Fractional order power battery SOC estimation method considering temperature and hysteresis effect

文档序号：1336736 发布日期：2020-07-17 浏览：10次中文

阅读说明：本技术 考虑温度及迟滞效应的分数阶动力电池soc估算方法 (Fractional order power battery SOC estimation method considering temperature and hysteresis effect ) 是由郑燕萍昌诚程虞杨于 2020-05-12 设计创作，主要内容包括：本发明提供一种考虑温度及迟滞效应的分数阶动力电池SOC估算方法,它能够准确地估算电池SOC,具有较强的鲁棒性,能在系统存在初始误差的情况下快速收敛。该方法是电池开路电压为UOCV的电压源、内阻R0、极化环串联形成动力电池的一阶分数阶等效电路模型,极化环中电容为分数阶CPE元件,电阻为极化内阻R1；CPE元件电容为C1,阶数为α1,UOCV可由试验测得；U0为内阻端电压；I为总电流；CPE元件上电流I1＝C1Dα1U1；极化环端电压U1＝(I-C1Dα1U1)R1；电池端电压Ut＝UOCV-U0-U1；<Image he="120" wi="619" file="DDA0002487948330000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>SOC(0)为初始SOC值；η为充放电容量折算系数；QN为电池额定容量。(The invention provides a fractional order power battery SOC estimation method considering temperature and hysteresis effect, which can accurately estimate the battery SOC, has stronger robustness and can quickly converge under the condition that the system has initial error. The method is that the open-circuit voltage of the battery is U OCV Voltage source, internal resistance R 0 The polarization ring is connected in series to form a first-order fractional order equivalent circuit model of the power battery, the capacitor in the polarization ring is a fractional order CPE element, and the resistor is polarization internal resistance R 1 (ii) a CPE element capacitance is C 1 Order of α 1 ，U OCV Can be measured by tests; u shape 0 Is the internal resistance terminal voltage; i is the total current; current I on CPE element 1 ＝C 1 D α 1 U 1 (ii) a Voltage U at the end of the polarization loop 1 ＝(I‑C 1 D α1 U 1 )R 1 (ii) a Terminal voltage U of battery t ＝U OCV ‑U 0 ‑U 1 ； SOC (0) is initial SOC value, η is charge-discharge capacity conversion coefficient, Q N The rated capacity of the battery.)

1. The fractional order power battery SOC estimation method considering the temperature and the hysteresis effect is characterized by comprising the following steps of:

open circuit voltage of the battery is U_OCVVoltage source, internal resistance R₀The first-order fractional order equivalent circuit model of the power battery is formed by connecting the polarization ring in series, wherein the capacitor in the polarization ring is a fractional order CPE element, and the resistor is polarization internal resistance R₁；I₁For current on CPE element, the capacitance of CPE element is C₁Order of α₁，U_OCVCan be measured by tests; u shape₀Is the internal resistance terminal voltage; u shape₁Is the voltage at the end of the polarization loop; u shape_tIs the battery terminal voltage, is the output variable of the whole battery system; i is total current, is an input variable of a battery system, and is negative during charging and positive during discharging;

the current on the CPE element is:

I₁＝C₁D^α1U₁(3)

the voltage on the polarization ring is:

U₁＝(I-C₁D^α1U₁)R₁(4)

the battery terminal voltage is:

U_t＝U_OCV-U₀-U₁(5)

the SOC calculation formula of the battery is as follows:

wherein SOC (0) is initial SOC value, η is charge-discharge capacity conversion coefficient, and Q_NThe rated capacity of the battery;

α therein₁Is the order, h is the sampling interval, n is t/h, t is the interval upper limit, k is 1, 2, 3 … … n;

considering the effect of gaussian white noise, the expression of the battery fractional order discretization space state is as follows:

wherein x (k) ═ soc (k), U₁(k)]^T；y(k)＝[Ut]； D(k)＝[-R₀]；h[x(k)]＝U_OCV[SOC(k)]-U₁(k) (ii) a Omega (k) is system noise, upsilon (k) is measurement noise, the noise type is Gaussian white noise, the system noise variance is Q, and the measurement noise variance is R.

2. The method for estimating the SOC of a fractional order power battery considering temperature and hysteresis effects as claimed in claim 1, wherein:

in the formula, η_dIs a discharge capacity conversion coefficient of η_cConverting the charge capacity into a coefficient; q_T,CdDischarge capacities at different temperatures and discharge currents; q_T,CcThe charge capacities at different temperatures and charge currents; q_NAs baseline capacity, in Ah; t is ambient temperature, T is 0 ℃,5 ℃,15 ℃,25 ℃,30 ℃,35 ℃; c_dTo discharge rate, C_d＝C/3,C/2,3C/4,C,5C/4,3C/2,7C/4,2C,9C/4；C_cTo charge rate, C_c＝C/3,C/2,3C/4,C。

3. The method for estimating the SOC of a fractional order power battery considering temperature and hysteresis effects as claimed in claim 1, wherein: u shape_OCV＝(U_{OCV_c}-U_{OCV_d})*0.25+U_{OCV_d}(14)

In the formula of U_{OCV_c}Open circuit voltage for charging state; u shape_{OCV_d}Open circuit voltage for discharge state; and uses a polynomial to split the open circuit voltage U_OCVAnd (6) fitting.

