CN104267354B  A kind of peak power Forecasting Methodology of electrokinetic cell  Google Patents
A kind of peak power Forecasting Methodology of electrokinetic cell Download PDFInfo
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 CN104267354B CN104267354B CN201410592570.4A CN201410592570A CN104267354B CN 104267354 B CN104267354 B CN 104267354B CN 201410592570 A CN201410592570 A CN 201410592570A CN 104267354 B CN104267354 B CN 104267354B
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Abstract
A kind of peak power Forecasting Methodology of electrokinetic cell, is related to the peak power Predicting Technique of electrokinetic cell.The present invention is the accuracy in order to improve the prediction of the peak power of electrokinetic cell.The method of the present invention includes two parts：The battery peak power Forecasting Methodology that A is decomposed based on zero state response and zero input response based on the electrochemical impedance spectroscopy equivalentcircuit model simplifying and the parameter Online Estimation of fractional order federated Kalman filtering, B.The present invention has selected the reference model that the simplification impedance spectrum model comprising fractional order element is predicted as battery peak power, therefore proposed by the present invention not only can accurately predict the maximum output in shortterm of battery it is also possible to peak power fanout capability in longer period for the Accurate Prediction battery based on the electrokinetic cell peak power Forecasting Methodology of this model.The present invention is applied to the prediction of electric automobile online peak power.
Description
Technical field
The present invention relates to the peak power Predicting Technique of electrokinetic cell.
Background technology
The content of the relevant battery peak power Forecasting Methodology disclosed in domestic patent is less, in paper periodical both domestic and external
The method having the prediction of some electrokinetic cell peak powers.
These methods mostly adopt the single order RC equivalentcircuit model of battery, using SOC, terminal voltage, electric current as its peak work
The restrictive condition of rate prediction, the power forecasting method of early stage adopts the complete battery pair of offline battery model supplemental characteristic to export/return
Feedback peak power prediction, but battery with the change of the environment such as aging or temperature, operating mode, model parameter also can change therewith
Become, therefore, the power estimation method reliability based on offline model supplemental characteristic is poor；
In the uptodate paper delivered, battery model supplemental characteristic is obtained online by method for parameter estimation, can effectively carry
The accuracy of high estimation, but because the error of single order RC model itself is larger, power prediction can only be confined to the shorter time
It is inside effective.
In order to reduce discretization error when for power prediction for the state equation, when adopting less discretization in paper
Between be spaced (such as taking time interval to be 1s or 0.1s), by the method for recurrence calculation, obtain battery 10s after current time
Predictive value at the peak power predictive value at place or 60s, the shortcoming of this method is that there is substantial amounts of recurrence calculation, realtime
Difference.In addition this method also cannot improve the power inaccurate problem of estimation causing due to model oneself error.
Content of the invention
The present invention is the peak power forecasting reliability in order to improve electrokinetic cell, reduces amount of calculation, thus providing one
Plant the peak power Forecasting Methodology of electrokinetic cell.
