CN105510829B - A kind of Novel lithium ion power battery SOC methods of estimation - Google Patents

Abstract

The invention discloses a novel method for estimating the SOC of a lithium-ion power battery. The equivalent circuit model of the battery is established, and the parameters of the established battery model are identified using the least squares algorithm; the battery open circuit voltage U _OCV and the corresponding The SOC relationship of SOC is obtained by combining the Shepherd model and the Nernst model to obtain the corresponding function, which fits the relationship between U _OCV and SOC; the state equation and observation equation for SOC estimation are built, and the STF algorithm has strong model uncertainty Robustness, strong ability to track sudden changes, through constant current discharge experiments and UDDS operating conditions, the EKF and STF algorithm estimation of SOC is verified, the results show that the STF algorithm is more accurate than the EKF algorithm in estimating SOC, and Convergence is better.

Description

A Novel SOC Estimation Method for Lithium-ion Power Batteries

technical field

The invention relates to a novel method for estimating the SOC of a lithium-ion power battery.

Background technique

The estimation of the battery state of charge has always been the focus and difficulty of the battery management system. Accurate estimation of the battery SOC is of great significance for improving battery usage efficiency, extending battery life, improving battery safety and reliability, and vehicle energy management, but SOC cannot Direct measurement can only be estimated by other battery parameters such as battery output voltage and current.

At present, the commonly used SOC estimation algorithms at home and abroad are: the ampere-hour integral method, which cannot give the initial value of SOC, and the inaccurate current measurement will lead to the cumulative error of SOC; the open circuit voltage method, which uses the corresponding relationship between the open circuit voltage of the battery and SOC It is simple and easy to estimate the SOC by measuring the open circuit voltage of the battery, but it needs to be estimated after the battery has stood for a period of time, which is not suitable for real-time online estimation of electric vehicles; The instrument measurement is rarely used in real vehicles; the neural network method requires a large amount of data for training, and the estimation error is greatly affected by the training data and training methods, so it has not been well applied yet. The extended Kalman filter algorithm to estimate SOC is a widely used estimation method at home and abroad. It regards SOC as an internal state variable of the battery system, and realizes the minimum variance estimation of SOC through a recursive algorithm. It is more dependent on the battery model. Strong, repeated charging and discharging of the battery during actual use will cause changes in the parameters of the battery model, so using the extended Kalman filter algorithm to estimate the SOC will produce inaccurate estimates or even divergence.

Contents of the invention

In order to solve the deficiencies in the prior art, the present invention discloses a novel method for estimating the SOC of a lithium-ion power battery, which uses a strong tracking filter to estimate the SOC to overcome the inaccurate shortcoming of the extended Kalman filter for estimating the SOC. The strong tracking filter consists of The extended Kalman filter is transformed, mainly for the inaccurate estimation and divergence of the filter caused by the uncertainty of the system model, and has the following advantages: (1) It has strong robustness to the model uncertainty; (2) The ability to track sudden changes is extremely strong, and even when the system reaches an equilibrium state, it still maintains the ability to track slow changes and sudden changes; (3) Moderate computational complexity.

To achieve the above object, the specific scheme of the present invention is as follows:

A novel lithium-ion power battery SOC estimation method, comprising the following steps:

Step 1: Establish a battery equivalent circuit model, and use the least squares algorithm to identify the parameters of the established battery model;

Step 2: According to the battery open-circuit voltage U _OCV and the corresponding SOC relationship identified by the parameters in step 1, the Shepherd model and the Nernst model are used to combine to obtain the corresponding function, which fits the relationship between U _OCV and SOC;

Step 3: Select the terminal voltage and SOC of the capacitor in the battery equivalent circuit model in step 1 as the state variables, build the state equation and observation equation for SOC estimation, adjust the covariance matrix and gain matrix of the state prediction error in real time, and estimate according to the SOC The state equation and observation equation are used to estimate the SOC of lithium-ion power batteries.

