CN110704790A - Lithium battery SOC estimation method based on IFA-EKF - Google Patents

Lithium battery SOC estimation method based on IFA-EKF Download PDF

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CN110704790A
CN110704790A CN201910842795.3A CN201910842795A CN110704790A CN 110704790 A CN110704790 A CN 110704790A CN 201910842795 A CN201910842795 A CN 201910842795A CN 110704790 A CN110704790 A CN 110704790A
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吴华伟
张远进
叶从进
杜聪聪
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Hubei University of Arts and Science
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Abstract

The invention provides an IFA-EKF-based lithium battery SOC estimation method, which comprises the following steps: establishing a second-order equivalent model of the lithium battery; performing parameter identification on the second-order equivalent model of the lithium battery; performing online optimization on the process noise covariance matrix and the measurement noise covariance matrix by using an IFA algorithm; and taking the determined optimal process noise covariance matrix and the optimal measurement noise covariance matrix as input, and performing lithium battery SOC estimation by adopting an EKF Kalman filtering algorithm to obtain a final lithium battery SOC estimation value. The lithium battery SOC estimation method based on IFA-EKF provided by the invention has the following advantages: the lithium battery SOC estimation method based on the IFA-EKF is based on an improved firefly optimization extended Kalman filter algorithm, and the EKF is optimized on line by adopting the IFA algorithm. The invention has more accurate SOC estimation effect and higher stability.

Description

Lithium battery SOC estimation method based on IFA-EKF
Technical Field
The invention belongs to the technical field of lithium battery SOC estimation, and particularly relates to an IFA-EKF-based lithium battery SOC estimation method.
Background
The battery soc (state of charge), i.e. the state of charge, of the electric vehicle is used to reflect the remaining capacity of the battery, and the value is defined as the ratio of the remaining capacity to the battery capacity, which is one of the key technologies for power distribution of the power system of the new energy vehicle. The SOC of the battery cannot be directly measured and is affected by factors such as ambient temperature, internal resistance and voltage. The accurate estimation of SOC can save battery cost, prolong battery service life, protect the battery, and provide important basis for realizing BMS balance control and other functions.
Currently, there are many approaches surrounding the research on battery SOC estimation. The open circuit voltage method is simple and effective, but is not suitable for dynamic SOC estimation. The ampere-hour method has the defects of accumulated errors, current loss and the like of a measuring instrument, and is not generally applied to a real vehicle. The neural network method has strong self-learning capability, but relies on a large number of samples to carry out data training. Compared with the first three methods, a Kalman Filtering (KF) algorithm has the advantages of high estimation precision, small calculated amount and the like, and is a hotspot of the current SOC estimation.
Although the KF algorithm greatly improves battery SOC management level and optimization control, the process noise covariance matrix Q is generally assumed when calculating using the KF algorithmkAnd measure the noise covariance matrix RkIs a random value. Thereby affecting the accuracy of the KF algorithm. When Q iskWhen the value is large, the uncertainty of KF operation is increased; when R iskLarger values result in divergence of the KF algorithm.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the lithium battery SOC estimation method based on the IFA-EKF, which can effectively solve the problems.
The technical scheme adopted by the invention is as follows:
the invention provides an IFA-EKF-based lithium battery SOC estimation method, which comprises the following steps:
step 1, establishing a second-order equivalent model of the lithium battery, wherein the state equation model is as follows:
Figure BDA0002194244830000021
in the formula:
QnΔ t is the time interval of the sampling sequence, SOC (k +1) is the battery SOC at time k +1, SOC (k) is the battery SOC at time k, I (k) is the current at time k, V is the current at time k1(k +1) is R at the time of k +11C1Voltage at loop terminal, V1(k) R at time k1C1Ring terminal voltage, R1Is a concentration difference polarization resistance, C1Polarizing capacitance by concentration difference, V2(k +1) is R at the time of k +12C2Voltage at loop terminal, V2(k) R at time k2C2Ring terminal voltage, R2For electrochemical polarization resistance, C2Is an electrochemical polarization capacitance;
