CN109839599B - Lithium ion battery SOC estimation method based on second-order EKF algorithm - Google Patents

Lithium ion battery SOC estimation method based on second-order EKF algorithm Download PDF

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CN109839599B
CN109839599B CN201811444425.6A CN201811444425A CN109839599B CN 109839599 B CN109839599 B CN 109839599B CN 201811444425 A CN201811444425 A CN 201811444425A CN 109839599 B CN109839599 B CN 109839599B
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黄梦涛
王超
刘宝
赵佳美
常正阳
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Xian University of Science and Technology
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Abstract

The invention discloses a lithium ion battery SOC estimation method based on a second-order EKF algorithm, which comprises the following steps: firstly, analyzing the external characteristics of the battery, which comprises the following specific processes: carrying out intermittent charge and discharge experiments on the battery to obtain an open-circuit voltage curve representing the hysteresis characteristic of the battery and a charge and discharge standing voltage curve representing the rebound characteristic of the battery; secondly, establishing an equivalent circuit model of the battery; thirdly, identifying parameters of an equivalent circuit model of the battery; and fourthly, estimating the SOC of the battery by adopting a second-order EKF algorithm to obtain a prediction result of the SOC of the battery. The method disclosed by the invention is novel and reasonable in design, convenient to implement, good in adaptability to the dynamic and static characteristics of the battery, high in estimation precision, strong in practicability and high in popularization and application value.

Description

Lithium ion battery SOC estimation method based on second-order EKF algorithm
Technical Field
The invention belongs to the technical field of battery SOC estimation, and particularly relates to a lithium ion battery SOC estimation method based on a second-order EKF algorithm.
Background
In the current era of advocating green economy and promoting sustainable development, the pure electric vehicle becomes the main direction of current research with the advantages of low noise, no pollution, high energy efficiency and the like. The power accumulator is used as the most main power supply system and power carrier of the electric automobile, and the quality of the running condition of the power accumulator is crucial to the whole electric automobile.
The lithium ion power battery has the advantages of high monomer voltage, high energy density, long cycle life and the like in performance, and is the first choice of many automobile manufacturers at home and abroad. However, the lithium ion power battery technology is still immature, and the disadvantages of short one-time charging driving range, poor safety performance, short service life of the battery and the like exist. Therefore, it is important to effectively manage and control the Battery Management System (BMS). In the BMS, the SOC operating state of the battery pack is accurately estimated, which is of great significance to the BMS system itself and the electric vehicle. However, the running condition of the electric vehicle is influenced by surrounding factors, and the SOC cannot be directly measured, so that the selection of the SOC estimation method suitable for the actual running of the power battery is the main direction of research by the researchers in the field. The invention relates to the problem of power battery residual capacity (SOC) estimation, in particular to a lithium ion battery SOC estimation method based on a second-order EKF.
In recent years, the research methods of battery SOC by scholars at home and abroad are mainly divided into three main categories.
The first type is a SOC estimation method based on the electrochemical properties of the battery, and representative methods are: ampere-hour integral (AH) method and Open Circuit Voltage (OCV) method. The SOC of the battery is estimated by combining a battery dynamic model with an AH method, the SOC of the battery can be effectively estimated under the conditions of temperature and current change, and the error range of the SOC is shown in an experimental result to be within 2.5 percent; based on a first-order equivalent circuit model, the OCV method is improved, the capacity and the SOC of the battery are respectively estimated by combining an EKF algorithm, and the final result shows that the SOC estimation precision is controlled within +/-5%. The method has the advantages that the principle is simple and easy to implement, but the method does not have real-time correction capability, and the SOC estimation error is obviously increased when the automobile is in a strong variable working condition state.
The second category is mainly emerging intelligent prediction algorithms based on artificial neural networks. The algorithm uses a neural network estimation method of input time delay, adopts a multilayer perceptron structure of a back propagation learning rule to adjust the weight among the neurons so as to realize accurate estimation, and simulation results show that: the root mean square error of the SOC estimation is less than 0.35%. However, the method is based on a large amount of sample data, is greatly influenced by the scale of the sample data and the rules of the training algorithm, has large calculation amount and increases the online cost.
The third method is mainly based on a Kalman filtering (Kalman Filter) algorithm of a battery model. The KF algorithm is directed at a linear system, and the algorithm directed at a power battery nonlinear system is mainly a first-order EKF algorithm, wherein the SOC of the battery is estimated by combining extended Kalman filtering on the basis of an electrochemical model of the battery, and an experimental result shows that the error is not more than 5%; under the consideration of the influence of discharge rate change on the battery capacity, a dual-power model is established, the SOC of the battery is estimated by using an extended Kalman filtering algorithm, and the final experimental result shows that the maximum estimation error is within 8% and the average error is within 5% through the verification of a constant-current discharge experiment. Compared with other SOC estimation methods, the first-order EKF algorithm not only has online estimation capability, but also is suitable for various batteries, and is a commonly used estimation method at present, but the method has strong dependence on a battery model and has the problem of low precision.
