CN105548896B

CN105548896B - Online closed-loop estimation method of power battery SOC based on N-2RC model

Info

Publication number: CN105548896B
Application number: CN201510990797.9A
Authority: CN
Inventors: 赵万忠; 孔祥创; 王春燕; 杨遵四
Original assignee: Nanjing University of Aeronautics and Astronautics
Current assignee: Nanjing University of Aeronautics and Astronautics
Priority date: 2015-12-25
Filing date: 2015-12-25
Publication date: 2019-04-09
Anticipated expiration: 2035-12-25
Also published as: CN105548896A

Abstract

The power battery SOC line closed loop estimation method based on N-2RC model that the invention discloses a kind of, this method combination electrochemical model and equivalent-circuit model, propose a kind of novel power battery model, N-2RC model proposed by the present invention replaces the electromotive force part of Order RC equivalent-circuit model using Nernst electrochemical model, more can accurately reflect cell emf and the one-to-one relationship of SOC；On the basis of this model, model parameter is picked out using the recursive least squares algorithm based on forgetting factor, realizes that the line closed loop of battery SOC is estimated using expanded Kalman filtration algorithm later；The characteristic of battery can be described well from the angle of electrochemistry by overcoming electrochemical model, but its structure is complex, be not suitable for the problem of being used alone, and it overcomes equivalent-circuit model and belongs to external characteristics model, the problem of can be good at expressing the C-V characteristic relationship of battery, but cannot reflecting the bulk properties of battery.

Description

Power battery SOC line closed loop estimation method based on N-2RC model

Technical field

The invention belongs to charge states of lithium ion batteries to predict field, be related to the power battery SOC based on N-2RC model and exist Line closed loop estimation method.

Background technique

In power battery management system, the prediction of battery charge state SOC (State Of Charge) has important meaning Justice, the accuracy of prediction, directly affects the control strategy of battery management system, to influence performance and the battery of battery performance The length in service life.

Meanwhile accurate battery model has great importance for the assessment algorithm of state-of-charge SOC, since battery has There is a non-linear behavior of height, the consistency of battery model and power battery is very good, can just obtain more accurately prediction knot Fruit.

Currently, common power battery model has three classes: electrochemical model, artificial nerve network model and equivalent circuit mould Type.The electrochemical reaction process of inside battery can be described in more detail in electrochemical model, but its structure is extremely complex, uncomfortable Close battery SOC estimation；Artificial nerve network model has the characteristics that the non-linear of height, fault-tolerance, the property learnt by oneself, and essence may be implemented True SOC estimation, but disadvantage is that need a large amount of experimental data to predict the performance of battery, and to battery history number According to dependence it is larger；Equivalent-circuit model forms circuit network by circuit elements such as traditional resistance, capacitor, constant pressure sources The external characteristics for describing power battery is often used by researcher since its structure is simple and can describe battery behavior well.

Power battery SOC estimation method mainly has: open circuit voltage method, current integration method, Kalman filtering method.Open-circuit voltage Method can only realize offline estimation in laboratory conditions, be unable to real-time estimation；Current integration method classics are easy-to-use, but its estimated accuracy It is affected by the precision of SOC initial value and current measurement value；Kalman filter method has Extended Kalman filter, without mark karr again The types such as graceful filtering, adaptive Kalman filter, Kalman filtering method can more accurately predict SOC value, be that battery SOC is estimated Meter studies most commonly used method.

Summary of the invention

The invention aims to solve power battery SOC On-line Estimation to be influenced by model, the low problem of estimated accuracy, Provide a kind of power battery SOC line closed loop estimation method based on N-2RC model.

