CN112630659A - Lithium battery SOC estimation method based on improved BP-EKF algorithm - Google Patents
Lithium battery SOC estimation method based on improved BP-EKF algorithm Download PDFInfo
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Abstract
The application discloses a lithium battery SOC estimation method based on an improved BP-EKF algorithm, which is characterized by comprising the following steps: the method comprises the following steps: 1) establishing an equivalent model of the lithium battery; 2) identifying parameters of the equivalent model through experiments to obtain accurate model parameters; 3) calculating an SOC estimation value of the lithium battery through an extended Kalman filtering algorithm; 4) optimizing a BP neural network algorithm, and adding a feed-forward design for pre-judging errors during denoising in a preprocessing stage of the BP neural network algorithm; 5) training the BP neural network algorithm optimized in the step 4); 6) optimizing and compensating the estimated value of the SOC of the lithium battery by the extended Kalman filtering by using the BP neural network algorithm trained in the step 5), and calculating to obtain the optimal state estimated value of the equivalent model. The method of the invention enables the SOC estimation algorithm to have better adaptivity and meet the requirements of actual operation conditions.
Description
Technical Field
The invention relates to a lithium battery SOC estimation method based on an improved BP-EKF algorithm, and belongs to the field of battery power management.
Background
With the popularization of the power internet of things and the energy internet strategy of the national power grid, the demand of renewable energy technology for replacing the traditional fossil energy is increasingly strengthened. As a new type of transportation means, the development and use of the electric vehicle will gradually become a mainstream life style. The power lithium battery is used as the core of the electric automobile, and has relatively better charging and discharging performance, energy ratio and high power bearing capacity. The development of the related technology of the power lithium battery is more and more emphasized by people. However, unlike conventional hydrocarbon energy utilization features, the current state of the battery is not directly measured and requires a series of state estimates, including state of charge (SOC), state of health (SOH), state of power (SOP), etc. Meanwhile, the state of charge of the battery is influenced by a plurality of factors, such as charge and discharge rate, discharge process, temperature and the like, and among various parameters, the precision and robustness of the state of charge of the lithium ion battery are extremely important to the performance of the battery.
At present, an ampere-hour integration method is the most commonly used method, but the method has an open-loop characteristic and is easy to generate divergence due to error accumulation in current measurement; the open-circuit voltage method is widely applied to an electrified vehicle storage battery management system, is easy to use and high in calculation speed, but has the main problems that accurate measurement and estimation can be carried out only when the battery is kept still for a long time to reach a stable state, so that the open-circuit voltage method is not suitable for being used in the actual working condition running process of a vehicle; the internal resistance measurement method has high requirements on measurement equipment and is difficult to use on electric automobiles. The EKF is widely applied to online estimation of the SOC of the battery, but the EKF needs an accurate battery model, and noise can cause filter divergence, thereby influencing the SOC estimation precision.
Disclosure of Invention
The invention provides a lithium battery SOC estimation method based on an improved BP-EKF algorithm.
In order to solve the technical problems, the technical scheme adopted by the invention is that the lithium battery SOC estimation method based on the improved BP-EKF algorithm comprises the following steps:
1) establishing an equivalent model of the lithium battery;
2) identifying parameters of the equivalent model through experiments to obtain accurate model parameters;
3) calculating an SOC estimation value of the lithium battery through an extended Kalman filtering algorithm;
4) optimizing a BP neural network algorithm, and adding a feed-forward design for pre-judging errors during denoising in a preprocessing stage of the BP neural network algorithm;
5) training the BP neural network algorithm optimized in the step 4);
6) optimizing and compensating the estimated value of the SOC of the lithium battery by the extended Kalman filtering by using the BP neural network algorithm trained in the step 5), and calculating to obtain the optimal state estimated value of the equivalent model.
In the optimized lithium battery SOC estimation method based on the improved BP-EKF algorithm, in the step 1), a Thevenin equivalent circuit is used as an equivalent model of a lithium battery; in the step 2), testing parameters of the equivalent model through an HPPC pulse experiment, wherein the testing process is as follows: performing discharge experiment on the model parameters, comparing the model parameters according to the selected worn Winan model, and accurately simulating the dynamic process of the battery when the maximum error is less than or equal to 4 percent
Preferably, in the method for estimating the SOC of the lithium battery based on the improved BP-EKF algorithm, in step 3), the process of calculating the SOC estimation value of the lithium battery by using the extended kalman filter algorithm includes the following steps:
(1) determining a discrete state equation and an observation equation of a Kalman filter;
(2) estimating the SOC of the lithium battery by combining the lithium battery equivalent model;
(3) discretizing the estimation model of the lithium battery SOC in the step (2) and determining a Kalman equation of the lithium battery SOC;
(4) determining a discretization state formula of an extended Kalman filtering algorithm;
(5) describing the relation between the SOC value and the open-circuit voltage of the lithium battery by using an extended Kalman filtering algorithm;
(6) and (4) estimating the SOC of the lithium battery by using an extended Kalman filtering algorithm in combination with the Kalman equation of the SOC of the lithium battery in the step (3).
