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

Abstract

The invention discloses a kind of Novel lithium ion power battery SOC methods of estimation, battery equivalent circuit model is established, the battery model parameter of foundation is recognized using least-squares algorithm；The battery open circuit voltage U come out according to step 1 parameter identification_OCVWith corresponding SOC relations, it is combined to obtain corresponding function using Shepherd models and Nernst models, Function Fitting U_OCVWith SOC relations；Build the state equation and observational equation of SOC estimations, STF algorithms have the stronger robustness on model uncertainty, the extremely strong ability of tracking on mutation status, SOC, which is verified, to be estimated to EKF and STF algorithms by constant-current discharge experiment and UDDS working condition experimentings, as a result show that STF algorithms are higher than EKF algorithm estimation SOC precision, and convergence is more preferable.

Description

Novel lithium ion power battery SOC estimation method

Technical Field

The invention relates to a novel lithium ion power battery SOC estimation method.

Background

The estimation of the state of charge of the battery is always the key and difficult point of a battery management system, the accurate estimation of the SOC of the battery has important significance for improving the service efficiency of the battery, prolonging the service life of the battery, improving the safety and reliability of the battery and managing the energy of the whole vehicle, but the SOC cannot be directly measured and can only be estimated through other battery parameters such as the output voltage and the current of the battery.

At present, the SOC estimation algorithm commonly used at home and abroad is as follows: an ampere-hour integration method cannot give an initial value of the SOC, and the SOC accumulation error can be caused by inaccurate current measurement; the open-circuit voltage method is simple and easy to implement, estimates the SOC by measuring the open-circuit voltage of the battery by utilizing the corresponding relation between the open-circuit voltage and the SOC of the battery, can estimate the SOC after the battery is kept still for a period of time, and is not suitable for the requirement of real-time online estimation of an electric automobile; the internal resistance method is suitable for SOC estimation at the later stage of battery discharge, needs special instrument measurement and is rarely used in practical vehicles; the neural network method needs a large amount of data for training, estimation errors are greatly influenced by the training data and the training method, and the neural network method is not well applied at present. The SOC is estimated by the extended Kalman filtering algorithm, which is a widely applied estimation method at home and abroad at present, the SOC is regarded as an internal state variable of a battery system, the minimum variance estimation of the SOC is realized by a recursion algorithm, the minimum variance estimation of the SOC has strong dependence on a battery model, and the battery is repeatedly charged and discharged in the actual use process to cause the change of parameters of the battery model, so that the estimation of the SOC by the extended Kalman filtering algorithm is inaccurate and even divergent.

Disclosure of Invention

In order to solve the defects in the prior art, the invention discloses a novel lithium ion power battery SOC estimation method, which adopts a strong tracking filter to estimate SOC, overcomes the defect of inaccurate SOC estimation of an extended Kalman filter, is formed by transforming the strong tracking filter by the extended Kalman filter, mainly aims at solving the problems of inaccurate estimation and divergence of the filter caused by uncertainty of a system model, and has the following advantages: (1) the robustness to model uncertainty is strong; (2) the tracking capability to the mutation state is extremely strong, and even when the system reaches the equilibrium state, the tracking capability to the slow change state and the mutation state is still maintained; (3) moderate computational complexity.

In order to achieve the purpose, the invention adopts the following specific scheme:

a novel lithium ion power battery SOC estimation method comprises 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 the capacitor in the battery equivalent circuit model in the first step as state variables, building 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.

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.

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)。

Terminal voltage of capacitor, C during charging_1cAnd C_2cAt the time of discharge is C_1dAnd C_2dAll referred to as C in the following description₁And C₂Instead.

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_OAre connected.

When the established battery model is identified, the nominal capacity of the battery is 6.2AH, the battery is discharged by 0.5C current under the condition that the experimental environment of the battery is 25 ℃, the battery stands for 30 minutes every time the battery discharges 10% of SOC (state of charge), the initial value of the SOC of the battery is 1, the battery is discharged after 10 pulses of discharge, and the parameter identification process is concretely implemented as follows: 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.

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

the SOC is a remaining capacity of the battery.

Determining a by using a custom function in a Curve Fitting Toolbox (Curve Fitting Toolbox) provided by Matlab software₁～a₅The parameter value of (2).

Said lambda_(k+1)The concrete formula is as follows:

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

wherein H_kMatrix for partial derivation of state variables for observation equations，R_k+1To measure the noise covariance, k is 0,1,2,3_k+1Denotes a residual at time k +1, r (1) denotes a residual at time k ═ 0, and S₀(k) in the equation, 0 ≦ ρ ≦ 1 is a forgetting factor, where ρ ≦ 0.95 is usually used, and β ≧ 1 is a weakening factor, in order to make the state estimation value smoother.

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)

E[x(k+1)-x(k+1|k+1)][x(k+1)-x(k+1|k+1)]^T＝min (11)

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, where x (k +1| k +1) represents the estimated value of the state at time k + 1.