Disclosure of Invention
The invention aims to solve the technical problem of providing a lithium ion battery SOC estimation method based on a second-order EKF algorithm aiming at the defects in the prior art, and the method has the advantages of novel and reasonable design, convenient implementation, better adaptability to the dynamic and static characteristics of the battery, higher estimation precision, strong practicability and high popularization and application values.
In order to solve the technical problems, the invention adopts the technical scheme that: a lithium ion battery SOC estimation method based on a second-order EKF algorithm comprises the following steps:
the method comprises the following steps of firstly, analyzing the external characteristics of the battery, and specifically comprising the following steps: carrying out intermittent charge and discharge experiments on the battery to obtain an open-circuit voltage curve representing the hysteresis characteristic of the battery and a charge and discharge standing voltage curve representing the rebound characteristic of the battery;
step two, establishing an equivalent circuit model of the battery, and the specific process is as follows:
step 201, establishing an SOC calculation model of a battery, establishing an equivalent voltage source model according to an open-circuit voltage curve of the battery, and establishing an equivalent impedance model according to a charge-discharge standing voltage curve of the battery;
202, combining an SOC calculation model, an equivalent voltage source model and an equivalent impedance model to establish an equivalent circuit model of the battery;
thirdly, identifying parameters of an equivalent circuit model of the battery;
and step four, estimating the SOC of the battery by adopting a second-order EKF algorithm to obtain a prediction result of the SOC of the battery.
In the second-order EKF algorithm-based SOC estimation method for the lithium ion battery, the specific process of performing the intermittent charge and discharge experiment on the battery in the first step is as follows:
step 101, emptying a battery;
102, charging at 1/3C discharge rate for 20min, executing step 104 when the battery voltage reaches 3.65V within 20min, otherwise executing step 103;
step 103, standing the battery for 30min, and then returning to step 102;
step 104, fully charging the battery;
105, discharging at 1/3C discharge rate for 20min, if the battery voltage is lower than 2.0V within 20min, entering step 107, otherwise, entering step 106;
step 106, standing the battery for 30min, and then returning to the step 105;
step 107, the battery is discharged at a low current of 0.02C.
In the above second-order EKF algorithm-based lithium ion battery SOC estimation method, in step 202, the SOC calculation model includes a capacitor CNAnd an equivalent battery B, the capacitor CNIs connected with the positive pole of the equivalent battery B, and the capacitor CNThe other end of the anode is connected with the cathode of the equivalent battery B; in step 202, the equivalent voltage source model includes a current source M and an inductor LhVoltage source U1And a voltage source U2Positive pole of the current source M and the inductor LhIs connected with the negative pole of the current source M and the inductance LhIs connected to the other end of the voltage source U1And a voltage source U2The cathode after series connection is connected with the cathode of the current source M; the equivalent impedance model in step 202 includes a resistance R0Resistance R1Resistance R2Capacitor C1And a capacitor C2Said resistance R0Resistance R1And a resistance R2In series, said capacitor C1And a resistor R1In parallel, the capacitor C2And a resistor R2Parallel connection; the cathode of the equivalent battery B and a voltage source U2The negative pole of (2) is connected, the resistor R0Resistance R1And a resistance R2Series rear resistor R0One end of (1) and a voltage source U1And a voltage source U2And the anodes after series connection are connected.
