Lithium battery SOC estimation method based on resistance-capacitance parameter filtering and AUKFTechnical Field
The invention relates to the technical field of lithium battery performance detection, in particular to a lithium battery SOC estimation method based on resistance-capacitance parameter filtering and AUKF.
Background
Accurate estimation of state of charge (SOC) of a lithium battery helps a battery management system to formulate an equalization strategy for a battery pack, extending battery pack life. The research students at home and abroad research the lithium battery SOC estimation method by adjusting the initial value P0 of the error covariance and the noise covariance Q and R in the Kalman filtering algorithm. The lithium battery SOC estimation method can be divided into a parameter offline identification method and a parameter online identification method, wherein the parameter offline identification method and the parameter online identification method can respectively obtain time-invariant and time-variant resistance-capacitance parameters, and the equivalent circuit model and the SOC estimation precision are improved.
However, the existing parameter online identification method has the problem that the resistance-capacitance parameters lack reasonable constraint, and meanwhile, the abnormal jitter phenomenon of the resistance-capacitance parameters is serious and the convergence speed of the SOC is reduced to influence the stability of the algorithm under the influence of the initial value and the working condition of an identification strategy.
Disclosure of Invention
The invention aims to solve the problems, and designs a lithium battery SOC estimation method based on resistance-capacitance parameter filtering and AUKF.
A lithium battery SOC estimation method based on resistance-capacitance parameter filtering and AUKF comprises the following steps of constructing a second-order RC lithium battery equivalent circuit model to describe the charge-discharge characteristics of a lithium battery, as shown in figure 2. Wherein Uoc is the open-circuit voltage of the battery, I is the charge-discharge current of the battery, RL、CL is the electrochemical polarization resistance and the polarization capacitance respectively, RS、CS is the concentration polarization resistance and the polarization capacitance respectively, U is the terminal voltage of the battery, and Ro is the equivalent internal resistance of the battery.
Setting [ SOC UL US]T as a state variable of lithium battery performance, and constructing a discrete state space equation:
U=Uoc(SOC)-US-UL-RoI(k) (2)
wherein US and UL are respectively RS and RL terminal voltages, τs and τl are respectively time constants RSCS and RLCL,Qc are battery capacities, Δt is a sampling interval, and k is a discrete time.
The mapping relationship between Uoc and SOC in equation (1) in FIG. 1 is established. Considering the higher order polynomial relationship of the open circuit voltage UOC and the SOC and the hysteresis effect, to reduce model errors, a BP neural network model is used to fit the nonlinear relationship of UOC -SOC, as shown in FIG. 3. Taking the SOC and the charging and discharging mean value of the corresponding UOC as training sets with a certain step length to obtain the formula (3).
UOC＝NNbp(SOC) (3)。
Identifying an unknown RC parameter Ro、RS、CS、RL、CL in FIG. 1, taking noise and battery aging into consideration, obtaining an RC parameter value by utilizing FFRLS, sampling voltage and current data of a lithium battery under a working condition as input of FFRLS to obtain an RC parameter online identification result, taking fixed voltage and current of the battery as input of FFRLS to obtain an RC parameter offline identification result, calculating a noise variance by combining the two identification results, setting a gain threshold according to the variation characteristic of Kalman gain, and calculating a self-adaptive RC parameter vector based on the Kalman gain. The specific implementation mode is as follows:
1) Defining a resistance-capacitance parameter vector based on an online identification method as Xk＝[Ro|k RS|k CS|k RL|k CL|k]T, carrying out Xk online identification by utilizing FFRLS, and recursively:
wherein θ is a coefficient vector to be determined, Ie is a homotype identity matrix, λ is a forgetting factor,For I and U at times K-2 to K, KLS is the gain factor and PLS is the covariance matrix.
The online identification parameter Xk may have instability, jitter, negative value, etc. under complex working conditions, and in order to ensure the parameter stability, an offline identification result is introduced to perform parameter correction.