the output equation is:
V(k)＝V0(k)-V1(k)-V2(k)-R0I(k) (2)
in the formula: v (k) is the end cell at time k, V0(k) Open circuit voltage at time k, V1(k) R at time k1C1Voltage at loop terminal, V2(k) R at time k2C2Ring terminal voltage, R0Ohmic internal resistance;
step 2, performing parameter identification on the second-order equivalent model of the lithium battery to respectively obtain open-circuit voltages V0Data relating to SOC and ohmic resistance R0Data relating to SOC, concentration difference polarization resistance R1Data relating to SOC, concentration difference polarization capacitance C1Data relating to SOC, electrochemical polarization resistance R2Data relating to SOC, and electrochemical polarization capacitance C2Data relating to SOC;
step 3, using IFA algorithm to process noise covariance matrix QkAnd measure the noise covariance matrix RkPerforming on-line optimization to obtain the optimal process noise covariance matrix Qk' and optimal measurement noise covariance matrix Rk'；
Step 4, the step ofStep 3 determined optimal process noise covariance matrix Qk' and optimal measurement noise covariance matrix RkTaking the parameter identification result determined in the step 2 as input, and performing lithium battery SOC estimation by adopting an EKF Kalman filtering algorithm to obtain a final lithium battery SOC estimation value, wherein the step specifically comprises the following steps:
step 4.1, order State variable xk＝[SOCkV1(k) V2(k)]TWherein T is the transpose of the matrix;
equation (1) is rewritten as the following matrix form:
Figure BDA0002194244830000031
order to
Figure BDA0002194244830000032
And adding the system process noise w at the moment kkThe state equation of the available battery model is:
xk＝Ak-1xk-1+Bk-1Ik-1+wk-1(15)
wherein: x is the number ofkIs a state variable at the moment k; x is the number ofk-1Is a state variable at the moment of k-1; i isk-1The current at the moment k-1; w is ak-1The system noise at the time k-1 is related to the measurement noise of the current; a. thek-1Is an intermediate amount; b isk-1Is an intermediate amount;
the lithium battery model output equation is:
Vk＝V0(SOCk)-V1(k)-V2(k)-R0Ik(16)
wherein: vkTerminal voltage at time k, V0(SOCk) Open circuit voltage at time k, V1(k) R at time k1C1Voltage at loop terminal, V2(k) R at time k2C2Ring terminal voltage, R0Ohmic internal resistance;
due to the open circuit voltage V0(SOCk) Is non-linear with SOC, so V0(SOCk) Is a non-linear function; let g (x)k,Ik)＝V0(SOCk)-V1(k)-V2(k)-R0IkAdding observation noise vkAnd obtaining an output equation of the lithium battery model as follows:
V'k＝g(xk,Ik)+vk(17)
wherein: v'kA correction value for the terminal voltage at time k;
step 4.2, setting an initial value, including: as a posterior value of a state variableSum mean square estimation error posteriori
Figure BDA0002194244830000042
Setting an initial value; determining the optimal process noise covariance matrix Q determined in step 3k' and optimal measurement noise covariance matrix Rk' as an initial value;
step 4.3, starting a recursion algorithm according to the initial value set in the step 4.2, substituting the recursion algorithm into the lithium battery model output equation determined in the step 4.1 to obtain the prior value of the state variable at the moment k
Figure BDA0002194244830000043
Mean square error prior value of sum timeComprises the following steps:
Figure BDA0002194244830000045
wherein:
Figure BDA0002194244830000046
the posterior value of the state variable at the moment of k-1;
Figure BDA0002194244830000047
estimating an error posterior value for the mean square at the time of k-1;
step 4.4, calculating Kalman filtering gain:
Figure BDA0002194244830000048
wherein: gkIs the Kalman filter gain; ckIs the system k moment output matrix;
Figure BDA0002194244830000049
in the step 4.5, the step of the method,
order to
Figure BDA00021942448300000410
According to terminal voltage measurement value V (k) at moment k and Kalman filtering gain GkObtaining the posterior value of the state variable at the k moment
Figure BDA0002194244830000051
And corresponding posterior value of mean square estimation error
Wherein:
Figure BDA0002194244830000054
the posterior value of the state variable at the moment k, I is current;
due to the state variable xk＝[SOCkV1(k) V2(k)]TThus, the battery SOC value at the time k is obtained, namely: SOCk；
And 4.6, then, making k equal to k +1, returning to the step 4.3, performing the next round of SOC estimation, and performing loop recursion to obtain the SOC value of the battery at each moment.