4. The method for estimating the SOC of a fractional order power battery considering temperature and hysteresis effects as claimed in claim 1, wherein: the fractional order equivalent circuit model is identified by adopting a particle swarm optimization algorithm of dynamic inertia weight, the weight is larger in the early stage of calculation so as to enlarge the search range, the global optimization capability is improved, the weight is smaller in the later stage of calculation so as to carry out local accurate calculation, and the result convergence speed and precision are improved.

5. The method of claim 4 for estimating the SOC of a fractional order power battery considering temperature and hysteresis effects, wherein: the method for identifying the fractional order equivalent circuit model by adopting the particle swarm optimization algorithm of the dynamic inertia weight comprises the following steps:

1) initialization

Defining the particle velocity v_max、v_minAnd a position limit theta_max、θ_minTo prevent ignoring the optimum and result overflow; initial velocity v of random particles_l,jAnd position theta_l,jWhere l is 1, 2, 3 … N, N is the number of particles, and j is the number of iterations; initial j is 0, particle position θ_l,jRepresents the parameter set [ R ] to be identified₀R₁C₁α₁]；

2) Calculating a fitness function

Setting a fitness function of each particle under the current iteration number asWhere n is the length of the test data, U_r(k) Measuring terminal voltage, U, for a battery at time k_m(k,θ_l,j) At particle position theta for fractional order model_l,jThe following terminal voltages are calculated as follows:

the transfer function of the fractional order capacitance element differential equation is as follows:

the voltage across the polarization ring is then:

U₁(s)＝(I-C₁s^α1U₁)R₁(17)

setting polarization ring and internal resistance R₀The voltage at both ends is U, then

Converted to a fractional order differential equation and defined in conjunction with the fractional order G-L:

then U is_m(k,θ_l,j)＝U_OCV(SOC(k))-U(k) (21)

Wherein h is the sampling interval; nc is the historical data amount involved in calculation, theoretically the number of all data points before the time k, but the calculation amount is increased rapidly along with the increase of time, so the invention comprehensively considers the particle swarm optimization calculation amount and the accuracy of the output end voltage of the fractional order model, sets the calculation truncation number Ne to be 800, and sets the calculation truncation number Ne to be k when Ne is less than k, and when Ne is more than or equal to k;

3) individual best fitness update

The position theta of each particle under the current iteration number is measured_l,jThe corresponding fitness value Fit (l, j) and the historical optimal position of the particleCorresponding fitness value F_best(l) For comparison, if Fit (l, j)<F_best(l) Then the current particle position is used to update the historical best position of the particle

4) Population best fitness update

The position theta of each particle under the current iteration number is measured_l,jThe corresponding fitness value Fit (l, j) and the global optimum position theta^bestCorresponding fitness value F_bestFor comparison, if Fit (l, j)<F_bestThen the global optimum position θ is updated with the current particle position^best；

5) Updating particle position and velocity

And updating the corresponding speed of each particle:

wherein ω is₁、ω₂Is weight and is used for adjusting the search range; m is the maximum iteration number; c. C₁、c₂Is an acceleration constant, c₁＝c₂＝2；r₁、r₂Is a random parameter, and takes a value range of [0,1 ]]To increase the randomness of particle search;

updating the corresponding positions of the particles:

θ_l,j+1＝θ_l,j+v_l,j+1(23)

6) judging whether the program is finished

If the iteration times are large or the fitness value is smaller than a preset value, the algorithm is ended, and the global optimal position theta is at the moment^bestAnd (3) obtaining the optimal solution, otherwise, iterating the times j +1 and returning to the step 2) to calculate the fitness function.

6. The method for estimating the SOC of a fractional order power battery considering temperature and hysteresis effects as claimed in claim 1, wherein: for the fractional order model, SOC estimation is carried out by adopting extended Kalman filtering, a Jacobian matrix is used for replacing a nonlinear part, and the specific steps are as follows:

in combination with equations (11) - (12), the state is predicted in one step:

wherein Nc is the historical data amount involved in calculation, theoretically the number of all data points before the time k, but the calculation amount is increased rapidly along with the increase of time, the particle swarm optimization calculation amount and the accuracy of the fractional order model output end voltage are comprehensively considered, the calculation truncation number Ne is set to be 800, and when Ne < k, Nc is Ne, and Ne is not less than k, Nc is k;

covariance one-step prediction:

kalman filter gain matrix:

K(k+1)＝P(k+1|k)H^T(HP(k+1|k)H^T+R)^-1(28)

h is a jacobian matrix to replace the nonlinear function H in the observation equation of equation (12):

and (3) estimation of observation error:

y (k +1) is the actually measured voltage at the moment of k + 1;

and (3) updating the covariance matrix:

P(k+1)＝(I_2x2-K(k+1)H)P(k+1|k) (32)

I_2x2is a 2-dimensional identity matrix;

and (3) updating the state:

Technical Field

The patent relates to a power battery SOC estimation method.