In the second-order EKF algorithm-based SOC estimation method for the lithium ion battery, the specific process of identifying the parameters of the equivalent circuit model of the battery in the third step is as follows:
step 301, identifying parameters of the equivalent voltage source model: the equilibrium potential EMF of the battery is expressed as
EMF＝0.5(EMFc+EMFd) (F1)
Hysteresis voltage V of batteryhIs shown as
Vh＝0.5(EMFc-EMFd) (F2)
Wherein EMFcFor charging a balanced potential, EMFdBalancing the potential for discharge;
step 302, identifying parameters of the equivalent impedance model: the voltage U at any time is expressed as
Figure GDA0003014223120000041
Wherein the OCVDThe voltage at the moment D of the charging and discharging standing voltage curve is the moment when the voltage does not change after the battery is discharged in the rebound stage; i is the value of the current flowing through the battery, R1Is a resistance R1Resistance value of1Is equal to the resistance R1Corresponding time constant and
Figure GDA0003014223120000042
R2is a resistance R2Resistance value of2Is equal to the resistance R2Corresponding time constant and
Figure GDA0003014223120000043
t is time;
expressing the fitting function as
f(x)＝A-B·exp(-ax)-C·exp(-bx) (F4)
Fitting the C-D stage of the charging and discharging standing voltage curve to obtain values of parameters A, B, C, a and b in a fitting function; the C-D stage of the charging and discharging standing voltage curve refers to a stage from sudden change of voltage at the moment of discharging the battery to the stage that the voltage is not changed after the battery is discharged and undergoes a rebound stage; and obtaining parameters of the equivalent impedance model according to the equation (F3) and the equation (F4) which are correspondingly equal to each other:
Figure GDA0003014223120000051
wherein, C1Is a capacitor C1Capacity value of C2Is a capacitor C2The capacity value of (c).
In the second-order EKF algorithm-based SOC estimation method for the lithium ion battery, the specific process of estimating the SOC of the battery by using the second-order EKF algorithm to obtain the prediction result of the SOC of the battery in the fourth step is as follows:
step 401, establishing a state space model of the battery system: according to the equivalent circuit model of the battery established in the step two, the SOC and the capacitance C of the battery are used1Voltage V across1And a capacitor C2Voltage V across2As the state variable of the system, the current value I flowing through the battery is input quantity, the terminal voltage V is output quantity, and the state space model equation of the battery system is deduced according to the circuit equation as follows:
Figure GDA0003014223120000052
the output equation is:
V(t)＝VOCV(SOC(t))-V1(t)-V2(t)-R0I(t) (F7)
wherein, CnIs the rated capacity of the battery, VOCVIs a voltage source U1And a voltage source U2The total voltage of (c);
step 402, linearizing a nonlinear state space model equation of the battery system through second-order Taylor expansion, wherein the specific process is as follows:
step 4021, performing second-order Taylor expansion on a state space model equation (F6) of the battery system at a state estimation point to obtain:
Figure GDA0003014223120000053
wherein, f (x)k,uk) As a function of the state transition, g (x)k,uk) As a measurement function, xkIs the state variable at time k, ukFor the control input of the system at time k,
Figure GDA0003014223120000061
is xkAn estimated value of (d);
step 4022, definition
Figure GDA0003014223120000062
Figure GDA0003014223120000063
Figure GDA0003014223120000064
Substituting formula (F8) into the state space model equation of the nonlinear discrete system
Figure GDA0003014223120000065
In the above, the linear equation of the battery system is obtained as follows:
Figure GDA0003014223120000066
wherein the content of the first and second substances,
Figure GDA0003014223120000067
Dk＝R0；R0is a resistance R0Δ t is the amount of change in time, ωkProcess noise, v, with mean value of zerokIs measurement noise with mean value of zero, and ωkAnd vkAre not related to each other, ωk～N(0,Qk)，vk～N(0,Rk) (ii) a I.e. omegakAnd vkObey a gaussian distribution with a mean value of 0;
step 403, estimating the SOC of the lithium ion battery by using a second-order EKF algorithm, which comprises the following specific steps:
step 4031, initialization phase:
Figure GDA0003014223120000068
wherein x is0In order to be the initial value of the state variable,
Figure GDA0003014223120000069
is x0Estimated value of (P)0Predicting an initialized value of an estimated error covariance matrix for the state variable;
step 4032, prediction phase:
predictive estimation of state variables:
Figure GDA00030142231200000610
wherein the content of the first and second substances,
Figure GDA00030142231200000611
is xk-1Estimate of (a), xk-1Is a state variable at time k-1, uk-1The control input quantity of the system at the moment k-1;
error covariance matrix of state variable prediction estimation:
Figure GDA00030142231200000612
wherein Q isk-1Covariance matrix of process noise at time k-1 and Qk-1＝Qk，QkA covariance matrix of the process noise at time k;
step 4033, correction phase:
kalman filter gain:
Figure GDA0003014223120000071
wherein R is a covariance matrix of observation noise;
modified estimation of state variables:
Figure GDA0003014223120000072
error covariance matrix of state variable correction estimation:
Pk＝(I-KkCk)Pk|k-1 (F15)
and step 4034, repeating the step 4032 and the step 4033 until the iteration number reaches a preset iteration termination value.
In the above lithium ion battery SOC estimation method based on the second-order EKF algorithm, in step 4032, Q is describedk-1Is taken as
Figure GDA0003014223120000073
In the above lithium ion battery SOC estimation method based on the second-order EKF algorithm, the value of R in step 4033 is 0.1.