A kind of peak power Forecasting Methodology of electrokinetic cell, it is realized by following steps：
Step A, the step of battery model parameter Online Estimation, specially：
Step A1, when modeling to secondary cell, due to electric automobile operating condition frequency characteristic, therefore battery electrochemical
The impedance operator of the medium frequency in impedance spectrum model can be by conventional purely resistive element R and the letter of normal phase element Q parallel circuit
Turn to purely resistive element R to describe, the battery electrochemical impedance spectrum equivalentcircuit model after being simplified；
Electrochemical impedance spectroscopy equivalentcircuit model after this simplification includes opencircuit voltage OCV_{e}, ohmic internal resistance R_{o}With weber resistance
Anti Z_{W}；
Step A2, according to step A1 obtain simplification after electrochemical impedance spectroscopy equivalentcircuit model set up fractional order karr
State equation needed for graceful wave filter and observational equation, specially：
Take total current I flowing through secondary cell_{L}It is on the occasion of data sampling period is 1s in electric discharge；
Wherein △^{r}For differential operator, r is differential order, when r is for decimal, △^{r}Represent fractional order differential operator, when r is
During integer, △^{r}For integer differential operator；
Take fractional order element Z_{W}Be both end voltage be U_{W}Quantity of state, have：
For battery model parameter, diffusion parameter X_{W}, opencircuit voltage OCV_{e}With ohmic internal resistance R_{o}With battery charge state
(SOC) change is slow, therefore：
Aforementioned four equation is rewritten as matrix form, obtains the state equation of fractional order Kalman integrated filter：
Take U_{L}For the observed quantity of system, then have：
U_{L}=OCV_{e}I_{L}R_{o}U_{W}
I_{L}The total current representing and flowing through battery；
Take：
Y=U_{L}
Obtain the observational equation of fractional order Kalman integrated filter：
After equation discretization, have：
Wherein, w, v represent statenoise and the observation noise of system respectively；
Series definition (being also called the definition of Gr ü nwaldLetnikov fractional order differential) according to fractional order differential：
Wherein,
Separately take：Obtain the discretization recursion expressionform of Fractional Differential Equation by above formula：
Definition：
According to the series definition of fractional order differential, wherein：Amount of calculation will increase over time
And constantly increase, this situation is not suitable for engineer applied, for this reason, above formula is rewritten as following form：
Step A3, the state equation needed for fractional order Kalman filter using step A2 structure and observational equation, right
State, parameter and covariance matrix carry out time renewal and measurement updaue according to fractional order federated Kalman filtering algorithm：
It is specially：
Initialization：
Wherein, E [x] represents the mathematic expectaion of x, is experience preset value when method calculates,Represent x in initial time (k
=0) estimated value,Represent the estimated value of the noise covariance in initial time (k=0) for the x；
The time of state, parameter and covariance matrix updates：
Wherein, Q_{k}It is noise w_{k}Covariance,For k moment state and model parameter x_{k}Predictive value,During for k1
Quarter state and model parameter x_{k1}Correction value,Noise covariance matrix P for k moment x_{k}Predictive value,During for k1
Carve the noise covariance matrix P of x_{k1}Correction value；
The measurement updaue of state, parameter and covariance matrix：
Wherein, R_{k}It is noise v_{k}Covariance, L_{k}It is k moment Kalman filter gain size；
Step A4, terminal voltage U of collection battery_{L}With total current I flowing through secondary cell_{L}, using the simplification of step A1 acquisition
Rear electrochemical impedance spectroscopy equivalentcircuit model and step A3 update after the state equation needed for fractional order Kalman filter
With observational equation, obtain opencircuit voltage OCV_{e}, ohmic internal resistance R_{o}, diffusion parameter X_{W}Estimated value, will obtain opencircuit voltage
OCV_{e}, ohmic internal resistance R_{o}, diffusion parameter X_{W}Estimated value as battery estimated result, complete based on fractional order joint karr
The secondary cell of graceful filtering simplifies impedance spectrum model parameter Online Estimation；
Step B, the battery model parameter Online Estimation result being obtained according to step A, the step carrying out power prediction：
Step B1, the weber impedance Z of derivation fractional order element_{W}Whether it is linear time invariant element：
If both end voltage U of fractional order element_{W}Initial value be 0, be I when applying amplitude_{L}Step current excitation
When, both end voltage U of fractional order element_{W}Voltage response situation after Ns is calculated as follows, and N is positive number：
If the opencircuit voltage OCV of battery model_{e}, ohmic internal resistance R_{o}, diffusion parameter X_{W}Numerical values recited during power prediction
It is constant；
Then U_{W}Voltage response in k=1s is：
Wherein, symbol ^ represents predictive value；
U_{W}Voltage response when k >=2 is：
Calculate：
After calculating：
By the voltage response that this recursion obtains 10s and 60s it is：
Thus, when battery model parameter X_{W}When constant or slowly varying, output valve U_{W}With I_{L}For linear relationship, infer and divide
Number rank element Z_{W}For linear time invariant element；