In the optimized lithium battery SOC estimation method based on the improved BP-EKF algorithm, in the step (1), the discrete state equation of the Kalman filtering algorithm is as follows: xt+1＝AtXt+BtUt+WtThe observation equation of the Kalman filtering algorithm is Yt+1＝CtXt+DtUt+VtWherein X istThe state vector of the system represents the estimated system state at the time t; u shapetThe control vector represents the control quantity of the outside on the system at the time t; y istRepresenting the estimated measured value at the time t as an observation vector; a. thetIs a state transition matrix, BtTo control a matrix, CtFor the observation matrix, DtIs a control matrix, determined by the system architecture; wtIs process noise, VtObserving noise;
in the step (2), the SOC of the lithium battery is estimated according to the Thevenin equivalent circuit, and the estimation equation is as follows:
and e (t) ═ i (t) R1+UC(t)+UC0(t), wherein e (t) is the electromotive force of the battery; u shapeC(t) is the terminal voltage of the polarization capacitor; u shapeC0(t) and I (t) are terminal voltage and current through the cell, respectively, which can be determined experimentally, t0Represents an initial value;
in the step (3), after discretizing the estimation equation of the lithium battery SOC, the SOC and the U are usedCAs a state variable, a kalman equation with the terminal voltage U as an observation variable is:
UC0,t＝Et-ItR1-UC,t (7)。
in the optimized lithium battery SOC estimation method based on the improved BP-EKF algorithm, in the step (4), the discretization state formula of the extended Kalman filter algorithm is determined as follows:
Xt＝f(Xt-1,Ut-1)+Wt-1 (8)
Yt＝g(Xt,Ut)+Vt (9)
wherein, XtIs a state vector of the system, YttTo observe the vector, f (X)t-1,Ut-1) And g (X)t,Ut) Respectively a state transition equation and an observation function of the nonlinear system;
in the step (5), the relationship between the SOC value and the open-circuit voltage of the lithium battery is described by using an extended Kalman filter algorithm as follows:
preferably, in the step (6), the estimating the SOC of the lithium battery by using the extended kalman filter algorithm includes: state initialization:
x0|0＝E(x0),
wherein P is a covariance matrix;
and (3) state estimation: calculating an estimated value at the time t: assuming that the system state value at the previous time is known as xt|t-1＝f(xt-1|t-1,Ut-1) (12)；
Error covariance prediction: by calculating the estimation error of X (t | t-1), the corresponding covariance matrix is found:
Pt-1|t-1＝At-1Pt-1|t-1At-1 T+Qt-1wherein A ist-1Being a state transition matrix, QtA covariance matrix that is the process noise;
updating Kalman gain coefficients:
wherein KtIs a gain factor, CtObservation matrix, RtA covariance matrix for the measured noise;
updating the state: and estimating the optimal estimation value of the existing state according to the open-circuit voltage value Ut obtained by real-time measurement:
Xt|t＝Xt|t-1+Kt(yt-g(Xt|t-1,Ut-1)) (15)；
updating the noise covariance according to the kalman gain and the noise covariance at the previous time instant: pt|t＝(I-KtCt)Pt -(16) Where I is an identity matrix represented by the formula Pt|t＝(I-KtCt)Pt -It can be seen that the gain coefficient decreases with decreasing and increases with decreasing, and the posterior estimate of the system state is obtained by combining the calculated gain coefficient with the measured value at time t, i.e. the optimal value can be solved; the system state estimation is repeated as the time update equation and the measurement update equation are calculated.
In the optimized lithium battery SOC estimation method based on the improved BP-EKF algorithm, in the step 4), the process of optimizing the BP neural network algorithm comprises the following steps: in the feedforward calculation, it is assumed that under the premise of a certain sample, the input calculation formula of the first neuron is:
where θ is the first neuron input layer error;
the second neuron outputs are calculated as:
wherein G (x) represents a second neuron output map;
the total input corresponding to the whole system is as follows:
meter for secondary error of each sampleThe calculation formula is expressed as:
wherein J is the quadratic error and t is the actual output;
further optimizing the whole recognition network, wherein the modified weighting formula is based on the inverse proportion of the change of W and the gradient of the function in the actual change:
wherein σ is a weighting coefficient;
the modification to the hidden layer function is:
where Z (x) is the implicit layer function mapping.