Background

For power battery SOC estimation, currently, commonly used integral order equivalent circuit models include a Rint model, a Thevein model and a PNGV model.

The resistance-capacitance characteristics of the lower end voltage of the battery in a charging and discharging and standing state are difficult to accurately simulate by the integer order equivalent circuit model, and particularly the accuracy of the output end voltage of the integer order equivalent circuit model cannot be ensured in a wider temperature range; the estimated SOC of the battery is accurate and low, and is difficult to adapt to the use requirement.

Disclosure of Invention

The invention aims to provide a fractional order power battery SOC estimation method considering temperature and hysteresis effect, which can accurately estimate the battery SOC, has stronger robustness and can quickly converge under the condition that the system has initial error; compared with an integral order equivalent circuit model, the fractional order model can accurately simulate the resistance-capacitance characteristics of the lower end voltage of the battery in the charging and discharging and standing states; the method can ensure the accuracy of the voltage of the output end of the fractional order equivalent circuit model in a wider temperature range and during the change of the charging and discharging states.

According to the technical scheme adopted by the patent, the fractional order power battery SOC estimation method considering temperature and hysteresis effect is adopted, and the open-circuit voltage of the battery is U_OCVVoltage source, internal resistance R₀The first-order fractional order equivalent circuit model of the power battery is formed by connecting the polarization ring in series, wherein the capacitor in the polarization ring is a fractional order CPE element, and the resistor is polarization internal resistance R₁；I₁For current on CPE element, the capacitance of CPE element is C₁Order of α₁，U_OCVCan be measured by tests; u shape₀Is the internal resistance terminal voltage; u shape₁Is the voltage at the end of the polarization loop; u shape_tIs the battery terminal voltage, is the output variable of the whole battery system; i is total current, is an input variable of a battery system, and is negative during charging and positive during discharging;

the current on the CPE element is:

I₁＝C₁D^α1U₁(3)

the voltage on the polarization ring is:

U₁＝(I-C₁D^α1U₁)R₁(4)

the battery terminal voltage is:

U_t＝U_OCV-U₀-U₁(5)

the SOC calculation formula of the battery is as follows:

wherein SOC (0) is initial SOC value, η is charge-discharge capacity conversion coefficient, and Q_NThe rated capacity of the battery;

α therein₁Is the order, h is the sampling interval, n is t/h, t is the interval upper limit, k is 1, 2, 3 … … n;

considering the effect of gaussian white noise, the expression of the battery fractional order discretization space state is as follows:

The above fractional order power battery SOC estimation method considering temperature and hysteresis effect,

U_OCV＝(U_{OCV_c}-U_{OCV_d})*0.25+U_{OCV_d}(14)

in the formula of U_{OCV_c}Open circuit voltage for charging state; u shape_{OCV_d}Open circuit voltage for discharge state; and uses a polynomial to split the open circuit voltage U_OCVAnd (6) fitting.

According to the fractional order power battery SOC estimation method considering the temperature and the hysteresis effect, the fractional order equivalent circuit model is identified by adopting a particle swarm optimization algorithm of dynamic inertia weight, the method has larger weight in the early stage of calculation to enlarge the search range and improve the global optimization capability, and has smaller weight in the later stage of calculation to facilitate local accurate calculation, so that the result convergence speed and precision are improved.

In the method for estimating the SOC of the fractional order power battery considering the temperature and the hysteresis effect, the step of identifying the fractional order equivalent circuit model by adopting the particle swarm optimization algorithm of the dynamic inertia weight is as follows:

1) initialization

Defining the particle velocity v_max、v_minAnd a position limit theta_max、θ_minTo prevent fromIgnoring the optimal value and result overflow; initial velocity v of random particles_l,jAnd position theta_l,jWhere l is 1, 2, 3 … N, N is the number of particles, and j is the number of iterations; initial j is 0, particle position θ_l,jRepresents the parameter set [ R ] to be identified₀R₁C₁α₁]；

2) Calculating a fitness function

the transfer function of the fractional order capacitance element differential equation is as follows:

the voltage across the polarization ring is then:

U₁(s)＝(I-C₁s^α1U₁)R₁(17)

setting polarization ring and internal resistance R₀The voltage at both ends is U, then

Converted to a fractional order differential equation and defined in conjunction with the fractional order G-L:

then U is_m(k,θ_l,j)＝U_OCV(SOC(k))-U(k) (21)

3) individual best fitness update

4) Population best fitness update

5) Updating particle position and velocity

And updating the corresponding speed of each particle:

updating the corresponding positions of the particles:

θ_l,j+1＝θ_l,j+v_l,j+1(23)

