CN111208437A - Power battery fusion modeling method - Google Patents
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Abstract
The invention provides a power battery fusion modeling method, which analyzes the precision of each model in each environment, establishes the corresponding model weight, embodies the model fusion rule through a neural network, maximally utilizes the advantages of each model, and can realize the high-precision prediction of the power battery voltage under complex working conditions. The neural network is used for expressing the rule of model fusion, so that the advantages and the disadvantages of the models in different working environments can be reflected, the weight information under various complex working conditions does not need to be stored, the complex table lookup is carried out, the hardware requirement is greatly reduced, the calculated amount is reduced, and the instantaneity is improved.
Description
Technical Field
The invention relates to the technical field of power battery management, in particular to a power battery system modeling technology and a battery management system.
Background
In the analysis and prediction of the power battery at the present stage, a power battery model is a more core mathematical tool. However, because the power battery has the characteristics of complex chemical reaction process, a plurality of reaction process influence factors, high uncertainty of the system and the like, the modeling research of the power battery is always a research hotspot and difficulty in multiple subjects and fields no matter in the academic or industrial field. At present, the commonly used power battery models can be roughly divided into an equivalent circuit model, a black box model and an electrochemical model. The equivalent circuit model has the advantages of simple structure and strong robustness, but as a semi-empirical model, the parameters of the equivalent circuit model lack practical significance; the black box model needs to be trained by a large number of experimental parameters, and the practicability of the black box model for the lithium ion battery is poor; as a mechanical model, the electrochemical model has strong practical significance of parameters, but the model has a complex structure and large corresponding calculated amount. In short, the common power battery models at present have various advantages and disadvantages, the application occasions are different, and various models have certain limitations for a system with a complex working environment, namely a power battery.
For the phenomenon that a single model cannot completely solve the modeling problem of the power battery, the idea of model fusion is widely concerned. However, most of the current model fusion modes adopt a form of fixed weight and online comparison of fitting results of a certain window period for fusion. The thought of fixing the weight cannot fully reflect the advantages and disadvantages of each model under different working environments, and the online comparison mode needs to store a certain amount of data, so that the real-time comparison and calculation have high requirements on hardware.
Disclosure of Invention
In view of the above, the present invention is to provide a method capable of analyzing the accuracy of each model under each environment and maximally utilizing the advantages of each model, so as to realize high-accuracy prediction of the power battery voltage.
The invention provides a power battery fusion modeling method, which specifically comprises the following steps:
establishing a plurality of single battery models according to the correlation theory of a battery system model, selecting a proper parameter identification method for each single battery model, and respectively identifying parameters by using experimental data;
fitting working condition data such as current, terminal voltage, temperature and the like under various working environments (aging states and temperatures) according to each established single battery model, and determining a weighting coefficient of each single battery model under each SOC according to a comparison result between an actual measurement value and a fitting value of the working condition data;
step three, establishing and training a neural network model by taking working environment parameters and SOC (state of charge) of the power battery as input and taking a weighting coefficient of each single battery model as output;
and fourthly, for any current excitation, respectively predicting the terminal voltage of each single battery model, and establishing a power battery weighted fusion model by combining the weighting coefficients obtained by the trained neural network model to finally obtain the predicted value of the terminal voltage of the power battery.
Further, single cell models include, but are not limited to: a pseudo two-dimensional model, a Thevenin model, a dual polarization model, and a fractional order model.
Further, the parameter identification method adopted in the first step includes but is not limited to: genetic algorithm, least square algorithm, minimum root mean square algorithm, particle swarm algorithm.
Further, in the second step, according to a comparison result between an actual measurement value and a fitting value of the operating condition data, a weighting coefficient of each single battery model under each SOC is determined, and the weighting coefficient is determined based on the following formula:
wherein, wiWeighting coefficients of the ith model under the SOC; sigmaiThe variance of the fitted value of the ith model at the SOC and the actual measured value is shown.
Further, in the second step, the SOC interval of 1% is used as a set of data for determining the weighting coefficient of the single battery model under each SOC.
Further, the neural network model selected in the third step includes but is not limited to: BP network model, Hopfield network model, BAM network model; methods for neural network model training include, but are not limited to: gradient descent method and its variants and modified algorithms, adagard algorithm, adapelta algorithm.
Further, in the weighted fusion process, selection is also performed based on an additional fusion rule: according to a fusion strategy for improving estimation accuracy additionally considered by a single battery model selected by a battery management system and a main working environment of the battery, for example, under low SOC (SOC is less than or equal to 5%), because a Thevenin model, a dual-polarization model and a fractional order model may have a vibration divergence phenomenon, if the selected model comprises an electrochemical model, a prediction result can be completely determined by the electrochemical model.