The covariance matrix P _k+1 of the state forecast error:

P _k+1 ＝λ _k+1 G _k P _k G ^T _k +Q _k (12)

Among them, λ _(k+1) is the time-varying fading factor, P _k+1 is the error covariance matrix at k+1 time, P _k is the error covariance matrix at k time, Q _k is the system noise covariance, G _k is the Jacobian matrix of the partial derivative of the state equation to the state variable.

The gain matrix K _k+1 :

K _k+1 =P _k+1 H ^T _k+1 [H _k+1 P _k+1 H ^T _k+1 +R _k ] ^-1 (7).

The terminal voltage of the capacitor is C _1c and C _2c when charging, and C _1d and C _2d when discharging, which are replaced by C ₁ and C ₂ in the following descriptions.

The battery equivalent circuit model includes polarization resistance R _1d , capacitance C _1d , polarization resistance R _1c and capacitance C _1c connected in series with corresponding diodes and then connected in parallel to form the first circuit, polarization resistance R _2d , capacitor C _2d , polarization resistor R _2c and capacitor C _2c are connected in series with the corresponding diodes to form the second circuit, and resistors R _od and R _oc are connected in series with the corresponding diodes to form the second circuit. Three circuits, the first circuit, the second circuit and the third circuit are connected in series, one end is connected to the open circuit voltage U _OCV of the battery, and the other end is connected to the open circuit voltage U _O.

When identifying the established battery model, the nominal capacity of the battery is 6.2AH. Under the condition of the battery experiment environment of 25°C, the battery is discharged at a current of 0.5C. When the battery discharges 10% of SOC, it is left to stand for 30 minutes. , the initial value of the battery SOC is 1, after 10 pulse discharges, the battery is fully discharged. The specific method of the parameter identification process: firstly extract the experimental data of each SOC point in the experiment, and use the least square function to perform parameter identification to get The battery model parameters in each state, and finally the parameters of each SOC point are listed in a table.

The formula of the function in the step 2 is:

Among them, SOC refers to the remaining capacity of the battery.

The parameter values of a ₁ to a ₅ were determined by using a custom function in the Curve Fitting Toolbox provided by Matlab software.

Described λ _(k+1) concrete formula is:

N(k+1)＝S ₀ (k+1)-H _k Q _k H ^T _k -βR _k+1 (16)

Among them, H _k is the matrix of the partial derivative of the observation equation to the state variable, R _k+1 is the measurement noise covariance, k=0,1,2,3,... represents the time, r _k+1 represents k+1 Time residual, r(1) represents the residual at time k=0, S ₀ (k) represents the covariance matrix of the residual. In the formula, 0≤ρ≤1 is the forgetting factor, usually ρ=0.95; β≥1 is the weakening factor, the purpose is to make the state estimate smoother.

The conditions satisfied by the gain matrix K _k+1 are:

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)

Among them, r(k+1+j) represents the residual at time k+1+j, x(k+1) represents the state variable at time k+1, and min represents the minimum value, where x(k+1|k +1) represents the estimated value of the state at time k+1.

Beneficial effects of the present invention:

In view of the problem that the estimation accuracy of the extended Kalman filter algorithm is greatly affected by the accuracy of the battery model and the estimation results are easy to diverge, this application proposes to use the strong tracking filter algorithm to estimate the battery SOC, STF on the basis of improving the second-order RC battery equivalent circuit model The algorithm has strong robustness to model uncertainty and strong ability to track sudden changes. Through constant current discharge experiments and UDDS operating conditions experiments, the EKF and STF algorithms are verified to estimate SOC. The results show that the STF algorithm Compared with the EKF algorithm, the SOC estimation accuracy is higher, and the convergence is better. The invention overcomes the shortcoming that the extended Kalman filter algorithm estimates the SOC depends on the accuracy of the battery model, and verifies the validity and correctness of the STF algorithm.