In the above lithium ion battery SOC estimation method based on the second-order EKF algorithm, the preset iteration termination value in step 4034 is 150.
Compared with the prior art, the invention has the following advantages:
1. the invention aims at the problem of inaccurate SOC estimation in a power battery management system, a lithium battery is taken as a main research object, and the defects of low precision and poor stability of the conventional first-order Extended Kalman Filter (EKF) are overcome.
2. According to the method, on one hand, the hysteresis voltage phenomenon of the battery is considered, on the other hand, the rebound voltage characteristic of the battery is fitted through RC circuits of different orders, and a second-order RC circuit model with the hysteresis voltage characteristic is established after the simplicity degree of the model and the approximation degree of the battery characteristic are comprehensively considered, so that the dynamic and static working characteristics of the battery can be simulated accurately, and a more accurate SOC estimation result can be obtained conveniently.
3. Because the power battery has higher nonlinear degree in the actual use process, and the first-order EKF algorithm has weaker nonlinear degree and low estimation precision because the first-order EKF algorithm ignores higher-order terms above the second order, the invention carries out second-order Taylor expansion on the state space equation of the nonlinear discrete system at the state estimation point, can keep the nonlinear degree of the battery and improve the estimation precision; along with the progress of the discharge process, the estimation result of the second order relative to the first order is closer to the true value, and the true value can be better tracked.
4. Experiments show that the error of the first-order EKF algorithm is within 5.5 percent and the error of the second-order EKF algorithm is not more than 3 percent in the whole discharging stage, thereby showing that the second-order EKF algorithm has better estimation precision compared with the first-order EKF algorithm.
In conclusion, the method disclosed by the invention is novel and reasonable in design, convenient to implement, good in adaptability to the dynamic and static characteristics of the battery, high in estimation precision, strong in practicability and high in popularization and application value.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a block diagram of the process flow of the present invention.
Fig. 2 is a schematic diagram of an equivalent circuit model of a battery constructed according to the present invention.
FIG. 3 is a block diagram of a process for estimating SOC of a battery according to the present invention using a second order EKF algorithm.
Detailed Description
As shown in fig. 1, the lithium ion battery SOC estimation method based on the second-order EKF algorithm of the present invention includes the following steps:
the method comprises the following steps of firstly, analyzing the external characteristics of the battery, and specifically comprising the following steps: carrying out intermittent charge and discharge experiments on the battery to obtain an open-circuit voltage curve representing the hysteresis characteristic of the battery and a charge and discharge standing voltage curve representing the rebound characteristic of the battery;
in this embodiment, the specific process of performing the intermittent charge and discharge experiment on the battery in the first step is as follows:
step 101, emptying a battery;
102, charging at 1/3C discharge rate for 20min, executing step 104 when the battery voltage reaches 3.65V within 20min, otherwise executing step 103;
step 103, standing the battery for 30min, and then returning to step 102;
step 104, fully charging the battery;
105, discharging at 1/3C discharge rate for 20min, if the battery voltage is lower than 2.0V within 20min, entering step 107, otherwise, entering step 106;
step 106, standing the battery for 30min, and then returning to the step 105;
step 107, the battery is discharged at a low current of 0.02C.
In steps 103 and 106, the battery standing time is set to 30min, so that the continuity of the experiment can be ensured.
To estimate the SOC of the battery using the EKF algorithm, an accurate battery model must be established for the battery, and the establishment of the battery model is based on external characteristic analysis of the battery, so the external characteristic analysis of the battery is the primary task. The charging and discharging balance potentials of the batteries at different SOC points are different, the phenomenon is called as the hysteresis characteristic of the batteries, and the hysteresis characteristic not only exists in lithium iron phosphate power batteries, but also exists in other types of lithium ion batteries. The voltage gradually rises at the time of the battery being left in a discharged state and gradually falls during the battery being left in a charged state, and this phenomenon is called a rebound characteristic of the battery, which is mainly affected by polarization resistance and polarization capacitance inside the battery.
