CN105548896A - Power-cell SOC online closed-loop estimation method based on N-2RC model - Google Patents

Abstract

The invention discloses a power-cell SOC online closed-loop estimation method based on an N-2RC model. In the invention, an electrochemical model and an equivalent circuit model are combined and a novel power cell model is provided. The N-2RC model uses a Nernst electrochemical model to replace an electromotive force portion of a second-order RC equivalent circuit model so that one to one correspondence of a cell electromotive force and SOC can be accurately reflected. Based on the model, a recursive least-square method based on a forgetting factor is used to identify a model parameter, and then an expansion Kalman filtering algorithm is used to realize on-line closed loop estimation of the cell SOC. The electrochemical model can well describe a cell characteristic on an electrochemical aspect, but the structure is complex and the model is not suitable for individually individual usage. And the equivalent circuit model belongs to an external characteristic model and can well express a volt-ampere characteristic relationship of the cell, but can not reflect an internal characteristic of the cell. By using the method in the invention, the above problems are overcome.

Description

Based on the electrokinetic cell SOC line closed loop method of estimation of N-2RC model

Technical field

The invention belongs to charge states of lithium ion battery prediction field, relate to the electrokinetic cell SOC line closed loop method of estimation based on N-2RC model.

Background technology

In power battery management system, the prediction of battery charge state SOC (StateOfCharge) is significant, the accuracy of its prediction, directly affects the control strategy of battery management system, thus affects the performance of battery performance and the length of battery life.

Meanwhile, accurate battery model has great importance for the assessment algorithm of state-of-charge SOC, and because battery has the non-linear behavior of height, the consistance of battery model and electrokinetic cell is very good, just can draw and predict the outcome more accurately.

At present, conventional electrokinetic cell model has three classes: electrochemical model, artificial nerve network model and equivalent-circuit model.Electrochemical model can be comparatively detailed the electrochemical reaction process of description inside battery, but its structure is very complicated, is not suitable for battery SOC and estimates; Artificial nerve network model has the features such as highly non-linear, fault-tolerance, self-study, and can realize accurate SOC estimates, but its weak point is to need a large amount of experimental datas to predict the performance of battery, and larger to the dependence of battery history data; Equivalent-circuit model describes the external characteristics of electrokinetic cell by circuit component built-up circuit networks such as traditional resistance, electric capacity, constant pressure sources, and because its structure is simple and well can describe battery behavior, normal studied person uses.

Electrokinetic cell SOC method of estimation mainly contains: open-circuit voltage method, ampere-hour integral method, Kalman filtering method.Open-circuit voltage method can only realize off-line in laboratory conditions and estimate, can not estimate in real time; Ampere-hour integral method classics are easy-to-use, but its estimated accuracy is larger by the Accuracy of SOC initial value and current measurement value; Kalman filter method has again the kinds such as EKF, Unscented kalman filtering, adaptive Kalman filter, and Kalman filtering method can predict SOC value more accurately, is that battery SOC Estimation Study uses maximum methods.

Summary of the invention

The present invention seeks to be subject to model impact to solve electrokinetic cell SOC On-line Estimation, the problem that estimated accuracy is low, provides a kind of electrokinetic cell SOC line closed loop method of estimation based on N-2RC model.

Electrokinetic cell SOC line closed loop method of estimation based on N-2RC model of the present invention, it comprises the following steps:

Step one: combined with electrochemical model and Order RC equivalent-circuit model, sets up the voltage-current relationship formula of N-2RC battery model;

Step 2: carry out pulse charge-discharge test to tested lithium battery, records each pulse charging-discharging cycle and leaves standstill the battery SOC after a period of time and battery open circuit voltage U _oc, found that value when same battery SOC point is larger than electric discharge to open-circuit voltage values during inductive charging, describe the delayed action of battery, get charge and discharge U _ocmean value as electro-motive force measurement value.By relational expression U _oc=K ₀+ K ₁in (SOC)+K ₂in (1-SOC) simulates a nonlinear curve, gets suitable K ₀, K ₁, K ₂value, makes matched curve approaching to reality value;

Step 3: the terminal voltage and the output current that gather tested ferric phosphate lithium ion battery, using the observed reading of measured value as identification algorithm, then based on the Recursive Least Squares containing forgetting factor, picks out time varying system parameter R _s, R ₁, R ₂, C ₁, C ₂;

Step 4: the time varying system parameter obtained according to step 3, the battery SOC carried out based on EKF is estimated, estimates that the SOC exported is as the input of SOC in battery open circuit voltage function, realizes the line closed loop estimation of battery SOC.

