CN105510829A - Novel lithium ion power cell SOC estimation method - Google Patents

Novel lithium ion power cell SOC estimation method Download PDF

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CN105510829A
CN105510829A CN201410514660.1A CN201410514660A CN105510829A CN 105510829 A CN105510829 A CN 105510829A CN 201410514660 A CN201410514660 A CN 201410514660A CN 105510829 A CN105510829 A CN 105510829A
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崔纳新
张文娟
刘苗
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Shandong University
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Abstract

The invention discloses a novel lithium ion power cell SOC estimation method. The novel lithium ion power cell SOC estimation method is characterized in that a cell equivalent circuit model can be established, and the identification of the parameters of the established cell model can be carried out by adopting the least squares algorithm; according to the cell open-circuit voltage UOCV acquired by identifying the parameters according to the step one and the corresponding SOC relation, a corresponding function can be acquired by adopting a Shepherd model and a Nernst model in a combined manner, and the function is used for the matching of the UOCV and the SOC relation; the state equation and the observation equation of the SOC estimation can be established, and the STF algorithm has the strong robustness related to the model uncertainty and the extremely strong tracking capability related to the breaking state. The verification of the SOC estimation by adopting the EKF algorithm and the STF algorithm can be carried out by the constant current discharging experiment and the UDDS working condition experiment, and according to the result, the accuracy of the SOC estimation is higher by adopting the STF algorithm than adopting the EKF algorithm, and the convergence performance is better.

Description

A kind of Novel lithium ion power battery SOC method of estimation
Technical field
The present invention relates to a kind of Novel lithium ion power battery SOC method of estimation.
Background technology
The estimation of battery charge state is the Focal point and difficult point of battery management system always, battery SOC is accurately estimated for raising battery availability factor and extending battery life, improve the safe reliability of battery, and car load energy management has great significance, but SOC can not directly measure, can only by other battery parameter as cell output voltage, electric current be estimated.
At present, SOC algorithm for estimating conventional both at home and abroad has: ampere-hour integral method, and the method cannot provide SOC initial value, and the inaccurate meeting of current measurement causes SOC cumulative errors; Open-circuit voltage method, utilizes the open-circuit voltage of battery and the corresponding relation of SOC, estimates SOC by the open-circuit voltage measuring battery, simple, but could estimate after needing battery standing a period of time, is not suitable for the requirement that electric automobile real-time online is estimated; Internal resistance method, is suitable for battery discharge later stage SOC and estimates, need special apparatus measures, real vehicle seldom uses; Neural network, needs a large amount of data to train, and evaluated error affects comparatively large by training data and training method, also well do not applied at present.Expanded Kalman filtration algorithm estimates that SOC is current domestic and international application method of estimation more widely, SOC is regarded as an internal state variable of battery system by it, the minimum variance estimate of SOC is realized by recursive algorithm, it is stronger to battery model dependence, battery is repeated charge in actual use, can cause the change of battery model parameter, therefore SOC can produce estimation and be forbidden, even occurs dispersing to adopt expanded Kalman filtration algorithm to estimate.
Summary of the invention
For solving the deficiency that prior art exists, the invention discloses a kind of Novel lithium ion power battery SOC method of estimation, SOC overcomes extended Kalman filter and estimates the shortcoming that SOC is inaccurate to adopt strong tracking filfer to estimate, strong tracking filfer is transformed by extended Kalman filter, cause wave filter to estimate inaccurate and divergence problem mainly for system model uncertainty, there is following advantage: (1) has stronger robustness to model uncertainty; (2) extremely strong to the tracking power of mutation status, even when system reaches equilibrium state, still keep the tracking power to soft phase and mutation status; (3) moderate computation complexity.
For achieving the above object, concrete scheme of the present invention is as follows:
A kind of Novel lithium ion power battery SOC method of estimation, comprises the following steps:
Step one: set up battery equivalent-circuit model, utilizes least-squares algorithm to carry out identification to the battery model parameter set up;
Step 2: according to step one parameter identification battery open circuit voltage U out oCVwith the SOC relation of correspondence, Shepherd model and Nernst model is utilized to carry out combining and obtain corresponding function, this Function Fitting U oCVwith SOC relation;
Step 3: in selecting step one, in battery equivalent-circuit model, the terminal voltage of electric capacity and SOC are state variable, build state equation and the observation equation of SOC estimation, the covariance matrix of real-time adjustment state forecast error and gain matrix, the state equation estimated according to SOC and observation equation are estimated lithium-ion-power cell SOC.