Preferably, step 3 specifically comprises:
step 3.1, initializing basic parameters of the firefly algorithm, including: process noise covariance matrix QkAnd measure the noise covariance matrix RkInitial value of (1), number of fireflies, population dimension of 2, maximum attraction beta0Light absorption coefficient gamma, maximum number of iterations;
step 3.2, randomly initializing the positions of all the fireflies, and calculating a target function value of each firefly as respective absolute fluorescence brightness;
specifically, the current requirement of the battery is used as input, and the absolute error of the measured value of the battery voltage and the voltage value of the equivalent second-order model of the lithium battery is used as the target function value of the IFA algorithm; the absolute brightness is expressed using the objective function value, i.e.: for any firefly I, the absolute fluorescence intensity I is establishediAnd an objective function, the value of the objective function being used to represent the absolute brightness, i.e. Ii＝f(x)；
Step 3.3, calculating the attraction beta of the firefly i to the firefly j according to the firefly attraction formulaijDetermining the moving direction of the firefly according to the absolute fluorescence brightness between the firefly i and the firefly j;
specifically, assuming that the absolute brightness of the firefly i is greater than the absolute brightness of the firefly j, the firefly i attracts the firefly j to move toward the firefly i; attraction beta of firefly i to firefly jijCalculated by the following formula:
wherein: gamma is the light absorption coefficient, beta0To the maximum attractive force, rijIs the cartesian distance from firefly i to firefly j, i.e.:
Figure BDA0002194244830000062
in the formula, xikIs firefly i institute at time kSpatial position of (a), xjkThe spatial position of the firefly j at the moment k, and d is the dimension of a variable; x is the number ofiIs firefly i; x is the number ofjIs firefly j;
step 3.4, updating the spatial position of the firefly according to a firefly position updating formula, and reordering the brightness of the firefly with the updated spatial position to find out the brightest firefly;
wherein: introducing an inertia weight linear decreasing strategy, wherein the formula after adjustment is as follows:
wherein: iter and itermaxExpressed as the current iteration number and the maximum iteration number, omegakRepresenting the current weight value, ωmax、ωminMaximum and minimum values, respectively; the new location update formula is as follows:
xj(t+1)＝ωt×xj(t)+βij(xi(t)-xj(t))+aεj(13)
wherein: x is the number ofj(t +1) is the spatial position of firefly j at the t +1 th iteration;
xj(t) is the spatial position of firefly j at the t-th iteration;
xi(t) is the spatial position of firefly i at the tth iteration;
xj(t) is the spatial position of firefly j at the t-th iteration;
alpha is a constant;
εjthe random number vector is obtained by uniform distribution, and t is the iteration frequency;
step 3.5, judging whether the iteration termination condition is met, if so, outputting the position of the optimal individual, namely, the optimal process noise covariance matrix Qk' and optimal measurement noise covariance matrix Rk'; if not, let t be t +1, return to step 3.3, enter the next iteration.
The lithium battery SOC estimation method based on IFA-EKF provided by the invention has the following advantages:
the lithium battery SOC estimation method based on the IFA-EKF is based on an improved firefly optimization extended Kalman filter algorithm, and the EKF is optimized on line by adopting the IFA algorithm. The invention has more accurate SOC estimation effect and higher stability.
Drawings
FIG. 1 is a schematic flow chart of a lithium battery SOC estimation method based on IFA-EKF provided by the invention;
FIG. 2 is a graph of experimental results of static conditions provided by the present invention;
FIG. 3 is a SOC estimation curve under a static condition according to the present invention;
FIG. 4 is a distribution diagram of SOC errors under a static condition according to the present invention;
FIG. 5 is a diagram of dynamic condition experimental results provided by the present invention;
FIG. 6 is a SOC estimation curve under dynamic conditions provided by the present invention;
FIG. 7 is a distribution diagram of SOC errors under dynamic conditions provided by the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects solved by the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the defects of the traditional KF algorithm in the aspect of a battery SOC estimation method, namely: the invention provides a battery SOC estimation method based on an IFA-EKF Algorithm, which is based on an improved Firefly Algorithm (FA) optimization Extended Kalman Filter (EKF) Algorithm. And adopting an IFA algorithm to perform online optimization on the EKF. The experimental result shows that the IFA-EKF algorithm has more accurate battery SOC estimation effect and higher stability than the EKF algorithm. Compared with the traditional EKF algorithm, the algorithm has better initial error adaptability and higher estimation precision of the SOC of the battery.