Correspondingly, the invention also provides a battery management system, which carries out weighted fusion prediction on the terminal voltage of the power battery based on the power battery fusion modeling method.
Compared with the prior art, the power battery fusion modeling method and the battery management system provided by the invention at least have the following beneficial effects:
according to the method, the corresponding model weight is determined through the precision analysis of each model under each environment, the model fusion rule is embodied through the neural network, the advantages of each model are utilized to the maximum extent, and the high-precision prediction of the power battery voltage under the complex working condition can be realized. The neural network is used for expressing the rule of model fusion, so that the advantages and the disadvantages of the models in different working environments can be reflected, the weight information under various complex working conditions does not need to be stored, the complex table lookup is carried out, the hardware requirement is greatly reduced, the calculated amount is reduced, and the instantaneity is improved.
Drawings
FIG. 1 is a flow chart of a method provided by the present invention;
fig. 2 is a Thevenin model of a power cell;
FIG. 3 is a power battery dual polarization model;
FIG. 4 is a power cell fractional order model;
FIG. 5 is a power cell electrochemical model;
FIG. 6 is a BP network model diagram;
FIG. 7 is a diagram of model weights in an embodiment of the present invention;
FIG. 8 shows simulation results of model voltages in an example of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a power battery fusion modeling method, as shown in fig. 1, which specifically comprises the following steps:
establishing a plurality of single battery models according to the correlation theory of a battery system model, selecting a proper parameter identification method for each single battery model, and respectively identifying parameters by using experimental data;
fitting working condition data such as current, terminal voltage, temperature and the like under various working environments (aging states and temperatures) according to each established single battery model, and determining a weighting coefficient of each single battery model under each SOC according to a comparison result between an actual measurement value and a fitting value of the working condition data;
step three, establishing and training a neural network model by taking working environment parameters and SOC (state of charge) of the power battery as input and taking a weighting coefficient of each single battery model as output;
and fourthly, for any current excitation, respectively predicting the terminal voltage of each single battery model, and establishing a power battery weighted fusion model by combining the weighting coefficients obtained by the trained neural network model to finally obtain the predicted value of the terminal voltage of the power battery.
In a preferred embodiment of the present invention, a single cell model is selected to include the Thevenin model shown in FIG. 2, which is derived from an ideal voltage source U representing the open circuit voltage of the power cellOCAnd an ideal resistance R for representing the ohmic internal resistance of the power batteryTPlus an internal resistance R of polarizationDAnd a polarization capacitor CDThe formed RC parallel network is connected with the three in seriesAnd (4) preparing the composition. In the figure, UtIs terminal voltage, iLFor applying current, UDThe voltage drop of the RC parallel network is used for simulating the polarization voltage of the power battery. The circuit equation of the circuit model can be expressed as:
in the formula of UDThe voltage drop of the RC parallel network is used for simulating the polarization voltage of the power battery;
representing the polarisation voltage UDA derivative with respect to time; i.e. iLIs the current applied to the cell; cDIs a polarization capacitor; rDIs the polarization internal resistance; rTOhmic internal resistance of Thevenin model; u shapetIs the battery terminal voltage; u shapeOCIs the battery open circuit voltage.
By performing discretization, we obtain:
Ut,k＝ΦTθT
in the formula, subscripts k and k-1 represent values at the time of k and k-1; Δ t is the sampling interval; phiTA data matrix which is a Thevenin model; thetaTA parameter matrix of the Thevenin model; c. C1,T、c2,T、c3,TThe coefficients of Thevenin model from which the values of the circuit elements in the circuit expression of Thevenin model can be solved, and the time constant τ is introduced for the simplicity of the expressionD＝CDRD。
Identifying model parameters using, for example, least squares algorithm and based on ideal voltage source UOCThe assumption of (1), open circuit voltage, was fitted to six of SOC according to open circuit voltage experimentsA function of degree, α0,…,α6：
UOC(SOC)＝α0+α1SOC+α2SOC2+α3SOC3+α4SOC4+α5SOC5+α6SOC6
Other single cell models may also be subjected to the above process.