The determination of N-2RC model equation in step one:

${\stackrel{\·}{U}}_1=I/C_1-U_1/\left(R_1{C}_1\right);---\left(1\right)$

${\stackrel{\·}{U}}_2=I/C_2-U_2/\left(R_2{C}_2\right);---\left(2\right)$

Ut＝Uoc-U ₁-U ₂-IRs；(3)

Uoc＝K ₀+K ₁In(SOC)+K ₂In(1-SOC)；(4)

Wherein, U _ocfor open-circuit voltage; U _tfor terminal voltage; I is electric current; R _sfor ohmic internal resistance; R ₁, C ₁represent concentration difference polarization reflection, R ₁for concentration difference polarization resistance, C ₁for concentration difference polarization capacity, U ₁for concentration difference polarizing voltage; R ₂, C ₂represent activation polarization reflection, R ₂for activation polarization internal resistance, C ₂for activation polarization electric capacity, U ₂for activation polarization voltage.

Battery impulse charge and discharge experiment is carried out in step 2.First be full of electricity to battery, shelve 5 hours; With C/3 constant-current discharge, stop electric discharge after releasing 10% of battery capacity, shelve 5 hours, measure the open-circuit voltage of battery; Repeat a process, until discharge cut-off voltage.With C/3 constant-current charge, stop charging after being charged to 10% of battery capacity, shelve 5 hours, measure the open-circuit voltage of battery; Repeat a process, until charging current is less than C/20.The mean value of the corresponding open-circuit voltage measured value of charge and discharge is as U _oc.By the U of 10% interval 0.1 to 100% correspondence _ocvalue and relational expression (4), by curve, obtain parameter K ₀, K ₁, K ₂.

The concrete steps of carrying out in step 3 based on the recursive least-squares parameter identification method of forgetting factor are:

Step 3.1: model difference equation is obtained to step one Chinese style (1), (2), (3) sliding-model control

Ut(k)＝m ₀+m ₁Ut(k-1)+m ₂Ut(k-2)+m ₃I(k)+m ₄I(k-1)+m ₅I(k-2)(5)

In formula, m ₀, m ₁, m ₂, m ₃, m ₄, m ₅for model difference equation undetermined coefficient, in its value and model, parameter to be identified has functional relation.

Formula (5) can be write as form, wherein

θ＝[m ₀，m ₁，m ₂，m ₃，m ₄，m ₅](7)

Step 3.2: based on the concrete estimation procedure of the recursive least-squares parameter identification method of forgetting factor.

Determine least square covariance P ₀with the initial value of parameter matrix θ.

Set up least square gain matrix K _k:

$K_k=P_{k-1}{h}_k{(h_k^T{P}_{k-1}{h}_k+\mathrm{\υ})}^{-1}---\left(8\right)$

In formula, υ is least square weighting factor.

Obtain calculating parameter estimated matrix θ after time-varied gain matrix _k:

${\mathrm{\θ}}_k={\mathrm{\θ}}_{k-1}+K_k(y_k-h_k^T{\mathrm{\θ}}_{k-1})---\left(9\right)$

Y in formula _kfor the terminal voltage measured value in k moment, θ _kfor θ _k-1estimates of parameters in the k-1 moment to the k moment.

The renewal of covariance matrix:

$P_k=(I-K_k{h}_k^T)P_{k-1}---\left(10\right)$

Like this, just complete a step recursion of the Recursive Least Squares based on forgetting factor, repeat this process, pick out m ₀, m ₁, m ₂, m ₃, m ₄, m ₅value, and then draw R _s, R ₁, C ₁, R ₂, C ₂value.

EKF algorithm for estimating in step 4:

Step 4.1: the determination based on N-2RC model estimate equation:

x _k＝A _k-1x _k-1+B _k-1u _k-1+ω _k-1(11)

y _k＝C _kx _k+D _ku _k+υ _k(12)

Wherein, x _kit is k moment state variable; y _kit is k moment observational variable; u _kit is the input control variable in k moment; ω _k, υ _kit is mutual incoherent system noise.