Referring to fig. 1, the lithium battery SOC estimation method based on IFA-EKF includes the following steps:
step 1, establishing a second-order equivalent model of the lithium battery, wherein the state equation model is as follows:
Figure BDA0002194244830000081
in the formula:
QnΔ t is the time interval of the sampling sequence, SOC (k +1) is the battery SOC at time k +1, SOC (k) is the battery SOC at time k, I (k) is the current at time k, V is the current at time k1(k +1) is R at the time of k +11C1Voltage at loop terminal, V1(k) R at time k1C1Ring terminal voltage, R1Is a concentration difference polarization resistance, C1Polarizing capacitance by concentration difference, V2(k +1) is R at the time of k +12C2Voltage at loop terminal, V2(k) R at time k2C2Ring terminal voltage, R2For electrochemical polarization resistance, C2Is an electrochemical polarization capacitance;
the output equation is:
V(k)＝V0(k)-V1(k)-V2(k)-R0I(k) (2)
in the formula: v (k) is the end cell at time k, V0(k) Open circuit voltage at time k, V1(k) R at time k1C1Voltage at loop terminal, V2(k) R at time k2C2Ring terminal voltage, R0Ohmic internal resistance;
step 2, performing parameter identification on the second-order equivalent model of the lithium battery to respectively obtain open-circuit voltages V0Data relating to SOC and ohmic resistance R0Data relating to SOC, concentration difference polarization resistance R1Data relating to SOC, concentration difference polarization capacitance C1Data relating to SOC, electrochemical polarization resistance R2Data relating to SOC, and electrochemical polarization capacitance C2Data relating to SOC;
the method comprises the following specific steps:
for V0The identification adopts an open-circuit voltage charging and discharging calibration experiment, and the specific experimental steps are as follows:
1) and (5) fully charging the battery, standing for 12h, and measuring the open-circuit voltage of the battery in a full state.
2) Discharging with a constant current of 1C to reduce the SOC by 0.1, standing for 1h, and measuring the voltage of the battery at the moment, namely the open-circuit voltage when the SOC is 0.9;
3) and returning to 2) until the electric quantity of the battery is discharged, and ending the experiment.
Then, a charging test was performed in which the procedure was substantially identical to that of the discharging test. Obtaining V under the charge-discharge experiment0After the data are obtained, the two are averaged to obtain V0The final data of (1).
TABLE 1V0Data related to SOC
Figure BDA0002194244830000091
For R0，R1，C1，R2，C2According to the Freedom CAR battery test manual, pulse power characteristics were tested. The ratio of the instantaneous voltage change and the discharge current at the beginning of the electrical pulse picking and placing is R0。
In the formula, Δ V is an instantaneous voltage change value at the start of the discharge pulse.
The time constant τ is known as RC, reflecting how fast the cell reaches steady state after discharge. To identify the resistance and the capacitance in the RC link, tau is firstly solved, and the following can be obtained by combining a time constant expression and solving:
Figure BDA0002194244830000093
Figure BDA0002194244830000101
in the formula, V1(0)，V2(0) The initial voltage at two ends of the capacitor at the moment of pulse ending, and t is the response time of the polarization effect.
According to the RC link zero input response, the terminal voltage can be expressed as:
Figure BDA0002194244830000102
in Matlab, the cftool box is used for laying aside the battery for 60s after pulse discharge, and a voltage change curve is fitted to obtain V1(0)，V2(0)，τ1，τ2。
According to the zero state response of the RC link, the voltages at two ends of the polarization capacitor are as follows:
the obtained V1(0)，V2(0)，τ1，τ2. Substituting the formula to obtain R1And R2Then, C is obtained from the expression of time constant1And C2。R0，R1，C1，R2，C2The results of the parameter identification are shown in table 2:
TABLE 2R0，R1，C1，R2，C2Parameter identification
Figure BDA0002194244830000105
Step 3, using IFA algorithm to process noise covariance matrix QkAnd measure the noise covariance matrix RkPerforming on-line optimization to obtain the optimal process noise covariance matrix Qk' and optimal measurement noise covariance matrix Rk'；
The Firefly Algorithm (FA) is proposed by Xin-she Yang in 2008, and is a relatively novel optimization Algorithm in the group intelligence Algorithm. For several common peak test function experiments, researchers find that the firefly algorithm is superior to the particle swarm algorithm and the genetic algorithm in the aspects of efficiency and success rate.