The invention has the beneficial effects that:

aiming at the problems that the estimation accuracy of the extended Kalman filtering algorithm is greatly influenced by the accuracy of a battery model and an estimation result is easy to disperse, the method provides that the battery SOC is estimated by using a strong tracking filtering algorithm on the basis of improving a second-order RC battery equivalent circuit model, the STF algorithm has strong robustness about model uncertainty and strong tracking capability about a mutation state, the estimation SOC of the EKF algorithm and the estimation SOC of the STF algorithm are verified through a constant current discharge experiment and a UDDS working condition experiment, and the result shows that the estimation SOC of the STF algorithm is higher in accuracy and better in convergence than that of the EKF algorithm.

Drawings

FIG. 1 is an improved second order RC equivalent circuit model;

fig. 2 is a schematic structural diagram of an embodiment of a state of charge estimation system for a lithium iron phosphate power battery;

FIG. 3 illustrates SOC comparison graphs estimated by two algorithms under UDDS conditions;

FIG. 4 shows SOC comparison graphs estimated by two algorithms under constant current discharge.

The specific implementation mode is as follows:

the invention is described in detail below with reference to the accompanying drawings:

in order to accurately estimate the state of charge (SOC) of a lithium ion power battery, aiming at the problems that the SOC estimated by the Extended Kalman Filter (EKF) algorithm which is widely applied at present is greatly influenced by the accuracy of a battery model and the estimation result is easy to diverge, on the basis of improving a second-order RC equivalent circuit model, the method is improved by applying a Strong Tracking Filter (STF) algorithm which has strong robustness about model uncertainty and strong tracking capability about a sudden change state.

The SOC of the battery needs to be estimated in the running process of the electric automobile, the SOC of the battery needs to be estimated by using an extended Kalman filter and a strong tracking filter, a model of the battery needs to be established, a second-order RC battery equivalent circuit model which is widely applied is selected for reflecting the characteristics of the battery and achieving simple and convenient operation, and the model shown in figure 1 is established on the basis of the second-order RC equivalent circuit model by considering the difference of charge and discharge direction parameters.

Parameters of the battery model can be identified by using a least square algorithm, each parameter in the model changes with the difference of the state of charge, and each parameter in the battery model can be obtained by referring to a Hybrid Pulse Power Test (HPPT) test in a free CAR battery test manual. The experimental research object of the application is a lithium ion power battery produced by a company in a country, the nominal capacity of the lithium ion power battery is 6.2AH, the battery is discharged at the current of 0.5C under the condition that the experimental environment of the battery is 25 ℃, the battery stands for 30 minutes when 10% of SOC electric quantity is discharged, the initial value of the SOC of the battery is 1, and the electric quantity of the battery is discharged after 10 pulses of discharge. The specific method of the parameter identification process is as follows: 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 as shown in table 1. The parameter identification process of the battery charging direction is similar to the battery discharging direction, and is not described herein again.

TABLE 1 second order RC model discharge direction parameter identification results

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

Battery open circuit voltage U identified according to the above parameters_OCVFitting U with corresponding SOC relationship by using formula 1 obtained by combining Shepherd model and Nernst model_OCVAnd the battery equivalent circuit model is more accurate due to the SOC relation. A can be determined by using a custom function in a Curve Fitting Toolbox (Curve Fitting Toolbox) provided by Matlab software₁～a₅The parameter values.

SOC estimation algorithm based on extended Kalman filtering: an extended Kalman filter algorithm is a recursive linear minimum variance estimation method, in order to apply the extended Kalman filter method, a state space equation of a system needs to be constructed, random interference and measurement noise of the system are considered to be combined with an ampere-hour integration method SOC estimation, and a capacitor C in an improved second-order RC equivalent battery model is selected on the basis of improving the second-order RC equivalent circuit model₁And C₂Terminal voltage of (charging C)₁Is C_1c，C₂Is C_2cAt time of discharge C₁Is C_1d，C₂Is C_2d) And SOC is a state variable and is builtThe state equation and observation equation for SOC estimation are shown as follows:

x_k+1＝Ax_k+Bu_k+w_k(2)

y_k+1＝Cx_k+1+v_k+1(3)

wherein x is_k、u_k、y_k+1Respectively a state variable, an input quantity and an output quantity of the system; w is a_kRepresenting process noise resulting from system perturbations and model inaccuracies, etc.; v. of_k+1Indicating observation noise generated by measurement error or the like; A. b, C are equation matching coefficients used to characterize the dynamics of the system.

Battery terminal voltage equation:

wherein

Wherein, U_B(k +1) is the terminal voltage of the battery at time k + 1; u shape_OCV(k +1) is the open circuit voltage of the battery at the moment k + 1; SOC_kThe remaining capacity of the battery at the moment k; u shape₁(k)、U₂(k) Are respectively a capacitor C₁、C₂Voltage across (i.e. C)_1d/C_1c、C_2d/C_2cTerminal voltage of C during charging_1c、C_2cAt the time of discharge is C_1d、C_2d)；τ₁＝R₁C₁,τ₂＝R₂C₂(at charging time R₁＝R_1c，C₁＝R_1c，R₂＝R_2c，C₂＝R_2cAt time of discharge, R₁＝R_1d，C₁＝R_1d，R₂＝R_2d，C₂＝R_2d)；Q_NIs the rated capacity of the battery. Δ t represents the time difference between time k and time k + 1.