Preferably, in the lithium battery SOC estimation method based on the improved BP-EKF algorithm, in step 5), training the BP neural network algorithm includes: firstly, performing a constant current pulse discharge experiment on a lithium battery according to a selected Thevenin equivalent model to obtain a plurality of groups of data required by training an improved BP neural network; training the neural network to enable the training error of the sampling point to be gradually close to the expected value; and when the training error of the sampling point reaches the expected error, finishing the required improved BP neural network training.
The optimized lithium battery SOC estimation method based on the improved BP-EKF algorithm optimizes and compensates the extended Kalman filter SOC estimation value by utilizing the training and learning ability of a teacher of the improved BP neural network algorithm, takes the weight and the threshold of the BP neural network as input, the state of an extended Kalman filter and the network output as observation to obtain the state estimation compensation of the extended Kalman filter algorithm, and then calculates to obtain the optimal state estimation value of the improved BP neural network combined with the EKF.
Under actual working conditions, the accurate model and noise influence are inherent defects of the EKF, the prediction effect of the EKF is reduced, and the problems can be effectively optimized by combining a BP neural network. The application provides an improved BP-EKF-based lithium ion battery SOC online estimation method, firstly, an improved BP neural network calculation model is constructed by optimizing BP neural network feedforward analysis and calculation according to the internal actual dynamic characteristics of a lithium battery, and the compensation error value identified by the BP neural network is used for optimizing EKF estimation SOC, and finally, simulation experiment results show that compared with the traditional EKF algorithm, the improved BP-EKF algorithm has the advantages that the SOC estimation precision is within 2%, the prediction and robustness are good, the SOC estimation precision of the lithium ion battery can be effectively improved, and the engineering application value is high.
Drawings
FIG. 1 is a diagram of an equivalent model of a Thevenin cell of the present application;
FIG. 2 is a parameter analysis diagram of a lithium battery discharge curve;
FIG. 3 is a SOC-OCV fit graph;
FIG. 4 is a diagram of a three-layer BP neural network architecture;
FIG. 5 is a flow chart of an improved BP-EKF in the present application;
FIG. 6 is a comparison graph of network training sample points;
FIG. 7 is a graph of network training sample point test errors;
FIG. 8 is a simulation curve diagram of a lithium battery SOC experiment;
FIG. 9 is a simulation curve error diagram of a lithium battery SOC experiment;
FIG. 10 is a table of corresponding values of SOC and various parameters of a lithium battery;
FIG. 11 is a SOC-OCV correspondence table;
FIG. 12 is a table of data statistics for the two algorithms in the example.
Detailed Description
The technical features of the present invention will be further described with reference to the following embodiments.
The invention relates to a lithium battery SOC estimation method based on an improved BP-EKF algorithm, which comprises the following steps:
1) establishing an equivalent model of the lithium battery;
2) identifying parameters of the equivalent model through experiments to obtain accurate model parameters;
3) calculating an SOC estimation value of the lithium battery through an extended Kalman filtering algorithm;
4) optimizing a BP neural network algorithm, and adding a feed-forward design for pre-judging errors during denoising in a preprocessing stage of the BP neural network algorithm;
5) training the BP neural network algorithm optimized in the step 4);
6) optimizing and compensating the estimated value of the SOC of the lithium battery by the extended Kalman filtering by using the BP neural network algorithm trained in the step 5), and calculating to obtain the optimal state estimated value of the equivalent model.
In the step 1), the Thevenin equivalent circuit is used as an equivalent model of the lithium battery, different battery equivalent models have different simulation accuracies on the battery, the equivalent model containing the RC has higher accuracy, and generally, the higher the RC order, the higher the accuracy, but the more complex the calculation, and the method is not suitable for a system with high real-time performance and limited hardware conditions. For lithium iron phosphate batteries, there are typically a Rint equivalent model, a thevenin equivalent model, a PNGV equivalent model, and the like.
The charging and discharging process of the battery is a complex nonlinear dynamic process, and the Thevenin battery model is a Thevenin equivalent circuit which is also called a first-order RC equivalent circuit. As shown in FIG. 1, R1、C1Respectively polarization internal resistance and polarization capacitance, for simulating polarization effect, R, of battery0Is the ohmic internal resistance of the battery, U0CIs the battery open circuit voltage and U is the load voltage.