Step two, establishing an equivalent circuit model of the battery, and the specific process is as follows:
step 201, establishing an SOC calculation model of a battery, establishing an equivalent voltage source model according to an open-circuit voltage curve of the battery, and establishing an equivalent impedance model according to a charge-discharge standing voltage curve of the battery;
202, combining an SOC calculation model, an equivalent voltage source model and an equivalent impedance model to establish an equivalent circuit model of the battery;
in this embodiment, as shown in fig. 2, the SOC calculation model in step 202 includes a capacitor CNAnd an equivalent battery B, the capacitor CNIs connected with the positive pole of the equivalent battery B, and the capacitor CNThe other end of the anode is connected with the cathode of the equivalent battery B; in step 202, the equivalent voltage source model includes a current source M and an inductor LhVoltage source U1And a voltage source U2Positive pole of the current source M and the inductor LhIs connected with the negative pole of the current source M and the inductance LhIs connected to the other end of the voltage source U1And a voltage source U2The cathode after series connection is connected with the cathode of the current source M; the equivalent impedance model in step 202 includes a resistance R0Resistance R1Resistance R2Capacitor C1And a capacitor C2Said resistance R0Resistance R1And a resistance R2In series, said capacitor C1And a resistor R1In parallel, the capacitor C2And a resistor R2Parallel connection; the cathode of the equivalent battery B and a voltage source U2The negative pole of (2) is connected, the resistor R0Resistance R1And a resistance R2Series rear resistor R0One end of (1) and a voltage source U1And a voltage source U2And the anodes after series connection are connected.
The equivalent circuit model of the battery established by the invention not only can describe the relation between the hysteresis voltage and the open-circuit voltage of the battery and the SOC of the battery, but also can directly estimate the SOC of the battery by an ampere-hour integration method.
Thirdly, identifying parameters of an equivalent circuit model of the battery;
in this embodiment, the specific process of performing parameter identification on the parameters of the equivalent circuit model of the battery in the third step is as follows:
step 301, identifying parameters of the equivalent voltage source model: the equilibrium potential EMF of the battery is expressed as
EMF＝0.5(EMFc+EMFd) (F1)
Hysteresis voltage V of batteryhIs shown as
Vh＝0.5(EMFc-EMFd) (F2)
Wherein EMFcFor charging a balanced potential, EMFdBalancing the potential for discharge;
step 302, identifying parameters of the equivalent impedance model: the voltage U at any time is expressed as
Figure GDA0003014223120000101
Wherein the OCVDThe voltage at the moment D of the charging and discharging standing voltage curve is the moment when the voltage does not change after the battery is discharged in the rebound stage; i is the value of the current flowing through the battery, R1Is a resistance R1Resistance value of1Is equal to the resistance R1Corresponding time constant and
Figure GDA0003014223120000102
R2is a resistance R2Resistance value of2Is equal to the resistance R2Corresponding time constant and
Figure GDA0003014223120000103
t is time;
expressing the fitting function as
f(x)＝A-B·exp(-ax)-C·exp(-bx) (F4)
Fitting the C-D stage of the charging and discharging standing voltage curve to obtain values of parameters A, B, C, a and b in a fitting function; the C-D stage of the charging and discharging standing voltage curve refers to a stage from sudden change of voltage at the moment of discharging the battery to the stage that the voltage is not changed after the battery is discharged and undergoes a rebound stage; and obtaining parameters of the equivalent impedance model according to the equation (F3) and the equation (F4) which are correspondingly equal to each other:
Figure GDA0003014223120000111
wherein, C1Is a capacitor C1Capacity value of C2Is a capacitor C2The capacity value of (c).
And step four, estimating the SOC of the battery by adopting a second-order EKF algorithm to obtain a prediction result of the SOC of the battery.
In this embodiment, as shown in fig. 3, the specific process of estimating the SOC of the battery by using the second-order EKF algorithm in step four to obtain the prediction result of the SOC of the battery is as follows:
step 401, establishing a state space model of the battery system (nonlinear discrete system): according to the equivalent circuit model of the battery established in the step two, the SOC and the capacitance C of the battery are used1Voltage V across1And a capacitor C2Voltage V across2As the state variables of the system, the current value I (discharging is negative and charging is positive) flowing through the battery is input quantity, the terminal voltage V is output quantity, and the state space model equation of the battery system is deduced according to the circuit equation as follows:
Figure GDA0003014223120000112
the output equation is:
V(t)＝VOCV(SOC(t))-V1(t)-V2(t)-R0I(t) (F7)
wherein, CnIs the rated capacity of the battery, VOCVIs a voltage source U1And a voltage source U2The total voltage of (c);
step 402, linearizing a nonlinear state space model equation of the battery system through second-order Taylor expansion, wherein the specific process is as follows:
step 4021, performing second-order Taylor expansion on a state space model equation (F6) of the battery system at a state estimation point to obtain:
Figure GDA0003014223120000121
wherein, f (x)k,uk) As a function of the state transition, g (x)k,uk) As a measurement function, xkIs the state variable at time k, ukFor the control input of the system at time k,
Figure GDA0003014223120000122
is xkAn estimated value of (d);
step 4022, definition
Figure GDA0003014223120000123
Figure GDA0003014223120000124
Figure GDA0003014223120000125
Substituting formula (F8) into the state space model equation of the nonlinear discrete system
Figure GDA0003014223120000126
In the above, the linear equation of the battery system is obtained as follows:
Figure GDA0003014223120000127
wherein the content of the first and second substances,
Figure GDA0003014223120000128
Dk＝R0；R0is a resistance R0Resistance value of,. DELTA.t is the amount of change in time, ωkProcess noise, v, with mean value of zerokIs measurement noise with mean value of zero, and ωkAnd vkAre not related to each other, ωk～N(0,Qk)，vk～N(0,Rk) (ii) a I.e. omegakAnd vkObey a gaussian distribution with a mean value of 0;
step 403, estimating the SOC of the lithium ion battery by using a second-order EKF algorithm, which comprises the following specific steps:
step 4031, initialization phase:
Figure GDA0003014223120000129
wherein x is0In order to be the initial value of the state variable,
Figure GDA00030142231200001210
is x0Estimated value of (P)0Predicting an initialized value of an estimated error covariance matrix for the state variable;
step 4032, prediction phase:
predictive estimation of state variables:
Figure GDA0003014223120000131
wherein the content of the first and second substances,
Figure GDA0003014223120000132
is xk-1Estimate of (a), xk-1Is a state variable at time k-1, uk-1The control input quantity of the system at the moment k-1;
error covariance matrix of state variable prediction estimation:
Figure GDA0003014223120000133
wherein Q isk-1Covariance matrix of process noise at time k-1 and Qk-1＝Qk，QkA covariance matrix of the process noise at time k;
in this embodiment, Q is described in step 4032k-1Is taken as
Figure GDA0003014223120000134
Step 4033, correction phase:
kalman filter gain:
Figure GDA0003014223120000135
wherein R is a covariance matrix of observation noise;
modified estimation of state variables:
Figure GDA0003014223120000136
error covariance matrix of state variable correction estimation:
Pk＝(I-KkCk)Pk|k-1 (F15)
in this embodiment, the value of R in step 4033 is 0.1.
And step 4034, repeating the step 4032 and the step 4033 until the iteration number reaches a preset iteration termination value.
In this embodiment, the preset iteration termination value in step 4034 is 150.
In order to verify the technical effect of the invention, a 18650 lithium iron phosphate battery produced by Tianjin Shen battery with limited shares is adopted as an experimental object, and the main performance parameters of the battery are shown in table 1.
TABLE 1 Main Performance parameters of the Battery
Figure GDA0003014223120000137
Figure GDA0003014223120000141
In order to investigate the external characteristics of the battery, an intermittent charge and discharge experiment was performed on the battery, and the standing time of the battery was set to 30min for the continuity of the experiment. The experimental procedure is shown in table 2.
TABLE 2 Experimental procedures for intermittent charging and discharging
Figure GDA0003014223120000142
An open-circuit voltage curve representing hysteresis characteristics of the battery and a charge-discharge standing voltage curve representing rebound characteristics of the battery are obtained through battery charge-discharge experiments. Establishing an SOC calculation model of the battery, establishing an equivalent voltage source model according to the hysteresis characteristic of the battery, and establishing an equivalent impedance model according to the rebound characteristic of the battery; when the parameter identification of the equivalent impedance model is performed, the comparison table of the fitting results of the RC networks with different orders is shown in Table 3.
TABLE 3 comparison of fitting results of RC networks of different orders
Figure GDA0003014223120000143
By comparing the fitting results in table 3, it can be seen that the fitting error of the second-order RC network is not much different from that of the third-order RC network, and the first-order fitting result is inferior to that of the second-order RC network and that of the third-order RC network. Compared with a first-order RC network, the second-order RC network is selected because the second-order RC network is simple, the later-stage parameter identification and algorithm estimation are convenient, and the external characteristics of the battery can be better described.
In this embodiment, a model diagram of an equivalent circuit of the battery is shown in fig. 2.
The state variables of the SOC estimation system of the battery by utilizing the second-order EKF algorithm are as follows: x is the number ofk＝[SOC(k)，V1(k)，V2(k)]TThe input quantity of the system is as follows: u. ofkI (k). State space of systemThe model equation linearizes the nonlinear equation through a second-order Taylor formula to obtain a matrix parameter after the second-order EKF algorithm is linearized. SOC is estimated based on a second order EKF algorithm. The ratio of the SOC estimation results of the first-order EKF algorithm and the second-order EKF algorithm under different simulation conditions is shown in Table 4.