The step 3 specifically comprises the following steps:
step 3.1, initializing basic parameters of the firefly algorithm, including: process noise covariance matrix QkAnd measure the noise covariance matrix RkInitial value of (1), number of fireflies, population dimension of 2, maximum attraction beta0Light absorption coefficient gamma, maximum number of iterations;
step 3.2, randomly initializing the positions of all the fireflies, and calculating a target function value of each firefly as respective absolute fluorescence brightness;
specifically, the current requirement of the battery is used as input, and the absolute error of the measured value of the battery voltage and the voltage value of the equivalent second-order model of the lithium battery is used as the target function value of the IFA algorithm; the absolute brightness is expressed using the objective function value, i.e.: for any firefly I, the absolute fluorescence intensity I is establishediAnd an objective function, the value of the objective function being used to represent the absolute brightness, i.e. Ii＝f(x)；
Step 3.3, calculating the attraction beta of the firefly i to the firefly j according to the firefly attraction formulaijDetermining the moving direction of the firefly according to the absolute fluorescence brightness between the firefly i and the firefly j;
specifically, assuming that the absolute brightness of the firefly i is greater than the absolute brightness of the firefly j, the firefly i attracts the firefly j to move toward the firefly i; attraction beta of firefly i to firefly jijCalculated by the following formula:
Figure BDA0002194244830000111
wherein: gamma is the light absorption coefficient, beta0To the maximum attractive force, rijIs the cartesian distance from firefly i to firefly j, i.e.:
Figure BDA0002194244830000112
in the formula, xikIs the spatial position, x, of the firefly i at time kjkThe spatial position of the firefly j at the moment k, and d is the dimension of a variable; x is the number ofiIs firefly i; x is the number ofjIs firefly j;
step 3.4, updating the spatial position of the firefly according to a firefly position updating formula, and reordering the brightness of the firefly with the updated spatial position to find out the brightest firefly;
although the FA algorithm shows significant advantages over the GA algorithm, the PSO algorithm. However, it is difficult to solve various problems in practical applications to avoid some of the drawbacks of other group intelligence optimization algorithms, such as: easy to fall into local optimum, easy to early mature and converge, etc. In order to improve the convergence speed and the convergence precision of the FA algorithm, the invention introduces an inertial weight linear decrement strategy in the standard FA algorithm.
Wherein: introducing an inertia weight linear decreasing strategy, wherein the formula after adjustment is as follows:
wherein: iter and itermaxExpressed as the current iteration number and the maximum iteration number, omegakRepresenting the current weight value, ωmax、ωminMaximum and minimum values, respectively; the new location update formula is as follows:
xj(t+1)＝ωt×xj(t)+βij(xi(t)-xj(t))+aεj(13)
wherein: x is the number ofj(t +1) is the spatial position of firefly j at the t +1 th iteration;
xj(t) is the spatial position of firefly j at the t-th iteration;
xi(t) is the spatial position of firefly i at the tth iteration;
xj(t) at the t-th iterationThe spatial location of firefly j;
alpha is a constant;
εjthe random number vector is obtained by uniform distribution, and t is the iteration frequency;
step 3.5, judging whether the iteration termination condition is met, if so, outputting the position of the optimal individual, namely, the optimal process noise covariance matrix Qk' and optimal measurement noise covariance matrix Rk'; if not, let t be t +1, return to step 3.3, enter the next iteration.
When the IFA algorithm is used for parameter optimization, the design of an objective function is an important link of the design of the IFA algorithm. Setting a covariance matrix QkAnd RkThe initial value of (1) is input by taking the current requirement of the battery as an input, and the absolute error of the voltage value of the equivalent second-order model of the lithium battery and the measured value of the voltage is taken as the target function value of the IFA algorithm. Using IFA algorithm to covariance matrix QkAnd RkAnd performing online optimization. Assigning the optimal solution to Q through the calculated IFA algorithmkAnd Rk. Optimized QkAnd RkAnd performing subsequent Kalman filtering as a new input parameter of the EKF algorithm.