Then, the power forecasting method of fractional order element is：
In order to predict voltage response at k+ Δ Ts for the fractional order elementThis voltage response is divided into zero state
ResponseAnd zero input response
Wherein zero state response is：
For k+10s moment, a=3.524；For k+60s moment, a=8.722；
Zero input responseDetermined by the data before the k moment, take time memory length L=of fractional order differential
60；
The zero input response in k+1 moment is：
The response of k+ Δ T moment fractional order element zero input voltage be can get by this recursion：
Wherein,It is battery model fractional order element Z_{W}Estimation between (k+1L)～k moment for the two ends terminal voltage
Value, when predicting k+10 moment, b=α, α are one group of constant coefficient matrix；
When predicting k+60 moment, b=β, β are another set constant coefficient matrix；
Thus, can get battery constantcurrent discharge electric current is I_{max}When battery the k+ Δ T moment terminal voltage predictive value：
Electric discharge peak value power prediction method be：
If battery charge state (SoC or SOC) is the restrictive condition of battery limit working condition, SoC_{min}It is battery discharge
Terminate the minima of stateofcharge, then obtain maximum discharge current value now：
Capacity is battery capacity value, and unit is ampere * hour (Ah), SoC_{k}For the battery charge state in k moment,
SoC_{min}The minimum stateofcharge limiting for battery discharge, the minimum stateofcharge that such as certain power battery for hybrid electric vehicle adopts
For SoC_{min}=30%；
If battery terminal voltage U_{L}For the restrictive condition of battery limit working condition, if now with maximum discharge current I_{max}Right
Battery discharge, battery model parameter OCV_{e}Predictive value in the k+ △ T moment is：
In above formula,It is by calculated battery model parameter OCV of fractional order federated Kalman filtering algorithm_{e}
In the estimated value in k moment,For OCV_{e}Predictive value in the k+ △ T moment；I_{max}It is as battery limit work in terminal voltage
Make maximum discharge current value during state limit condition, be value to be solved,It is the maximum discharge current of battery；OCV_{k}It is in k
The battery open circuit voltage values in moment, can be calculated by OCV (SoC) predefined function and obtain it is generally recognized that OCV and SoC has clearly
Corresponding relation；The functional relationship of the predefined function of OCV and SoC can be obtained by handbook of batteries or test；For electricity
Pond in the k+ △ T moment it is assumed that withCorresponding battery open circuit voltage values during constantcurrent discharge, equally can be predefined by OCV (SoC)
Function calculates and obtains；Due in most cases, the change of OCV is all less and slow, it can thus be assumed that opening within the △ T period
Road voltage variety is linear with discharge current；
And then calculate it is assumed that battery is I in discharge current_{max}When, estimated value U of battery terminal voltage_{L,k+△T}：
Wherein, the estimated value of terminal voltage be k moment opencircuit voltage estimated value, open circuit voltage variations value, ohm in the △ T period
Internal resistance voltage difference, fractional order element Z_{W}Zero state response magnitude of voltage, zero input response magnitude of voltage sum；
Thus release, when with terminal voltage U_{L}As the extreme working position of battery constraints when, the maximum work of battery
As electric current it is：
When the k+ Δ T moment reaches crest discharge power, consider abovementioned restrictive condition, maximum discharge current value is：
The crest discharge power in k+ Δ T moment is：
The Forecasting Methodology of feedback current peak power of battery is with the Forecasting Methodology of abovementioned discharge power in the same manner：
If I_{L}Be on the occasion of；
If SoC is the restrictive condition of battery limit working condition, SoC_{max}It is the maximum SOC of battery, then obtain
Minimum feedback current value now：
If U_{L}For the restrictive condition of battery limit working condition, then obtain minimum feedback current value now：
When the k+ Δ T moment reaches peak value feedback power, consider abovementioned restrictive condition, minimum feedback current value is：
Thus, obtain the peak power of battery current feedback：
Complete the peak power prediction of electrokinetic cell.
In step A, due to the electrochemical impedance spectroscopy test data based on battery for the battery model, battery mould used in method
Shape parameter has clear and definite physical significance, ohmic internal resistance R_{o}Physical significance be：
R_{o}≈R_{Ω}+R_{SEI}+R_{ct}
Wherein, R_{Ω}For high frequency ohmage, R_{SEI}For SEI membrane impedance, R_{ct}For Chargetransfer resistance；
In addition, weber impedance to be defined by below equation：
Wherein, W is ionic diffusion coefficient, for the ease of impedance parameter Online Estimation, takes：
Obtain：
Beneficial effects of the present invention：
1st, the present invention has selected the ginseng that the simplification impedance spectrum model comprising fractional order element is predicted as battery peak power
Examine model, because fractional order element has the memory characteristic of long period, the power based on this model therefore proposed by the present invention
Battery peak power Forecasting Methodology not only can accurately predict the maximum output in shortterm of battery it is also possible to Accurate Prediction is electric
Peak power fanout capability in longer period for the pond.
