CN103439668B

CN103439668B - The charge state evaluation method of power lithium-ion battery and system

Info

Publication number: CN103439668B
Application number: CN201310400509.0A
Authority: CN
Inventors: 党选举; 伍锡如; 姜辉; 杨青; 张向文; 许勇; 刘振丙; 赵龙阳; 许凯; 莫妍; 陈波
Original assignee: Guilin University of Electronic Technology
Current assignee: Guilin University of Electronic Technology
Priority date: 2013-09-05
Filing date: 2013-09-05
Publication date: 2015-08-26
Anticipated expiration: 2033-09-05
Also published as: CN103439668A

Abstract

The present invention is charge state evaluation method and the system of power lithium-ion battery, this method first step sets up the circuit model of battery eliminator, discharge and recharge is carried out to battery and obtains volt-time curve, by formula identification model parameter, the nonlinear relationship obtaining open-circuit voltage OCV and SoC with standing experiment, timing sampling; Second step, based on Kalman Algorithm, with status predication, predicated error variance, filter gain, state estimation and estimation error variance equal matrix, obtain SoC maximum likelihood estimate.Native system analog to digital converter, program storage, programmable storage, timer and display are connected with microprocessor respectively, and electric current, voltage sensor are connected in the circuit that mesuring battary is connected with load respectively, export and access analog to digital converter.Programmable storage stores the battery model parameter of experiment gained, and program storage stores the estimation program of this method.SoC estimation precision of the present invention can reach 1%, and more stable; System provides SoC estimated value in real time.

Description

Charge state estimation method and system of power lithium ion battery

Technical Field

The invention relates to the technical field of charge state estimation of automobile power lithium batteries, in particular to a charge state (SoC) estimation method and system of a power lithium battery by adopting multi-state decomposition Kalman filtering.

Background

The power battery is the key for the development of new energy automobiles, and in the field of electric automobiles, lithium ion batteries are mostly adopted as power sources. The lithium ion battery has the advantages of high energy, long cycle life, no memory effect, safety, no public hazard, quick charge and discharge, wide working temperature range and the like.

The state of charge soc (state of charge) of the battery is an important parameter in a battery Management system bms (battery Management system), which is an important parameter for ensuring the safe life of the battery. However, SoC estimation is a problem difficult to solve, and due to uncertainty of battery working conditions and influences of factors such as current, temperature, self-discharge and aging, particularly high nonlinearity of the battery in the using process, the SoC estimation difficulty of the battery is increased. The current battery SoC estimation method comprises an electric quantity accumulation method, an open-circuit voltage method impedance method, a Kalman filtering method, a neural network method and the like. In all of the methods, a battery pack used by an electric automobile can be regarded as a dynamic system consisting of input and output, a state equation of the system is established, and estimation of internal states of the system, such as a charge state and the like, which cannot be directly measured is obtained by using information of the output of a battery.

The classical Kalman (Kalman) filtering method is only applicable to linear systems. Since the chemical characteristics inside the battery are complex nonlinear processes, they cannot be directly used to estimate the SoC of the battery. The extended Kalman filtering method EKF (extended Kalman Filter) is suitable for a nonlinear system, has strong correction effect on the initial value deviation of the SoC, and is a better method in the SoC of the conventional power battery. However, the noise statistical characteristics change along with the severe fluctuation of the actual working conditions, which may cause the estimation error to become larger, and even the filtering estimation process diverges. Therefore, in order to accurately estimate the SoC of the battery and effectively improve the estimation accuracy, the conventional EKF still needs to be improved.

Disclosure of Invention

The invention aims to design a charge state estimation method of a power lithium ion battery, which comprises the steps of establishing a three-order RC equivalent Circuit model, and identifying model parameters through charging and constant current discharging experiments to obtain a nonlinear relation between an Open Circuit Voltage (OCV) (open Circuit voltage) and an SoC (system on chip); and secondly, Kalman filtering is adopted, the open-circuit voltage of the battery is separately and independently estimated for the multi-state variables, and the SoC estimation value is finally obtained by combining the nonlinear relation between the battery open-circuit voltage and the SoC.

The invention also aims to design a charge state estimation system of the power lithium ion battery based on a computer signal processing system by adopting the charge state estimation method of the power lithium ion battery, so as to realize real-time display of the charge state of the power lithium ion battery estimated online.

The charge state estimation method of the power lithium ion battery designed by the invention comprises two steps,

first, model, experiment and formula identification model parameters are established

I. Modeling

Establishing a three-order RC equivalent circuit model of an equivalent power lithium ion battery, wherein the model comprises the following components: polarization resistance R₁、R₂And R₃Respectively and a capacitor C₁、C₂And C₃Three RC circuits are formed, and then the three RC circuits which are connected in series with the open Circuit voltage OCV (open Circuit voltage) and the ohmic internal resistance R of the power lithium ion battery₀₀The terminal voltage of the equivalent circuit model is the output end voltage Y of the power lithium ion battery_L。

The corresponding mathematical model is as follows:

\begin{matrix} \frac{{dU}^{1}}{dt} = - \frac{U^{1}}{R_{1} C_{1}} + \frac{I}{C_{1}} \\ \frac{{dU}^{2}}{dt} = - \frac{U^{2}}{R_{2} C_{2}} + \frac{I}{C_{2}} \\ \frac{{dU}^{3}}{dt} = - \frac{U^{3}}{R_{3} C_{3}} + \frac{I}{C_{3}} \\ Y_{L} = OCV (SoC) - {IR}_{00} - U^{1} - U^{2} - U^{3} \end{matrix}\} - - - (1)

wherein Y is_LIs the output terminal voltage, R, of the power lithium ion battery₀₀Is ohmic internal resistance, U¹、U²、U³Respectively represent a capacitor C₁、C₂、C₃The terminal voltage of (1); r₁、R₂、R₃For polarization internal resistance, I is the current value in the equivalent circuit model.