Power battery SOC line closed loop estimation method of the present invention based on N-2RC model, it the following steps are included:

Step 1: in conjunction with electrochemical model and Order RC equivalent-circuit model, the voltage and current of N-2RC battery model is established Relational expression；

Step 2: carrying out pulse charge-discharge test to tested lithium battery, records each pulse charging-discharging cycle and stands one section Battery SOC and open-circuit voltage U after time_oc, as a result, it has been found that open-circuit voltage values when same battery SOC point is to inductive charging want bigger Value when electric discharge, illustrates the delayed action of battery, takes the average value of charge and discharge measured value as open-circuit voltage U_oc.By closing It is formula U_oc=K₀+K₁In(SOC)+K₂In (1-SOC) fits a nonlinear curve, takes suitable K₀、K₁、K₂Value, makes to be fitted Curve approaching to reality value；

Step 3: the end voltage and output electric current of tested ferric phosphate lithium ion battery are acquired, is calculated using measured value as identification The observation of method is then based on the recursive least squares algorithm containing forgetting factor, picks out time varying system parameter R_s、R₁、R₂、C₁、C₂；

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

The determination of N-2RC model equation in step 1:

U_t=U_oc-U₁-U₂-IR_S； (3)

U_oc=K₀+K₁ln(SOC)+K₂ln(1-SOC)； (4)

Wherein, U_ocFor open-circuit voltage；U_tTo hold voltage；I is electric current；R_sFor ohmic internal resistance；R₁、C₁Indicate concentration difference polarization Reflection, R₁For concentration difference polarization resistance, C₁For concentration difference polarization capacity, U₁For concentration difference polarizing voltage；R₂、C₂Indicate electrochemistry pole Change reflection, R₂For activation polarization internal resistance, C₂For activation polarization capacitor, U₂For activation polarization voltage.

Battery impulse charge and discharge experiment is carried out in step 2.It is first fully charged to battery, it shelves 5 hours；It is put with C/3 constant current Electricity stops electric discharge after releasing the 10% of battery capacity, shelves 5 hours, measure the open-circuit voltage of battery；A upper process is repeated, directly To discharge cut-off voltage.With C/3 constant-current charge, stops charging after being charged to the 10% of battery capacity, shelve 5 hours, measure battery Open-circuit voltage；A upper process is repeated, until charging current is less than C/20.The corresponding open-circuit voltage measured value of charge and discharge is averaged Value is used as U_oc.By 10% 0.1 to 100% corresponding U of interval_ocValue and relational expression (4) find out parameter K by curve matching₀、 K₁、K₂。

The specific steps of the recursive least-squares parameter identification method based on forgetting factor are carried out in step 3 are as follows:

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

U_t(k)=m₀+m₁U_t(k-1)+m₂U_t(k-2)+m₃I(k)+m₄I(k-1)+m₅I(k-2) (5)

In formula, m₀、m₁、m₂、m₃、m₄、m₅For model difference equation undetermined coefficient, parameter Cheng Han to be identified in value and model Number relationship.

Formula (5) can be write asForm, wherein

θ=[m₀, m₁, m₂, m₃, m₄, m₅] (7)

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

Determine least square covariance P₀With the initial value of parameter matrix θ.

Establish least square gain matrix K_k:

υ is least square weighted factor in formula.

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

Y in formula_kFor the end voltage measuring value at k moment, θ_kFor θ_k-1At the k-1 moment to the estimates of parameters at k moment.

The update of covariance matrix:

In this way, just completing a step recursion of the recursive least squares algorithm based on forgetting factor, this process, identification are repeated M out₀、m₁、m₂、m₃、m₄、m₅Value, and then obtain R_s、R₁、C₁、R₂、C₂Value.

Extended Kalman filter algorithm for estimating in step 4:

Step 4.1: based on the determination of N-2RC model estimation 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 at k moment；ω_k、υ_k It is irrelevant system noise.

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

Battery observational equation is known by formula (3) are as follows:

U_t(k)=U_oc[SOC(k)]-U₁(k)-U₂(k)-I(k)R_S (14)

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

U in observational equation_oc(SOC) it is nonlinear function about SOC, the first order Taylor of equation is taken to be unfolded to be linearized Processing, obtains observing matrix

Step 4.2: determining the state error covariance matrix initial value P of Extended Kalman filter₀, system covariance Q₀And R₀, Start expanded Kalman filtration algorithm.