2nd, the method for the present invention, under multiple electric automobile operating conditions, can keep preferable peak power prediction energy
Power, the adaptability for working condition of the inventive method is better than the online power prediction algorithm based on single order RC model for the tradition.
3rd, the method adopts zero state response and the method for zero input response decomposition to predict in k+10 moment and k+60 moment
Voltage response situation, eliminate k～k+10, the state recursion link between k～k+60, greatly reduce peak power prediction
Amount of calculation it is adaptable to electric automobile online peak power prediction.
Brief description
Fig. 1 is the battery impedance spectroscopy equivalentcircuit model simplifying；
Fig. 2 is that the current value emulation schematic diagram collecting when work operating mode is run simulated by electrokinetic cell battery；
This simulated condition is made up of the United States Federal's city operating mode (FUDS operating mode) and discharge and recharge pulse operation, for authentication
The reliability of method.
Fig. 3 is the comparison diagram that battery terminal voltage predicted the outcome and surveyed terminal voltage；
Wherein UL surveys terminal voltage for battery, and ULd10 assumes that battery reaches during electric discharge peak value working condition in 10s
Terminal voltage predictive value, ULd60 assumes that battery reaches terminal voltage predictive value during electric discharge peak value working condition, ULr60 in 60s
Assume that battery reaches terminal voltage predictive value during energy feedback peak value working condition in 10s.Contrast is it is found that ULd10
With ULd60 respectively at 10s discharge pulse operating mode and 60s discharge pulse operating mode with UL closely, thus it can be extrapolated that the present invention
Method has preferable battery discharge characteristic predictive ability.
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 preferable electric discharge peak value power prediction ability.
Specific embodiment
Specific embodiment one, a kind of peak power Forecasting Methodology of electrokinetic cell,
The invention discloses a kind of peak estimation method of electrokinetic cell, the method includes two parts：A is based on the electricity simplifying
Chemical impedance composes the parameter Online Estimation of equivalentcircuit model and fractional order federated Kalman filtering, B is based on zero state response and
The battery peak power Forecasting Methodology that zero input response is decomposed.
The method be specially：Based on the electrochemical impedance spectroscopy equivalentcircuit model simplifying, the filter of fractional order federated Kalman
The power of battery Forecasting Methodology that ripple, zero state response and zero input response are decomposed.It is realized by following steps：
Step one, the electrochemical impedance spectroscopy test result according to battery, due in impedance spectrum, by electrochemical impedance spectroscopy etc.
Effect circuit model has done and has simplified further, the electrochemical impedance spectroscopy equivalentcircuit model after being simplified, as shown in figure 1, U_{t}And I_{L}
Represent the terminal voltage of battery and the total current flowing through battery respectively.
The impedance spectrum equivalentcircuit model of this simplification includes OCV_{e}、R_{o}And Z_{W}Three elements.
Wherein, OCV_{e}For being combined opencircuit voltage, main reflection battery open circuit voltage characteristic, because equivalentcircuit model simplifies
Many processes of cell dynamics processes, and have ignored each dynamic (dynamical) boundary condition of battery charge and discharge process, because
This is due to this battery model error of itself, OCV_{e}It is the approximation of OCV, numerically mainly contain OCV and least a portion of
Other chemical reaction potential value such as ion diffusion polarization potential.
OCV_{e}≈OCV
R_{o}For being combined ohmic internal resistance, this parameter mainly reflects the mediumhigh frequency ohm impedance characteristic of battery electrochemical impedance spectrum
(frequency is more than 0.5Hz), this parameter numerically approximates high frequency ohmage (R_{Ω}), SEI membrane impedance (R_{SEI}), electric charge transfer
Impedance (R_{ct}) impedance sum.