Description of drawings

The improved second-order RC equivalent circuit model of Fig. 1;

Fig. 2 Schematic diagram of the embodiment of the state of charge estimation system for lithium iron phosphate power battery;

Fig. 3 Comparison chart of SOC estimated by two algorithms under UDDS working condition;

Fig. 4 Comparison chart of SOC estimated by two algorithms under constant current discharge.

Detailed ways:

The present invention is described in detail below in conjunction with accompanying drawing:

In order to accurately estimate the state of charge (SOC) of lithium-ion power batteries, the Extended Kalman Filter (EKF) algorithm, which is widely used at present, is greatly affected by the accuracy of the battery model to estimate SOC and the estimation results are easy to diverge. Based on the first-order RC equivalent circuit model, a strong tracking filter (STF) algorithm with strong robustness to model uncertainty and strong tracking ability to sudden changes is proposed for improvement.

The SOC of the battery needs to be estimated during the operation of the electric vehicle. To estimate the SOC of the battery by using the extended Kalman filter and the strong tracking filter, it is necessary to establish a model of the battery. First-order RC battery equivalent circuit model, and on the basis of the second-order RC equivalent circuit model, the model shown in Figure 1 is established considering the different parameters of the charging and discharging directions.

The parameters of the battery model can be identified using the least squares algorithm. Each parameter in the model changes with the state of charge. Refer to the Hybrid Pulse PowerTest (HPPT) test in the "Freedom CAR Battery Test Manual", which can Get the various parameters in the battery model. The experimental research object of this application is a lithium-ion power battery produced by a domestic company. Its nominal capacity is 6.2AH. Under the condition of the battery experiment environment of 25°C, it is discharged at a current of 0.5C. When the battery discharges 10% of SOC, After standing for 30 minutes, the initial value of the battery SOC is 1, and the battery is fully discharged after 10 pulse discharges. The specific method of the parameter identification process: firstly extract the experimental data of each SOC point in the experiment, and use the least square function to perform parameter identification to obtain the battery model parameters in each state, and finally list the parameters of each SOC point as shown in the table 1. The parameter identification process of the charging direction of the battery is similar to that of the discharging direction, and will not be repeated here.

Table 1 Identification results of discharge direction parameters of the second-order RC model

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 the relationship between the battery open circuit voltage U _OCV and the corresponding SOC identified by the above parameters, the relationship between U _OCV and SOC is fitted by using the formula 1 obtained by combining the Shepherd model and the Nernst model, making the battery equivalent circuit model more accurate. The values of parameters a ₁ to a ₅ can be determined by using a custom function in the Curve Fitting Toolbox provided by Matlab software.

SOC estimation algorithm based on extended Kalman filter: the extended Kalman filter algorithm is a linear minimum variance estimation method using recursion. In order to use the extended Kalman filter method, it is necessary to construct the state space equation of the system, taking into account the random interference of the system Combined with the measurement noise and the SOC estimation of the ampere-hour integration method, on the basis of the improved second-order RC equivalent circuit model, the terminal voltages of capacitors C ₁ and C ₂ in the improved second-order RC equivalent battery model are selected (C ₁ is C _1c , C ₂ is C _2c , C ₁ is C _1d , C ₂ is C _2d ) and SOC is the state variable during discharge, and the state equation and observation equation for SOC estimation are constructed as follows:

x _k+1 ＝Ax _k +Bu _k +w _k (2)

y _k+1 ＝Cx _k+1 +v _k+1 (3)

Among them, x _k , u _k , y _k+1 are the state variables, input and output of the system respectively; w _k represents the process noise caused by system disturbance and model inaccuracy; v _k+1 represents the measurement error etc.; A, B, and C are the equation matching coefficients used to reflect the dynamic characteristics of the system.