Battery status equation is listed according to ampere-hour integral formula and formula (1), (2):

$\left[\begin{array}{c}SOC\left(k\right)\\ U_1\left(k\right)\\ U_2\left(k\right)\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1-\frac{T}{R_1{C}_1}& 0\\ 0& 0& 1-\frac{T}{R_2{C}_2}\end{array}\right]*\left[\begin{array}{c}SOC(k-1)\\ U_1(k-1)\\ U_2(k-1)\end{array}\right]+\left[\begin{array}{c}-\frac{\mathrm{\η}T}{Q_n}\\ \frac{T}{C_1}\\ \frac{T}{C_2}\end{array}\right]*I(k-1)---\left(13\right)$

Know that battery observation equation is by formula (3):

Ut(k)＝Uoc[SOC(k)]-U ₁(k)-U ₂(k)-I(k)Rs(14)

In formula (13), (14), order:

$A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1-\frac{T}{R_1{C}_1}& 0\\ 0& 0& 1-\frac{T}{R_2{C}_2}\end{array}\right],B=\left[\begin{array}{c}-\frac{\mathrm{\η}T}{Q_n}\\ \frac{T}{C_1}\\ T\\ C_2\end{array}\right],$ C＝[Uoc(SOC)-1-1]，D＝[-R _s]

U in observation equation _oc(SOC) be nonlinear function about SOC, the first order Taylor getting equation launches to carry out linearization process, obtains observing matrix $H_k=\[\begin{array}{ccc}\frac{\∂Uoc}{\∂SOC}& -1& -1\end{array}\].$

Step 4.2: the state error covariance matrix initial value P determining EKF ₀, system covariance Q ₀and R ₀, start expanded Kalman filtration algorithm.

EKF predictive equation:

The estimation of state variable: x _k=A _k-1x _k-1+ B _k-1u _k-1+ ω _k-1(15)

State covariance is estimated: $P_k=A_{k-1}{P}_{k-1}{A}_{k-1}^T+Q_{k-1}---\left(16\right)$

Kalman gain matrix: K _k=P _kh ^t(HP _kh ^t+ R _k) ^-1(17)

State-updating: x _k+1=x _k+ K _k(y _k-Hx _k) (18)

State covariance is estimated to upgrade: P _k+1=(I-K _kh) P _k(19)

In EKF, terminal voltage estimates that belonging to closed loop estimates, after some step iteration upgrade, and terminal voltage U _tapproaching to reality value gradually; U simultaneously ₁and U ₂value calculated by systematic parameter, then estimate cell emf U according to observation equation (3) _oc; Estimate battery SOC by formula (4), be updated in state equation, utilize ampere-hour integral method to calculate new state estimation, realize the line closed loop method of estimation of SOC.

The present invention adopts above technical scheme compared with prior art, has following technique effect:

Present invention incorporates Nernst electrochemical model and can describe electrokinetic cell internal-response process and the strong advantage such as dynamically adapting characteristic and dynamic simulation precision of Order RC model more all sidedly; Then the recursive least-squares method based on forgetting factor is adopted to achieve the on-line parameter identification of N-2RC model; Finally based on time the systematic parameter that the becomes line closed loop that completes battery SOC by expanded Kalman filtration algorithm estimate, suitable battery model and the expanded Kalman filtration algorithm of line closed loop ensure that the precision comparison that battery SOC is estimated is high.

Accompanying drawing explanation

Below with reference to accompanying drawing, the invention will be further described:

Fig. 1 is N-2RC model cootrol process schematic proposed by the invention;

Fig. 2 is the implementing procedure figure of the inventive method;

Fig. 3 tests the single lithium battery voltage pattern recorded under UDDS operating mode;

Fig. 4 tests the single lithium battery map of current recorded under UDDS operating mode;

Fig. 5 is the terminal voltage measured value and estimated value comparison diagram that use EKF to obtain under UDDS operating mode;

Fig. 6 is the terminal voltage measured value and estimated value Error Graph that use EKF to obtain under UDDS operating mode;

Fig. 7 is the battery SOC estimated value and reference value comparison diagram that use EKF to obtain under UDDS operating mode;

Fig. 8 is the battery SOC estimated value and reference value Error Graph that use EKF to obtain under UDDS operating mode.

Embodiment

The invention provides the electrokinetic cell SOC line closed loop method of estimation based on N-2RC model, for making object of the present invention, clearly, clearly, and the present invention is described in more detail with reference to accompanying drawing examples for technical scheme and effect.Should be appreciated that concrete enforcement described herein is only in order to explain the present invention, is not intended to limit the present invention.