R_{o}≈R_{Ω}+R_{SEI}+R_{ct}
Z_{W}It is used to describe the weber impedance (Warburg) of the ion diffusion polarization characteristic of battery, U_{W}For weber impedance two ends
Voltage.Many phenomenons of nature meet fractional order characteristic, and the ion diffusion property process of battery charge and discharge process is especially such as
This.It is that knowable to Qwest's figure, ion diffusion process meets fractional order differential characteristic, and this characteristic is normal from the electrochemical impedance spectroscopy of battery
Represented with fractional order physical component weber impedance.Weber impedance to be defined by below equation：
Wherein, W is ionic diffusion coefficient, for the ease of impedance parameter Online Estimation, takes：Obtain：
The feature of this impedance spectrum equivalentcircuit model is a simplified Conventional impedance and composes the high frequency (frequency in equivalentcircuit model
More than 1kHz) and intermediate frequency impedance (frequency is more than 0.5Hz, and is less than 1kHz), from the associated description of test data and other paper
From the point of view of, abovementioned simplification impedance spectrum model can effectively reduce model parameter quantity, is suitable for the Online Estimation of model parameter.
Step 2：State equation according to needed for abovementioned equivalentcircuit model sets up fractional order Kalman filter and observation
Equation：
Quantity of state based on fractional order Kalman integrated filter estimating circuit and parameter value, specific method is as follows.
First, take I_{L}It is on the occasion of data sampling period is 1s in electric discharge.
1st, row write state equation and the observational equation of fractional order Kalman integrated filter：
Wherein：△^{r}For differential operator, r is differential order, when r is for decimal, △^{r}Represent fractional order differential operator, when r is
During integer, △^{r}For integer differential operator.
Take fractional order element Z_{W}It is both end voltage U_{W}For quantity of state, have：
For parameter X_{W}, OCV_{e}, R_{o}Change with battery charge state (SoC) is slow, therefore：
Aforementioned four equation is rewritten as matrix form, has：
Take U_{L}For the observed quantity of system, then have：
U_{L}=OCV_{e}I_{L}R_{o}U_{W}
Take：
Y=U_{L}
Then have：
After abovementioned equation discretization, have：
Wherein, w, v represent statenoise and the observation noise of system respectively, generally it will be assumed that both are independent noise.
Defined according to Gr ü nwaldLetnikov fractional order differential：
Wherein：
Separately take：
Arrive the discretization recursion expressionform of Fractional Differential Equation as available from the above equation：
Definition：
According to Gr ü nwaldLetnikov fractional order differential definition, whereinAmount of calculation will be with
The increase of time and constantly increase, this situation is not suitable for engineer applied, for this reason, above formula is rewritten as following form：
Step 2, utilize fractional order Kalman integrated filter estimated state and parameter value
Initialization：
Wherein, E [x] represents the mathematic expectaion of x, is experience preset value when method calculates,Represent x in initial time (k
=0) estimated value,Represent the estimated value of the noise covariance in initial time (k=0) for the x.
The time of state, parameter and covariance matrix updates：
Wherein, Q_{k}It is noise w_{k}Covariance,For k moment state and model parameter x_{k}Predictive value,For the k1 moment
State and model parameter x_{k1}Correction value,Noise covariance matrix P for k moment x_{k}Predictive value,For k1 moment x
Noise covariance matrix P_{k1}Correction value.
The measurement updaue of state, parameter and covariance matrix：
Wherein, R_{k}It is noise v_{k}Covariance, L_{k}It 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 electrokinetic cell by load characteristic.Different load classes
Type, load operating mode all can lead to the power of battery to export the difference of situation.The purpose of maximum output prediction is in reliability
While protection battery system, predict the maximum power output ability in certain moment for the battery, to have given play to the maximality of battery
Energy.The premise of peak power prediction is reliably to protect battery system, prevents its supercharge superdischarge.
Key point has two：The reference operating mode of the constraints of cell operating status and power prediction；
The limiting constraint of cell operating status：The instruction manual of reference battery, the major constraints of cell operating status
Condition has：Maximum charging current, maximum discharge current, charge cutoff voltage, discharge cutoff voltage, SoC operation interval etc..At this
In invention, obtaining current, voltage, SoC are as constraints.