Battery terminal voltage equation:

in

Among them, U _B (k+1) is the terminal voltage of the battery at time k+1; U _OCV (k+1) is the open circuit voltage of the battery at time k+1; SOC _k is the remaining capacity of the battery at time k; U ₁ (k ), U ₂ (k) are the voltages across capacitors C ₁ and C ₂ respectively (i.e. the terminal voltages of C _1d /C _1c , C _2d /C _2c , which are C _1c and C _2c when charging, and C _1d and C 2c when discharging. C _2d ); τ ₁ ＝R ₁ C ₁ , τ ₂ ＝R ₂ C ₂ (R ₁ ＝R _1c , C ₁ ＝R _1c , R ₂ ＝R _2c , C ₂ ＝R _2c , during discharge, R ₁ =R _1d , C ₁ =R _1d , R ₂ =R _2d , C ₂ =R _2d ); Q _N is the rated capacity of the battery. Δt represents the time difference between time k and k+1 time.

The recursive process of SOC estimation based on the extended Kalman filter algorithm is shown in the following formula.

(1) Predict the state value at time k+1: predict the error covariance matrix at time k+1, calculate the gain matrix K _k+1 , update the state estimation value according to the observed value, and update the error covariance matrix.

x _k+1 =Ax _k +Bu _k (5)

(2) Predict the error covariance matrix at time k+1:

(3) Calculate the gain matrix K _k+1 :

K _k+1 ＝P _k+1 H ^T _k+1 [H _k+1 P _k+1 H ^T _k+1 +R _k ] ^-1 (7)

(4) Update state estimates based on observations:

x _k+1 ＝x _k+1 +K _k+1 r _k+1 (8)

(5) Update the error covariance matrix:

P _k+1 ＝(IK _k+1 H _k+1 )P _k+1 (9)

In the above formula, the residual r _k+1 = y _k+1 -y _k+1 , y _k+1 is the actual measured value, y _k+1 is the estimated value corresponding to the state x _k+1 , Q _k is the system noise covariance, R _k is the measurement noise covariance, and P _k+1 is the error covariance, which reflects the degree of inconsistency between the estimated value and the real value of the state variable. G _k is the Jacobian matrix of the partial derivative of the state equation to the state variable at time k.

The strong tracking filter is an improvement of the Kalman filter, and the sufficient condition for the establishment of the strong tracking filter is to select the appropriate time-varying gain matrix K _k+1 so that the following formula holds.

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 influence of model uncertainty, the estimated actual value of the filter will be inaccurate, which must be reflected in the mean and amplitude of the output residual sequence. If the system can automatically adjust the gain matrix K _k+1 online, the formula (10 ) is established, that is, the output residual is forced to have a property similar to Gaussian white noise, which extracts the effective information in the output residual. If the uncertainty of the model does not exist, the strong tracking filter does not play a regulating role, and the strong tracking filter is a Kalman filter at this time. The improvement of the strong tracking filter to the Kalman filter is: real-time adjustment of the covariance matrix and gain matrix of the state forecast error, modifying the formula (6) as

P _k+1 ＝λ _k+1 G _k P _k G ^T _k +Q _k (12)

where λ _(k+1) is the time-varying fading factor:

N(k+1)＝S ₀ (k+1)-H _k Q _k H ^T _k -βR _k+1 (16)

In the formula, 0≤ρ≤1 is the forgetting factor, usually ρ=0.95; β≥1 is the weakening factor, the purpose is to make the state estimate smoother.

Experiment verification analysis: In order to verify the effectiveness of the strong tracking filter algorithm for estimating SOC, the AVL-Estorage equipment platform is used to conduct experiments covering the entire range of battery SOC on the battery. The test equipment can simulate urban road conditions and charge and discharge the battery with constant current , UDDS working conditions and other experiments. The structure diagram of an embodiment of the state of charge estimation system for lithium iron phosphate power battery is shown in Figure 2, including a temperature control box, voltage/current detection equipment, a controller and a display. The controller includes a microprocessor, program memory, CAN bus interface, several IO ports, etc. The controller is connected to the temperature control box and voltage/current detection equipment through the CAN bus. The temperature control box is used to keep the ambient temperature constant. The software of the tester can be programmed to set the battery experiment limit conditions to prevent the battery from overcharging and over-discharging, and can record the test current, voltage, SOC and temperature in detail. In the single charge and discharge process of the battery, the ampere-hour measurement method is more accurate in estimating the SOC, so the SOC value obtained by the ampere-hour integration method is used as the actual value of the SOC in this experiment. The experimental object is a lithium iron phosphate battery with a capacity of 6.2AH produced by a domestic company, and the ambient temperature is controlled at 25°C.