Embodiment adopts a kind of urban highway traffic operating mode (UDDS) as the load of lithium ion battery, this operating mode curent change is larger, difficulty is added to On-line Estimation battery SOC, but can the well applicability of verification model and the estimated accuracy of algorithm for estimating.Fig. 3, Fig. 4 are the battery terminal voltage and output current that gather.The implementation step of the present embodiment is illustrated below in conjunction with Fig. 2.

Step one: set up N-2RC model equation as shown in Figure 1:

${\stackrel{\·}{U}}_1=I/C_1-U_1/\left(R_1{C}_1\right);---\left(1\right)$

${\stackrel{\·}{U}}_2=I/C_2-U_2/\left(R_2{C}_2\right);---\left(2\right)$

Ut＝Uoc-U ₁-U ₂-IRs；(3)

Uoc＝K ₀+K ₁In(SOC)+K ₂In(1-SOC)；(4)

Wherein, U _ocfor open-circuit voltage; U _tfor terminal voltage; I is electric current; R _sfor ohmic internal resistance; R ₁, C ₁represent concentration difference polarization reflection, R ₁for concentration difference polarization resistance, C ₁for concentration difference polarization capacity, U ₁for concentration difference polarizing voltage; R ₂, C ₂represent activation polarization reflection, R ₂for activation polarization internal resistance, C ₂for activation polarization electric capacity, U ₂for activation polarization voltage.

Step 2: carry out charging, discharging electric batteries pulse test.First be full of electricity to battery, shelve 5 hours; With C/3 constant-current discharge, stop electric discharge after releasing 10% of battery capacity, shelve 5 hours, measure the open-circuit voltage of battery; Repeat a process, until discharge cut-off voltage.With C/3 constant-current charge, stop charging after being charged to 10% of battery capacity, shelve 5 hours, measure the open-circuit voltage of battery; Repeat a process, until charging current is less than C/20.The mean value of the corresponding open-circuit voltage measured value of charge and discharge is as U _oc.By the U of 10% interval 0.1 to 100% correspondence _ocvalue and relational expression (4), by curve, obtain parameter K ₀, K ₁, K ₂.

Step 3: the concrete steps based on the recursive least-squares parameter identification method of forgetting factor are:

Step 3.1: model difference equation is obtained to step one Chinese style (1), (2), (3) sliding-model control

Ut(k)＝m ₀+m ₁Ut(k-1)+m ₂Ut(k-2)+m ₃I(k)+m ₄I(k-1)+m ₅I(k-2)(5)

In formula, m ₀, m ₁, m ₂, m ₃, m ₄, m ₅for model difference equation undetermined coefficient, in its value and model, parameter to be identified has functional relation.

Formula (5) can be write as form, wherein

θ＝[m ₀，m ₁，m ₂，m ₃，m ₄，m ₅](7)

Step 3.2: based on the concrete estimation procedure of the recursive least-squares parameter identification method of forgetting factor.

Determine least square covariance P ₀with the initial value of parameter matrix θ.

Set up least square gain matrix K _k:

$K_k=P_{k-1}{h}_k{(h_k^T{P}_{k-1}{h}_k+\mathrm{\υ})}^{-1}---\left(8\right)$

In formula, υ is least square weighting factor, gets υ=0.98.

Obtain calculating parameter estimated matrix θ after time-varied gain matrix _k:

${\mathrm{\θ}}_k={\mathrm{\θ}}_{k-1}+K_k(y_k-h_k^T{\mathrm{\θ}}_{k-1})---\left(9\right)$

Y in formula _kfor the terminal voltage measured value in k moment, θ _kfor θ _k-1estimates of parameters in the k-1 moment to the k moment.

The renewal of covariance matrix:

$P_k=(I-K_k{h}_k^T)P_{k-1}---\left(10\right)$

Like this, just complete a step recursion of the Recursive Least Squares based on forgetting factor, repeat this process, pick out m ₀, m ₁, m ₂, m ₃, m ₄, m ₅value, and then draw R _s, R ₁, C ₁, R ₂, C ₂value.