The charge state SoC mathematical model of the power lithium ion battery is defined as follows:

<math> <mrow> <mi>SoC</mi> <mo>=</mo> <mi>So</mi> <msub> <mi>C</mi> <mi>initial</mi> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>C</mi> <mi>n</mi> </msub> </mfrac> <mo>&Integral;</mo> <mi>ηIdt</mi> </mrow> </math>

SoC_initialis an initial value of SoC, eta is coulombic efficiency, C_nThe rated capacity of the power lithium ion battery.

The three-order RC equivalent circuit model of the battery has the following parameters to be identified: ohmic internal resistance R₀₀Capacitor C₁、C₂、C₃Internal resistance to polarization R₁、R₂、R₃The parameters are obtained by identification through experiments and a multiple nonlinear regression method.

II. Power lithium ion battery charging, constant current discharging and standing experiment

The experiment for identifying the model parameters comprises the processes of charging, constant-current discharging and standing of the power lithium ion battery, in the experiment process, the current and the output end voltage of a circuit after the power lithium ion battery is connected with a load are measured with high precision, the output end voltage of the battery is sampled according to a certain sampling frequency, the sampling frequency is 0.5-2 seconds, and a voltage and time curve in the experiment process is obtained.

II-1, charging

The power lithium ion battery is charged with constant current and constant voltage, and the voltage of the output end reaches the rated voltage U of the output end of the battery₀；

II-2, constant current discharge

Constant current discharging is carried out at normal temperature, when the rated capacity of the battery is M ampere, the discharging current value is 18-22% M, namely the discharging rate is 0.18-0.22, and the voltage Y of the output end of the power lithium ion battery is_LxRapidly decreases, continuously discharges for 500-2000 s, stops constant current discharge, and the corresponding battery output end voltage is U_B；

II-3, at the moment of stopping constant current discharge, the voltage jump of the output end of the battery rises to U_B，The ratio of the abrupt voltage to the constant current is ohmic internal resistance R₀₀A parameter value;

namely, it is

II-4, standing

Standing after stopping constant current discharge, and controlling the voltage Y at the output end of the power lithium ion battery_LsSlowly rising, wherein the voltage difference value of the two sampling before and after the voltage is within 5 percent of the voltage value at the position, namely entering a steady state, and the steady state voltage is U_C，U_CIs the open circuit voltage OCV;

III, obtaining the nonlinear relation between the open-circuit voltage OCV and the SoC

III-1, in the step II-4, the voltage of the output end of the power lithium ion battery rises, and the voltage characteristics of 3 resistance-capacitance circuits are zero input response voltage output values, so that

Wherein: y is_IsIs the voltage output value of the battery rising section, tau₁＝R₁C₁，τ₂＝R₂C₂，τ₃＝R₃C₃. (2) In the formula t₁The discharge end time t is any time in the time interval from the discharge end time to the voltage steady state standing end time₁＝0。

According to the time voltage experimental data obtained in the step II-4, a least square method is adopted to obtain a undetermined coefficient b₀、b₁、b₂、b₃、τ₁、τ₂、τ₃。

III-2, outputting voltage of a voltage reduction section at the output end of the power lithium ion battery in the step II

Wherein, Y_LXIs the voltage output value of the battery falling section, U₀Step I, the output end voltage of the power lithium ion battery after charging is obtained, and the parameter tau obtained by the formula (2) is used₁、τ₂、τ₂Substituting the formula (3), and obtaining the polarization resistance R by adopting a least square method according to the time voltage experimental data obtained in the step II₁、R₂、R₃. (3) In the formula t₂Is any time in the time interval from the discharge starting time to the discharge stopping time, the discharge starting time t₂＝0。

Repeating the experiment of the step II for 3-5 times, calculating each parameter according to III-1 and III-2 after each experiment, and respectively averaging the parameters obtained in each experiment to serve as corresponding parameter values.

III-3, in the charging and discharging processes of different constant current values, measuring the current and the corresponding open-circuit voltage U of the circuit of the power lithium ion battery connected with the load with high precision_CSimultaneously, an SoC value corresponding to the open-circuit voltage is obtained according to the definition of the SoC, and ohmic internal resistance R is obtained according to the experiment₀₀Capacitor C₁、C₂、C₃Internal resistance to polarization R₁、R₂、R₃The parameter value of (2) can obtain the non-linear relationship OCV (OCC) of the open-circuit voltage OCV and the SoC from the mathematical model equation set (1) of the three-order RC equivalent circuit of the battery_k-1)The following are:

OCV ({SoC}_{k - 1}) = k_{1} So C_{k - 1}^{8} + k_{2} So C_{k - 1}^{7} + k_{3} So C_{k - 1}^{6} + k_{4} {SoC}_{k - 1}^{5} + k_{5} {SoC}_{k - 1}^{4}

+ k_{6} {SoC}_{k - 1}^{3} + k_{7} So C_{k - 1}^{2} + k_{8} So C_{k - 1} + k_{9} . - - - (4)

(4) in-type SoC_kIs the SoC at the current sampling time and k time_k-1Is the SoC at the previous sampling instant, k-1.