The covariance matrix P of described state forecast error k+1:
P k+1=λ k+1G kP kG T k+Q k(12)
Wherein, λ (k+1)for time become fading factor, P k+1for the error co-variance matrix in k+1 moment, P kfor the error co-variance matrix in k moment, Q ksystem noise covariance, G kfor state equation to ask the Jacobian matrix of local derviation to state variable.
Described gain matrix K k+1:
K k+1=P k+1H T k+1[H k+1P k+1H T k+1+R k] -1(7)。
The terminal voltage of electric capacity is C during charging 1cand C 2c, be C during electric discharge 1dand C 2d, below describe in all with C 1and C 2replace.
Described battery equivalent-circuit model comprises polarization resistance R 1d, electric capacity C 1d, polarization resistance R 1cand electric capacity C 1ccircuit after being in series with corresponding diode forms the first circuit, polarization resistance R after distinguishing parallel connection again 2d, electric capacity C 2d, polarization resistance R 2cand electric capacity C 2ccircuit after being in series with corresponding diode forms second circuit, resistance R after parallel connection more respectively odwith R ocafter being in series with corresponding diode, circuit is in parallel composition tertiary circuit, the open-circuit voltage U of one end and battery after described first circuit, second circuit and tertiary circuit are in series oCVbe connected, the other end and open-circuit voltage U obe connected.
When the described battery model to setting up carries out identification, the nominal capacity of battery is 6.2AH, under Cell Experimentation An environment is 25 DEG C of conditions, with the current discharge of 0.5C, the electricity of 10%SOC often released by battery, leave standstill 30 minutes, battery SOC initial value is 1, after experiencing 10 pulsed discharges, battery electric quantity discharges, parameter identification process specific practice: first the experimental data of each SOC point of experiment is extracted respectively, utilize least square function carry out parameter identification can obtain each state under battery model parameter, finally the parameter of each SOC point is listed.
In described step 2, the formula of function is:
U OCV = a 1 + a 2 ln ( SOC ) + a 3 ln ( 1 - SOC ) + a 4 SOC + a 5 SOC - - - ( 1 )
Wherein, SOC refers to the residual capacity of battery.
In the Curve Fitting Toolbox (CurveFittingToolbox) that application Matlab software provides, self-defining function determines a 1~ a 5parameter value.
Described λ (k+1)concrete formula is:
&lambda; k + 1 = &lambda; 0 &lambda; 0 > 1 1 &lambda; 0 < 1 - - - ( 13 )
&lambda; 0 = tr [ N ( k + 1 ) ] tr [ M ( k + 1 ) ] - - - ( 14 )
N(k+1)=S 0(k+1)-H kQ kH T k-βR k+1(16)
M ( k + 1 ) = H k G k P k G k T H K T - - - ( 17 )
S 0 ( k + 1 ) = r ( 1 ) r T ( 1 ) k = 0 &rho; S 0 ( k ) + r k + 1 r T k + 1 1 + &sigma; k &GreaterEqual; 1 - - - ( 15 )
Wherein, H kfor observation equation to ask the matrix of local derviation to state variable, R k+1for measurement noises covariance, k=0,1,2,3 ... represent the moment, r k+1represent k+1 moment residual error, r (1) represents the residual error in k=0 moment, S 0k () represents the covariance matrix of residual error.In formula, 0≤ρ≤1 is forgetting factor, usually gets ρ=0.95; β >=1 is for weakening the factor, and object makes state estimation more level and smooth.
Described gain matrix K k+1the condition met is:
E[r(k+1+j)r T(k+1+j)]=0,k=0,1,2,...,j=1,2,3,...(10)
E[x(k+1)-x(k+1|k+1)][x(k+1)-x(k+1|k+1)] T=min(11)
Wherein, r (k+1+j) represents the residual error in k+1+j moment, and x (k+1) represents the state variable in k+1 moment, and min expression obtains minimum value, and wherein x (k+1|k+1) represents the estimated value of k+1 moment state.
Beneficial effect of the present invention:
This problem is easily dispersed by battery model Accuracy is larger with estimated result for expanded Kalman filtration algorithm estimated accuracy, the application is on the basis of improving Order RC battery equivalent-circuit model, proposition utilizes strong tracking filter to estimate battery SOC, STF algorithm has the stronger robustness about model uncertainty, the extremely strong tracking power about mutation status, by constant-current discharge experiment and UDDS working condition experimenting, EKF and STF algorithm is estimated that SOC verifies, result shows than EKF algorithm, STF algorithm estimates that SOC precision is higher, and convergence is better, instant invention overcomes expanded Kalman filtration algorithm and estimate that SOC depends on the shortcoming of battery model accuracy, demonstrate validity and the correctness of STF algorithm.