Step 4, determining the optimal process noise covariance matrix Q in step 3k' and optimal measurement noise covariance matrix RkTaking the parameter identification result determined in the step 2 as input, and performing lithium battery SOC estimation by adopting an EKF Kalman filtering algorithm to obtain a final lithium battery SOC estimation value, wherein the step specifically comprises the following steps:
step 4.1, order State variable xk＝[SOCkV1(k) V2(k)]TWherein T is the transpose of the matrix;
equation (1) is rewritten as the following matrix form:
Figure BDA0002194244830000131
order to
Figure BDA0002194244830000132
And adding the system process noise w at the moment kkThe state equation of the available battery model is:
xk＝Ak-1xk-1+Bk-1Ik-1+wk-1(15)
wherein: x is the number ofkIs a state variable at the moment k; x is the number ofk-1Is a state variable at the moment of k-1; i isk-1The current at the moment k-1; w is ak-1The system noise at the time k-1 is related to the measurement noise of the current; a. thek-1Is an intermediate amount; b isk-1Is an intermediate amount;
the lithium battery model output equation is:
Vk＝V0(SOCk)-V1(k)-V2(k)-R0Ik(16)
wherein: vkTerminal voltage at time k, V0(SOCk) Open circuit voltage at time k, V1(k) R at time k1C1Voltage at loop terminal, V2(k) R at time k2C2Ring terminal voltage, R0Ohmic internal resistance;
due to the open circuit voltage V0(SOCk) Is non-linear with SOC, so V0(SOCk) Is a non-linear function; let g (x)k,Ik)＝V0(SOCk)-V1(k)-V2(k)-R0IkAdding observation noise vkAnd obtaining an output equation of the lithium battery model as follows:
V'k＝g(xk,Ik)+vk(17)
wherein: v'kA correction value for the terminal voltage at time k;
step 4.2, setting an initial value, including: as a posterior value of a state variable
Figure BDA0002194244830000141
Sum mean square estimation error posterioriSetting an initial value; determining the optimal process noise covariance matrix Q determined in step 3k' and optimal measurement noise covariance matrix Rk' as an initial value;
step 4.3, starting a recursion algorithm according to the initial value set in the step 4.2, substituting the recursion algorithm into the lithium battery model output equation determined in the step 4.1 to obtain the prior value of the state variable at the moment k
Figure BDA0002194244830000143
Mean square error prior value of sum timeComprises the following steps:
Figure BDA0002194244830000145
wherein:
Figure BDA0002194244830000146
the posterior value of the state variable at the moment of k-1;
Figure BDA0002194244830000147
estimating an error posterior value for the mean square at the time of k-1;
step 4.4, calculating Kalman filtering gain:
Figure BDA0002194244830000148
wherein: gkIs the Kalman filter gain; ckIs the system k moment output matrix;
Figure BDA0002194244830000149
in the step 4.5, the step of the method,
order to
Figure BDA0002194244830000151
According to terminal voltage measurement value V (k) at moment k and Kalman filtering gain GkObtaining the posterior value of the state variable at the k moment
Figure BDA0002194244830000152
And corresponding posterior value of mean square estimation error
Wherein:
Figure BDA0002194244830000155
the posterior value of the state variable at the moment k, I is current;
due to the state variable xk＝[SOCkV1(k) V2(k)]TThus, the battery SOC value at the time k is obtained, namely: SOCk；
And 4.6, then, making k equal to k +1, returning to the step 4.3, performing the next round of SOC estimation, and performing loop recursion to obtain the SOC value of the battery at each moment.
The SOC estimation process is a continuous recursion process, the initial value is corrected by observing the estimated value, the measured value and the filter gain, noise is removed gradually, the estimated value is closer to the true value, the optimal estimation of the state variable is obtained, and the optimal estimation of the SOC is obtained.
And 5: experimental verification
Setting an initial value: IFA algorithm parameter initialization: the number of the populations is 50; the number of iterations is 1000; omegamaxIs 0.9; omegaminIs 0.4; alpha is 0.2; beta is 0.2; gamma is 1.
Initialization of an EKF algorithm:
in the static working condition, a constant current experiment with the discharge rate of 1C as shown in figure 2 is adopted, and the battery is fully charged and then stands for 1h before the test is started. The results of the IFA-EKF algorithm and the EKF algorithm under static conditions are shown in FIGS. 3 and 4.
TABLE 1 comparison of static Condition test results
Figure BDA0002194244830000161
As can be seen from fig. 3, 4 and table 1, both the IFA-EKF algorithm and the EKF algorithm can converge to the measured value quickly when the initial estimation is inaccurate, and the absolute value of the maximum SOC error of the former is 0.0063 lower than that of the latter. As the simulation time progresses, the absolute value of the SOC error of the EKF algorithm is larger and larger. In the experiment, the SOC average error absolute value of the IFA-EKF algorithm is 0.0185, the SOC average error absolute value of the EKF algorithm is 0.0332, and the SOC estimation based on the IFA-EKF algorithm shows stronger accuracy.
The dynamic working condition adopts a dynamic current experiment under a certain city typical working condition as shown in figure 5, and the battery is fully charged and then stands for 1 hour before the experiment is started. The results of the IFA-EKF algorithm and the EKF algorithm under static conditions are shown in FIGS. 6 and 7.
TABLE 2 comparison of dynamic working conditions
Figure BDA0002194244830000162
As can be seen from fig. 6, fig. 7, and table 2, both the IFA-EKF algorithm and the EKF algorithm can still converge to the measured value quickly even if the initial estimation is inaccurate, but the absolute value of the SOC maximum error of the EKF algorithm is 0.0187 higher than that of the IFA-EKF algorithm. The IFA-EKF algorithm has an absolute value of SOC mean error of 0.0246, while the EKF algorithm has an absolute value of SOC mean error of 0.0407, and battery SOC estimation based on the IFA-EKF algorithm shows higher estimation accuracy.