(1) UDDS operating condition experiment SOC estimation verification

This article uses the international general urban road cycle conditions (Urban Dynamometer Driving Schedule, abbreviated as UDDS), using the standard test conditions as a reference, according to the actual situation of the laboratory lithium iron phosphate battery, through a certain ratio to obtain the UDDS conditions used in the experiment Current, the lithium iron phosphate battery is discharged under the UDDS working condition with the initial SOC value of 0.99206. This working condition includes 6 UDDS working condition cycles. Assuming that the STF estimated and EKF estimated SOC initial values are both 0.7, the actual value of the SOC in the UDDS working condition experiment , The comparison of STF estimated SOC value and EKF estimated SOC value is shown in Figure 3.

(2) Constant current discharge experiment SOC estimation verification

A constant current discharge experiment with an initial value of SOC of 0.996 is carried out on a lithium iron phosphate battery. Assuming that the initial value of SOC estimated by STF and EKF is both 0.8, the actual value of SOC in constant current discharge experiment, the estimated SOC value of STF algorithm and the estimated SOC of EKF algorithm are relatively For example, as shown in Figure 4

From the verification results in Figures 3 to 4 above, it can be seen that the estimation of SOC based on the STF algorithm is more accurate than the estimation of the SOC by the EKF algorithm, and the convergence speed of the estimated initial value is faster. The STF algorithm overcomes the disadvantage that the estimation of the SOC by the EKF algorithm is easy to diverge.

Claims (6)

1. A novel lithium ion power battery SOC estimation method is characterized by comprising the following steps:

the method comprises the following steps: establishing a battery equivalent circuit model, and identifying the parameters of the established battery model by using a least square algorithm;

step two: battery open circuit voltage U identified according to step one parameter_OCVAnd combining the corresponding SOC relation with the Shepherd model and the Nernst model to obtain a corresponding function, wherein the function fits U_OCVAnd SOC relationship;

step three: selecting the terminal voltage and the SOC of a capacitor in the battery equivalent circuit model in the first step as state variables, constructing a state equation and an observation equation of SOC estimation, adjusting a covariance matrix and a gain matrix of a state prediction error in real time, and estimating the SOC of the lithium ion power battery according to the state equation and the observation equation of the SOC estimation;

the battery equivalent circuit model comprises a polarization resistor R_1dCapacitor C_1dPolarization resistance R_1cAnd a capacitor C_1cThe circuits connected in series with the corresponding diodes are connected in parallel to form a first circuit, and the polarization resistor R_2dCapacitor C_2dPolarization resistance R_2cAnd a capacitor C_2cThe circuits connected in series with the corresponding diodes are respectively connected in parallel to form a second circuit, and a resistor R_odAnd R_ocThe circuit is connected in parallel with the corresponding diode to form a third circuit, and one end of the first circuit, the second circuit and the third circuit is connected in series and then is connected with the open-circuit voltage U of the battery_OCVConnected with the other end of the open circuit voltage U_OConnecting;

the formula of the function in the second step is as follows:

<mrow> <msub> <mi>U</mi> <mrow> <mi>O</mi> <mi>C</mi> <mi>V</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mi>ln</mi> <mrow> <mo>(</mo> <mi>S</mi> <mi>O</mi> <mi>C</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <mi>ln</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>S</mi> <mi>O</mi> <mi>C</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>a</mi> <mn>4</mn> </msub> <mrow> <mi>S</mi> <mi>O</mi> <mi>C</mi> </mrow> </mfrac> <mo>+</mo> <msub> <mi>a</mi> <mn>5</mn> </msub> <mi>S</mi> <mi>O</mi> <mi>C</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

wherein SOC is the remaining capacity of the battery, a₁～a₅Is the parameter to be solved.