Solving the nonlinear relation model parameter k of OCV and SoC by adopting a least square method₁～k₉。

Second step, SoC estimation based on Kalman filtering

And (3) separately and independently estimating the open-circuit voltage of the battery for the multi-state variables by adopting a Kalman filtering method, and estimating the current value of the SoC by combining the nonlinear relation between the open-circuit voltage of the power lithium ion battery obtained in the first step and the SoC.

Aiming at an extended Kalman (Kalman) algorithm (EKF) of a nonlinear system, and combining a mathematical model of a three-order RC equivalent circuit of the battery established in the first step, selecting an SoC and a capacitor C₁、C₂、C₃The terminal voltage of (b) is a state variable, namely:

X_{k} = {[\begin{matrix} X 1 & X 2 & X 3 & X 4 \end{matrix}]}^{T}

= {[\begin{matrix} {SoC}_{k} & U_{k}^{1} & U_{k}^{2} & U_{k}^{3} \end{matrix}]}^{T} - - - (5)

wherein, SoC_kIs SoC at time k;is the capacitance C at time k₁A terminal voltage;is the capacitance C at time k₂A terminal voltage;is the capacitance C at time k₃Terminal voltage, T, is a mathematical symbol transposed to vector.

Discretizing the equation set (1) of the first step according to the above equation (5), and taking system noise into consideration, obtaining a state equation (6) and a measurement equation (7) thereof, which are respectively as follows:

Y_{k} = OCV (So C_{k - 1}) - I_{k} R_{00} - U_{k}^{1} - U_{k}^{2} {- U}_{k}^{3} {+ v}_{k} - - - (7)

wherein: y is_kIs the battery output terminal voltage at time k; Δ t is the sampling time; i is_kThe current of the battery loop at the moment k is the system control input quantity; eta_iIs the coulomb efficiency; OCV (SoC)_k-1) Shows the battery open-circuit voltage OCV obtained by fitting experimental data and the SOC at the previous moment_k-1A non-linear functional relationship therebetween; tau is₁＝R₁C₁，τ₂＝R₂C₂，τ₃＝R₃C₃；w_kAnd v_kProcess noise and measurement noise, respectively.

The internal characteristics of the power battery show complex nonlinearity, noise exists when the working condition of an actual hybrid electric vehicle is changed violently, the SOC of the battery is directly estimated by using an EKF algorithm, the error of the estimation result is large, and even filtering estimation divergence occurs.

The method is a novel SOC estimation method based on EKF, which can accurately estimate the SOC and other parameters of the battery. As can be seen from the third-order RC equivalent circuit model of the battery established in the first step, there is more than one state variable of the system, and when the SoC is actually estimated, a plurality of state variables need to be estimated at the same time. In the estimation process, because the plurality of state variables have correlation, coupling and influence, the more the state variables are, the more complicated the relationship among the state variables is, and the larger the operation amount of state estimation is. Especially when the system noise interference is large, the filter estimation is easy to diverge. From the measurement equation (7), the battery output terminal voltage Y_kIs OCV (SoC)_k-1)、i_kR₀₀Is linearly combined of Y_kRegarded as OCV (SoC)_k-1)、I_kR₀₀、The measurement equation can be decomposed into four independent measurement equation subsystems through linear superposition, each subsystem independently observes corresponding state variables, estimation of the state variables is not affected mutually, coupling relation among the state variables during estimation is effectively eliminated, and estimation accuracy is improved. In particular toThe method comprises the following steps:

the measurement equation (7) is decomposed as follows:

\begin{matrix} Y_{k, x 1} = OCV ({SoC}_{k - 1}) - I_{k} R_{k} \\ Y_{k, x 2} {= - U}_{k}^{R_{1} C_{1}} \\ Y_{k, x 3} = {- U}_{k}^{R_{1} C_{2}} \\ Y_{k, x 4} = {- U}_{k}^{R_{3} C_{3}} \end{matrix}\} - - - (8)

combining the formula (6) and the formula (8), and applying EKF algorithm to the state variable X1 ═ SoC_kThe estimation is carried out, and the state prediction of the EKF algorithm recursive process is as follows:

i. state prediction matrix

Wherein, I_K-1Is the loop current in the circuit after the battery is connected to the load at time k-1, the state transition matrix:

system control input matrix:

ii. Prediction error variance matrix

Wherein Q_kIs the system zero mean random process noise w_kThe covariance matrix of (2).

iii, a filter gain matrix

K_{k} = P_{k | k - 1} H_{k}^{T} {(H_{k} P_{k | k - 1} H_{k}^{T} + R_{k})}^{- 1} - - - (13)

Wherein the observation matrix is:

<math> <mrow> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <msub> <mi>H</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mrow> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>Y</mi> </mrow> <mrow> <mi>k</mi> <mo>,</mo> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>&PartialD;</mo> <mi>X</mi> </mrow> </mfrac> <mo>|</mo> </mrow> <mrow> <mi>X</mi> <mo>=</mo> <mover> <mi>S</mi> <mo>^</mo> </mover> <mi>o</mi> <msub> <mi>C</mi> <mi>k</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>H</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>H</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow> </math>

whereinIs an estimate of the SoC at time k, i.e. a state prediction matrixRow 1, column 1 data; r_kIs the system measurement noise v_kThe covariance of (a);

iv, state estimation matrix

{\hat{X}}_{k | k} = {\hat{X}}_{k | k - 1} + K_{k} (Y_{m | k} - {\hat{Y}}_{k}) - - - (15)