The invention provides the lithium battery SOC estimation method based on the IFA-EKF algorithm by taking the KF algorithm and the FA algorithm as theoretical bases and combining a battery second-order equivalent model, and verifies that the method has better precision and practicability.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and improvements can be made without departing from the principle of the present invention, and such modifications and improvements should also be considered within the scope of the present invention.

Claims (2)

1. An IFA-EKF-based lithium battery SOC estimation method is characterized by comprising the following steps:
step 1, establishing a second-order equivalent model of the lithium battery, wherein the state equation model is as follows:
Figure FDA0002194244820000011
in the formula:
QnΔ t is the time interval of the sampling sequence, SOC (k +1) is the battery SOC at time k +1, SOC (k) is the battery SOC at time k, I (k) is the current at time k, V is the current at time k1(k +1) is R at the time of k +11C1Voltage at loop terminal, V1(k) R at time k1C1Ring terminal voltage, R1Is a concentration difference polarization resistance, C1Polarizing capacitance by concentration difference, V2(k +1) is R at the time of k +12C2Voltage at loop terminal, V2(k) R at time k2C2Ring terminal voltage, R2For electrochemical polarization resistance, C2Is an electrochemical polarization capacitance;
the output equation is:
V(k)＝V0(k)-V1(k)-V2(k)-R0I(k) (2)
in the formula: v (k) is the end cell at time k, V0(k) Open circuit voltage at time k, V1(k) R at time k1C1Voltage at loop terminal, V2(k) R at time k2C2Ring terminal voltage, R0Ohmic internal resistance;
step 2, performing parameter identification on the second-order equivalent model of the lithium battery to respectively obtain open circuitsVoltage V0Data relating to SOC and ohmic resistance R0Data relating to SOC, concentration difference polarization resistance R1Data relating to SOC, concentration difference polarization capacitance C1Data relating to SOC, electrochemical polarization resistance R2Data relating to SOC, and electrochemical polarization capacitance C2Data relating to SOC;
step 3, using IFA algorithm to process noise covariance matrix QkAnd measure the noise covariance matrix RkPerforming on-line optimization to obtain the optimal process noise covariance matrix Qk' and optimal measurement noise covariance matrix Rk′；
Step 4, determining the optimal process noise covariance matrix Q in step 3k' and optimal measurement noise covariance matrix RkTaking the parameter identification result determined in the step 2 as input, and performing lithium battery SOC estimation by adopting an EKF Kalman filtering algorithm to obtain a final lithium battery SOC estimation value, wherein the step specifically comprises the following steps:
step 4.1, order State variable xk＝[SOCkV1(k) V2(k)]TWherein T is the transpose of the matrix;
equation (1) is rewritten as the following matrix form:
order to
Figure FDA0002194244820000022
And adding the system process noise w at the moment kkThe state equation of the available battery model is:
xk＝Ak-1xk-1+Bk-1Ik-1+wk-1(15)
wherein: x is the number ofkIs a state variable at the moment k; x is the number ofk-1Is a state variable at the moment of k-1; i isk-1The current at the moment k-1; w is ak-1The system noise at the time k-1 is related to the measurement noise of the currentClosing; a. thek-1Is an intermediate amount; b isk-1Is an intermediate amount;
the lithium battery model output equation is:
Vk＝V0(SOCk)-V1(k)-V2(k)-R0Ik(16)
wherein: vkTerminal voltage at time k, V0(SOCk) Open circuit voltage at time k, V1(k) R at time k1C1Voltage at loop terminal, V2(k) R at time k2C2Ring terminal voltage, R0Ohmic internal resistance;
due to the open circuit voltage V0(SOCk) Is non-linear with SOC, so V0(SOCk) Is a non-linear function; let g (x)k,Ik)＝V0(SOCk)-V1(k)-V2(k)-R0IkAdding observation noise vkAnd obtaining an output equation of the lithium battery model as follows:
V'k＝g(xk,Ik)+vk(17)
wherein: v'kA correction value for the terminal voltage at time k;
step 4.2, setting an initial value, including: as a posterior value of a state variable
Figure FDA0002194244820000031
Sum mean square estimation error a posteriori value P0 +Setting an initial value; determining the optimal process noise covariance matrix Q determined in step 3k' and optimal measurement noise covariance matrix Rk' as an initial value;
step 4.3, starting a recursion algorithm according to the initial value set in the step 4.2, substituting the recursion algorithm into the lithium battery model output equation determined in the step 4.1 to obtain the prior value of the state variable at the moment k
Figure FDA0002194244820000032
Mean square error prior value of sum timeComprises the following steps:
Figure FDA0002194244820000034
wherein:
Figure FDA0002194244820000035
the posterior value of the state variable at the moment of k-1;
Figure FDA0002194244820000036
estimating an error posterior value for the mean square at the time of k-1;
step 4.4, calculating Kalman filtering gain:
Figure FDA0002194244820000037
wherein: gkIs the Kalman filter gain; ckIs the system k moment output matrix;
Figure FDA0002194244820000038
in the step 4.5, the step of the method,
order to
Figure FDA0002194244820000039
According to terminal voltage measurement value V (k) at moment k and Kalman filtering gain GkObtaining the posterior value of the state variable at the k moment
Figure FDA00021942448200000310
And corresponding posterior value of mean square estimation error
Figure FDA00021942448200000311
Figure FDA0002194244820000041
Wherein:
Figure FDA0002194244820000042
the posterior value of the state variable at the moment k, I is current;
due to the state variable xk＝[SOCkV1(k) V2(k)]TThus, the battery SOC value at the time k is obtained, namely: SOCk；
And 4.6, then, making k equal to k +1, returning to the step 4.3, performing the next round of SOC estimation, and performing loop recursion to obtain the SOC value of the battery at each moment.
2. The IFA-EKF-based SOC estimation method for lithium batteries as claimed in claim 1, wherein the step 3 is specifically:
step 3.1, initializing basic parameters of the firefly algorithm, including: process noise covariance matrix QkAnd measure the noise covariance matrix RkInitial value of (1), number of fireflies, population dimension of 2, maximum attraction beta0Light absorption coefficient gamma, maximum number of iterations;
step 3.2, randomly initializing the positions of all the fireflies, and calculating a target function value of each firefly as respective absolute fluorescence brightness;
specifically, the current requirement of the battery is used as input, and the absolute error of the measured value of the battery voltage and the voltage value of the equivalent second-order model of the lithium battery is used as the target function value of the IFA algorithm; the absolute brightness is expressed using the objective function value, i.e.: for any firefly I, the absolute fluorescence intensity I is establishediAnd an objective function, the value of the objective function being used to represent the absolute brightness, i.e. Ii＝f(x)；
Step 3.3, calculating the attraction beta of the firefly i to the firefly j according to the firefly attraction formulaijDetermining the moving direction of the firefly according to the absolute fluorescence brightness between the firefly i and the firefly j;
specifically, assuming that the absolute brightness of the firefly i is greater than the absolute brightness of the firefly j, the firefly i attracts the firefly j to move toward the firefly i; attraction beta of firefly i to firefly jijCalculated by the following formula:
Figure FDA0002194244820000043
wherein: gamma is the light absorption coefficient, beta0To the maximum attractive force, rijIs the cartesian distance from firefly i to firefly j, i.e.:
Figure FDA0002194244820000051
in the formula, xikIs the spatial position, x, of the firefly i at time kjkThe spatial position of the firefly j at the moment k, and d is the dimension of a variable; x is the number ofiIs firefly i; x is the number ofjIs firefly j;
step 3.4, updating the spatial position of the firefly according to a firefly position updating formula, and reordering the brightness of the firefly with the updated spatial position to find out the brightest firefly;
wherein: introducing an inertia weight linear decreasing strategy, wherein the formula after adjustment is as follows:
Figure FDA0002194244820000052
wherein: iter and itermaxExpressed as the current iteration number and the maximum iteration number, omegakRepresenting the current weight value, ωmax、ωminMaximum and minimum values, respectively; the new location update formula is as follows:
xj(t+1)＝ωt×xj(t)+βij(xi(t)-xj(t))+aεj(13)
wherein: x is the number ofj(t +1) is the spatial position of firefly j at the t +1 th iteration;
xj(t) isThe spatial position of firefly j at the t-th iteration;
xi(t) is the spatial position of firefly i at the tth iteration;
xj(t) is the spatial position of firefly j at the t-th iteration;
alpha is a constant;
εjthe random number vector is obtained by uniform distribution, and t is the iteration frequency;
step 3.5, judging whether the iteration termination condition is met, if so, outputting the position of the optimal individual, namely, the optimal process noise covariance matrix Qk' and optimal measurement noise covariance matrix Rk'; if not, let t be t +1, return to step 3.3, enter the next iteration.
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