Step 4: EKF algorithm for estimating:

Step 4.1: the determination based on N-2RC model estimate equation:

x _k＝A _k-1x _k-1+B _k-1u _k-1+ω _k-1(11)

y _k＝C _kx _k+D _ku _k+υ _k(12)

Wherein, x _kit is k moment state variable; y _kit is k moment observational variable; u _kit is the input control variable in k moment; ω _k, υ _kit is mutual incoherent system noise.

Battery status equation is listed according to ampere-hour integral formula and formula (1), (2):

$\left[\begin{array}{c}SOC\left(k\right)\\ U_1\left(k\right)\\ U_2\left(k\right)\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1-\frac{T}{R_1{C}_1}& 0\\ 0& 0& 1-\frac{T}{R_2{C}_2}\end{array}\right]*\left[\begin{array}{c}SOC(k-1)\\ U_1(k-1)\\ U_2(k-1)\end{array}\right]+\left[\begin{array}{c}-\frac{\mathrm{\η}T}{Q_n}\\ \frac{T}{C_1}\\ \frac{T}{C_2}\end{array}\right]*I(k-1)---\left(13\right)$

Know that battery observation equation is by formula (3):

Ut(k)＝Uoc[SOC(k)]-U ₁(k)-U ₂(k)-I(k)Rs(14)

In formula (13), (14), order:

$A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1-\frac{T}{R_1{C}_1}& 0\\ 0& 0& 1-\frac{T}{R_2{C}_2}\end{array}\right],B=\left[\begin{array}{c}-\frac{\mathrm{\η}T}{Q_n}\\ \frac{T}{C_1}\\ T\\ C_2\end{array}\right],$ C＝[Uoc(SOC)-1-1]，D＝[-R _s]

U in observation equation _oc(SOC) be nonlinear function about SOC, the first order Taylor getting equation launches to carry out linearization process, obtains observing matrix $H_k=\[\begin{array}{ccc}\frac{\∂Uoc}{\∂SOC}& -1& -1\end{array}\].$

Step 4.2: the state error covariance matrix initial value P determining EKF ₀, system covariance Q ₀and R ₀, start expanded Kalman filtration algorithm.

EKF predictive equation:

The estimation of state variable: x _k=A _k-1x _k-1+ B _k-1u _k-1+ ω _k-1(15)

State covariance is estimated: $P_k=A_{k-1}{P}_{k-1}{A}_{k-1}^T+Q_{k-1}---\left(16\right)$

Kalman gain matrix: K _k=P _kh ^t(HP _kh ^t+ R _k) ^-1(17)

State-updating: x _k+1=x _k+ K _k(y _k-Hx _k) (18)

State covariance is estimated to upgrade: P _k+1=(I-K _kh) P _k(19)

In EKF, terminal voltage estimates that belonging to closed loop estimates, after some step iteration upgrade, and terminal voltage U _tapproaching to reality value gradually; U simultaneously ₁and U ₂value calculated by systematic parameter, then estimate cell emf U according to observation equation (3) _oc; Estimate battery SOC by formula (4), be updated in state equation, utilize ampere-hour integral method to calculate new state estimation, realize the line closed loop method of estimation of SOC.

Design sketch of the present invention is as shown in Fig. 5 to Fig. 8, and Fig. 5 is the comparison diagram of battery terminal voltage estimated value and experiment value under UDDS operating mode, and the fluctuation of terminal voltage measured value is comparatively large as can be seen from Figure, but estimated value is still very close to measured value.Fig. 6 more directly describes the accuracy that terminal voltage is estimated, wherein U _tmaximum error at about 0.05V, the error of most of the time is at about 0.02V.Fig. 7 is the comparison diagram of battery SOC estimated value and reference value under UDDS operating mode, and due to the nonlinearity characteristic of battery, real SOC value is difficult to obtain, and the present invention adopts laboratory reference value as SOC true value.Fig. 8 shows that the maximum error of SOC estimated value is about 4%, and the error of most of the time is about 2%.The battery model and the SOC method of estimation which illustrate the present invention's proposition can be good at being applicable to battery SOC estimation.

To the above-mentioned explanation of the disclosed embodiments, professional and technical personnel in the field are realized or uses the present invention.To be apparent for those skilled in the art to the multiple amendment of these embodiments, General Principle as defined herein can without departing from the spirit or scope of the present invention, realize in other embodiments.Therefore, the present invention can not be restricted to these embodiments shown in this article, but will meet the widest scope consistent with principle disclosed herein and features of novelty.