Wherein the state estimation matrixRow 1, column 1 data of (a) is SoC_kThe optimal estimated value of (a); y is_m|kIs the observed value of the voltage at the output end of the battery at the moment k, and comprises measurement noise v_k；The estimated value of the voltage of the output end of the battery at the moment k is obtained by calculating according to the following formula:

in the calculation process, according toThe first step obtains a non-linear model between the open-circuit voltage OCV and the SOC, and combines the obtained open-circuit voltage OCV and the SOC at the previous moment_k-1The open-circuit voltage OCV (SoC) in the formulas (8) and (16) can be obtained by estimating_k-1)。

v, estimating error variance matrix

P_k|k＝(I-K_kH_k)P_k|k-1 (17)

Steps i to v are the state variable X1 ═ SoC_kEstimation procedure, estimating the matrix at a given stateAnd estimating an error variance matrix P_k|kThe initial value of each element is 0.001-0.005, and the initial value can be obtained by recursionThe 1 st row and 1 st column data are SoC_kThe optimal estimate of.

The charge state estimation system of the power lithium ion battery designed according to the charge state estimation method of the power lithium ion battery comprises a microprocessor, a current sensor, a voltage sensor, an analog-to-digital (A/D) converter, a program memory, a programmable memory, a timer and a display. The analog-to-digital converter, the program memory, the programmable memory, the timer and the display are respectively connected with the microprocessor, the current sensor is connected in series in a circuit formed by connecting the power lithium ion battery to be tested with a load, and the voltage sensor is connected in parallel on the circuit. The outputs of the current sensor and the voltage sensor are connected to an analog-to-digital converter, and the measured circuit current and the output end voltage of the power lithium ion battery after the power lithium ion battery is connected with a load are transmitted.

The programmable memory stores the equivalent model parameters of the power lithium ion battery obtained by the experiment, including the ohmic internal resistance R₀₀Capacitor C₁、C₂、C₃Internal resistance to polarization R₁、R₂、R₃Open circuit voltage and SoC_k-1Of the nonlinear model parameter k₁～k₉. Storing Kalman filtering SoC in program memory_kEstimation model and open-Circuit Voltage OCV (SOC)_K-1) And SoC_k-1A non-linear relationship model;

kalman filtering SoC_kThe estimation model includes:

i. state prediction matrix

Wherein the state transition matrix:

system control input matrix:

ii. Prediction error variance matrix

Wherein Q_kIs the system zero mean random process noise w_kThe covariance matrix of (a);

iii, a filter gain matrix

K_{k} = P_{k | k - 1} H_{k}^{T} {(H_{k} P_{k | k - 1} H_{k}^{T} + R_{k})}^{- 1}

Wherein the observation matrix is:

<math> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <msub> <mi>H</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mrow> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>Y</mi> </mrow> <mrow> <mi>k</mi> <mo>,</mo> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>&PartialD;</mo> <mi>X</mi> </mrow> </mfrac> <mo>|</mo> </mrow> <mrow> <mi>X</mi> <mo>=</mo> <mover> <mi>S</mi> <mo>^</mo> </mover> <mi>o</mi> <msub> <mi>C</mi> <mi>k</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>H</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>H</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math>

iv, state estimation matrix

{\hat{X}}_{k | k} = {\hat{X}}_{k | k - 1} + K_{k 1} (Y_{m | k} - {\hat{Y}}_{k})

wherein:is an SoC_k-1Estimated value of (1), open circuit voltage OCV (SOC)_K-1) And SoC_k-1The nonlinear relationship model is as follows:

OCV ({SoC}_{k - 1}) = k_{1} {SoC}_{k - 1}^{8} + k_{2} {SoC}_{k - 1}^{7} + k_{3} {SoC}_{k - 1}^{6} + k_{4} {SoC}_{k - 1}^{5} + k_{5} {SoC}_{k - 1}^{4}

+ k_{6} {SoC}_{k - 1}^{3} + k_{7} {SoC}_{k - 1}^{2} + k_{8} {SoC}_{k - 1} + k_{9} .

according to SoC_k-1Is estimated byTo obtain

v, estimating error variance matrix

P_k|k＝(I-K_kH_k)P_k|k-1 ；

SoC in timer control program memory_kEstimating the current SoC of program start and interrupt operation and microprocessor operation result_kAnd the estimated value is displayed in real time through a display.

Compared with the prior art, the charge state estimation method and the charge state estimation system of the power lithium ion battery have the advantages that: 1. on the basis of an extended Kalman algorithm (EKF), according to the superposition principle, a measurement equation is decomposed, multiple state variables are respectively and independently estimated, the coupling among the state variables is eliminated, and the SoC is reduced_kThe operation amount of state estimation is increased, and SoC is improved_kThe estimation precision is improved, and experiments prove that compared with the classical EKF, the EKF Kalman filtering gain matrix of state decomposition estimation has stronger correction effect and more stability; 2. considering the noise in the practical application of the power battery, the error of the estimation result is reduced, the filtering estimation divergence is prevented, and the experiment proves that the SoC estimation precision of the invention can reach 1%; 3. the estimation program can be stored in a microprocessor-based system, and the charge state value of the power battery can be accurately obtained in real time, so that important parameters are provided for safe operation of the power battery.