6) judging whether the program is finished

In the method for estimating the fractional order power battery SOC considering the temperature and the hysteresis effect, the SOC is estimated by adopting the extended Kalman filtering for the fractional order model, and a Jacobian matrix is used for replacing a nonlinear part, and the method specifically comprises the following steps:

in combination with equations (11) - (12), the state is predicted in one step:

covariance one-step prediction:

kalman filter gain matrix:

K(k+1)＝P(k+1|k)H^T(HP(k+1|k)H^T+R)^-1(28)

h is a jacobian matrix to replace the nonlinear function H in the observation equation of equation (12):

and (3) estimation of observation error:

y (k +1) is the actually measured voltage at the moment of k + 1;

and (3) updating the covariance matrix:

P(k+1)＝(I_2x2-K(k+1)H)P(k+1|k) (32)

I_2x2is a 2-dimensional identity matrix;

and (3) updating the state:

the beneficial effect of this patent:

the method establishes an equivalent circuit model based on a fractional order theory, researches the capacity characteristic and the open-circuit voltage characteristic of the lithium iron phosphate battery at different temperatures, provides a simplified modeling method considering the hysteresis characteristic of the open-circuit voltage, identifies the parameters of the fractional order equivalent circuit model at different temperatures based on a PSO (particle swarm optimization) optimization method, and finally establishes a fractional order extended Kalman filtering algorithm model to realize the dynamic estimation of the SOC of the power battery, wherein the proposed estimation method has the following advantages:

1. under the same order, compared with an integer order equivalent circuit model, the fractional order model can accurately simulate the resistance-capacitance characteristics of the lower end voltage of the battery in the charging and discharging and standing states;

2. the accuracy of the voltage at the output end of the fractional order equivalent circuit model can be ensured in a wider temperature range and when the charging and discharging state changes;

3. the extended Kalman filter based on the fractional order can estimate the SOC of the battery more accurately than the extended Kalman filter based on the integral order, and has stronger robustness under the condition of larger initial error.

Drawings

FIG. 1 is a fractional order equivalent circuit model;

fig. 2 is a schematic view of a charge and discharge test stand.

Detailed Description

Introduction to 1

The integer order equivalent circuit model is difficult to accurately simulate the resistance-capacitance characteristics of the lower end voltage of the battery in a charging and discharging and standing state, and the estimated SOC of the battery is accurate and low and is difficult to adapt to the use requirements. Therefore, the invention provides a fractional order power battery SOC estimation method considering temperature and hysteresis effect, which can accurately estimate the battery SOC.

2 fractional order model

2.1 fractional order theory

Fractional order is essentially the expansion of integral order calculus operation to any non-integral order calculus, and is widely applied to subjects of viscoelasticity mechanics, soft material mechanics and the like at present, and has primary application in the aspect of batteries along with the development of a new energy automobile SOC estimation method. Partial documents show the rationality of applying the fractional calculus theory to the battery, and the accuracy of the terminal voltage of the model can be improved by establishing a battery equivalent circuit model based on the fractional theory.

At present, fractional calculus definitions mainly comprise four types, namely G-L type, R-L type, Caputo type and Weyl type, while the most widely applied type in the aspect of a battery equivalent circuit model is G-L type, which is generalized by an integer order derivative difference approximation recursion formula, and when the fractional order α >0, the fractional order is defined as follows:

wherein a is the lower limit of the interval; t is the upper limit of the interval; h is the sampling interval, and n is t/h. For convenience of writing, hereinafterCan be represented as D^αx(t)。

2.2 fractional order equivalent circuit model

The current commonly used integer order equivalent circuit model comprises a Rint model, a Thevein model and a PNGV model, the fractional order equivalent circuit model is mostly modified and replaced by elements on the basis of the integer order equivalent circuit model, the patent considers that the fractional order has data memory characteristics to cause the calculated amount to be larger than that of the integer order, and in order to reduce the difficulty of parameter identification, the first order Thevein model is modified, and the capacitor in the polarization ring is replaced by a fractional order CPE element to obtain the first order fractional order equivalent circuit model, as shown in figure 1. Wherein U is_OCVThe open-circuit voltage of the battery is one of important parameters influencing the SOC estimation of the power battery, and is also equivalent to a nonlinear characteristic part in a circuit model, and the nonlinear characteristic part can be measured by a test; u shape₀Is the internal resistance terminal voltage; u shape₁Is the voltage at the end of the polarization loop; u shape_tIs the battery terminal voltage, is the output variable of the whole battery system; i is the total current, which is the input variable of the battery system, and this patent specifies negative for charging and positive for discharging. I is₁Current on CPE (constant phase angle) element; r₀The internal resistance can embody the voltage characteristic of the battery at the charging and discharging moment; r₁For polarization internal resistance, the CPE element capacitance is C₁Order of α₁The combination of the two can show the polarization characteristics of the battery in the processes of charging, discharging and standing.