Thevenin battery model belongs to first-order nonlinear model, and design parameter is less, and simple structure can guarantee better precision under constant current charge-discharge, accurately simulates the charge-discharge action of battery, and occupation resource space is few in BMS embedded system, and the advantage is obvious, based on this, will choose to use Thevenin battery equivalent model for use in this application, and in the resource limited embedded system like BMS, its advantage will be more obvious, more can the accurate state of charge who predicts the battery.
In the step 2), when the parameters of the equivalent model are tested through an HPPC pulse experiment, a lithium battery with the battery model capacity of 10Ah is adopted in a laboratory, a battery test platform is built, the battery is discharged for 180s at the current of 1C and then stands for 180s, and the discharge rule of the lithium battery is drawn as shown in FIG. 2. The release can be found by a curveAt the moment of electricity discharge stopping, the battery voltage has a sudden change, and then slowly changes. The sudden change in voltage is due to the ohmic internal resistance of the cell itself, Δ U in FIG. 21The slow voltage change is shown to be due to the presence of polarization effects inside the cell, corresponding to the zero state response of the equivalent model RC loop, Δ U in fig. 22As shown.
HPPC pulse experiments are carried out to test the model parameters, and the model parameters are discharged circularly to the required voltage, and the discharge amount of each time is about 10%. The test results are shown in table 1, the laboratory battery is subjected to a discharge test through determined model parameters, the maximum error is not more than 4% according to the comparison of the selected worn Winan model, and the dynamic process of the simulated battery is accurate.
In order to determine the correspondence relationship with the SOC value, the battery was still subjected to a load pulse test, and the open circuit voltage was read, and in the test, the open circuit voltage was closely correlated with the open circuit voltage in the range of 20% to 90%, and the data thereof is shown in fig. 11.
Polynomial curve fitting was performed on the data in this range, the results were
F(SOCt)＝4.373×10-7SOCt 3-0.00009244SOCt 2+0.006819SOCt+3.824 (1)
After fitting, the curve and the variance are 0.00002476, the fitting coefficient is 0.9964, and the relation between the open-circuit voltage and the SOC is accurately fitted.
The process for calculating the SOC estimation value of the lithium battery through the extended Kalman filtering algorithm comprises the following steps:
(1) determining a discrete state equation and an observation equation of a Kalman filter;
(2) estimating the SOC of the lithium battery by combining the lithium battery equivalent model;
(3) discretizing the estimation model of the lithium battery SOC in the step (2) and determining a Kalman equation of the lithium battery SOC;
(4) determining a discretization state formula of an extended Kalman filtering algorithm;
(5) describing the relation between the SOC value and the open-circuit voltage of the lithium battery by using an extended Kalman filtering algorithm;
(6) and (4) estimating the SOC of the lithium battery by using an extended Kalman filtering algorithm in combination with the Kalman equation of the SOC of the lithium battery in the step (3).
The basic idea of the Kalman filter is to estimate the optimal state estimation value of the state quantity of the random linear system in the state of the minimum root mean square error by using the state space concept of signal process and noise. The discrete state equation and the observation equation are as follows:
equation of state
Xt+1＝AtXt+BtUt+Wt (2)
The observation equation:
Yt+1＝CtXt+DtUt+Vt (3)
wherein, XtThe state vector of the system represents the estimated system state at the time t; u shapetThe control vector represents the control quantity of the outside on the system at the time t; y istRepresenting the estimated measured value at the time t as an observation vector; a. thetIs a state transition matrix, BtTo control a matrix, CtFor the observation matrix, DtIs a control matrix, determined by the system architecture; wtIs process noise, VtThe observed noise is generally white noise with an average value of 0, and the two are independent of each other.
In combination with the Thevenin battery equivalent model, the method comprises the following steps of estimating the SOC of the lithium battery
E(t)＝I(t)R1+UC(t)+UC0(t) (5)
Wherein E (t) is the electromotive force of the battery; u shapeC(t) is the terminal voltage of the polarization capacitor; u shapeC0(t) and I (t) are terminal voltage and current through the cell, respectively, which can be determined experimentally, t0Indicating an initial value. Discretizing the data into SOC and UCAs a state variable, a kalman equation with the terminal voltage U as an observation variable is:
UC0,t＝Et-ItR1-UC,t (7)
the Kalman filtering algorithm is to calculate the optimal SOC estimation in the sense of the minimum variance at the next moment according to the SOC value at a certain moment. The accuracy control can be well realized in the calculation process, and the influence of external factors can be effectively reduced. The method has the disadvantages that each parameter in the battery needs to be determined in detail, but the parameters are difficult to determine and the calculation amount is large.