Accompanying drawing explanation
The Order RC equivalent-circuit model that Fig. 1 improves;
Fig. 2 lithium iron phosphate dynamic battery state-of-charge estimating system example structure schematic diagram;
Under Fig. 3 UDDS operating mode, two kinds of algorithms estimate SOC comparison diagram;
Under Fig. 4 constant-current discharge, two kinds of algorithms estimate SOC comparison diagram.
Embodiment:
Below in conjunction with accompanying drawing, the present invention is described in detail:
In order to accurately estimate the state-of-charge (SOC) of lithium-ion-power cell, for current Application comparison widely EKF (EKF) algorithm estimate that SOC easily disperses this problem by the Accuracy of battery model is larger with estimated result, on the basis of improving Order RC equivalent-circuit model, propose to apply Strong tracking filter (STF) algorithm with the stronger robustness about model uncertainty and the extremely strong tracking power about mutation status and improve.
Need in electric automobile operational process to estimate the SOC of battery, extended Kalman filter and strong tracking filfer is utilized to estimate battery SOC, need the model setting up battery, in order to reflect that battery behavior again can simple operation, select Application comparison Order RC battery equivalent-circuit model widely, and on the basis of Order RC equivalent-circuit model, consider the difference of discharge and recharge direction parameter, set up model as shown in Figure 1.
The parameter of battery model can utilize least-squares algorithm to carry out identification, parameters in model changes along with the difference of state-of-charge, with reference to the mixed pulses experiment (HybridPulsePowerTest in " FreedomCAR battery testing handbook ", HPPT) test, the parameters in battery model can be obtained.The application's experimental study object is the lithium-ion-power cell that certain domestic corporation produces, its nominal capacity is 6.2AH, under Cell Experimentation An environment is 25 DEG C of conditions, with the current discharge of 0.5C, the electricity of 10%SOC often released by battery, leave standstill 30 minutes, battery SOC initial value is 1, and after experiencing 10 pulsed discharges, battery electric quantity discharges.Parameter identification process specific practice: first the experimental data of each SOC point of experiment is extracted respectively, utilize least square function carry out parameter identification can obtain each state under battery model parameter, finally the Argument List of each SOC point is become as shown in table 1.Parameter identification process and the course of discharge in battery charging direction are similar, do not repeat them here.
Table 1 Order RC model course of discharge parameter identification result
SOC Uocv(V) R(mΩ) R1(mΩ) C1(F) R2(mΩ) C2(F)
0.0028 2.9792 33.75 29.80 24901.12 28.95 1294.66
0.10003 3.212 29.44 5.76 87318.81 8.88 3661.89
0.20005 3.2558 29.24 6.45 85260.83 7.66 4956.27
0.30005 3.2846 29.28 7.66 73577.30 7.20 5678.10
0.40005 3.2913 28.83 4.74 102356.69 6.97 5755.12
0.50004 3.2952 28.68 3.98 141531.77 6.15 5529.76
0.60004 3.3116 28.14 7.04 108991.73 6.22 6196.12
0.70004 3.3291 27.85 8.49 53941.98 7.30 5513.29
0.80004 3.3306 28.61 4.08 115293.37 7.80 4613.10
0.90006 3.3313 28.56 3.42 166961.48 6.18 5174.26
1 3.4315 28.56 3.42 166961.48 6.18 5174.26
According to above-mentioned parameter identification battery open circuit voltage U out oCVwith the SOC relation of correspondence, Shepherd model and Nernst model is utilized to combine the formula 1 obtained, matching U oCVwith SOC relation, make battery equivalent-circuit model more accurate.In the Curve Fitting Toolbox (CurveFittingToolbox) that application Matlab software provides, self-defining function can determine a 1~ a 5parameter value.