According to the fractional order theory, the current on the CPE device is:

I₁＝C₁D^α1U₁(3)

the voltage on the polarization ring is:

U₁＝(I-C₁D^α1U₁)R₁(4)

according to kirchhoff's voltage law, the battery terminal voltage is:

U_t＝U_OCV-U₀-U₁(5)

the SOC calculation formula of the battery is as follows:

wherein SOC (0) is initial SOC value, η is charge-discharge capacity conversion coefficient, and Q_NThe rated capacity of the battery;

when h takes a small positive number, equation (1) can be approximated as:

if f (k-i) is substituted for f (t-ih), equation (7) can be rewritten as:

discretizing formula (4) can obtain:

in combination with the fractional order approximation calculation formula of equation (8), equation (9) can be further derived:

finishing to obtain:

if the influence of Gaussian white noise is considered, the battery fractional order discretization space state expression is as follows:

3 Battery characteristics under different influence factors

This patent selects A123 company to produce pure electric automobile lithium iron phosphate monomer power battery as the research object, battery capacity characteristic and open circuit voltage characteristic research under the influence of different factors have been carried out, battery rated capacity is 20Ah, rated voltage 3.2V, constant voltage charging cutoff voltage is 3.65V, constant current charging cutoff current is 0.5A, for guaranteeing battery life, the discharging cutoff voltage sets to 2.5V, the charge-discharge test rack comprises charge-discharge tester BT2016, host computer, ambient temperature case and multi-functional ammeter HP34401A, as shown in figure 2.

3.1 Capacity characteristics

The battery capacity is a key factor influencing the SOC estimation accuracy, but the influence of the battery temperature and the charge-discharge rate is large in the actual use process, so in order to improve the SOC estimation accuracy, the battery charge-discharge capacity needs to be tested under different temperatures and different charge-discharge rates to obtain a charge-discharge capacity conversion coefficient η to correct the battery SOC, according to 2015 electric vehicle battery test manual, the patent calculates η by taking the capacity under the conditions of 30 ℃ and 3/C rate as a reference, as shown in formula (13), the specific test method is as follows:

discharge capacity test

Because pure electric vehicles's power battery is in the in-service use in-process, the big multiplying power is discharge operating mode less continuously, and during the battery test moreover, during the battery test, need consider the battery in the security of constant current discharge operating mode moreover, avoid electrode impaired influence follow-up test. Therefore, in the test, the maximum discharge rate of the battery is selected to be 9C/4(45A), the minimum discharge rate is selected to be C/3(6.67A), the test workload and the test precision are comprehensively considered, and the discharge rate test node is set as follows: c/3, C/2, 3C/4, C, 5C/4, 3C/2, 7C/4, 2C, 9C/4. In consideration of the temperature setting range of the constant temperature environment box and the low-temperature performance loss of the battery, the lowest test environment temperature is selected to be 0 ℃ in the test, and meanwhile, the highest test environment temperature is selected to be 35 ℃ in order to guarantee the safety of the battery in the high-temperature test. Therefore, the experimental ambient temperature node is set to: 0 ℃,5 ℃,15 ℃,25 ℃,30 ℃ and 35 ℃.

The operation steps of the specific discharge capacity test are as follows: firstly, a group of environment temperature nodes and discharge rate nodes are selected. Under the environment temperature, the battery is charged with C/3 constant current to cut-off voltage of 3.65V, and then charged with 3.65V constant voltage until the charging current is less than 0.025C, and because the temperature of the battery is slightly higher during charging, the battery is kept still for 1 hour to make the temperature equal to the environment temperature. And then, constant-current discharge is carried out according to the selected discharge rate node until the terminal voltage is reduced to 2.5V of discharge cut-off voltage, and the discharge capacity under the conditions of the temperature and the discharge rate node is recorded. And circulating the steps until all the combinations of the environment temperature and the discharge multiplying factor nodes are finished.

Test of charging Capacity

The maximum acceptable charging rate of the lithium iron phosphate battery is generally less than 2C, and in order to ensure the safety of the battery in a charging capacity test and prevent an electrode from being irreversibly damaged so as not to influence a subsequent test, the maximum charging rate of the battery is 1C in the test. Therefore, the charge capacity test charge rate node is set to: c/3, C/2, 3C/4, C. The environment temperature node of the charge capacity test is the same as the environment temperature node of the discharge capacity test, and the nodes are as follows: 0 ℃,5 ℃,15 ℃,25 ℃,30 ℃ and 35 ℃.

The specific operation steps of the charge capacity test are as follows: firstly, selecting a corresponding temperature node and charging rate node combination. Under the selected environment temperature, the battery is fully charged under the same condition, then discharged by C/3 constant current until the terminal voltage is reduced to be the discharge cut-off voltage of 2.5V, and kept stand for 1 hour to ensure that the temperature of the battery is equal to the environment temperature. And (5) carrying out constant current charging according to the selected charging rate until the terminal voltage rises to be the charging cut-off voltage of 3.65V, and recording the charging capacity at the temperature and the charging rate node. And circulating the steps until all temperature and charging rate node combinations are completed.