The SOC estimation recursion process based on the extended Kalman filtering algorithm is shown in the following formula.

(1) Predicting the state value at the k +1 moment: predicting the error covariance matrix at the time K +1, and calculating the gain matrix K_k+1And updating the state estimation value according to the observation value and updating the error covariance matrix.

x_k+1＝Ax_k+Bu_k(5)

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

(3) calculating a 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)

(4) Updating the state estimation value according to the observation value:

x_k+1＝x_k+1+K_k+1r_k+1(8)

(5) updating the error covariance matrix:

P_k+1＝(I-K_k+1H_k+1)P_k+1(9)

residual error r in the above formula_k+1＝y_k+1-y_k+1，y_k+1Is the actual measured value, y_k+1Is in an AND state x_k+1The corresponding estimated value of the signal,Q_kis the system noise covariance, R_kIs to measure the noise covariance, P_k+1Is the error covariance, reflecting the degree of inconsistency between the estimated value and the true value of the state variable. G_kAnd solving a Jacobian matrix of the partial derivatives of the state variables for the state equation at the time k.

The improvement of the strong tracking filter on the Kalman filter is characterized in that the strong tracking filter is satisfied with the following sufficient conditions: selecting a suitable time-varying gain array K_k+1The following equation is established.

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)

Because of the uncertain influence of the model, the estimated actual value of the filter is inaccurate and is necessarily reflected on the mean value and the amplitude value of the output residual sequence, and if the system can automatically adjust the gain array K on line_k+1The equation (10) is satisfied, that is, the output residual is forced to have the property of white gaussian noise, so that the effective information in the output residual is extracted. And if the uncertainty of the model does not exist, the strong tracking filter does not play a role in regulation, and the strong tracking filter is the Kalman filter. The improvement of the strong tracking filter to the Kalman filter is as follows: adjusting the covariance matrix and the gain matrix of the state prediction error in real time, and modifying the formula (6) to

P_k+1＝λ_k+1G_kP_kG^T _k+Q_k(12)

Wherein λ_(k+1)As time-varying fading factor:

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

where ρ ≦ 0 ≦ 1 is a forgetting factor, where ρ ≦ 0.95 is usually taken, and β ≧ 1 is a weakening factor in order to make the state estimation value smoother.

Experimental verification and analysis: in order to verify the effectiveness of the strong tracking filtering algorithm in estimating the SOC, an AVL-Estroage equipment platform is used for carrying out an experiment covering the whole range of the SOC of the battery on the battery, and the test equipment can simulate urban road working conditions, carry out constant-current charging and discharging on the battery, carry out UDDS working conditions and other experiments. The schematic structural diagram of an embodiment of the state of charge estimation system for a lithium iron phosphate power battery is shown in fig. 2, and the system comprises a temperature control box, a voltage/current detection device, a controller and a display. The controller comprises a microprocessor, a program memory, a CAN bus interface, a plurality of IO ports and the like, is connected with a temperature control box and a voltage/current detection device through a CAN bus, is used for keeping the ambient temperature constant, CAN set the experimental limit conditions of the battery in a programming mode through software of the controller so as to prevent the battery from being overcharged and overdischarged, and CAN record the test current, the test voltage, the SOC, the test temperature and the like in detail. In the single charge-discharge process of the battery, the ampere-hour measurement method is accurate to SOC estimation, so the SOC value obtained by the ampere-hour integration method is used as the actual value of the SOC in the experiment. The experimental object is a lithium iron phosphate battery with the capacity of 6.2AH produced by a company in a certain country, and the environmental temperature is controlled at 25 ℃.

(1) SOC estimation verification of UDDS working condition experiment

The method comprises the steps of using an international universal Urban road circulation working condition (UDDS), obtaining UDDS working condition current used in an experiment by reducing a certain proportion according to the actual condition of a laboratory lithium iron phosphate battery by taking a standard test working condition as reference, and carrying out UDDS working condition discharge with an initial value of SOC of 0.99206 on the lithium iron phosphate battery, wherein the working condition comprises 6 UDDS working condition cycles, and assuming that the initial values of the SOC are both 0.7 in STF estimation and EKF estimation, the actual value of the SOC in the UDDS working condition experiment, the estimated SOC value of the STF and the estimated SOC value of the EKF are as shown in fig. 3.

(2) SOC estimation verification of constant current discharge experiment

Performing a constant current discharge experiment with an initial value SOC of 0.996 on the lithium iron phosphate battery, assuming that the SOC initial values of the STF estimation and the EKF estimation are both 0.8, comparing the SOC actual value, the STF algorithm estimation SOC value and the EKF algorithm estimation SOC value of the constant current discharge experiment with the SOC ratio shown in FIG. 4

From the verification results of the above fig. 3-4, it can be seen that compared with the EKF algorithm, SOC estimation based on the STF algorithm has higher accuracy and faster convergence speed of the estimated initial value, and the STF algorithm overcomes the disadvantage that the SOC estimation result of 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.