TABLE 4 comparison of errors of different simulation condition algorithms
Figure GDA0003014223120000151
Performing characteristic experimental analysis on the lithium iron phosphate battery, establishing a second-order equivalent circuit model with hysteresis voltage, and performing parameter identification; on the basis of the equivalent model, the SOC of the battery is estimated by using a first-order EKF algorithm and a second-order EKF algorithm, the estimation precision of the algorithm is verified by simulating different working conditions of the battery, and the final experimental result shows that: the second-order EKF algorithm is superior to the first-order EKF algorithm in the estimation error precision of the battery SOC under different simulation working conditions, and has good dynamic adaptability to the battery and higher precision.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. It is not intended to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and its practical application to enable one skilled in the art to make and use various exemplary embodiments of the invention and various alternatives and modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims and their equivalents.

Claims (6)

1. A lithium ion battery SOC estimation method based on a second-order EKF algorithm is characterized in that: the method comprises the following steps:
the method comprises the following steps of firstly, analyzing the external characteristics of the battery, and specifically comprising the following steps: carrying out intermittent charge and discharge experiments on the battery to obtain an open-circuit voltage curve representing the hysteresis characteristic of the battery and a charge and discharge standing voltage curve representing the rebound characteristic of the battery;
step two, establishing an equivalent circuit model of the battery, and the specific process is as follows:
step 201, establishing an SOC calculation model of a battery, establishing an equivalent voltage source model according to an open-circuit voltage curve of the battery, and establishing an equivalent impedance model according to a charge-discharge standing voltage curve of the battery;
202, combining an SOC calculation model, an equivalent voltage source model and an equivalent impedance model to establish an equivalent circuit model of the battery;
the SOC calculation model comprises a capacitance CNAnd an equivalent battery B, the capacitor CNIs connected with the positive pole of the equivalent battery B, and the capacitor CNThe other end of the anode is connected with the cathode of the equivalent battery B; the equivalent voltage source model comprises a current source M and an inductor LhVoltage source U1And a voltage source U2Positive pole of the current source M and the inductor LhIs connected with the negative pole of the current source M and the inductance LhIs connected to the other end of the voltage source U1And a voltage source U2The cathode after series connection is connected with the cathode of the current source M; the equivalent impedance model includes a resistance R0Resistance R1Resistance R2Capacitor C1And a capacitor C2Said resistance R0Resistance R1And a resistance R2In series, said capacitor C1And a resistor R1In parallel, the capacitor C2And a resistor R2Parallel connection; the cathode of the equivalent battery B and a voltage source U2The negative pole of (2) is connected, the resistor R0Resistance R1And a resistance R2Series rear resistor R0One end of (1) and a voltage source U1And a voltage source U2Connecting the anodes after series connection;
thirdly, identifying parameters of an equivalent circuit model of the battery;
estimating the SOC of the battery by adopting a second-order EKF algorithm to obtain a prediction result of the SOC of the battery;
step 401, establishing a state space model of the battery system: according to the cell established in step twoEquivalent circuit model based on SOC and capacitance C of battery1Voltage V across1And a capacitor C2Voltage V across2As the state variable of the system, the current value I flowing through the battery is input quantity, the terminal voltage V is output quantity, and the state space model equation of the battery system is deduced according to the circuit equation as follows:
Figure FDA0003014223110000021
the output equation is:
V(t)＝VOCV(SOC(t))-V1(t)-V2(t)-R0I(t) (F7)
wherein, CnIs the rated capacity of the battery, VOCVIs a voltage source U1And a voltage source U2The total voltage of (c);
step 402, linearizing a nonlinear state space model equation of the battery system through second-order Taylor expansion, wherein the specific process is as follows:
step 4021, performing second-order Taylor expansion on a state space model equation (F6) of the battery system at a state estimation point to obtain:
Figure FDA0003014223110000022
wherein, f (x)k,uk) As a function of the state transition, g (x)k,uk) As a measurement function, xkIs the state variable at time k, ukFor the control input of the system at time k,
Figure FDA0003014223110000023
is xkAn estimated value of (d);
step 4022, definition
Figure FDA0003014223110000024
Figure FDA0003014223110000025
Figure FDA0003014223110000026