Drawings

FIG. 1 is a schematic diagram of a three-order RC equivalent circuit model of a power lithium ion battery according to an embodiment of a state of charge estimation method for a power lithium ion battery;

FIG. 2 is a graph of voltage and time obtained from the power lithium ion battery charging, constant current discharging and standing experiments according to the method for estimating the state of charge of the power lithium ion battery;

fig. 3 is a schematic structural diagram of an embodiment of a state of charge estimation system of a power lithium ion battery.

Detailed Description

Embodiment of charge state estimation method of power lithium ion battery

I. Modeling

Establishing a three-order RC equivalent circuit model of an equivalent power lithium ion battery, as shown in FIG. 1, with a polarization resistance R₁、R₂And R₃Respectively and a capacitor C₁、C₂And C₃Three RC circuits are formed and then connected in series with the open-circuit voltage OCV and the ohmic internal resistance R of the power lithium ion battery₀₀The terminal voltage of the equivalent circuit model is the output end voltage Y of the power lithium ion battery_L。

The corresponding mathematical model is as follows:

\begin{matrix} \frac{{dU}^{1}}{dt} = - \frac{U^{1}}{R_{1} C_{1}} + \frac{I}{C_{1}} \\ \frac{{dU}^{2}}{dt} = - \frac{U^{2}}{R_{2} C_{2}} + \frac{I}{C_{2}} \\ \frac{{dU}^{3}}{dt} = - \frac{U^{3}}{R_{3} C_{3}} + \frac{I}{C_{3}} \\ Y_{L} = OCV (SoC) - {IR}_{00} - U^{1} - U^{2} - U^{3} \end{matrix}\}

<math> <mrow> <mi>SoC</mi> <mo>=</mo> <msub> <mi>SoC</mi> <mi>initial</mi> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>C</mi> <mi>n</mi> </msub> </mfrac> <mo>&Integral;</mo> <mi>ηIdt</mi> </mrow> </math>

The test experimental equipment is an electric vehicle battery test system-EVTS of Arbin corporation in the United states. Rated capacity C of power lithium ion battery_nη is coulombic efficiency at 60Ah, η is 0.95 at the time of charge, and η is 1 at the time of discharge.

The experiment for identifying the model parameters comprises the processes of charging, constant-current discharging and standing of the power lithium ion battery, the whole process is carried out at normal temperature, in the experiment process, the current and the output end voltage of a circuit of the power lithium ion battery connected with a load are measured at high precision, the sampling period is 1 second, and the voltage and time curve in the experiment process is obtained, as shown in fig. 2.

II-1, charging

The power lithium ion battery is charged with constant current and constant voltage, and reaches the point A in figure 2, and the rated voltage of the output end of the battery is U₀＝79.48V；

II-2, constant current discharge

Constant current discharging is carried out at normal temperature, the rated capacity of the battery is 60Ah, the discharging current I is 60 multiplied by 20 percent to 12A, the discharging time T is 700s, and the output end voltage Y of the power lithium ion battery_LxRapidly decreases to point B in FIG. 2, corresponding to a battery output voltage of U_BWhen the voltage is 77.8V, the constant current discharge is stopped;

II-3, at the moment of stopping constant current discharge, the voltage jump of the output end of the battery rises to a point B' in figure 2, and the point is U_B' -79.18V; the point B and the point B' are inflection points, and the angle between BB and a horizontal line is close to 90 degrees; the ratio of the abrupt voltage to the constant current is ohmic internal resistance R₀₀A parameter value;

namely, it is

II-4, standing

Standing after stopping constant current, wherein the duration time of the example is 4300s, and the voltage Y of the output end of the power lithium ion battery_LsSlowly rises until the voltage difference value of the two previous and next samplings is within 5 percent of the voltage value at the current position, enters a steady state, namely a steady-state voltage U_C79.4V, point C, U in fig. 2_CIs the open circuit voltage OCV of the present battery.

III-1, in the step II-4, the voltage characteristics of 3 resistance-capacitance links in the rising section BB' of the output end voltage of the power lithium ion battery are zero input response, and the voltage value of the output end of the battery is

Wherein: y is_LSIs the voltage output value of the battery rising section, tau₁＝R₁C₁，τ₂＝R₂C₂，τ₃＝R₃C₃. (2) In the formula t₁Ending the discharge time t to any time within the time interval from the ending of the discharge time to the ending of the voltage steady state and the standing₁＝0。

According to the time voltage experimental data obtained in the step II-4, the undetermined coefficient b is obtained by adopting a least square method₀、b₁、b₂、b₃、τ₁、τ₂、τ₃。

III-2, outputting the voltage of the voltage drop section AB of the power lithium ion battery output end in the step II

Wherein, Y_LXIs the voltage output value of the battery falling section, U₀The output end voltage of the power lithium ion battery at the point A after the charging in the step I is finished, and the parameter tau obtained by the formula (2) is used₁、τ₂、τ₂Substituting the formula (3), and obtaining the polarization resistance R by adopting a least square method according to the time voltage experimental data obtained in the step II₁、R₂、R₃. (3) Formula t₂At any time in the interval from the discharge start time to the discharge stop time, the discharge start time t₂＝0。

Repeating the experiment of the step II for 3 times, calculating each parameter according to III-1 and III-2 after each experiment, and respectively averaging the parameters obtained in each experiment to serve as corresponding parameter values.