U OCV = a 1 + a 2 ln ( SOC ) + a 3 ln ( 1 - SOC ) + a 4 SOC + a 5 SOC - - - ( 1 )
SOC algorithm for estimating based on EKF: expanded Kalman filtration algorithm is a kind of linear minimum-variance estimation method utilizing recursion, in order to use EKF method, need the state space equation of tectonic system, consider that random disturbance and the measurement noise of system are estimated in conjunction with ampere-hour integral method SOC, on the basis of improving Order RC equivalent-circuit model, choose and improve electric capacity C in Order RC battery eliminator model 1and C 2terminal voltage (C during charging 1for C 1c, C 2for C 2c, C during electric discharge 1for C 1d, C 2for C 2d) and SOC be state variable, build SOC estimation state equation and the following formula of observation equation shown in:
x k+1=Ax k+Bu k+w k(2)
y k+1=Cx k+1+v k+1(3)
Wherein, x k, u k, y k+1be respectively the state variable of system, input quantity and output quantity; w krepresent the process noise produced by the out of true of system disturbance and model etc.; v k+1represent the observation noise produced by measuring error etc.; A, B, C are the equation matching factor for embodying system dynamic characteristic.
Battery terminal voltage equation:
U B ( k + 1 ) = U OCV ( k + 1 ) - R 0 ( k + 1 ) * i k + 1 + 0 - 1 - 1 T * SOC ( k + 1 ) U 1 ( k + 1 ) U 2 ( k + 1 ) + v k + 1 - - - ( 4 )
Wherein
A = 1 0 0 0 exp ( - &Delta;t / &tau; 1 ) 0 0 0 exp ( - &Delta;t / &tau; 2 )
B = - &Delta;t / ( Q N ) R 1 * ( 1 - exp ( - &Delta;t / &tau; 1 ) ) R 2 * ( 1 - exp ( - &Delta;t / &tau; 2 ) )
C = d U B dSOC d U B d U 1 d U B d U 2 = d U OCV dSOC - 1 - 1
x k = SOC k U 1 ( k ) U 2 ( k ) .
Wherein, U b(k+1) be the terminal voltage of k+1 moment battery; U oCV(k+1) be the open-circuit voltage of k+1 moment battery; SOC kfor the residual capacity of k moment battery; U 1(k), U 2k () is respectively electric capacity C 1, C 2voltage (the i.e. C at two ends 1d/ C 1c, C 2d/ C 2cterminal voltage, be C during charging 1c, C 2c, be C during electric discharge 1d, C 2d); τ 1=R 1c 1, τ 2=R 2c 2(R during charging 1=R 1c, C 1=R 1c, R 2=R 2c, C 2=R 2c, during electric discharge, R 1=R 1d, C 1=R 1d, R 2=R 2d, C 2=R 2d); Q nfor the rated capacity of battery.Δ t represents the mistiming between k moment and k+1 moment.
Based on expanded Kalman filtration algorithm SOC estimate recursive process as the following formula shown in.
(1) state value in k+1 moment is predicted: the error co-variance matrix in prediction k+1 moment, calculated gains matrix K k+1, upgrade state estimation according to observed reading, upgrade error co-variance matrix.
x k+1=Ax k+Bu k(5)
(2) error co-variance matrix in k+1 moment is predicted:
P k + 1 = G k P k G k T + Q k - - - ( 6 )
(3) calculated gains matrix K k+1:
K k+1=P k+1H T k+1[H k+1P k+1H T k+1+R k] -1(7)
(4) state estimation is upgraded according to observed reading:
x k+1=x k+1+K k+1r k+1(8)
(5) error co-variance matrix is upgraded:
P k+1=(I-K k+1H k+1)P k+1(9)
Residual error r in above-mentioned formula k+1=y k+1-y k+1, y k+1actual measured value, y k+1for with state x k+1corresponding estimated value, G k = &PartialD; &PartialD; x ( Ax + Bu ) | x = x k , H k + 1 = &PartialD; &PartialD; x ( Cx ) | x = x ( k + 1 ) , Q ksystem noise covariance, R kmeasurement noises covariance, P k+1be error covariance, reacted inconsistent degree between the estimated value of state variable and actual value.G kfor k moment state equation to ask the Jacobian matrix of local derviation to state variable.
Strong tracking filfer to the improvement of Kalman filter, Strong tracking filter set up adequate condition: select suitable time-varying gain battle array K k+1, following formula is set up.