Substituting formula (F8) into the state space model equation of the nonlinear discrete system
Figure FDA0003014223110000027
In the above, the linear equation of the battery system is obtained as follows:
Figure FDA0003014223110000028
wherein the content of the first and second substances,
Figure FDA0003014223110000029
Dk＝R0；R0is a resistance R0Δ t is the amount of change in time, ωkProcess noise, v, with mean value of zerokIs measurement noise with mean value of zero, and ωkAnd vkAre not related to each other, ωk～N(0,Qk)，vk～N(0,Rk) (ii) a I.e. omegakAnd vkObey a gaussian distribution with a mean value of 0;
step 403, estimating the SOC of the lithium ion battery by using a second-order EKF algorithm, which comprises the following specific steps:
step 4031, initialization phase:
Figure FDA0003014223110000031
wherein x is0In order to be the initial value of the state variable,
Figure FDA0003014223110000032
is x0Estimated value of (P)0Predicting an initialized value of an estimated error covariance matrix for the state variable;
step 4032, prediction phase:
predictive estimation of state variables:
Figure FDA0003014223110000033
wherein the content of the first and second substances,
Figure FDA0003014223110000034
is xk-1Estimate of (a), xk-1Is a state variable at time k-1, uk-1The control input quantity of the system at the moment k-1;
error covariance matrix of state variable prediction estimation:
Figure FDA0003014223110000035
wherein Q isk-1Covariance matrix of process noise at time k-1 and Qk-1＝Qk，QkA covariance matrix of the process noise at time k;
step 4033, correction phase:
kalman filter gain:
Figure FDA0003014223110000036
wherein R is a covariance matrix of observation noise;
modified estimation of state variables:
Figure FDA0003014223110000037
error covariance matrix of state variable correction estimation:
Pk＝(I-KkCk)Pk|k-1 (F15)
and step 4034, repeating the step 4032 and the step 4033 until the iteration number reaches a preset iteration termination value.
2. The lithium ion battery SOC estimation method based on the second-order EKF algorithm of claim 1, wherein: the specific process of carrying out the intermittent charge-discharge experiment on the battery in the first step is as follows:
step 101, emptying a battery;
102, charging at 1/3C discharge rate for 20min, executing step 104 when the battery voltage reaches 3.65V within 20min, otherwise executing step 103;
step 103, standing the battery for 30min, and then returning to step 102;
step 104, fully charging the battery;
105, discharging at 1/3C discharge rate for 20min, if the battery voltage is lower than 2.0V within 20min, entering step 107, otherwise, entering step 106;
step 106, standing the battery for 30min, and then returning to the step 105;
step 107, the battery is discharged at a low current of 0.02C.
3. The lithium ion battery SOC estimation method based on the second-order EKF algorithm of claim 1, wherein: the specific process of identifying the parameters of the equivalent circuit model of the battery in the third step is as follows:
step 301, identifying parameters of the equivalent voltage source model: the equilibrium potential EMF of the battery is expressed as
EMF＝0.5(EMFc+EMFd) (F1)
Hysteresis voltage V of batteryhIs shown as
Vh＝0.5(EMFc-EMFd) (F2)
Wherein EMFcFor charging a balanced potential, EMFdBalancing the potential for discharge;
step 302, identifying parameters of the equivalent impedance model: the voltage U at any time is expressed as
Figure FDA0003014223110000041
Wherein the OCVDThe voltage at the moment D of the charging and discharging standing voltage curve is the moment when the voltage does not change after the battery is discharged in the rebound stage; i is the value of the current flowing through the battery, R1Is a resistance R1Resistance value of1Is equal to the resistance R1Corresponding time constant and
Figure FDA0003014223110000042
R2is a resistance R2Resistance value of2Is equal to the resistance R2Corresponding time constant and
Figure FDA0003014223110000043
t is time;
expressing the fitting function as
f(x)＝A-B·exp(-ax)-C·exp(-bx) (F4)
Fitting the C-D stage of the charging and discharging standing voltage curve to obtain values of parameters A, B, C, a and b in a fitting function; the C-D stage of the charging and discharging standing voltage curve refers to a stage from sudden change of voltage at the moment of discharging the battery to the stage that the voltage is not changed after the battery is discharged and undergoes a rebound stage; and obtaining parameters of the equivalent impedance model according to the equation (F3) and the equation (F4) which are correspondingly equal to each other:
Figure FDA0003014223110000051
wherein, C1Is a capacitor C1Capacity value of C2Is a capacitor C2The capacity value of (c).
4. The lithium ion battery SOC estimation method based on the second-order EKF algorithm of claim 1, wherein: q in step 4032k-1Is taken as
Figure FDA0003014223110000052
5. The lithium ion battery SOC estimation method based on the second-order EKF algorithm of claim 1, wherein: in step 4033, the value of R is 0.1.
6. The lithium ion battery SOC estimation method based on the second-order EKF algorithm of claim 1, wherein: the preset iteration end value in step 4034 is 150.
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