III-3, in the charging and discharging processes of different constant current values, measuring the current and the corresponding open-circuit voltage of a circuit of the power lithium ion battery after the power lithium ion battery is connected with a load with high precision, obtaining an SoC value corresponding to the open-circuit voltage according to the definition of SoC, and obtaining the ohmic internal resistance R according to the experiment₀₀Capacitor C₁、C₂、C₃Internal resistance to polarization R₁、R₂、R₃The parameter value of (2) can obtain the non-linear relationship OCV (OCC) of the open-circuit voltage OCV and the SoC from the mathematical model equation set (1) of the three-order RC equivalent circuit of the battery_k-1) Polynomial ofThe types are as follows:

\begin{matrix} OCV ({SoC}_{k - 1}) = k_{1} {SoC}_{k - 1}^{8} + k_{2} {SoC}_{k - 1}^{7} + k_{3} {SoC}_{k - 1}^{6} + k_{4} {SoC}_{k - 1}^{5} + k_{5} {SoC}_{k - 1}^{4} \\ + k_{6} {SoC}_{k - 1}^{3} + k_{7} {SoC}_{k - 1}^{2} + k_{8} {SoC}_{k - 1} + k_{9} . \end{matrix}

in-type SoC_kIs the SoC at the current sampling moment and k moment_k-1Is the SoC at the previous sampling instant, k-1.

Non-linear relationship OCV (open circuit voltage) of OCV and SoC_k-1)

Second step, SoC estimation based on Kalman filtering

i. State prediction matrix

Wherein the state transition matrix:

system control input matrix:

ii. Prediction error variance matrix

iii, a filter gain matrix

K_{k} = P_{k | k - 1} H_{k}^{T} {(H_{k} P_{k | k - 1} H_{k}^{T} + R_{k})}^{- 1}

Wherein the observation matrix is:

<math> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <msub> <mi>H</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>Y</mi> </mrow> <mrow> <mi>k</mi> <mo>,</mo> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>&PartialD;</mo> <mi>X</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>X</mi> <mo>=</mo> <mover> <mi>S</mi> <mo>^</mo> </mover> <mi>o</mi> <msub> <mi>C</mi> <mi>k</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>H</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>H</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math>

whereinIs an estimate of the SoC at time k, i.e. a state prediction matrixRow 1, column 1 data; r_kIs the system measurement noise v_kThe covariance of (a); in this example, when estimating X1, the estimate is defined based on test data in combination with covariance, in this example R is taken_k0.0473, the system of this example is zero-mean random process noise w_kCovariance matrix of (2):

Q_{k} = (\begin{matrix} 0.012 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{matrix})

iv, state estimation matrix

{\hat{X}}_{k | k} = {\hat{X}}_{k | k - 1} + K_{k} (Y_{m | k} - {\hat{Y}}_{k})

v, estimating error variance matrix

P_k|k=(I-K_kH_k)P_k|k-1

Steps i to v are state variable X1= SoC_kEstimation procedure, let k =2 be the start time, estimating the matrix in a given stateAnd estimating an error variance matrix P_k|kTaking the initial value ofAnd P_k|kThe elements of the two matrixes are 0.001, and the state estimation matrix can be obtained through recursionWith row 1, column 1 data being SoC_kThe optimal estimate of. In the calculation process, according to the non-linear model between the open-circuit voltage OCV and the SOC obtained in the first step, the obtained open-circuit voltage OCV and the SOC at the previous moment are combined_k-1The open-circuit voltage OCV (SoC) in the formula (16) can be obtained by estimating_k-1)。

By recursive computation of i to v, the SoC is obtained in this example_kWith an estimation accuracy of 1%.

Charge state estimation system embodiment of power lithium ion battery

An embodiment of the present state of charge estimation system for a power lithium ion battery is shown in fig. 3 and includes a microprocessor, a current sensor, a voltage sensor, an analog-to-digital (a/D) converter, a program memory, a programmable memory, a timer, and a display. The analog-to-digital converter, the program memory, the programmable memory, the timer and the display are respectively connected with the microprocessor, the current sensor is connected in series in a circuit connecting the power lithium ion battery to be tested and the load, and the voltage sensor is connected in parallel on the circuit. The outputs of the current sensor and the voltage sensor are connected to an analog-to-digital converter, and the measured load current and the output end voltage of the power lithium ion battery are transmitted. The microprocessor, the analog-to-digital converter, the program memory, the programmable memory and the timer of the present example are installed on the same computer motherboard.

The programmable memory stores power lithium ion battery parameters including battery rated capacity and ohmic internal resistance R₀₀Capacitor C₁、C₂、C₃Internal resistance to polarization R₁、R₂、R₃Open circuit voltage and SoC_k-1Of the nonlinear model parameter k₁～k₉。

Storing Kalman filtering SoC in program memory_kEstimation model and open-Circuit Voltage OCV (SOC)_K-1) And SoC_k-1A non-linear relationship model;

kalman filtering SoC_kThe estimation model includes:

i. state prediction matrix

Wherein the state transition matrix:

system control input matrix:

ii. Prediction error variance matrix

iii, a filter gain matrix

K_{k} = P_{k | k - 1} H_{k}^{T} {(H_{k} P_{k | k - 1} H_{k}^{T} + R_{k})}^{- 1}

Wherein the observation matrix is:

<math> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <msub> <mi>H</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>Y</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>x</mi> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <mi>X</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>X</mi> <mo>=</mo> <mover> <mi>S</mi> <mo>^</mo> </mover> <msub> <mi>oC</mi> <mi>k</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>H</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>H</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math>

iv, state estimation matrix

{\hat{X}}_{k | k} = {\hat{X}}_{k | k - 1} + K_{k} (Y_{m | k} - {\hat{Y}}_{k})

wherein,is an SoC_k-1Estimated value of (1), open circuit voltage OCV (SOC)_K-1) And SoC_k-1The nonlinear relationship model is as follows:

OCV ({SoC}_{k - 1}) = k_{1} {SoC}_{k - 1}^{8} + k_{2} {SoC}_{k - 1}^{7} + k_{3} {SoC}_{k - 1}^{6} + k_{4} {SoC}_{k - 1}^{5} + k_{5} {SoC}_{k - 1}^{4}

+ k_{6} {SoC}_{k - 1}^{3} + k_{7} {SoC}_{k - 1}^{2} + k_{8} {SoC}_{k - 1} + k_{9} .

v, estimating error variance matrix

P_k|k=(I-K_kH_k)P_k|k-1；

Display of this exampleFor LCD displays, the programmable memory is electrically erasable²PROM programmable memory.

The above-described embodiments are only specific examples for further explaining the object, technical solution and advantageous effects of the present invention in detail, and the present invention is not limited thereto. Any modification, equivalent replacement, improvement and the like made within the scope of the disclosure of the present invention are included in the protection scope of the present invention.

Claims

1. The charge state estimating method for power lithium ion cell includes two steps,

I, establishing a model

Establishing a three-order RC equivalent circuit model of an equivalent power lithium ion battery, wherein the model comprises the following components: polarization resistance R₁、R₂And R₃Respectively and a capacitor C₁、C₂And C₃Three RC circuits are formed, and the three series RC circuits are connected with the power lithium ion battery in seriesOpen circuit voltage OCV and ohmic internal resistance R₀₀The terminal voltage of the equivalent circuit model is the output end voltage Y of the power lithium ion battery_L；

The corresponding mathematical model is as follows:

\begin{matrix} \frac{{dU}^{1}}{dt} = - \frac{U^{1}}{R_{1} C_{1}} + \frac{I}{C_{1}} \\ \frac{{dU}^{2}}{dt} = - \frac{U^{2}}{R_{2} C_{2}} + \frac{I}{C_{2}} \\ \frac{d U^{3}}{dt} = - \frac{U^{3}}{R_{3} C_{3}} + \frac{I}{C_{3}} \\ Y_{L} = OCV (SoC) - {IR}_{00} - U^{1} - U^{2} - U^{3} \end{matrix}\} - - - (1)

wherein Y is_LIs the output terminal voltage, R, of the power lithium ion battery₀₀Is ohmic internal resistance, U¹、U²、U³Respectively representCapacitor C₁、C₂、C₃The terminal voltage of (1); r₁、R₂、R₃The polarization internal resistance is, and I is a current value in the equivalent circuit model;

SoC_initialis an initial value of SoC, eta is coulombic efficiency, C_nThe rated capacity of the power lithium ion battery;

II, power lithium ion battery charging, constant current discharging and standing experiment

The experiment for identifying the model parameters comprises the processes of charging, constant-current discharging and standing of the power lithium ion battery, wherein in the experiment process, the current and the output end voltage of a circuit after the power lithium ion battery is connected with a load are measured with high precision, the output end voltage of the battery is sampled according to a certain sampling frequency, and the sampling period is 0.5-2 seconds, so that a voltage and time curve in the experiment process is obtained;

II-1, charging

II-2, constant current discharge

Constant current discharging is carried out at normal temperature, when the rated capacity of the battery is M ampere, the discharging current value is 18-22 percent, namely the discharging rate is 0.18-0.22, and the voltage Y of the output end of the power lithium ion battery is_LxRapidly decreases, continuously discharges to 500 s-2000 s, stops constant current discharge, and the corresponding battery output end voltage is U_B；

II-3, at the moment of stopping constant current discharge, the voltage jump of the output end of the battery rises to U_B’The ratio of the abrupt voltage to the constant current is ohmic internal resistance R₀₀A parameter value;

namely, it is

II-4, standing

Standing after stopping constant current discharge, and controlling the voltage Y at the output end of the power lithium ion battery_LsSlowly rising, wherein the voltage difference value of the two sampling before and after the voltage is within 5 percent of the voltage value at the position, namely entering a steady state, and the steady state voltage is U_C,U_CIs the open circuit voltage OCV;

III-1, in the step II-4, the voltage of the output end of the power lithium ion battery rises, and the voltage characteristics of 3 resistance-capacitance circuits are voltage output values with zero input response, so that

Wherein: y is_LsIs the voltage output value of the battery rising section, tau₁＝R₁C₁，τ₂＝R₂C₂，τ₃＝R₃C₃(ii) a In the formula t₁Ending the discharge time t to any time within the time interval from the ending of the discharge time to the ending of the voltage steady state and the standing₁＝0；

According to the time voltage experimental data obtained in the step II-4, a least square method is adopted to obtain a undetermined coefficient b₀、b₁、b₂、b₃、τ₁、τ₂、τ₃；

III-2, outputting voltage of the voltage reduction section at the output end of the power lithium ion battery in the step II

Wherein, Y_LXIs the voltage output value of the battery falling section, U₀Step I, the output end voltage of the power lithium ion battery after charging is obtained, and the parameter tau obtained by the formula (2) is used₁、τ₂、τ₃Substituting the formula (3), and obtaining the polarization resistance R by adopting a least square method according to the time voltage experimental data obtained in the step II₁、R₂、R₃(ii) a (3) In the formula t₂Is any time in the time interval from the discharge starting time to the discharge stopping time, the discharge starting time t₂＝0；