2) Defining the resistance-capacitance parameter vector of off-line identification asSuppressing Xk jitter and possible outliers. From the zero state response and zero input response of the voltages and currents in FIG. 4, calculated using FFRLS
3) Adding a Gaussian white noise simulation environment, battery aging and other factors toIs a function of (a) and (b). A noise term wg＝[wowrs wcs wrl wcl]T is defined, and a variance vector σ= [ σo σrs σcs σrl σcl]T. Wherein wo-N(0,σo),wrs-N(0,σrs),wcs-N(0,σcs),wrl-N(0,σrl),wcl-N(0,σcl). calculates the value of each element of σ from the variance calculation formula (7).
Wherein sigmaj andRespectively sigma,Xk,j is the j element of Xk, and vector elements should be limited to ensure the digital stability of Cholesky decomposition operation
4) According to the obtained Xk,And wg, designing an adaptive resistance-capacitance parameter vector Xa, and calculating Xa by combining the Kalman gain K as shown in a formula (8).
Wherein epsilon is a step function and gamma is a gain threshold.
5) And (5) judging an abnormal value. When Xk output elements are positive, gamma takes 0.1, and when Xk output contains negative numbers, gamma becomes a positive integer much larger than K.
Substituting the RC parameter vector filtering method into an UKF recursive process, constructing an AUKF algorithm, and carrying out lithium battery SOC estimation.
Based on the nonlinear characteristics of the lithium battery output, the formulas (1) and (2) are rewritten as:
xk+1＝f(xk,uk,w) (9)
yk＝h(xk,uk,v) (10)
wherein, w and Q are system process noise and covariance thereof, and v and R are system measurement noise and covariance thereof.
Based on classical UKF, a resistance-capacitance parameter self-adaptive module is added, a recursive Kalman gain coefficient is substituted into the resistance-capacitance parameter self-adaptive module, kalman gain closed-loop control is constructed, synchronous iteration of the resistance-capacitance parameter vector is realized, the convergence speed and stability of an algorithm are improved, an AUKF algorithm is obtained, and the recursive process is as follows:
1) 2n+1 sigma points are set, and n takes a value of 3 according to the dimension of the state vector xk＝[SOCk UL,k US,k]T in the equation (9).
Wherein: is the mean value of SOC and UL、US, Px is the oblique variance matrix of the state vector, and the matrixIs defined as the ith column of the square root matrix obtained by decomposing (n+lambdau)Px by Cholesky), lambdau is a scaling factor and is obtained by the formula (13).
λu＝α2(n+ki)-n (13)
Wherein, alpha is a small positive number, ki takes 0 under the single state variable, 3-n under the multi-state variable, and n is 3, so the value of ki takes 0.
2) The mean weight Wim and variance weight Wic of the sigma sample points are set to
Wherein beta is a super parameter reflecting the history information of the high-order state.
3) And (3) inputting the Kalman gain Kk at the moment K into a resistance-capacitance parameter self-adaptive module, constructing closed-loop feedback, and calculating the moment K Xa by combining the feedback with the moment (8).
4) Optimizing the time updating process of sigma sampling points, substituting Xa into formula (9) to obtain the mean value and variance of the one-step prediction state vector as follows:
5) The sampling point of the state vector predicted value is updated as
6) Optimizing the measurement updating process of sigma sampling points, substituting Xa into the formula (10) to obtain the mean value, variance and covariance of the one-step prediction measurement vector, wherein the mean value, variance and covariance are as follows:
7) The Kalman gain, state estimation and covariance matrix at time k+1 are calculated, where xk+1＝[SOCk+1UL,k+1US,k+1]T.
Advantageous effects
The lithium battery SOC estimation method based on the resistance-capacitance parameter filtering and the AUKF, which is manufactured by utilizing the technical scheme of the invention, has the following advantages:
1. correcting an online identification result by utilizing an offline identification result of the RC parameter, calculating a noise variance, combining a Kalman gain threshold to realize RC parameter filtering, and constructing an AUKF algorithm to realize quick estimation of the SOC of the lithium battery;
2. The AUKF algorithm has good convergence, robustness and effectiveness when estimating the SOC of the lithium battery, and provides a selection range of a gain threshold, and the maximum error of the SOC estimation after the AUKF algorithm is converged is lower than 1%.