Extended Kalman filter 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 estimation:

Kalman gain matrix:

State-updating: x_k+1=x_k+K_k(y_k-H_kx_k) (18)

State covariance estimation updates: P_k+1=(I-K_kH_k)P_k (19)

The estimation of Extended Kalman filter middle-end voltage belongs to closed loop estimation, after the update of several step iteration, holds voltage U_t Gradually approaching to reality value；U simultaneously₁And U₂Value be calculated by system parameter, estimate electricity further according to observation equation (3) Pond electromotive force U_oc；Battery SOC is estimated by formula (4), is updated in state equation, new state is calculated using current integration method and estimates Evaluation realizes the line closed loop estimation method of SOC.

The invention adopts the above technical scheme compared with prior art, has following technical effect that

Present invention incorporates Nernst electrochemical models can more fully describe power battery interior reaction process and two The advantages such as the strong dynamically adapting characteristic of rank RC model and dynamic simulation precision；Then the recursion minimum two based on forgetting factor is used Multiply method realize N-2RC model on-line parameter identification；Finally the system parameter based on time-varying passes through Extended Kalman filter Algorithm completes the line closed loop estimation of battery SOC, the expanded Kalman filtration algorithm of suitable battery model and line closed loop It ensure that the precision of battery SOC estimation is relatively high.

Detailed description of the invention

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

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

Fig. 2 is the implementation flow chart of the method for the present invention；

Fig. 3 is that the single lithium battery voltage pattern measured is tested under UDDS operating condition；

Fig. 4 is that the single lithium battery current graph measured is tested under UDDS operating condition；

Fig. 5 is the end voltage measuring value and estimated value comparison diagram obtained under UDDS operating condition using Extended Kalman filter；

Fig. 6 is the end voltage measuring value and estimate error figure obtained under UDDS operating condition using Extended Kalman filter；

Fig. 7 is the battery SOC estimated value obtained under UDDS operating condition using Extended Kalman filter and reference value comparison diagram；

Fig. 8 is the battery SOC estimated value and reference value Error Graph obtained under UDDS operating condition using Extended Kalman filter.

Specific embodiment

The present invention provides the power battery SOC line closed loop estimation method based on N-2RC model, to make mesh of the invention , technical solution and effect are clearer, clear, and referring to attached drawing and give an actual example that the present invention is described in more detail.It answers Work as understanding, specific implementation described herein is not intended to limit the present invention only to explain the present invention.

Embodiment uses a kind of load of urban highway traffic operating condition (UDDS) as lithium ion battery, this operating condition electric current becomes Change larger, increases difficulty to On-line Estimation battery SOC, can but verify the applicability of model and the estimation of algorithm for estimating well Precision.Fig. 3, Fig. 4 are the battery terminal voltage and output electric current of acquisition.The implementation step of the present embodiment is illustrated below with reference to Fig. 2 Suddenly.

Step 1: N-2RC model equation as shown in Figure 1 is established:

U_t=U_oc-U₁-U₂-IR_S； (3)

U_oc=K₀+K₁ln(SOC)+K₂ln(1-SOC)； (4)

Step 2: charging, discharging electric batteries pulse test is carried out.It is first fully charged to battery, it shelves 5 hours；It is put with C/3 constant current Electricity stops electric discharge after releasing the 10% of battery capacity, shelves 5 hours, measure the open-circuit voltage of battery；A upper process is repeated, directly To discharge cut-off voltage.With C/3 constant-current charge, stops charging after being charged to the 10% of battery capacity, shelve 5 hours, measure battery Open-circuit voltage；A upper process is repeated, until charging current is less than C/20.The corresponding open-circuit voltage measured value of charge and discharge is averaged Value is used as U_oc.By 10% 0.1 to 100% corresponding U of interval_ocValue and relational expression (4) find out parameter K by curve matching₀、 K₁、K₂。

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

U_t(k)=m₀+m₁U_t(k-1)+m₂U_t(k-2)+m₃I(k)+m₄I(k-1)+m₅I(k-2) (5)

Formula (5) can be write asForm, wherein

θ=[m₀, m₁, m₂, m₃, m₄, m₅] (7)

Establish least square gain matrix K_k:

υ is least square weighted factor in formula, takes υ=0.98.