The reference operating mode of power prediction：If prediction battery, in the power output capacity in k+ Δ T moment, needs to know k～k+
Battery applying working condition between 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, the amount of calculation minimum of battery peak power is solved based on constant current operating mode and battery can be reflected
Power output capacity, therefore takes constant current operating mode can effectively prevent overcharging of battery mistake as the work operating mode between k～k+ Δ T
Put.
1st, the Z of derivation fractional order element_{W}Whether it is linear time invariant element：
Assume U_{W}Initial value be 0, be I when applying amplitude_{L}Step current excitation when, voltage after Ns for the Uw rings
Situation is answered to be calculated as follows：
Assume battery model parameter OCV_{e}、R_{o}、X_{W}During power prediction, numerical values recited is constant.
U_{W}Voltage response in k=1s is：
U_{W}Voltage response when k >=2 is：
Calculate：
Can obtain after calculating：
By the voltage response that this recursion obtains 10s and 60s it is：
Thus it is easy to infer Z_{W}Element is linear time invariant element.
Power prediction：
Due to Z_{W}Element is linear time invariant element, and response under current excitation for the element can be according to the superposition theorem of circuit
Decomposed.In order to predict Z_{W}Voltage response at k+ Δ Ts, is classified as zero state response and zero input response：
Wherein：
Wherein zero state response is：
For k+10s moment, a=3.524；For k+60s moment, a=8.722.
Zero input responseDetermined by the data before the k moment, take time memory length L=of fractional order differential
60.
The zero input response in k+1 moment is：
K+ Δ T moment battery model element Z be can get by this recursion_{W}Locate zero input voltage response：
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 get battery constantcurrent discharge electric current is I_{max}When battery the k+ Δ T moment voltage prediction value.
For the peak power prediction of energy type electrokinetic cell, take SoC bound, bound blanking voltage, maximum charge and discharge
Electric current is as the extreme working position of battery.
When wherein, any one parameter value preferentially reaches during its restrained boundary it is believed that battery is assigned for this numerical value in this parameter
To extreme working position, the now peak power predictive value in calculated input/output performance number as 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 working condition,：
If U_{L}For the restrictive condition of battery limit working condition, then：
Thus release, when terminal voltage U_{t}As the extreme working position of battery constraints when, operating current is：
When the k+ Δ T moment reaches crest discharge power, discharge current value is：
The crest discharge power in k+ Δ T moment is：
Similar with electric discharge peak value power method, the feedback current peak power of battery can be calculated：
Now I_{L}Be on the occasion of.
If SoC is the restrictive condition of battery limit working condition,：
If U_{L}For the restrictive condition of battery limit working condition, then：
When the k+ Δ T moment reaches peak value feedback power, feedback current value is：
Thus, obtain the peak power of battery current feedback：
If it follows that battery is run with constant current mode in k to k+ Δ T time, the electric discharge its peak work in k+ Δ T moment
Rate, current feedback peak power are obtained by above formula prediction respectively.
If battery operated under other mode of operations, such as constant voltage or constant power mode, made with abovementioned peak power
Extreme working position for battery can effectively prevent from overcharging of battery from crossing putting.
