, Q knoise w kcovariance, for k moment state and model parameter x kpredicted value, for k-1 moment state and model parameter x k-1modified value, for the noise covariance matrix P of k moment x kpredicted value, for the noise covariance matrix P of k-1 moment x k-1modified value;
The measurement updaue of state, parameter and covariance matrix:
L k = P k - ( C k ) T [ C k P k - ( C k ) T + R k ] - 1
x ^ k + = x ^ k - + L k x [ y k - g ( x ^ k - , I L , k ) ]
P k + = ( I - L k C k ) P k -
Wherein, R knoise v kcovariance, L kit is k moment Kalman filter gain size;
The terminal voltage U of steps A 4, collection battery lwith the total current I flowing through secondary cell l, the state equation needed for fractional order Kalman filter after the electrochemical impedance spectroscopy equivalent-circuit model after the simplification utilizing steps A 1 to obtain and steps A 3 upgrade and observation equation, obtain open-circuit voltage OCV e, ohmic internal resistance R o, diffusion parameter X westimated value, by obtain open-circuit voltage OCV e, ohmic internal resistance R o, diffusion parameter X westimated value as the estimated result of battery, the secondary cell completed based on fractional order federated Kalman filtering simplifies impedance spectrum model parameter On-line Estimation;
Step B, the battery model parameter On-line Estimation result obtained according to steps A, carry out the step of power prediction:
The weber impedance Z of step B1, derivation fractional order element wwhether be linear time invariant element:
If the both end voltage U of fractional order element winitial value be 0, when applying amplitude is I lstep current excitation time, the both end voltage U of fractional order element wvoltage responsive situation after Ns is calculated as follows, and N is positive number:
If the open-circuit voltage OCV of battery model e, ohmic internal resistance R o, diffusion parameter X win power prediction process, numerical values recited is constant;
Then U wvoltage responsive when k=1s is:
U ^ W , 1 = X ^ W , 0 I L - ( - 1 ) 1 0.5 1 U W , 0
Wherein, symbol ^ represents predicted value;
U wvoltage responsive when k>=2 is:
U ^ W , k + 1 = X ^ W , 0 I L - Σ j = 1 L ( - 1 ) j 0.5 j U ^ W , k + 1 - j + w
Calculate:
U ^ W , 1 = X ^ W I L
U ^ W , 2 = X ^ W , 0 I L - ( ( - 1 ) 1 0.5 1 U ^ W , 1 + ( - 1 ) 2 0.5 2 U W , 0 )
After calculating:
U ^ W , 2 = 1.5 X ^ W , 0 I L
Recursion obtains the voltage responsive at 10s and 60s place and is thus:
U ^ W , 10 = 3.524 X ^ W , 0 I L
U ^ W , 60 = 8.722 X ^ W , 0 I L
Thus, as battery model parameter X wconstant or when slowly changing, output valve U wwith I lfor linear relationship, infer fractional order element Z wfor linear time invariant element;
Then, the power forecasting method of fractional order element is:
In order to predict the voltage responsive of fractional order element at k+ Δ Ts place this voltage responsive is divided into zero state response and zero input response
U ^ W , k + ΔT = U ^ W , k + ΔT zs + U ^ W , k + ΔT zi
Wherein zero state response is:
U ^ W , k + ΔT zs = a X ^ W , k I max
For the k+10s moment, a=3.524; For the k+60s moment, a=8.722;
Zero input response determined by the data before the k moment, get length L=60 time memory of fractional order differential;
The zero input response in k+1 moment is:
U ^ W , k + 1 zi = - Σ j = 1 L ( - 1 ) j 0.5 j U ^ W , k + 1 - j zi
Recursion can obtain the input voltage response of k+ Δ T moment fractional order element place zero thus:
U ^ W , k + ΔT zi = Σ j = 1 L b k + 1 - j U ^ W , k + 1 - j
Wherein, battery model fractional order element Z wthe estimated value of two ends terminal voltage between (k+1-L) ~ k moment, when the prediction k+10 moment, b=α, α are one group of constant coefficient matrix;
When the prediction k+60 moment, b=β, β are other one group of constant coefficient matrix;
Thus, can obtain battery constant-current discharge electric current is I maxtime battery in the terminal voltage predicted value in k+ Δ T moment:
The method of electric discharge peak value power prediction is:
If battery charge state is the restrictive condition of battery limit duty, SoC minbe the minimum value that battery discharge stops state-of-charge, then obtain maximum discharge current value now:
I max , SoC = ( SoC k - SoC min ) × Capacity ΔT
Capacity is battery capacity value, and unit is ampere * hour (Ah), SoC kfor the battery charge state in k moment, SoC minfor the minimum state-of-charge that battery discharge limits;
If battery terminal voltage U lfor the restrictive condition of battery limit duty, if now with maximum discharge current I maxto battery discharge, battery model parameter OCV ein the predicted value in k+ △ T moment be:
In above formula, for the battery model parameter OCVe that calculated by fractional order federated Kalman filtering algorithm is in the estimated value in k moment, for OCV ein the predicted value in k+ △ T moment; I maxbeing in terminal voltage as maximum discharge current value during battery limit duty restrictive condition, is value to be solved, it is the maximum discharge current of battery; OCV kit is the battery open circuit voltage values in the k moment; for battery is in the k+ △ T moment, assuming that with battery open circuit voltage values corresponding during constant-current discharge; Due in most cases, the change of OCV is all less and slowly, therefore can think open circuit voltage variations amount within the △ T period and discharge current linear;
And then calculate, suppose that battery is I at discharge current maxtime, the estimated value U of battery terminal voltage l, k+ △ T:
Wherein, the estimated value of terminal voltage be k moment open-circuit voltage estimated value, open circuit voltage variations value, ohmic internal resistance voltage difference, fractional order element Z in the △ T period wzero state response magnitude of voltage, zero input response magnitude of voltage sum;
Release thus, when with terminal voltage U lduring constraint condition as the extreme working position of battery, the maximum operating currenbt of battery is:
The k+ Δ T moment, when reaching crest discharge power, considers above-mentioned restrictive condition, and maximum discharge current value is:
I max = min ( I max , SoC , I max , U L , I max lim )
The crest discharge power in k+ Δ T moment is:
The Forecasting Methodology of the feedback current peak power of battery and the Forecasting Methodology of above-mentioned discharge power be in like manner:
If I lfor on the occasion of;
If SoC is the restrictive condition of battery limit duty, SoC maxbe the maximum SOC of battery, then obtain minimum feedback current value now:
I min , SoC = ( SoC k - SoC max ) × Capacity ΔT
If U lfor the restrictive condition of battery limit duty, then obtain minimum feedback current value now:
The k+ Δ T moment, when reaching peak value feedback power, considers above-mentioned restrictive condition, and minimum feedback current value is:
I min = max ( I min , SoC , I min , U L , I min lim )
Thus, the peak power of battery current feedback is obtained:
Complete the peak power prediction of electrokinetic cell.
2. the peak power Forecasting Methodology of a kind of electrokinetic cell according to claim 1, is characterized in that in steps A,
Because the battery model that uses in method is based on the electrochemical impedance spectroscopy test data of battery, battery model parameter has clear and definite physical significance, ohmic internal resistance R ophysical significance be:
R o≈R Ω+R SEI+R ct
Wherein, R Ωfor high frequency ohmage, R sEIfor SEI membrane impedance, R ctfor Charge-transfer resistance;
In addition, weber impedance is defined by following formula:
Z W = 1 W ( jw ) 0.5
Wherein, W is ionic diffusion coefficient, for the ease of impedance parameter On-line Estimation, gets:
X W = 1 W
Obtain:
Z W = X W ( jw ) 0.5 .
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CN115113046B (en) * 2022-07-14 2022-12-16 河南新太行电源股份有限公司 Test method for rapidly evaluating maximum discharge rate of battery
CN116388343B (en) * 2023-05-29 2023-09-19 重庆大学 Charging load prediction method based on charging controller software data
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