Drawings
FIG. 1 is a flow chart of a lithium battery SOC estimation method based on resistance-capacitance parameter filtering and AUKF;
FIG. 2 is a schematic diagram of an equivalent circuit of a lithium battery according to the present invention;
FIG. 3 is a diagram of a BP neural network according to the present invention;
FIG. 4 is a graph of voltage parameters according to the present invention;
FIG. 5 is a physical diagram of the lithium battery test platform according to the invention;
FIG. 6 is a graph comparing experimental data of HPPC according to the present invention;
FIG. 7 is a graph of the charge-discharge relationship of UOC -SOC according to the present invention;
FIG. 8 is a graph of current waveforms in accordance with the present invention;
FIG. 9 is a time sequence diagram of the on-line identification of RL and CL according to the present invention;
FIG. 10 is a graph of SOC estimation under intermittent constant current discharge conditions according to the present invention;
FIG. 11 is a graph showing the variation trend of the Kalman gain according to the present invention;
FIG. 12 is a comparative plot of the convergence of the P0 variables according to the present invention;
FIG. 13 is a graph comparing the convergence of Q variables according to the present invention;
FIG. 14 is a comparative graph of the convergence of R-variables according to the present invention;
FIG. 15 is a graph comparing the convergence of the gamma variables according to the present invention;
FIG. 16 is a graph of the current waveforms of the DST test according to the present invention;
FIG. 17 is a graph of experimental data for SOC estimation with an initial value of 0.2 according to the present invention;
FIG. 18 is a graph of experimental data for SOC estimation with an initial value of 0.5 according to the present invention;
FIG. 19 is a graph showing outliers of CS and RS according to the present invention;
FIG. 20 is a time series diagram of RS and CS according to the present invention;
FIG. 21 is a diagram of SOC estimation during outlier disturbance according to the present invention;
fig. 22 is a graph of the external characteristics of the battery according to the present invention;
FIG. 23 is a graph of the capacity change according to the present invention;
FIG. 24 is a diagram of an aged battery SOC estimation according to the present invention;
FIG. 25 is a table of analysis of Uoc -SOC data according to the present invention;
FIG. 26 is a table of identifying offline parameters according to the present invention;
Detailed Description
Examples
The 18650 ternary lithium battery with rated capacity of 1800mAh, highest voltage of 4.2V and cut-off voltage of 2.5V is taken as an experimental object. And designing an HPPC experiment, a DST experiment, an intermittent constant current discharge experiment and a cyclic aging lithium battery SOC estimation experiment.
According to Freedom CAR battery test handbook, standard HPPC experiment is carried out to establish an equivalent circuit model, intermittent constant-current discharge experiment is designed to verify convergence of a design algorithm according to absolute error lower than 2%, DST working condition experiment is carried out to verify stability of the algorithm, cyclic aging lithium battery SOC estimation experiment is carried out to verify effectiveness and accuracy of full life cycle SOC estimation based on AUKF algorithm under the condition that external characteristics of the lithium battery are changed.
The experimental equipment is shown in fig. 5, and comprises a high-performance battery detection platform and a constant temperature and humidity box. The constant temperature was maintained at 26℃and the sampling interval was 0.5s.
1. HPPC experiments and analysis
The battery was charged to a maximum voltage of 4.2V and discharged to a cut-off voltage of 2.5V, and an HPPC experiment was performed as shown in fig. 6. The corresponding Uoc -SOC discrete values at the time of discharging and charging are obtained respectively as shown in Table 1.
The Uoc -SOC mapping is constructed according to Table 1, as shown in FIG. 7. According to fig. 2, the mean value of the SOC and the corresponding UOC is used as a training set to construct a BP neural network, and the maximum fitting relative error is 0.1%. The maximum relative error is 0.3% by polynomial fit as in equation (21). The result shows that the Uoc -SOC relation fitting by using the neural network algorithm has higher precision.