Can be identified by least square method [ (1-c)1,T)UOC,kc1,Tc2,Tc3,T]TFurther obtain the model parameter [ R ]TRDCD]T。
Fig. 3 shows a dual-polarization model that can be selected as a single battery model, which is formed by further connecting an RC parallel network in series on the basis of Thevenin model, that is, 2 RC parallel networks are connected in series in the model. In the figure, iLFor applying current, UtIs terminal voltage, UOCIs the open circuit voltage, R, of the batterysIs ohmic internal resistance, two RC parallel networks respectively describe electrochemical polarization and concentration polarization of the battery, UD1、RD1And CD1Electrochemical polarization voltage, charge transfer impedance and charge transfer capacitance, U, of the cellD2、RD2And CD2Respectively, the concentration polarization voltage, the concentration impedance and the concentration capacitance of the cell. The circuit equation of the circuit model is as follows:
in the formula of UD1Is an electrochemical polarization voltage;
represents the electrochemical polarization voltage UD1A derivative with respect to time; rD1Is the charge impedance; cD1Is a charge transfer capacitor; u shapeD2Is a concentration polarization voltage;
representing concentration polarization voltage UD2A derivative with respect to time; rD2Is the concentration impedance; cD2Is a concentration capacitance; i.e. iLIs the current applied to the cell; rsOhmic internal resistance of the dual-polarization model; u shapetIs the battery terminal voltage; u shapeOCIs the battery open circuit voltage.
Discretizing the above formula to obtain
Ut,k＝Φsθs
In the formula, subscripts k, k-1 and k-2 represent the values at the time of k, k-1 and k-2; Δ t is the sampling interval; phisA data matrix which is a dual-polarization model; thetasA parameter matrix of the dual-polarization model; c. C1,s、c2,s、c3,s、c4,s、c5,sThe coefficients of the dual-polarization model can be used for solving the values of circuit elements in the dual-polarization model circuit expression; for the simplicity of the expression, an auxiliary variable a ═ 1+2R is introducedD1CD1+2RD2CD2+4RD1CD1RD2CD2And time constant τ1＝RD1CD1、τ2＝RD2CD2。
Can be identified by least square method [ (1-c)1,s-c2,s)UOC,kc1,sc2,sc3.sc4,sc5,s]TFurther obtain the model parameter [ R ]sRD1CD1RD2CD2]T。
Fig. 4 shows that a fractional order model circuit can be constructed by replacing the capacitance in the above described Thevenin model RC parallel network with a constant phase angle element, optionally as a single cell model. The circuit equation of the model is:
in the formula of UOCIs the open circuit voltage of the cell; rFIs the ohmic internal resistance of the fractional order model; i.e. iLTo apply a current; u shapetIs terminal voltage; u shapeFVoltage drop for a parallel network; zarcA resistor of a parallel network; zCPEResistance of a constant phase angle element; riIs the resistance of the resistor in the parallel network, omega is the angular frequency, Y and α are two parameters of the constant phase angle element, the dimension of Y is sαΩ-1α is a dimensionless number used to characterize the degree to which a constant phase angle element deviates from a purely capacitive element.
The discretization of the above formula by adopting a short memory criterion is carried out by
Ut,k＝ΦFθF
In the formula, subscripts k and k-j represent values at the time of k and k-j; phiFA data matrix which is a fractional order model; thetaFA parameter matrix of the fractional order model; l is the memory length;
is a binomial coefficient; dαThe fractional order operator represents the fractional order with the differential order of α, and the specific expression is shown in the following formula:
in the formula, f represents an arbitrary parameter for fractional order operation.
Can be identified by least squares methodF+RiRFRiY(1+RiYDα)UOC,kRiY]TFurther obtain the model parameter [ R ]FRiY]T。
Fig. 5 shows a diagram of a quasi-two-dimensional electrochemical model, which can be selected as a single cell model, and which divides the cell into two phases (solid and liquid), three regions (positive, negative, and separator) to simplify the description of the internal structure of the cell, and which is modeled with spherical solid-phase particles in the solid phase of the positive and negative electrodes. The physical equations of the various parts are shown in table 1.
TABLE 1 quasi-two-dimensional electrochemical model physical equations
Wherein, subscripts p, n and sep respectively represent three areas of a positive electrode, a negative electrode and a diaphragm; c. CsIs the lithium ion concentration in the solid phase; r is the radial position in the solid phase particle; dsIs the diffusion coefficient of lithium ions in the solid phase; rsIs the radius of the solid phase particle; j is a function ofrIs the lithium ion flow density at the solid-liquid interface; epsiloneIs the liquid phase volume fraction; c. CeIs the liquid-phase lithium ion concentration; x is the distance along the thickness direction of the polar plate;
is the effective diffusion coefficient of lithium ions in the liquid phase; sigmaeffEffective diffuse conductivity in the solid phase; phi is asIs the potential in the solid phase; i.e. isIs the current density in the solid phase; i is the external current density when the battery is in operation; kappaeffIs the effective ionic conductivity in the liquid phase; phi is aeIs the potential in the liquid phase; i.e. ieIs the current density in the liquid phase; r is a molar gas constant, and R is 8.314J/(mol K); t is the temperature of the working environment of the battery; f is a Faraday constant, and F is 96485C/mol;
is the transfer coefficient of lithium ions in the liquid phase; i.e. iLIs an external current; s isThe effective area of the electrode; a is the specific surface area of the active particles, which is the ratio of their total surface area to the volume of the electrode; i.e. i0α reflecting the difficulty of electrode reaction to exchange current densitycAnd αaThe anode and cathode transmission coefficients, respectively, are taken to be the usual values of 0.5, η is the surface overpotential of the particles, ksIs the electrochemical reaction constant; c. Cs,maxIs the maximum value of the lithium ion concentration inside the active material; c. CsurfThe concentration of lithium ions at the solid-liquid interface; eOCVIs the open circuit potential of the electrode material.