The update of covariance matrix:

Step 4: Extended Kalman filter algorithm for estimating:

Step 4.1: based on the determination of N-2RC model estimation 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)

Battery observational equation is known by formula (3) are as follows:

U_t(k)=U_oc[SOC(k)]-U₁(k)-U₂(k)-I(k)R_S (14)

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

Extended Kalman filter 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 estimation:

Kalman gain matrix:

State-updating: x_k+1=x_k+K_k(y_k-H_kx_k) (18)

State covariance estimation updates: P_k+1=(I-K_kH_k)P_k (19)

For effect picture of the invention as shown in Fig. 5 to Fig. 8, Fig. 5 is battery terminal voltage estimated value and experiment value under UDDS operating condition Comparison diagram, hold voltage measuring value fluctuation larger as can be seen from Figure, but estimated value is still very close to measured value.Fig. 6 is more direct Illustrate the accuracy of end voltage estimation, wherein U_tWorst error in 0.05V or so, the error of most of the time is in 0.02V Left and right.Fig. 7 is the comparison diagram of battery SOC estimated value and reference value under UDDS operating condition, due to the nonlinearity characteristic of battery, very Real SOC value is difficult to obtain, and the present invention is using laboratory reference value as SOC true value.Fig. 8 shows the worst error of SOC estimation 4% or so, the error of most of the time is 2% or so.This illustrates battery model and SOC estimation method proposed by the present invention It can be good at being suitable for battery SOC estimation.

The foregoing description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, as defined herein General Principle can be realized in other embodiments without departing from the spirit or scope of the present invention.Therefore, of the invention It is not intended to be limited to the embodiments shown herein, and is to fit to and the principles and novel features disclosed herein phase one The widest scope of cause.

Claims

1. An online closed-loop estimation method of power battery SOC based on the N-2RC model, characterized in that the method comprises the following steps:

Step 1: Combine the electrochemical model and the second-order RC equivalent circuit model to establish the voltage-current relationship of the N-2RC battery model;

Step 2: Perform pulse charge and discharge experiments on the lithium battery under test, record the battery SOC and open circuit voltage measurement values after each pulse charge and discharge cycle for a period of time, and take the average value of the charge and discharge open circuit voltage measurements as the open circuit voltage U _oc , a nonlinear curve is fitted by the relationship U _oc =K ₀ +K ₁ In(SOC)+K ₂ In(1-SOC), and appropriate K ₀ , K ₁ , and K ₂ values are selected to fit the The curve approximates the true value;

Step 3: Collect the terminal voltage and output current of the lithium-ion battery under test, take the measured value as the observation value of the identification algorithm, and then identify the system parameters that change with time based on the recursive least squares algorithm with forgetting factor;

Step 4: Carry out battery SOC estimation based on extended Kalman filter according to the time-varying system parameters obtained in step 3, and use the estimated output SOC as the input of SOC in the open-circuit voltage function to realize online closed-loop estimation of battery SOC.

2. The power battery SOC online closed-loop estimation method based on the N-2RC model according to claim 1, wherein the determination process of the N-2RC model equation described in step 1 is:

U _t =U _oc -U ₁ -U ₂ -IR _S ; (3)

U _oc =K ₀ +K ₁ ln(SOC)+K ₂ ln(1-SOC); (4)

Among them, U _oc is the open circuit voltage; U _t is the terminal voltage; I is the current; R _s is the ohmic internal resistance; R ₁ and C ₁ represent the concentration difference polarization reflection, R ₁ is the concentration difference polarization internal resistance, and C ₁ is the Concentration difference polarization capacitance, U ₁ is the concentration difference polarization voltage; R ₂ and C ₂ represent the electrochemical polarization reflection, R ₂ is the electrochemical polarization internal resistance, C ₂ is the electrochemical polarization capacitance, and U ₂ is the electrical polarization Chemical polarization voltage.

3. The power battery SOC online closed-loop estimation method based on the N-2RC model according to claim 2, wherein the specific process of performing the battery pulse charge-discharge experiment in the step 2 is:

Fully charge the battery first and leave it for 5 hours; discharge with a constant current of C/3, stop discharging after 10% of the battery capacity is released, leave it for 5 hours, and measure the open circuit voltage of the battery; repeat the previous process until the discharge cut-off voltage;

Then charge with a constant current of C/3, stop charging after charging to 10% of the battery capacity, leave it for 5 hours, and measure the open-circuit voltage of the battery; repeat the previous process until the charging current is less than C/20; among them, the charging and discharging are correspondingly open-circuit The average value of the voltage measurements is taken as the open circuit voltage U _oc , and the parameters K ₀ , K ₁ , and K ₂ are obtained by curve fitting from the U _oc value corresponding to the 10% interval 0.1 to 100% and the relational formula (4).