In the actual operation process of the lithium battery pack of the electric automobile, the system is a nonlinear system, and the extended Kalman filtering algorithm can enable SOC estimation to be adapted to a Kalman filtering method by linearizing the nonlinear system. The discretization state formula is as follows:
Xt＝f(Xt-1,Ut-1)+Wt-1 (8)
Yt＝g(Xt,Ut)+Vt (9)
wherein, XtIs a state vector of the system, YttTo observe the vector, f (X)t-1,Ut-1) And g (X)t,Ut) Respectively a state transfer equation and an observation function of the nonlinear system, wherein in the SOC estimation, for the observation function of the system, Taylor series expansion is carried out on a surrounding state vector of the observation function every time of prediction, and high-order infinite small quantity is omitted for describing the relation between an SOC value and an open-circuit voltage to obtain
When the SOC is estimated by the extended Kalman filter combined with the formula (6), the system is represented in a linear mode.
The estimation of the SOC of the lithium battery by using the extended Kalman filtering algorithm comprises the following steps:
EKF estimation of lithium battery SOC
The estimation steps are as follows:
the first step is as follows: state initialization:
x0|0＝E(x0),
where P is the covariance matrix.
The second step is that: and (3) state estimation:
calculating an estimated value at the time t: assuming that the system state value at the previous time is known as
xt|t-1＝f(xt-1|t-1,Ut-1) (12)
The third step: error covariance prediction:
by calculating the estimation error of X (t | t-1), the corresponding covariance matrix is found:
Pt-1|t-1＝At-1Pt-1|t-1At-1 T+Qt-1 (13)
wherein A ist-1Being a state transition matrix, QtIs the covariance matrix of the process noise.
The fourth step: updating Kalman gain coefficients:
wherein KtIs a gain factor, CtObservation matrix, RtIs a covariance matrix of the measured noise.
And fifthly, updating the state. And estimating the optimal estimation value of the existing state according to the open-circuit voltage value Ut obtained by real-time measurement:
Xt|t＝Xt|t-1+Kt(yt-g(Xt|t-1,Ut-1)) (15)
and a sixth step: updating the noise covariance according to the kalman gain and the noise covariance at the previous time instant:
Pt|t＝(I-KtCt)Pt - (16)
where I is an identity matrix, it can be seen from equation (16) that the decrease is followed by a decrease and the increase is followed by a decrease, and the posterior estimate of the system state is obtained by combining the calculated gain factor with the measured value at time t, and the optimum value can be found. The system state estimation is repeated as the time update equation and the measurement update equation are calculated.
The BP neural network is essentially a forward feedback learning neural network, and the feedback learning is performed through a connection mode structure, and the structure diagram of the BP neural network is shown in fig. 4. L in the figureA、LB、LCRespectively representing an input layer, a hidden layer and an output layer. { Xi}、{Yi}、{OiDenotes the corresponding output vector, W, respectivelyijRepresents LALayer to LBTransfer weight of layer, VijRepresents LBLayer to LCThe transfer weight of the layer.
The neural network adopts a method of instructor training, and the learning process of the BP neural network algorithm is a feedforward learning process. Essentially, this is a process of error back-propagation, while correcting the weight coefficients of each layer. Feedback learning includes adjusting connection patterns, weights and thresholds for each neuron, and identification of the entire network.
Compared with a standard BP neural network algorithm, the improved algorithm provided by the application mainly focuses on the improvement of feedforward calculation, and mainly solves the problem that the signal-to-noise ratio is low in initialization and processing of the traditional BP algorithm. A feed-forward design is added in a preprocessing stage, and the main function of the feed-forward design is to judge errors in advance during denoising and adjust in advance when the errors exceed a threshold value. The method can solve the error problem from the source, thereby reducing the burden of subsequent filtration. In the above feed forward calculation, it is assumed that, on the premise of a certain sample, the input of the first neuron is calculated as shown in equation (17),
where θ is the first neuron input layer error.
The calculation formula of the second neuron output is shown in formula (18)
Where G (x) represents a second neuron output map.
The total input corresponding to the whole system is shown as a formula (19)
The calculation formula of the secondary error of each sample is shown as formula (20).
Where J is the quadratic error and t is the actual output.
In the feedforward calculation, the optimized weight coefficient of the BP neural network is improved by utilizing the optimized feedforward calculation. To further optimize the overall recognition network, the variation of W is inversely proportional to the gradient of the function in the actual variation.
The modified weighting formula is shown in formula (21).
Where the sigma weighting factor.
For the hidden layer function modification as shown in equation (22)
Where Z (x) is the implicit layer function mapping.