In order to simplify the solution of the solid-phase diffusion partial differential equation, assuming that the contribution of each spherical particle to the lithium ion flux density is completely the same, the lithium ion flux density in the entire region can be approximately replaced by the average value of the lithium ion flux density in the electrode region, i.e., the lithium ion flux density in the entire region
In the formula LnIs the length of the negative electrode region in the x direction; l ispIs the length of the positive electrode region in the x direction; a isnIs the active particle specific surface area of the negative electrode region; a ispIs the active particle specific surface area of the positive electrode region; snAn electrode effective area that is a negative electrode region; spThe effective area of the electrode in the positive electrode area;
and
is the average flow density of the corresponding region.
Then, the difference is used to replace the differential, and the spherical particles are meshed into 10 parts along the radial direction, taking the negative electrode area as an example:
it is briefly described as
In the formula cn,iIs shown in
The concentration of lithium ions; Δ rn＝Rs,n/10。
The iteration process adopts a three-order Runge-Kutta method, and comprises the following steps:
in the formula, subscripts k and k-1 represent values at the time of k and k-1;
for R ═ Rs,nThe concentration of lithium ions in (b) is csurf,nIs provided with
Meanwhile, neglecting the influence of the lithium ion concentration distribution in the electrolyte on the liquid phase potential distribution, the terminal voltage expression can be rearranged from table 1 as follows:
wherein OCV is the open circuit voltage of the battery ηn、ηpAuxiliary variables taken to simplify the expression; l issepIs the length of the membrane region in the x-direction; ssepIs the effective area of the diaphragm; r0For compensating errors caused by various approximations assumed in simplifying the model and voltage drops caused by electrochemical processes such as the formation of an SEI film associated with battery aging.
Parameter vectors can be identified according to the formula by adopting a particle swarm algorithm
In a preferred embodiment of the present application, in step three, taking a BP network model as an example, a neural network model is established, and a complex nonlinear mapping relationship between the weight and the operating environment (aging state, temperature, etc.) and SOC of the power battery is fitted.
The BP network model imitates biological neural network, is formed by multilayer network (input layer, hidden layer, output layer), the structure is as shown in figure 6, it is the most complete and most widely applied neural network model of the present theory, theoretically, only by enough hidden layer and hidden layer nodes, it can approach arbitrary nonlinear mapping relation, it has strong generalization ability, therefore can imitate the relation of weight and SOC, power battery working condition well. The input of the BP network is SOC and the working state of a power battery, the number of the BP network is 2-4, the output is the weight of four models, and the number of hidden nodes can be appropriately 8-10. By adjusting the connection weight of each layer through training methods such as a gradient descent method, the complex nonlinear mapping relation between the weight and the working state (aging state and temperature) and SOC of the power battery can be approached, and the more data used for learning, the more accurate the result.
Here, taking the gradient descent method as an example, the BP neural network is trained, and the specific process is as follows:
Input x for hidden neuronsjFor all inputs xiIs a weighted sum of
In the formula, wijThe connection weight between the hidden layer and the input layer.
Output of hidden layer neuron x'jDetermined by the excitation function, here for example the excitation of the S-function is taken, in the form of
Then the output of hidden layer neuron x'jPartial derivatives of the input of
Output x of output layer neuronslIs a weighted sum of hidden neuron outputs, i.e.
In the formula wjlIs the connection weight between the output layer and the hidden layer.
Net ith output and corresponding ideal output
An error of
The error performance indicator function of the p-th sample is
In the formula, N is the number of the neurons of the network output layer.