Claims (2)
1. a kind of peak power Forecasting Methodology of electrokinetic cell, is characterized in that：It is realized by following steps：
Step A, the step of battery model parameter Online Estimation, specially：
Step A1, when modeling to secondary cell, due to electric automobile operating condition frequency characteristic, therefore battery electrochemical impedance
The impedance operator of the medium frequency in spectrum equivalentcircuit model is by conventional purely resistive element R and the letter of normal phase element Q parallel circuit
Turn to purely resistive element R to describe, the battery electrochemical impedance spectrum equivalentcircuit model after being simplified；
Battery electrochemical impedance spectrum equivalentcircuit model after this simplification includes opencircuit voltage OCV_{e}, ohmic internal resistance R_{o}And fractional order
Element Z_{W}；
Opencircuit voltage OCV_{e}Positive pole and ohmic internal resistance R_{o}One end connect；Described ohmic internal resistance R_{o}The other end and fractional order unit
Part Z_{W}One end connect；Opencircuit voltage OCV_{e}Negative pole and fractional order element Z_{W}The other end as cell voltage U_{L}Two ends；
Step A2, according to step A1 obtain simplification after battery electrochemical impedance spectrum equivalentcircuit model set up fractional order joint
State equation needed for Kalman filter and observational equation, specially：
Take total current I flowing through secondary cell_{L}It is on the occasion of data sampling period is 1s in electric discharge；
Wherein Δ^{r}For differential operator, r is differential order, when r is for decimal, Δ^{r}Represent fractional order differential operator, when r is integer
When, Δ^{r}For integer differential operator；
Take fractional order element Z_{W}Be both end voltage be U_{W}Quantity of state, have：
For battery model parameter, diffusion parameter X_{W}, opencircuit voltage OCV_{e}With ohmic internal resistance R_{o}With battery charge state SoC's
Change is slow, therefore：
Will：
It is rewritten as matrix form, obtain the state equation of fractional order Kalman integrated filter：
Take U_{L}For the observed quantity of system, then have：
U_{L}=OCV_{e}I_{L}RoU_{W}
I_{L}The total current representing and flowing through battery；
Take：
Y=U_{L}
Obtain the observational equation of fractional order Kalman integrated filter：
After the observational equation discretization of this fractional order Kalman integrated filter, have：
Wherein, w, v represent statenoise and the observation noise of system respectively；
Series definition according to fractional order differential：
Wherein,
Separately take：Obtain the discretization recursion expressionform of Fractional Differential Equation by above formula：
Definition：
According to the series definition of fractional order differential, wherein：Amount of calculation will increase over time and not
Disconnected increase, this situation is not suitable for engineer applied, for this reason, above formula is rewritten as following form：
Step A3, the state equation needed for fractional order Kalman integrated filter using step A2 structure and observational equation, right
State, parameter and covariance matrix carry out time renewal and measurement updaue according to fractional order federated Kalman filtering algorithm：
It is specially：
Initialization：
Wherein, E [x] represents the mathematic expectaion of x, is experience preset value when method calculates,Represent the estimation in initial time for the x
Value,Represent the estimated value of the noise covariance in initial time for the x；
The time of state, parameter and covariance matrix updates：
Wherein, Q_{k}It is noise w_{k}Covariance,For k moment state and model parameter x_{k}Predictive value,For k1 moment state
With model parameter x_{k1}Correction value,Noise covariance matrix P for k moment x_{k}Predictive value,For making an uproar of k1 moment x
Sound covariance matrix P_{k1}Correction value；
The measurement updaue of state, parameter and covariance matrix：
Wherein, R_{k}It is noise v_{k}Covariance, L_{k}It is k moment Kalman filter gain size；
Step A4, terminal voltage U of collection battery_{L}With total current I flowing through secondary cell_{L}, using after the simplification that step A1 obtains
The state needed for fractional order Kalman integrated filter after battery electrochemical impedance spectrum equivalentcircuit model and the renewal of step A3
Equation and observational equation, obtain opencircuit voltage OCV_{e}, ohmic internal resistance R_{o}, diffusion parameter X_{W}Estimated value, will obtain opencircuit voltage
OCV_{e}, ohmic internal resistance R_{o}, diffusion parameter X_{W}Estimated value as battery estimated result, complete based on fractional order joint karr
The secondary cell of graceful filtering simplifies impedance spectrum model parameter Online Estimation；
Step B, the battery model parameter Online Estimation result being obtained according to step A, the step carrying out power prediction：
Step B1, derivation fractional order element Z_{W}Whether it is linear time invariant element：
If both end voltage U of fractional order element_{W}Initial value be 0, be I when applying amplitude_{L}Step current excitation when, point
Both end voltage U of number rank element_{W}Voltage response situation after N s is calculated as follows, and N is positive number：