In the formula, η_dIs a discharge capacity conversion coefficient of η_cConverting the charge capacity into a coefficient; q_T,CdDischarge capacities at different temperatures and discharge currents; q_T,CcThe charge capacities at different temperatures and charge currents; q_NThe reference capacity is 20.2Ah through tests; t is ambient temperature, T is 0 ℃,5 ℃,15 ℃,25 ℃,30 ℃,35 ℃; c_dTo discharge rate, C_d＝C/3,C/2,3C/4,C,5C/4,3C/2,7C/4,2C,9C/4；C_cTo charge rate, C_c＝C/3,C/2,3C/4,C。

3.2 open Circuit Voltage characteristic

The influence of the battery open-circuit voltage on the output voltage of the battery model is very large, and for the lithium iron phosphate battery, the open-circuit voltage has strong nonlinear characteristic and hysteresis characteristic along with the change of the SOC. The open circuit voltage test scheme considering the influence of different temperatures and charge and discharge states of the battery is as follows:

open circuit voltage test in discharge state

Firstly, selecting a corresponding temperature node, charging the test battery to a charging cut-off voltage of 3.65V by using a C/3 constant current, and then charging the test battery to a constant voltage of 3.65V until the charging current is reduced to 0.025C, wherein the battery is in a full-charge state. After standing for 1h, the battery terminal voltage was recorded as a discharge state open circuit voltage at which the battery SOC became 100%. Then, the constant current of C/3 is used for discharging until the SOC is 95%, and the discharged electricity quantity is equal to 5% of the discharged electricity quantity at the current environment temperature and discharge multiplying factor. After standing for 1h, the battery terminal voltage was recorded as a discharge state open circuit voltage at which SOC was 95%. And (4) sequentially circulating, wherein each time of discharging is reduced by 5% according to the SOC of the battery until the SOC is equal to 0%, recording the terminal voltage of standing for 1h after each time of discharging, and taking the terminal voltage as the open-circuit voltage value of the discharging state when the SOC of the battery corresponds to, thus finishing the open-circuit voltage test of the discharging state at the environment temperature node. And repeating the steps until all the environment temperature nodes are finished. And (5) collating the test data to obtain open-circuit voltage values corresponding to SOC points of the discharge state at different temperatures.

State of charge open circuit voltage test

Firstly, selecting a corresponding temperature node, and discharging the lithium iron phosphate battery at a constant current of C/3 until the voltage at the battery terminal is reduced to the discharge cut-off voltage of 2.5V. At this time, the battery was considered to be in a dead state, and after standing for 1 hour, the terminal voltage was recorded as a charged state open circuit voltage value at which the battery SOC became 0%, and then C/3 constant current charging was performed until the battery SOC became 5%. At this time, the amount of charge should be equal to 5% of the battery charge capacity at the current ambient temperature and charge rate. After standing for 1h, terminal voltage data was recorded as a state-of-charge open circuit voltage value at which the battery SOC became 5%. And (4) circulating in sequence, increasing the SOC of the battery by 5% until the SOC of the battery is 95% each time of charging, and recording the open-circuit voltage value of standing for 1h after each time of charging. Finally, the battery is charged with a constant current of C/3 to a charge cut-off voltage of 3.65V, and then charged with a constant voltage of 3.65V until the charge current drops to 0.025C. And (4) standing the battery for 1h when the battery is in a full-charge state, and recording terminal voltage data as a charging state open-circuit voltage value when the battery SOC is equal to 100%, so that the battery charging state open-circuit voltage value measurement test under the environment temperature node is finished. And repeating the steps until all the environment temperature nodes are finished. And (5) collating the test data to obtain open-circuit voltage values corresponding to SOC points of the charging state at different temperatures.

When the pure electric vehicle runs, the power battery is in a discharge state for most of time, so in order to simplify the algorithm and consider the hysteresis characteristic of the open-circuit voltage and make the open-circuit voltage biased to the discharge state, the calculation method comprises the following steps:

U_OCV＝(U_{OCV_c}-U_{OCV_d})*0.25+U_{OCV_d}(14)

in the formula of U_{OCV_c}Open circuit voltage for charging state; u shape_{OCV_d}Is the open circuit voltage in the discharge state.

This patent uses 8 th order polynomials to carry out the fitting to open circuit voltage OCV, and it can each OCV test data point of well fitting. 4 fractional order equivalent circuit model parameter identification based on PSO

4.1PSO Algorithm identification

Compared with an integer order model, the fractional order model has a relation with a historical state, data has a memory effect, so that a calculation process is slow, the particle swarm optimization algorithm is widely concerned and applied in recent years as an evolutionary algorithm by virtue of the advantages of high calculation speed, few calling parameters, simple programming and the like, the dynamic inertial weight particle swarm optimization algorithm is adopted to identify the fractional order equivalent circuit model, the fractional order equivalent circuit model can have large weight in the early calculation stage to enlarge a search range and improve the global optimization capability, and has small weight in the later calculation stage to perform local accurate calculation, so that the result convergence speed and precision are improved. The specific method is as follows:

1) initialization

2) Calculating a fitness function

the transfer function of the fractional order capacitance element differential equation is as follows:

the voltage across the polarization ring is then:

U₁(s)＝(I-C₁s^α1U₁)R₁(17)

setting polarization ring and internal resistance R₀The voltage at both ends is U, then

Converted to a fractional order differential equation and defined in conjunction with the fractional order G-L:

then U is_m(k,θ_l,j)＝U_OCV(SOC(k))-U(k) (21)

3) individual best fitness update

4) Population best fitness update

5) Updating particle position and velocity

And updating the corresponding speed of each particle:

updating the corresponding positions of the particles:

θ_l,j+1＝θ_l,j+v_l,j+1(23)

6) judging whether the program is finished

4.2 identification test

The state change of the power battery is complex in the working process, the equivalent circuit model parameters of the power battery can change along with self factors and external states, pulse tests are required to be carried out under different charging and discharging states, SOC (state of charge) and ambient temperatures of the battery in order to obtain accurate fractional order equivalent circuit model parameters of the battery, and the test scheme is shown as follows.

(I) discharge State parameter identification test

The environmental temperature node of the discharge state parameter identification test is the same as the environmental temperature node of the discharge capacity test, and the nodes are as follows: 0 deg.C, 5 deg.C, 15 deg.C, 25 deg.C, 30 deg.C, 35 deg.C. Considering that when the SOC of the battery is low or high, the model parameters change very severely, the parameter identification is difficult, and the battery is generally not fully charged in order to prolong the cycle life, so the SOC nodes of the battery are divided into: 0.9,0.8,0.7,0.6,0.5,0.4,0.3,0.2,0.1. The specific test steps are as follows:

firstly, selecting an environment temperature node, after the battery temperature is stabilized at the environment temperature, carrying out C/3 constant current charging on the battery until the charging cut-off voltage is 3.65V, and then carrying out constant voltage charging until the charging current is reduced to 0.025C, wherein the SOC of the battery is in a full state of 100%. After standing for 1h, discharging the battery at a constant current of C/3 until the SOC is reduced to 90 percent, namely the discharged electric quantity is equal to 10 percent of the discharged electric quantity measured under the corresponding environment temperature and C/3 discharge rate in a discharge capacity test. And standing for 1h to enable the battery to be in a balanced state, and performing double-pulse discharge, namely standing for 10s first, then discharging with 2C for 10s constant current, standing for 40s, then discharging with 2C for 10s constant current, and then standing for 40 s. After the double-pulse discharge test is finished, the battery is also kept stand for 1h, then is discharged at a constant current of C/3 until the SOC of the battery is reduced to 80%, and then is kept stand for 1h to carry out double-pulse discharge. And sequentially circulating, performing a group of double-pulse discharge tests at intervals of 10% of SOC (state of charge) each time to obtain parameter identification data, and ending the discharge parameter identification test at the temperature node until the double-pulse discharge test in the state of SOC being 10% is completed. And extracting a double-pulse discharge test value under each SOC node as parameter identification data, wherein 9 segments of data are contained in each environment temperature node, the time length of each segment of data is 110s, and the sampling interval of the rack is 0.2s, so that 550 test data points are contained in total. And similarly, testing all the environment temperature nodes according to the test steps. And finishing the discharge state double-pulse parameter identification test data under all the temperature nodes, wherein the total number of the discharge state double-pulse parameter identification test data is 54, and the duration of each section is 110s, so that the discharge state double-pulse parameter identification test data is used for identifying the discharge state equivalent circuit parameters.

(II) Charge State parameter identification test

The ambient temperature node and the SOC node of the charging state parameter identification test are the same as those of the discharging state parameter identification test.

The specific test steps are as follows:

firstly, selecting an environment temperature node, and after the battery temperature is equal to the environment temperature, performing C/3 constant current discharge on the battery until the discharge cut-off voltage is 2.5V (SOC is 0%). And after standing for 1h, charging the battery at a constant current of C/3 until the SOC of the battery is 10%, namely the charged electric quantity is equal to 10% of the charging capacity measured under the corresponding environment temperature and C/3 charging rate in a charging capacity test, standing for 1h, then performing double-pulse charging, namely standing for 10s, then continuing to charge at a constant current of 10s at 2C, standing for 40s, continuing to charge at a constant current of 10s at 2C, and then standing for 40 s. And then standing for 1h, charging the battery at a constant current of C/3 until the SOC of the battery is 20%, standing for 1h, and then performing double-pulse charging. And sequentially circulating, performing a group of double-pulse charging tests at intervals of 10% of SOC each time to be used as parameter identification data, and ending the charging parameter identification test at the temperature node until the double-pulse charging test at the state that the SOC of the battery is 90% is completed, and extracting a double-pulse charging test value at each SOC node to be used as the parameter identification data. And similarly, performing the test steps until the test of all the environment temperature nodes is completed. And (4) sorting the charging state double-pulse parameter identification test data under all the temperature nodes, wherein the total number of the charging state double-pulse parameter identification test data is 54, and the duration of each section is 110s, so that the charging state double-pulse parameter identification test data is used for charging state equivalent circuit parameter identification.