② backward propagation, using gradient descent method to adjust the weight between layers
Connection weight w between output layer and hidden layerjlThe learning algorithm is
The influence of the last weight value on the weight value change of the time is considered by adding a momentum factor α, and the weight value of the network at the moment k +1 is
wjl(k+1)＝wjl(k)+Δwjl+α(wjl(k)-wjl(k-1))
Connection weight w between hidden layer and input layerijThe learning algorithm is
The influence of the last weight value on the weight value change of the time is considered by adding a momentum factor α, and the weight value of the network at the moment k +1 is
wij(k+1)＝wij(k)+Δwij+α(wij(k)-wij(k-1))
In the above equation, η denotes a learning rate, α denotes a momentum factor, and both values are 0 to 1.
And ③, judging an end condition, if the end condition is met, ending the training, if the end condition is not met, k is k +1, returning to step ①, and obtaining a commonly used end condition that the training algebra of the algorithm reaches a set maximum evolution algebra or the error performance index is smaller than a given precision.
In an embodiment of the present application, the above-mentioned single battery models are used, and a BP network model is selected as the neural network model; the working environment of the battery is temperature and aging state. Particularly, under low SOC (SOC ≦ 5%), since the Thevenin model, the dual-polarization model and the fractional order model may have oscillation divergence, the prediction result is completely determined by the electrochemical model, that is, under low SOC (5%), the result output by the BP network model is adjusted to be 1 for the quasi-two-dimensional electrochemical model weight and 0 for the rest, which is used as an additional fusion rule. An NMC battery with the rated voltage of 3.8V and the rated capacity of 2Ah is taken as an experimental object, a fusion model of the power battery is established and verified, and end voltage estimation errors are shown in a table 2. FIG. 7 shows the weights of each single model. Fig. 8 shows the simulation results of the end-to-end voltage and the terminal voltage measurement values of the single models and the fusion models.
TABLE 2 statistical table of power battery model errors
As can be seen from table 2, the maximum error of the power battery fusion model established by the method is reduced compared with that of a single model, which indicates that the method can effectively utilize the high-precision sections of the models. And the accuracy of each model is greatly changed among different sections from the view of the average error and the error root mean square, so that the fused model can keep lower average error and root mean square error, and the stability and reliability of the estimation result are ensured.
It should be understood that, the sequence numbers of the steps in the embodiments of the present invention do not mean the execution sequence, and the execution sequence of each process should be determined by the function and the inherent logic of the process, and should not constitute any limitation on the implementation process of the embodiments of the present invention.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (7)
1. A power battery fusion modeling method is characterized in that: the method specifically comprises the following steps:
establishing a plurality of single battery models according to the correlation theory of a battery system model, selecting a proper parameter identification method for each single battery model, and respectively identifying parameters by using experimental data;
fitting the working condition data under various working environments according to each established single battery model, and determining the weighting coefficient of each single battery model under each SOC according to the comparison result between the actual measurement value and the fitting value of the working condition data;
step three, establishing and training a neural network model by taking working environment parameters and SOC (state of charge) of the power battery as input and taking a weighting coefficient of each single battery model as output;
and fourthly, for any current excitation, respectively predicting the terminal voltage of each single battery model, and establishing a power battery weighted fusion model by combining the weighting coefficients obtained by the trained neural network model to finally obtain the predicted value of the terminal voltage of the power battery.
2. The method of claim 1, wherein: the single cell model includes: a pseudo two-dimensional model, a Thevenin model, a dual polarization model, and a fractional order model.
3. The method of claim 1, wherein: the parameter identification method adopted in the first step comprises the following steps: genetic algorithm, least square algorithm, minimum root mean square algorithm, particle swarm algorithm.
4. The method of claim 1, wherein: in the second step, the weighting coefficient of each single battery model under each SOC is determined according to the comparison result between the actual measurement value and the fitting value of the working condition data, and the weighting coefficient is determined based on the following formula:
wherein, wiWeighting coefficients of the ith model under the SOC; sigmaiThe variance of the fitted value of the ith model under the SOC and the actual measured value is taken as the standard deviation;
in the second step, the SOC interval of 1% is used as a set of data for determining the weighting coefficient of the single battery model under each SOC.
5. The method of claim 1, wherein: the neural network model selected in the third step comprises: BP network model, Hopfield network model, BAM network model; the method for training the neural network model comprises the following steps: gradient descent method and its variants and modified algorithms, adagard algorithm, adapelta algorithm.
6. The method of claim 1, wherein: in the weighted fusion process, the accuracy is also compensated based on additional fusion rules: and (3) a fusion strategy for improving estimation accuracy according to a single battery model selected by the battery management system and additionally considered by the main working environment of the battery.
7. A battery management system, characterized by: based on the power battery fusion modeling method as claimed in any one of claims 1-6, the terminal voltage of the power battery is weighted fusion predicted.
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