UOC＝0.9748SOC5-5.533SOC4+9.803SOC3
-6.654SOC2+2.35SOC+3.24 (21)
Based on the data of fig. 7, the 0.1SOC is taken as a step length, the equation (5) and the equation (6) are combined, the time-invariant resistance-capacitance parameters are obtained through offline identification, and the average value of the parameters is taken as an effective value of an identification result, as shown in table 2.
2. Convergence experiment and analysis under intermittent constant-current discharge working condition
In the SOC estimation experiment, a comparison group is set to be compared with AUKF combined with RC parameter vector filtering method:
1) A comparison group 1, UKF algorithm of the RC parameter on-line identification result is utilized;
2) And a comparison group 2, namely utilizing the UKF algorithm of the RC parameter offline identification result.
The initial discharge SOC of the lithium battery is set to be 0.9, the end discharge SOC is set to be 0.6, and the terminal voltage of the battery is measured by a built-in high-precision sensor of experimental equipment. And the discharge is intermittently kept stand for 1 hour, so that the internal temperature of the battery is ensured to be fully dispersed, and the influence of temperature noise on the experimental result is reduced. The intermittent constant current discharge current waveform is shown in fig. 8. The result of partial RC parameter online identification is shown in FIG. 9.
The convergence of the SOC estimation is observed through the approximation process of the state variable to the true value, and the same P0, Q, R are selected for the control group 1, the control group 2, and the AUKF, and the result is shown in fig. 10.
According to FIG. 10, control group 1 converged after 300s, the convergence rate was low, the maximum error after convergence was less than 1%, control group 2 rapidly approached the true value in the [0s,50s ] interval, but the maximum error of SOC was greater than 2% in the [50s,1250s ] interval, the convergence performance was poor, and SOC estimation was performed based on AUKF algorithm, with the maximum error of SOC after convergence being less than 1% in 50 s. The result shows that the AUKF algorithm estimates the SOC, the convergence speed is higher than that of the control group 1, and the accuracy is higher than that of the control group 2.
And analyzing the relation between the Kalman gain variation trend and the SOC convergence speed. The [0s,300s ] Kalman gain variation is truncated as shown in FIG. 11. According to the Kalman filtering algorithm principle, the larger the Kalman gain is, the faster the convergence speed is. And in [0s,50s ], the average value of the Kalman gains of the AUKF, the control group 2 and the control group 1 is respectively 0.51, 0.5 and 0.42, so that the AUKF algorithm estimated SOC has better convergence.
Different P0 and Q, R influence the convergence speed and accuracy of the algorithm, and also influence the variation trend of the Kalman gain. The experiment was repeated with the modifications P0, Q, R, and the results are shown in FIGS. 12-14, respectively.
As can be seen from fig. 12 (a) and (b), increasing P0 can increase the convergence rate of the SOC estimation, the maximum error after convergence is greater than 2% for the comparison group 2, the maximum error after convergence is less than 1% for the comparison group 1, but the convergence rate is slow, and the AUKF convergence rate is higher than that for the comparison group 1, and the maximum error after convergence is less than 1%.
As can be seen from fig. 13 (a), (b) and fig. 14 (a), (b), the decrease Q, R can increase the convergence rate of the SOC estimation, and the SOC estimation based on the AUKF is higher than the convergence rate of the control group 1 and the estimation accuracy of the control group 2, and the maximum error after convergence is less than 1%.
As can be seen from fig. 12 (c) and (d), fig. 13 (c) and (d) and fig. 14 (c) and (d), changing P0 and Q, R does not affect the final convergence section of the AUKF kalman gain. After 200s the Kalman gain converges to the [0.05,0.2] range, and the gain threshold gamma can be adjusted within the [0.05,0.2] range. As shown in fig. 15, the maximum error after convergence is lower than 1% for the convergence curves of the SOC estimation values when the γ values are 0.05, 0.1, 0.15, and 0.2, respectively. Wherein, the convergence can be completed within 100s when the gamma is 0.1 or 0.15, the convergence can be completed within 130s when the gamma is 0.2, and the convergence can be completed within 160s when the gamma is 0.05. And adjusting the gamma value can change the convergence performance of the AUKF estimation SOC.