E[r(k+1+j)r T(k+1+j)]=0,k=0,1,2,...,j=1,2,3,...(10)
E[x(k+1)-x(k+1|k+1)][x(k+1)-x(k+1|k+1)] T=min(11)
Due to the uncertain impact of model, wave filter can be made to estimate, and actual value is forbidden, and the inevitable average at output residual sequence and amplitude embody, if system can automatic on-line adjustment gain battle array K k+1, formula (10) is set up, and namely force and export the character that residual error has similar white Gaussian noise, this just extracts the effective information exported in residual error.If when the uncertainty of model does not exist, strong tracking filter does not play regulatory role, and now strong tracking filfer is exactly Kalman filter.The improvements of strong tracking filfer to Kalman filter are: the covariance matrix and the gain matrix that adjust state forecast error in real time, amendment formula (6) is
P k+1=λ k+1G kP kG T k+Q k(12)
Wherein λ (k+1)for time become fading factor:
&lambda; k + 1 = &lambda; 0 &lambda; 0 > 1 1 &lambda; 0 < 1 - - - ( 13 )
&lambda; 0 = tr [ N ( k + 1 ) ] tr [ M ( k + 1 ) ] - - - ( 14 )
S 0 ( k + 1 ) = r ( 1 ) r T ( 1 ) k = 0 &rho; S 0 ( k ) + r k + 1 r T k + 1 1 + &sigma; k &GreaterEqual; 1 - - - ( 15 )
N(k+1)=S 0(k+1)-H kQ kH T k-βR k+1(16)
M ( k + 1 ) = H k G k P k G k T H K T - - - ( 17 )
In formula, 0≤ρ≤1 is forgetting factor, usually gets ρ=0.95; β >=1 is for weakening the factor, and object makes state estimation more level and smooth.
Experimental verification is analyzed: in order to verify that strong tracking filter estimates the validity of SOC, utilize AVL-Estorage equipment platform to contain the experiment of battery SOC gamut to battery, this testing apparatus can simcity road condition, the experiment such as constant current charge-discharge, UDDS operating mode is carried out to battery.Lithium iron phosphate dynamic battery state-of-charge estimating system example structure schematic diagram as shown in Figure 2, comprises temperature control box, voltage/current detection equipment, controller and display.This controller inside comprises microprocessor, program storage, CAN interface, some I/O ports etc., controller is connected with voltage/current detection equipment with temperature control box by CAN, temperature control box is in order to keep environment temperature constant, setting Cell Experimentation An restrictive condition can be programmed to prevent battery overcharge, overdischarge by the software of controller, and measuring current, voltage, SOC and temperature etc. can be recorded in detail.In battery single charge and discharge process, Ah counting method is estimated more accurate to SOC, so the SOC value drawn by ampere-hour integral method tests the actual value of SOC as this.Experimental subjects is the capacity that certain domestic corporation produces is the ferric phosphate lithium cell of 6.2AH, and environment temperature controls at 25 DEG C.
(1) UDDS working condition experimenting SOC estimates checking
Use international Metro cycle operating mode (UrbanDynamometerDrivingSchedule herein, write a Chinese character in simplified form UDDS), with the measurement condition of standard as a reference, the experimentally actual conditions of room ferric phosphate lithium cell, reduced by certain proportion and obtain testing UDDS operating mode electric current used, the UDDS operating mode electric discharge that SOC initial value is 0.99206 is carried out to ferric phosphate lithium cell, this operating mode comprises 6 UDDS Operation mode cycles, suppose that STF estimates and EKF estimates that SOC initial value is 0.7, UDDS working condition experimenting SOC actual value, STF estimates that SOC value and EKF estimate SOC value contrast as shown in Figure 3.
(2) constant-current discharge experiment SOC estimates checking
Carry out to ferric phosphate lithium cell the constant-current discharge experiment that initial value SOC is 0.996, suppose that the SOC initial value that STF estimates and EKF estimates is 0.8, constant-current discharge experiment SOC actual value, STF algorithm estimate that SOC value and EKF algorithm estimate SOC contrast as shown in Figure 4
3 ~ 4 the results can be found out and estimate that SOC estimates that SOC precision is higher compared to EKF algorithm, estimates that initial value speed of convergence is faster based on STF algorithm from the graph, and STF algorithm overcomes EKF algorithm and estimates the shortcoming that SOC result is easily dispersed.

Claims (8)

1. a Novel lithium ion power battery SOC method of estimation, is characterized in that, comprises the following steps:
Step one: set up battery equivalent-circuit model, utilizes least-squares algorithm to carry out identification to the battery model parameter set up;
Step 2: according to step one parameter identification battery open circuit voltage U out oCVwith the SOC relation of correspondence, Shepherd model and Nernst model is utilized to carry out combining and obtain corresponding function, this Function Fitting U oCVwith SOC relation;
Step 3: in selecting step one, in battery equivalent-circuit model, the terminal voltage of electric capacity and SOC are state variable, build state equation and the observation equation of SOC estimation, the covariance matrix of real-time adjustment state forecast error and gain matrix, the state equation estimated according to SOC and observation equation are estimated lithium-ion-power cell SOC.