Through the improvement, compared with the traditional BP neural network algorithm, the weight segmentation technology is added, the problem of low signal-to-noise ratio can be solved, the system identification precision is optimized, and meanwhile the defect caused by the large accumulation of data of the traditional auxiliary algorithm is overcome.
In the EKF linearization process, due to the influence of noise filtering and the existence of errors, the SOC estimation value of the extended Kalman filtering is optimized and compensated by using the training and learning ability of a teacher for improving the BP neural network algorithm, the error degree is reduced, so that the object model problem is converted into the state parameter estimation problem, the weight and the threshold of the BP neural network are used as input, the state of the extended Kalman filter is used, and the network output is used as observation. The algorithm process is as follows:
and (3) a training process of the BP neural network algorithm.
Firstly, a constant-current pulse discharge experiment is carried out on a lithium iron phosphate 18650 type battery with 10Ah in a laboratory according to a selected Thevenin equivalent model, and 3000 groups of data required by training an improved BP neural network are obtained. And then training the designed neural network to ensure that the training error of the sampling point is gradually close to the expected value, and when the training error is within the expected error, proving that the required training of the improved BP neural network is finished.
BP optimized EKF algorithm.
The structure of the algorithm is first given as shown in fig. 5. The essence of the algorithm is that the trained improved BP neural network process is combined into the EKF algorithm, accurate model parameters are obtained by parameter identification in the process of continuously updating battery information, then filtering processing is carried out through an extended Kalman filter, initial data are input into the trained improved BP neural network, state estimation compensation of the extended Kalman filter algorithm is obtained, and then the optimal state estimation value of the improved BP neural network combined with the EKF is obtained by calculation.
For the same problem, the final results may be consistent by using different algorithms, but the time resources consumed in the operation process are greatly different. The time complexity is used for describing the increment relation between the algorithm execution time and the data scale, and compared with the algorithm performance test, the complexity analysis has the advantages of independence on the execution environment, high efficiency, strong guidance and the like, and is beneficial to reducing the system development and maintenance cost. The algorithmic time metric, usually expressed in mathematical terms, is defined as t (n) as the number of times an algorithmic statement is executed, the problem size is set to n, and if some auxiliary function f (n) is present, the limit of t (n)/f (n) is constant and not equal to 0 when n approaches infinity, i.e. t (n) and f (n) are considered to be the same-magnitude functions, i.e.:
T(n)＝O(f(n)) (23)
equation (23) is the progressive temporal complexity of the algorithm, referred to as temporal complexity for short.
In time complexity analysis, the large O representation is usually used as a measure of the algorithm speed. Common large O operation times are O (log n), O (n × log n), O (n)2) O (n! ) And the like. For the improved BP-EKF algorithm in the application, in a 3-layer BP neural network, the number of neurons in each layer is respectively assumed to be n1、n2、n3If for a sample n 11, two matrix operations are needed to perform feedforward calculation, and the essence of the two matrix multiplications is vector and matrix multiplication, and n is needed to perform n1*n2And n2*n 33 times of calculation, due to the number n of nodes of the input layer and the final output layer1And n3Is deterministic and can therefore be regarded as a constant, the number n of hidden layers in between2The feedforward computation time complexity for one sample under self-setting is:
O(n1*n2+n2*n3)＝O(n2) (24)
the same time complexity in back propagation is calculated as in the feed-forward process, and assuming that there are m training samples in total, each training sample is only trained once, the time complexity for training a neural network is O (m × n)2)。
EXAMPLES analysis of results
Neural network training experiment
Firstly, a Matlab neural network tool box is utilized to establish a 3-layer BP neural network, the neuron number of an input layer is 4, the neuron number of an implicit layer is 10, the neuron number of an output layer is 1, the maximum iteration number is 6000, and the expected value is 1 multiplied by 10-5. And inputting 2500 groups of data obtained by 3000 groups of data required by training the improved BP neural network into the neural network, and when the test is iterated to 2200 times, meeting the precision requirement and finishing the training. The training results were validated for an additional 500 sets of data, with the results shown in figure 6,
the test error of the neural network training sampling point is within 1 percent, as shown in figure 7. The trained neural network has higher precision and can be used for improving the BP-EKF neural network.