Claims (5)

1., based on the electrokinetic cell SOC line closed loop method of estimation of N-2RC model, it is characterized in that, the method comprises the following steps:

Step one: combined with electrochemical model and Order RC equivalent-circuit model, sets up the voltage-current relationship formula of N-2RC battery model;

Step 2: carry out pulse charge-discharge test to tested lithium battery, records each pulse charging-discharging cycle and leaves standstill the battery SOC after a period of time and battery open circuit voltage U _oc, get charge and discharge open-circuit voltage U _ocmean value as electro-motive force measurement value, by relational expression U _oc=K ₀+ K ₁in (SOC)+K ₂in (1-SOC) simulates a nonlinear curve, gets suitable K ₀, K ₁, K ₂value, makes matched curve approaching to reality value;

Step 3: the terminal voltage and the output current that gather tested lithium ion battery, using the observed reading of measured value as identification algorithm, then based on the Recursive Least Squares containing forgetting factor, picks out time varying system parameter;

Step 4: the time varying system parameter obtained according to step 3, the battery SOC carried out based on EKF is estimated, estimates that the SOC exported is as the input of SOC in battery open circuit voltage function, realizes the line closed loop estimation of battery SOC.

2. a kind of electrokinetic cell SOC line closed loop method of estimation based on N-2RC model according to claim 1, it is characterized in that, the deterministic process of the model equation of N-2RC described in step one is:

${\stackrel{\·}{U}}_1=I/C_1-U_1/\left(R_1{C}_1\right);---\left(1\right)$

${\stackrel{\·}{U}}_2=I/C_2-U_2/\left(R_2{C}_2\right);---\left(2\right)$

Ut＝Uoc-U ₁-U ₂-IRs；(3)

Uoc＝K ₀+K ₁In(SOC)+K ₂In(1-SOC)；(4)

Wherein, U _ocfor open-circuit voltage; U _tfor terminal voltage; I is electric current; R _sfor ohmic internal resistance; R ₁, C ₁represent concentration difference polarization reflection, R ₁for concentration difference polarization resistance, C ₁for concentration difference polarization capacity, U ₁for concentration difference polarizing voltage; R ₂, C ₂represent activation polarization reflection, R ₂for activation polarization internal resistance, C ₂for activation polarization electric capacity, U ₂for activation polarization voltage.

3. a kind of electrokinetic cell SOC line closed loop method of estimation based on N-2RC model according to claim 2, it is characterized in that, the detailed process of carrying out charging, discharging electric batteries pulse test in described step 2 is,

First be full of electricity to battery, shelve 5 hours; With C/3 constant-current discharge, stop electric discharge after releasing 10% of battery capacity, shelve 5 hours, measure the open-circuit voltage of battery; Repeat a process, until discharge cut-off voltage;

Again with C/3 constant-current charge, stop charging after being charged to 10% of battery capacity, shelve 5 hours, measure the open-circuit voltage of battery; Repeat a process, until charging current is less than C/20; Wherein, the mean value of the corresponding open-circuit voltage measured value of charge and discharge is as battery open circuit voltage U _oc, by the U of 10% interval 0.1 to 100% correspondence _ocvalue and relational expression (4), by curve, obtain parameter K ₀, K ₁, K ₂.

4. a kind of electrokinetic cell SOC line closed loop method of estimation based on N-2RC model according to claim 2, it is characterized in that, the concrete steps of carrying out in step 3 based on the recursive least-squares parameter identification method of forgetting factor are:

Step 3.1: model difference equation is obtained to step one Chinese style (1), (2), (3) sliding-model control

Ut(k)＝m ₀+m ₁Ut(k-1)+m ₂Ut(k-2)+m ₃I(k)+m ₄I(k-1)+m ₅I(k-2)(5)

In formula, m ₀, m ₁, m ₂, m ₃, m ₄, m ₅for model difference equation undetermined coefficient, in its value and model, parameter to be identified has functional relation;

Formula (5) is write as form, wherein

θ＝[m ₀，m ₁，m ₂，m ₃，m ₄，m ₅](7)

Step 3.2: the concrete estimation procedure based on the recursive least-squares parameter identification method of forgetting factor:

Determine least square covariance P ₀with the initial value of parameter matrix θ;

Set up least square gain matrix K _k:

$K_k=P_{k-1}{h}_k{(h_k^T{P}_{k-1}{h}_k+\mathrm{\υ})}^{-1}---\left(8\right)$

In formula, υ is least square weighting factor, obtains calculating parameter estimated matrix θ after time-varied gain matrix _k:

${\mathrm{\θ}}_k={\mathrm{\θ}}_{k-1}+K_k(y_k-h_k^T{\mathrm{\θ}}_{k-1})---\left(9\right)$

Y in formula _kfor the terminal voltage measured value in k moment, θ _kfor θ _k-1estimates of parameters in the k-1 moment to the k moment; The renewal of covariance matrix:

$P_k=(I-K_k{h}_k^T)P_{k-1}---\left(10\right)$

Said process completes a step recursion of the Recursive Least Squares based on forgetting factor, repeats this process, picks out m ₀, m ₁, m ₂, m ₃, m ₄, m ₅value, and then draw R _s, R ₁, C ₁, R ₂, C ₂value.

5. a kind of electrokinetic cell SOC line closed loop method of estimation based on N-2RC model according to claim 2, it is characterized in that, the EKF algorithm for estimating described in step 4 is specially:

Step 4.1: the determination drawing estimate equation based on N-2RC model:

x _k＝A _k-1x _k-1+B _k-1u _k-1+ω _k-1(11)

y _k＝C _kx _k+D _ku _k+υ _k(12)

Wherein, x _kit is k moment state variable; y _kit is k moment observational variable; u _kit is the input control variable in k moment; ω _k, υ _kit is mutual incoherent system noise;

Battery status equation is listed according to ampere-hour integral formula and formula (1), (2):

$\left[\begin{array}{c}SOC\left(k\right)\\ U_1\left(k\right)\\ U_2\left(k\right)\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1-\frac{T}{R_1{C}_1}& 0\\ 0& 0& 1-\frac{T}{R_2{C}_2}\end{array}\right]*\left[\begin{array}{c}SOC(k-1)\\ U_1(k-1)\\ U_2(k-1)\end{array}\right]+\left[\begin{array}{c}-\frac{\mathrm{\η}T}{Q_n}\\ \frac{T}{C_1}\\ \frac{T}{C_2}\end{array}\right]*I(k-1)---\left(13\right)$

Know that battery observation equation is by formula (3):

Ut(k)＝Uoc[SOC(k)]-U ₁(k)-U ₂(k)-I(k)Rs(14)

In formula (13), (14), order:

$A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1-\frac{T}{R_1{C}_1}& 0\\ 0& 0& 1-\frac{T}{R_2{C}_2}\end{array}\right],$ $B=\left[\begin{array}{c}-\frac{\mathrm{\η}T}{Q_n}\\ \frac{T}{C_1}\\ T\\ C_2\end{array}\right],$ C＝[Uoc(SOC)-1-1]，D＝[-R _s]

U in observation equation _oc(SOC) be nonlinear function about SOC, the first order Taylor getting equation launches to carry out linearization process, obtains observing matrix $H_k=\left[\begin{array}{ccc}\frac{\∂Uoc}{\∂SOC}& -1& -1\end{array}\right];$

Step 4.2: the state error covariance matrix initial value P determining EKF ₀, system covariance Q ₀and R ₀, start expanded Kalman filtration algorithm;

Wherein, EKF predictive equation is:

The estimation of state variable: x _k=A _k-1x _k-1+ B _k-1u _k-1+ ω _k-1(15)

State covariance is estimated: $P_k=A_{k-1}{P}_{k-1}{A}_{k-1}^T+Q_{k-1}---\left(16\right)$

Kalman gain matrix: K _k=P _kh ^t(HP _kh ^t+ R _k) ^-1(17)

State-updating: x _k+1=x _k+ K _k(y _k-Hx _k) (18)

State covariance is estimated to upgrade: P _k+1=(I-K _kh) P _k(19)

In EKF, terminal voltage estimates that belonging to closed loop estimates, after some step iteration upgrade, and terminal voltage U _tapproaching to reality value gradually; Concentration difference polarizing voltage U simultaneously ₁with activation polarization voltage U ₂value calculated by systematic parameter, then estimate open-circuit voltage and cell emf U according to observation equation (3) _oc; Estimate battery SOC by formula (4), be updated in state equation, utilize ampere-hour integral method to calculate new state estimation, realize the line closed loop method of estimation of SOC.