4. The power battery SOC online closed-loop estimation method based on N-2RC model according to claim 2, is characterized in that, the concrete steps of carrying out the recursive least squares parameter identification method based on forgetting factor in step 3 are:

Step 3.1: Discretize equations (1), (2) and (3) in step 1 to obtain the model difference equation

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

In the formula, m ₀ , m ₁ , m ₂ , m ₃ , m ₄ , m ₅ are the undetermined coefficients of the model difference equation, and their values have a functional relationship with the parameters to be identified in the model;

Write equation (5) as in the form of

θ=[m ₀ , m ₁ , m ₂ , m ₃ , m ₄ , m ₅ ] (7)

Step 3.2: The specific estimation process of the recursive least squares parameter identification method based on the forgetting factor:

Determine the initial value of the least squares covariance P ₀ and the parameter matrix θ;

Build the least squares gain matrix K _k :

where υ is the least square weighting factor, and the parameter estimation matrix θ _k is calculated after obtaining the gain matrix that changes with time:

In the formula, y _k is the terminal voltage measurement value at time k, θ _k is the parameter estimation value of θ _k-1 at time k-1 at time k; the update of the covariance matrix:

The above process completes the one-step recursion of the recursive least squares algorithm based on the forgetting factor. Repeat this process to identify the values of m ₀ , m ₁ , m ₂ , m ₃ , m ₄ , and m ₅ , and then obtain R _s , R ₁ , C ₁ , R ₂ , C ₂ values.

5. The power battery SOC online closed-loop estimation method based on the N-2RC model according to claim 2, wherein the extended Kalman filter estimation algorithm described in step 4 is specifically:

Step 4.1: Determine the estimation equation based on the N-2RC model:

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

y _k =C _k x _k +D _k u _k +υ _k (12)

Among them, x _k is the state variable at time k; y _k is the observed variable at time _k ; uk is the input control variable at time k; ω _k , υ _k are uncorrelated system noises;

According to the ampere-hour integral formula and formulas (1) and (2), the battery state equation is listed:

From equation (3), we know that the battery observation equation is:

U _t (k)=U _oc [SOC(k)]-U ₁ (k)-U ₂ (k)-I(k)R _S (14)

In formulas (13) and (14), let:

C=[U _oc (SOC) -1 -1], D=[-R _s ]

In the observation equation, U _oc (SOC) is a nonlinear function of SOC. Taking the first-order Taylor expansion of the equation to linearize it, the observation matrix is obtained.

Step 4.2: Determine the initial value of the state error covariance matrix P ₀ , the system covariance Q ₀ and the observation covariance R ₀ of the extended Kalman filter, where Q _k-1 is the system noise covariance at time k-1 , where R _k in equation (17) is the observation noise co-prevention difference at time k, and the extended Kalman filter algorithm is activated;

Among them, the extended Kalman filter prediction equation is:

Estimation of state variables: x _k =A _k-1 x _k-1 +B _k-1 u _k-1 +ω _k-1 (15)

State covariance estimate:

Kalman gain matrix:

State estimate update: x _k+1 = x _k +K _k (y _k -H _k x _k ) (18)

State covariance estimation update: P _k+1 = (IK _k H _k )P _k (19)

The terminal voltage estimation in the extended Kalman filter belongs to the closed-loop estimation. After several steps of iterative updating, the terminal voltage U _t gradually approaches the real value; at the same time, the values of the concentration difference polarization voltage U ₁ and the electrochemical polarization voltage U ₂ are calculated by the system parameters Obtained, and then according to the observation equation (3) to estimate the open circuit voltage U _oc that is the battery electromotive force; from the equation (4) to estimate the battery SOC, substitute it into the state equation, and use the ampere-hour integration method to calculate a new state estimate value to achieve SOC The online closed-loop estimation method for .