Pulse discharge experiment
According to a BP neural network tool box in Matlab/Simulink, firstly, a trained BP neural network structure is generated into a Simulink network module. The experimental simulation platform was constructed according to the modified BP-EKF flowchart shown in fig. 5. The initial value of the SOC is set to be 100%, the test temperature is set to be a normal temperature state, the real SOC value of the battery cannot be directly measured, and the SOC theoretical value is calculated by using the obtained data such as current, temperature and time through an ampere-hour integration method. Programming on a Matlab platform by respectively adopting an improved BP-EKF algorithm and an EKF algorithm, constructing a simulation experiment, carrying out SOC estimation, and comparing an estimation result with an SOC estimation theoretical value carried out by an ampere-hour integral method. The process noise Q adopted by each algorithm is [1 × 10 ═ d -9 1×10-9 1×10-9 1×10-8]TThe observation noise is R0.01, and the initial state is x0＝[0 0 0 1]TThe state error covariance error is P (0) ═ diag (1, 1). The experimental results for the modified BP-EKF and EKF algorithms are shown in FIG. 8 and FIG. 9.
According to pulse discharge simulation experiment analysis, compared with the EKF algorithm, the BP-EKF algorithm can quickly and quickly correct the SOC estimated value in real time according to the predicted value, is stabilized near the true value, and ensures the real-time battery health state.
EKF and BF-EKF algorithms were evaluated and compared experimentally, and the quantitative performance comparison is shown in FIG. 12.
As can be seen from fig. 12, and the improved BP-EKF algorithm herein is superior to the conventional EKF algorithm, the maximum error can be reduced to within 2%, indicating that the improved algorithm has higher accuracy in estimation result. When the SOC estimation value converges to the true value, the maximum relative error of the single EKF algorithm is much larger and is about 5.53%, and the maximum relative error of the SOC estimation value adopting the improved BP-EKF algorithm is about 1.56%, which has higher accuracy than the traditional estimation method and is more suitable for SOC estimation of the electric vehicle.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art should understand that they can make various changes, modifications, additions and substitutions within the spirit and scope of the present invention.
Claims (9)
1. A lithium battery SOC estimation method based on an improved BP-EKF algorithm is characterized by comprising the following steps: the method comprises the following steps:
1) establishing an equivalent model of the lithium battery;
2) identifying parameters of the equivalent model through experiments to obtain accurate model parameters;
3) calculating an SOC estimation value of the lithium battery through an extended Kalman filtering algorithm;
4) optimizing a BP neural network algorithm, and adding a feed-forward design for pre-judging errors during denoising in a preprocessing stage of the BP neural network algorithm;
5) training the BP neural network algorithm optimized in the step 4);
6) optimizing and compensating the estimated value of the SOC of the lithium battery by the extended Kalman filtering by using the BP neural network algorithm trained in the step 5), and calculating to obtain the optimal state estimated value of the equivalent model.
2. The improved BP-EKF algorithm-based lithium battery SOC estimation method according to claim 1, wherein: in the step 1), a Thevenin equivalent circuit is used as an equivalent model of a lithium battery; in the step 2), testing parameters of the equivalent model through an HPPC pulse experiment, wherein the testing process is as follows: and (4) carrying out a discharge experiment on the model parameters, comparing according to the selected worn Winan model, and when the maximum error is less than or equal to 4%, accurately simulating the dynamic process of the battery.
3. The improved BP-EKF algorithm-based lithium battery SOC estimation method according to claim 1, wherein: in the step 3), the process of calculating the SOC estimation value of the lithium battery through the extended Kalman filtering algorithm comprises the following steps:
(1) determining a discrete state equation and an observation equation of a Kalman filter;
(2) estimating the SOC of the lithium battery by combining the lithium battery equivalent model;
(3) discretizing the estimation model of the lithium battery SOC in the step (2) and determining a Kalman equation of the lithium battery SOC;
(4) determining a discretization state formula of an extended Kalman filtering algorithm;
(5) describing the relation between the SOC value and the open-circuit voltage of the lithium battery by using an extended Kalman filtering algorithm;
(6) and (4) estimating the SOC of the lithium battery by using an extended Kalman filtering algorithm in combination with the Kalman equation of the SOC of the lithium battery in the step (3).