2. a kind of Novel lithium ion power battery SOC method of estimation as claimed in claim 1, is characterized in that, the covariance matrix P of described state forecast error k+1:
P k+1=λ k+1G kP kG T k+Q k(12)
Wherein, λ (k+1)for time become fading factor, P k+1for the error co-variance matrix in k+1 moment, P kfor the error co-variance matrix in k moment, Q ksystem noise covariance, G kfor state equation to ask the Jacobian matrix of local derviation to state variable.
3. a kind of Novel lithium ion power battery SOC method of estimation as claimed in claim 1, is characterized in that, described gain matrix K k+1:
K k+1=P k+1H T k+1[H k+1P k+1H T k+1+R k] -1(7)
Wherein, r kit is measurement noises covariance.
4. a kind of Novel lithium ion power battery SOC method of estimation as claimed in claim 1, is characterized in that, described battery equivalent-circuit model comprises polarization resistance R 1d, electric capacity C 1d, polarization resistance R 1cand electric capacity C 1ccircuit after being in series with corresponding diode forms the first circuit, polarization resistance R after distinguishing parallel connection again 2d, electric capacity C 2d, polarization resistance R 2cand electric capacity C 2ccircuit after being in series with corresponding diode forms second circuit, resistance R after parallel connection more respectively odwith R ocafter being in series with corresponding diode, circuit is in parallel composition tertiary circuit, the open-circuit voltage U of one end and battery after described first circuit, second circuit and tertiary circuit are in series oCVbe connected, the other end and open-circuit voltage U obe connected.
5. a kind of Novel lithium ion power battery SOC method of estimation as claimed in claim 1, it is characterized in that, when the described battery model to setting up carries out identification, the nominal capacity of battery is 6.2AH, under Cell Experimentation An environment is 25 DEG C of conditions, with the current discharge of 0.5C, the electricity of 10%SOC often released by battery, leave standstill 30 minutes, battery SOC initial value is 1, after experiencing 10 pulsed discharges, battery electric quantity discharges, parameter identification process specific practice: first the experimental data of each SOC point of experiment is extracted respectively, utilize least square function carry out parameter identification can obtain each state under battery model parameter, finally the parameter of each SOC point is listed.
6. a kind of Novel lithium ion power battery SOC method of estimation as claimed in claim 1, is characterized in that, in described step 2, the formula of function is:
U OCV = a 1 + a 2 ln ( SOC ) + a 3 ln ( 1 - SOC ) + a 4 SOC + a 5 SOC - - - ( 1 )
Wherein, SOC refers to the residual capacity of battery, a 1~ a 5for parameter to be asked.
7. a kind of Novel lithium ion power battery SOC method of estimation as claimed in claim 2, is characterized in that, described λ (k+1)concrete formula is:
&lambda; k + 1 = &lambda; 0 &lambda; 0 > 1 1 &lambda; 0 < 1 - - - ( 13 )
&lambda; 0 = tr [ N ( k + 1 ) ] tr [ M ( k + 1 ) ] - - - ( 14 )
N(k+1)=S 0(k+1)-H kQ kH T k-βR k+1(16)
M ( k + 1 ) = H k G k P k G k T H K T - - - ( 17 )
S 0 ( k + 1 ) = r ( 1 ) r T ( 1 ) k = 0 &rho; S 0 ( k ) + r k + 1 r T k + 1 1 + &sigma; k &GreaterEqual; 1 - - - ( 15 )
Wherein, H kfor observation equation to ask the matrix of local derviation to state variable, R k+1for measurement noises covariance, k=0,1,2,3 ... represent the moment, r k+1represent k+1 moment residual error, r (1) represents the residual error in k=0 moment, S 0k () represents the covariance matrix of residual error, in formula, 0≤ρ≤1 is forgetting factor, usually gets ρ=0.95; β>=1 is for weakening the factor.
8. a kind of Novel lithium ion power battery SOC method of estimation as claimed in claim 3, is characterized in that, described gain matrix K k+1the condition met is:
E[r(k+1+j)r T(k+1+j)]=0,k=0,1,2,...,j=1,2,3,...(10)
E[x(k+1)-x(k+1|k+1)][x(k+1)-x(k+1|k+1)] T=min(11)
Wherein, r (k+1+j) represents the residual error in k+1+j moment, and x (k+1) represents the state variable in k+1 moment, and min expression obtains minimum value, and wherein x (k+1|k+1) represents the estimated value of k+1 moment state.
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