2. The SOC estimation method for Li-ion power battery as claimed in claim 1, wherein the covariance matrix P of the state prediction error_k+1：

P_k+1＝λ_k+1G_kP_kG^T _k+Q_k(12)

Wherein λ is_(k+1)Being a time-varying fading factor, P_k+1Is the error covariance matrix at time k +1, P_kIs the error covariance matrix at time k, Q_kIs the system noise covariance, G_kThe Jacobian matrix of the state variables is derived for the state equations.

3. The novel lithium-ion power battery SOC estimation method according to claim 2, wherein the 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_kthe method is to measure the covariance of noise, x is the state variable of the system, and C is the equation matching coefficient used for representing the dynamic characteristic of the system.

4. The method according to claim 1, wherein when identifying the established battery model, the nominal capacity of the battery is 6.2AH, the battery is discharged at a current of 0.5C under a battery experimental environment of 25 ℃, the battery is left standing for 30 minutes every time 10% of SOC of the battery is discharged, the initial value of the battery SOC is 1, the battery is discharged after 10 pulses of discharge, and the parameter identification process specifically comprises: firstly, respectively extracting experimental data of each SOC point of an experiment, carrying out parameter identification by using a least square function to obtain battery model parameters under each state, and finally listing the parameters of each SOC point into a table.

5. The novel lithium-ion power battery SOC estimation method according to claim 2, wherein λ is_(k+1)The concrete formula is as follows:

<mrow> <msub> <mi>&amp;lambda;</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>&amp;lambda;</mi> <mn>0</mn> </msub> </mtd> <mtd> <mrow> <msub> <mi>&amp;lambda;</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <msub> <mi>&amp;lambda;</mi> <mn>0</mn> </msub> <mo>&lt;</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>&amp;lambda;</mi> <mn>0</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mi>t</mi> <mi>r</mi> <mo>&amp;lsqb;</mo> <mi>N</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>t</mi> <mi>r</mi> <mo>&amp;lsqb;</mo> <mi>M</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>

N(k+1)＝S₀(k+1)-H_kQ_kH^T _k-βR_k+1(16)

<mrow> <mi>M</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>H</mi> <mi>k</mi> </msub> <msub> <mi>G</mi> <mi>k</mi> </msub> <msub> <mi>P</mi> <mi>k</mi> </msub> <msubsup> <mi>G</mi> <mi>k</mi> <mi>T</mi> </msubsup> <msubsup> <mi>H</mi> <mi>k</mi> <mi>T</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>S</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>r</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <msup> <mi>r</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <msub> <mi>&amp;rho;S</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>r</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <msub> <msup> <mi>r</mi> <mi>T</mi> </msup> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>&amp;rho;</mi> </mrow> </mfrac> </mtd> <mtd> <mrow> <mi>k</mi> <mo>&amp;GreaterEqual;</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>

wherein H_kMatrix of state variables partial derivatives for the observation equation, R_k+1To measure the noise covariance, k is 0,1Denotes the time, r_k+1Denotes a residual at time k +1, r (1) denotes a residual at time k ═ 0, and S₀(k) and expressing a covariance matrix of residual errors, wherein rho is more than or equal to 0 and less than or equal to 1 and is a forgetting factor, and the rho is generally equal to 0.95 and beta is more than or equal to 1 and is a weakening factor.

6. The novel lithium-ion power battery SOC estimation method according to claim 3, wherein the gain matrix K_k+1The conditions are satisfied as follows:

E[r(k+1+j)r^T(k+1+j)]＝0，k＝0,1,2,...，j＝1,2,3,... (10)

<mrow> <mi>E</mi> <mo>&amp;lsqb;</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>=</mo> <mi>min</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>

where r (k +1+ j) represents the residual at time k +1+ j, x (k +1) represents the state variable at time k +1, and min represents the minimum value, whereRepresenting an estimate of the state at time k + 1.