4. The improved BP-EKF algorithm-based lithium battery SOC estimation method according to claim 3, wherein: in the step (1), the discrete state equation of the Kalman filtering algorithm is as follows: xt+1＝AtXt+BtUt+WtThe observation equation of the Kalman filtering algorithm is Yt+1＝CtXt+DtUt+VtWherein X istThe state vector of the system represents the estimated system state at the time t; u shapetThe control vector represents the control quantity of the outside on the system at the time t; y istRepresenting the estimated measured value at the time t as an observation vector; a. thetIs a state transition matrix, BtTo control a matrix, CtFor the observation matrix, DtIs a control matrix, determined by the system architecture; wtIs process noise, VtObserving noise;
in the step (2), the SOC of the lithium battery is estimated according to the Thevenin equivalent circuit, and the estimation equation is as follows:
and e (t) ═ i (t) R1+UC(t)+UC0(t), wherein e (t) is the electromotive force of the battery; u shapeC(t) is the terminal voltage of the polarization capacitor; u shapeC0(t) and I (t) are terminal voltage and current through the cell, respectively, which can be determined experimentally, t0Represents an initial value;
in the step (3), after discretizing the estimation equation of the lithium battery SOC, the SOC and the U are usedCAs a state variable, a kalman equation with the terminal voltage U as an observation variable is:
UC0,t＝Et-ItR1-UC,t (7)。
5. the improved BP-EKF algorithm-based lithium battery SOC estimation method according to claim 3, wherein:
in the step (4), determining a discretization state formula of the extended Kalman filtering algorithm as follows:
Xt＝f(Xt-1,Ut-1)+Wt-1 (8)
Yt＝g(Xt,Ut)+Vt (9)
wherein, XtIs a vector of the states of the system,
to observe the vector, f (X)t-1,Ut-1) And g (X)t,Ut) Respectively a state transition equation and an observation function of the nonlinear system;
in the step (5), the relationship between the SOC value and the open-circuit voltage of the lithium battery is described by using an extended Kalman filter algorithm as follows:
6. the improved BP-EKF algorithm-based lithium battery SOC estimation method according to claim 3, wherein: in the step (6), the step of estimating the SOC of the lithium battery by using the extended Kalman filter algorithm comprises the following steps: state initialization:
x0|0＝E(x0),
wherein P is a covariance matrix;
and (3) state estimation: calculating an estimated value at the time t: assuming that the system state value at the previous time is known as xt|t-1＝f(xt-1|t-1,Ut-1) (12)；
Error covariance prediction: by calculating the estimation error of X (t | t-1), the corresponding covariance matrix is found:
Pt-1|t-1＝At-1Pt-1|t-1At-1 T+Qt-1wherein A ist-1Being a state transition matrix, QtA covariance matrix that is the process noise;
updating Kalman gain coefficients:
wherein KtIs a gain factor, CtObservation matrix, RtA covariance matrix for the measured noise;
updating the state: and estimating the optimal estimation value of the existing state according to the open-circuit voltage value Ut obtained by real-time measurement:
Xt|t＝Xt|t-1+Kt(yt-g(Xt|t-1,Ut-1)) (15)；
updating the noise covariance according to the kalman gain and the noise covariance at the previous time instant: pt|t＝(I-KtCt)Pt -(16) Where I is an identity matrix represented by the formula Pt|t＝(I-KtCt)Pt -It can be seen that the decrease is followed by a decreaseDecreasing and increasing, and obtaining the posterior estimation of the system state by combining the calculated gain coefficient with the measured value at the time t, thus obtaining the optimal value; the system state estimation is repeated as the time update equation and the measurement update equation are calculated.
7. The improved BP-EKF algorithm-based lithium battery SOC estimation method according to claim 3, wherein: in step 4), the process of optimizing the BP neural network algorithm comprises the following steps:
in the feedforward calculation, it is assumed that under the premise of a certain sample, the input calculation formula of the first neuron is:
where θ is the first neuron input layer error;
the second neuron outputs are calculated as:
wherein G (x) represents a second neuron output map;
the total input corresponding to the whole system is as follows:
the calculation formula of the quadratic error of each sample is expressed as:
wherein J is the quadratic error and t is the actual output;
further optimizing the whole recognition network, wherein the modified weighting formula is based on the inverse proportion of the change of W and the gradient of the function in the actual change:
wherein σ is a weighting coefficient;
the modification to the hidden layer function is:
where Z (x) is the implicit layer function mapping.
8. The improved BP-EKF algorithm-based lithium battery SOC estimation method according to claim 3, wherein: in step 5), training the BP neural network algorithm comprises: firstly, performing a constant current pulse discharge experiment on a lithium battery according to a selected Thevenin equivalent model to obtain a plurality of groups of data required by training an improved BP neural network; training the neural network to enable the training error of the sampling point to be gradually close to the expected value; and when the training error of the sampling point reaches the expected error, finishing the required improved BP neural network training.
9. The improved BP-EKF algorithm-based lithium battery SOC estimation method according to claim 3, wherein: optimizing and compensating the extended Kalman filtering SOC estimation value by using the training learning capability of a teacher of the improved BP neural network algorithm, taking the weight and the threshold of the BP neural network as input, taking the state of the extended Kalman filter and the network output as observation to obtain the state estimation compensation of the extended Kalman filtering algorithm, and then calculating to obtain the optimal state estimation value of the improved BP neural network combined with the EKF.
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