If the opencircuit voltage OCV of battery model_{e}, ohmic internal resistance R_{o}, diffusion parameter X_{W}During power prediction, numerical values recited is not
Become；
Then U_{W}Voltage response in k=1s is：
Wherein, symbol ^ represents predictive value；
U_{W}Voltage response when k >=2 is：
Calculate：
After calculating：
By the voltage response that this recursion obtains 10s and 60s it is：
Thus, when battery model parameter X_{W}When constant or slowly varying, output valve U_{W}With I_{L}For linear relationship, infer fractional order
Element Z_{W}For linear time invariant element；
Then, the power forecasting method of fractional order element is：
In order to predict voltage response at k+ Δ Ts for the fractional order elementThis voltage response is divided into zero state responseAnd zero input response
Wherein zero state response is：
For k+10s moment, a=3.524；For k+60s moment, a=8.722；
Zero input responseDetermined by the data before the k moment, take time memory length L=60 of fractional order differential；
The zero input response in k+1 moment is：
The response of k+ Δ T moment fractional order element zero input voltage be can get by this recursion：
Wherein,It is battery model fractional order element Z_{W}Estimated value between (k+1L)～k moment for the two ends terminal voltage,
When predicting k+10 moment, b=α, α are one group of constant coefficient matrix；
When predicting k+60 moment, b=β, β are another set constant coefficient matrix；
Thus, can get battery constantcurrent discharge electric current is I_{max}When battery the k+ Δ T moment terminal voltage predictive value：
Electric discharge peak value power prediction method be：
If battery charge state is the restrictive condition of battery limit working condition, SoC_{min}It is that battery discharge terminates stateofcharge
Minima, then obtain maximum discharge current value now：
Capacity is battery capacity value, and unit is ampere * hour (Ah), SoC_{k}For the battery charge state in k moment, SoC_{min}For
The minimum stateofcharge that battery discharge limits；
If battery terminal voltage U_{L}For the restrictive condition of battery limit working condition, if now with maximum discharge current I_{max}Battery is put
Electricity, battery model parameter OCV_{e}Predictive value in the k+ Δ T moment is：
In above formula,It is by calculated battery model parameter OCV of fractional order federated Kalman filtering algorithm_{e}In k
The estimated value carved,For OCV_{e}Predictive value in the k+ Δ T moment；I_{max}It is as battery limit working condition in terminal voltage
Maximum discharge current value during restrictive condition, is value to be solved,It is the maximum discharge current of battery；OCV_{k}It is in the k moment
Battery open circuit voltage values；For battery in k+ Δ_{T}Moment it is assumed that withCorresponding battery open circuit electricity during constantcurrent discharge
Pressure value；Due in most cases, the change of OCV is all less and slow, it can thus be assumed that the opencircuit voltage within the Δ T period becomes
Change amount is linear with discharge current；
And then calculate it is assumed that battery is I in discharge current_{max}When, estimated value U of battery terminal voltage_{L,k+ΔT}：
Wherein, the estimated value of terminal voltage be k moment opencircuit voltage estimated value, open circuit voltage variations value, ohmic internal resistance in the Δ T period
Voltage difference, fractional order element Z_{W}Zero state response magnitude of voltage, zero input response magnitude of voltage sum；
Thus release, when with terminal voltage U_{L}As the extreme working position of battery restrictive condition when, the maximum operating currenbt of battery
For：
When the k+ Δ T moment reaches electric discharge peak power, consider the restrictive condition of the extreme working position of abovementioned battery, maximum
Discharge current value is：
The electric discharge peak power in k+ Δ T moment is：
The Forecasting Methodology of the Forecasting Methodology of current peak feedback power and abovementioned electric discharge peak power is in the same manner：
If I_{L}Be on the occasion of；
If SoC is the restrictive condition of battery limit working condition, SoC_{max}It is the maximum SOC of battery, then obtain now
Minimum feedback current value：
If U_{L}For the restrictive condition of battery limit working condition, then obtain minimum feedback current value now：
When the k+ Δ T moment reaches current peak feedback power, consider abovementioned restrictive condition, minimum feedback current value is：
Thus, obtain battery current peak value feedback power：
Complete the peak power prediction of electrokinetic cell.
2. a kind of peak power Forecasting Methodology of electrokinetic cell according to claim 1 is it is characterised in that in step A,
Due to the electrochemical impedance spectroscopy test data based on battery for the battery model used in method, battery model parameter has clearly
Physical significance, ohmic internal resistance R_{o}Physical significance be：
R_{o}≈R_{Ω}+R_{SEI}+R_{ct}
Wherein, R_{Ω}For high frequency ohmage, R_{SEI}For SEI membrane impedance, R_{ct}For Chargetransfer resistance；
In addition, weber impedance to be defined by below equation：
Wherein, W is ionic diffusion coefficient, for the ease of impedance parameter Online Estimation, takes：
Obtain：
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