3. Robustness experiment and analysis under DST working condition
The DST experiment is designed to simulate complex working conditions, the initial discharging SOC is set to be 0.7, the state variable SOC initial value is set to be 0.2, and the robustness of SOC estimation is verified. The set current waveform is shown in fig. 16, and the SOC estimation result is shown in fig. 17.
According to fig. 17, control group 2 completed convergence after 350s, the maximum error of SOC after convergence was greater than 2%, the average error was greater than 1%, and control group 1 completed convergence before 200s, the maximum error of SOC after convergence was less than 1%. AUKF converges within 200s at a higher convergence rate than that of control group 1, and the maximum error of SOC after convergence is lower than 1%.
The state variable SOC initial value is changed to 0.5 in consideration of randomness of the state variable SOC initial value, as shown in fig. 18. The control group 2 can quickly approach the true value, the convergence is completed within 100 seconds, but overshoot exists, the average error after the convergence is more than 1.5%, and the maximum error is more than 2%. The control group 1 completes convergence within 150s, and the maximum error of the SOC after convergence is less than 1%. AUKF completes convergence within 100s, the maximum error is less than 1%, and SOC estimation is performed at a higher convergence rate than that of the comparison group 1 and at a higher accuracy than that of the comparison group 2, so that the comprehensive performance is good.
As shown in fig. 19 (a) and (b), the parameters were subjected to numerical jitter at the early stages of online recognition RS and CS, the amplitudes exceeded 500F, 0.05Ω, respectively, and RS and CS were subjected to abnormal negative values around 10 s. Jitter and outliers result in RC-link divergence and non-positive definite matrices that Cholesky decomposition cannot handle.
As shown in fig. 20, when jitter and outliers occur, the AUKF can circumvent the disturbance, RS is less than 0.035 Ω in [0s,100s ], CS is less than 100F in [0s,100s ], and RS and CS have no outlier negative values. At this time, the SOC is estimated based on the AUKF, as shown in fig. 21. The convergence is completed within 100s, the maximum error after the convergence is lower than 1%, and the stability is good.
In conclusion, the AUKF algorithm adaptively acquires the system equation resistance-capacitance parameters according to the actual working conditions, the convergence is rapid, the high accuracy is achieved, and the high robustness requirement under the complex working conditions is met.
4. Effectiveness test and analysis under aging conditions of batteries
The voltage characteristics of the HPPC test after 0 and 300 charge and discharge cycles of the lithium battery are shown in fig. 22. After 300 times of cyclic aging, the external characteristics of the lithium battery are changed, the terminal voltage is reduced, and the maximum voltage difference exceeds 0.3V. And verifying the validity of an AUKF algorithm on the SOC estimation of the lithium battery, and designing a DST working condition experiment under the aging condition of the battery.
The initial discharge SOC was set to 0.7, the state variable SOC estimation initial value was set to 0.4, the capacity change curve correction Qc measured by an experimental instrument was used to exclude the influence of discharge rate on the SOC estimation result, as shown in FIG. 23, the capacity ratio represents the ratio of the current capacity to the maximum capacity, and Qc is 0.9 times the maximum capacity after 300 cycles. The SOC estimation result is shown in fig. 24.
As can be seen from fig. 24, the battery aging aggravates the estimation error of the control group 2, the average error exceeds 2% after convergence, the maximum error exceeds 2.5%, the SOC estimation maximum error of the control group 1 and the AUKF algorithm is lower than 1%, but the AUKF algorithm is 20s earlier than the control group 1 to complete convergence.
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The above technical solution only represents the preferred technical solution of the present invention, and some changes that may be made by those skilled in the art to some parts of the technical solution represent the principles of the present invention, and the technical solution falls within the scope of the present invention.