4.3 verification of identification results

Dynamic Stress Test (DST) is simplified from the UDDS, and includes 10 discharge stages, 5 charge stages and 5 standing stages, wherein each cycle is 360s, and the working condition is easy to realize and can better simulate the actual operation condition of the battery, which is a common simulated charge-discharge working condition for verifying the accuracy of the equivalent circuit model of the battery and the effectiveness of the SOC estimation method at present.

This patent adopts 26 continuous DST circulation operating modes to test the test battery altogether, and ambient temperature is 28 ℃. The result shows that the voltage at the end of the fractional order equivalent circuit can well track the actually measured voltage, the average voltage error is 0.0034V, the average error rate is 0.107%, and the error is larger only when the charging and discharging current is larger, the maximum error is 0.0196V, and the error rate is 0.613%. The integral order equivalent circuit model terminal voltage is integrally larger than the actually measured voltage and the fractional order terminal voltage, the average voltage error is 0.0086V, the average error rate is 0.0269%, and the error is larger, so that the fractional order model parameter identification result based on the PSO and the SOC-OCV simplification method considering the hysteresis characteristic can better simulate the battery voltage characteristic and provide better model precision for the later SOC estimation of the Kalman filter.

5 fractional order based extended Kalman SOC estimation

Kalman filtering is an optimal estimation method based on minimum variance estimation, but is only suitable for a linear system, a vehicle-mounted power battery has strong nonlinear characteristics in the actual operation process, and the problem can be well solved by taking extended Kalman filtering as a Kalman filtering improvement form, so that the method has wide application in the aspect of SOC estimation.

5.1FEKF SOC estimation

The extended Kalman filtering linearization method based on the fractional order model is the same as the integer order extended Kalman, a Jacobian matrix is used for replacing a nonlinear part, and the extended Kalman filtering method based on the fractional order model comprises the following steps:

in combination with equations (11) - (12), the state is predicted in one step:

wherein N is_cHas the same meaning as formula (20).

Covariance one-step prediction:

kalman filter gain matrix:

K(k+1)＝P(k+1|k)H^T(HP(k+1|k)H^T+R)^-1(28)

h is a jacobian matrix to replace the nonlinear function H in the observation equation of equation (12):

and (3) estimation of observation error:

y (k +1) is the voltage measured at the moment k + 1.

And (3) updating the covariance matrix:

P(k+1)＝(I_2x2-K(k+1)H)P(k+1|k) (32)

I_2x2is a 2-dimensional identity matrix.

And (3) updating the state:

5.2 validation of estimation results

The test environment temperature is set to be 28 ℃, the working conditions are 26 continuous DST working conditions in section 4.3, the FEKF is verified and compared with the integer-order EKF, the initial SOC of the working conditions is 0.9, and the initial SOC of the FEKF and the initial SOC of the EKF are the same as the initial values of the working conditions.

The verification result shows that errors of the FEKF and the EKF are relatively large in the early estimation stage, but the FEKF can quickly keep up with the SOC true value and enable the errors to fluctuate above and below 0, the SOC average error is 0.0036, the error rate is 0.52%, but the EKF always keeps large errors with the true value due to problems of equivalent circuit model accuracy and the like, the average error is 0.0224, and the error rate is 3.2%. Because the accuracy of the fractional order model is higher than that of the integral order, the voltage of the output end of the KEKF filter can better follow the measured voltage than that of the EKF, and because of the effect of the covariance, compared with the voltage error of the output end of the equivalent circuit model without the effect of the filter in section 4.3, the voltage error of the end can fluctuate above and below 0, thereby achieving better balance between the reliability of the model and the reliability of the measured value.

The method selects the FEKF initial SOC to be 0.85,0.8,0.7 and 0.6 respectively to carry out simulation test to verify the robustness of the FEKF under the condition that the filter parameter noise covariance and the initial covariance are not changed.

The result shows that the FEKF can achieve a better convergence effect through a period of time of SOC and output end voltage under different initial error conditions, the FEKF can enable the error to be reduced rapidly in the early stage under the condition of larger initial error, and the convergence speed is ensured, wherein the error of the output voltage of the filter in the early stage of estimation is increased along with the increase of the initial error of the SOC, because the larger the initial SOC error is, the smaller the state is predicted in one step, the smaller the SOC is, the end voltage is reduced due to the reduction of the open-circuit voltage of the model, but the estimated state can be gradually converged to a test value along with the feedback effect of the actually measured voltage.

In summary, compared with the EKF, the FEKF adopted by the method can estimate the SOC of the battery more accurately, has stronger robustness and can quickly converge under the condition that the system has initial errors.

19页详细技术资料下载

上一篇：一种医用注射器针头装配设备

下一篇：一种模拟车辆工况动力电池荷电状态SOC估算优化方法

Fractional order power battery SOC estimation method considering temperature and hysteresis effect

相关技术

网友询问留言