III-3, in the charging and discharging processes with different constant current values, measuring the current and the corresponding open-circuit voltage U of the circuit of the power lithium ion battery connected with the load with high precision_CSimultaneously, an SoC value corresponding to the open-circuit voltage is obtained according to the definition of the SoC, and ohmic internal resistance R is obtained according to the experiment₀₀Capacitor C₁、C₂、C₃Internal resistance to polarization R₁、R₂、R₃The parameter value of (1) can be obtained by the mathematical model equation of the three-order RC equivalent circuit of the battery in the step I to obtain the non-linear relationship OCV (OCV) between the open-circuit voltage OCV and the SoC_k-1)；

\begin{matrix} OCV ({SoC}_{k - 1}) = k_{1} {SoC}_{k - 1}^{8} + k_{2} {SoC}_{k - 1}^{7} + k_{3} {SoC}_{k - 1}^{6} + k_{4} {SoC}_{k - 1}^{5} + k_{5} {SoC}_{k - 1}^{4} \\ + k_{6} {SoC}_{k - 1}^{3} + k_{7} {SoC}_{k - 1}^{2} + k_{8} {SoC}_{k - 1} + k_{9} . \end{matrix}

Wherein the SoC_kIs the SoC at the current sampling moment and k moment_k-1Is the SoC at the previous sampling time, time k-1;

according to SoC_k-1Is estimated byTo obtain

Solving the nonlinear relation model parameter k of OCV and SoC by adopting a least square method₁～k₉；

Second step, SoC estimation based on Kalman filtering

The state prediction of the extended kalman algorithm recursion process of the nonlinear system is as follows:

i, state prediction matrix

Wherein the state transition matrix:

system control input matrix:

ii, predicting error variance matrix

iii, filter gain matrix

K_{k} = P_{k | k - 1} H_{k}^{T} {(H_{k} P_{k | k - 1} H_{k}^{T} + R_{k})}^{- 1}

Wherein the observation matrix is:

iv, state estimation matrix

{\hat{X}}_{k | k} = {\hat{X}}_{k | k - 1} + K_{k} (Y_{m | k} - {\hat{Y}}_{k})

wherein,is the capacitance C at time k₁A terminal voltage;is the capacitance C at time k₂A terminal voltage;is the capacitance C at time k₃A terminal voltage;

v, estimating an error variance matrix

P_k|k＝(I-K_kH_k)P_k|k-1

Steps i to v are the state variable X1 ═ SoC_kEstimation procedure, estimating the matrix at a given stateAnd estimating an error variance matrix P_k|kEach element is 0.001-0.005, and SoC is obtained through recursion_kThe optimal estimated value of (a); in the calculation process, according to the non-linear model between the open-circuit voltage OCV and the SOC obtained in the first step, the obtained open-circuit voltage OCV and the SOC at the previous moment are combined_k-1The value estimation yields the open-circuit voltage OCV (SoC)_k-1)。

2. The state-of-charge estimation method of a power lithium ion battery of claim 1, characterized in that:

and repeating the experiment of the step II for 3-5 times, calculating each parameter according to III-1 and III-2 after each experiment, and averaging the parameters obtained in each experiment to serve as corresponding parameter values.

3. The system for estimating the state of charge of a power lithium ion battery designed according to the method for estimating the state of charge of a power lithium ion battery of claim 1 or 2, is characterized in that:

the device comprises a microprocessor, a current sensor, a voltage sensor, an analog-to-digital converter, a program memory, a programmable memory, a timer and a display; the analog-to-digital converter, the program memory, the programmable memory, the timer and the display are respectively connected with the microprocessor, the current sensor is connected in series in a circuit formed by connecting the power lithium ion battery to be tested with a load, and the voltage sensor is connected in parallel on the circuit; the outputs of the current sensor and the voltage sensor are connected to an analog-to-digital converter, and the measured load current and the output end voltage of the power lithium ion battery are transmitted;

the programmable memory stores the equivalent model parameters of the power lithium ion battery obtained by the experiment, including the ohmic internal resistance R₀₀Capacitor C₁、C₂、C₃Internal resistance to polarization R₁、R₂、R₃Open circuit voltage and SoC_k-1Of the nonlinear model parameter k₁～k₉；

kalman filtering SoC_kThe estimation model includes:

i, state prediction matrix

Wherein the state transition matrix:

system control input matrix:

ii, predicting error variance matrix

Wherein Q_kIs the system zero mean random process noiseSound w_kThe covariance matrix of (a);

iii, filter gain matrix

K_{k} = P_{k | k - 1} H_{k}^{T} {(H_{k} P_{k | k - 1} H_{k}^{T} + R_{k})}^{- 1}

Wherein the observation matrix is:

iv, state estimation matrix

{\hat{X}}_{k | k} = {\hat{X}}_{k | k - 1} + K_{k} (Y_{m | k} - {\hat{Y}}_{k})

\begin{matrix} OCV ({SoC}_{k - 1}) = k_{1} {SoC}_{k - 1}^{8} + k_{2} {SoC}_{k - 1}^{7} + k_{3} {SoC}_{k - 1}^{6} + k_{4} {SoC}_{k - 1}^{5} + k_{5} {SoC}_{k - 1}^{4} \\ + k_{6} {SoC}_{k - 1}^{3} + k_{7} {SoC}_{k - 1}^{2} + k_{8} {SoC}_{k - 1} + k_{9} . \end{matrix}

v, estimating an error variance matrix

P_k|k＝(I-K_kH_k)P_k|k-1；