CN105891724B - Charge states of lithium ion battery On-line Estimation method based on extension individual-particle model - Google Patents
Charge states of lithium ion battery On-line Estimation method based on extension individual-particle model Download PDFInfo
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Abstract
The invention discloses a kind of charge states of lithium ion battery On-line Estimation methods based on extension individual-particle model, method includes the following steps: 1) establishing lithium ion battery individual-particle model；2) liquid phase lithium concentration distribution problem is solved based on BP neural network；3) it is distributed using the liquid phase lithium concentration that trained BP neural network solves each region in individual-particle model, optimizes individual-particle model；4) based on extension individual-particle model, the On-line Estimation of charge states of lithium ion battery is realized using Unscented kalman filtering.The present invention considers the liquid phase lithium concentration distribution in each region in individual-particle model, improves the simulation accuracy of individual-particle model, compensates for the individual-particle model disadvantage low in middle high magnification operating condition drag precision.Extension individual-particle model can better describe the nonlinear characteristic of battery, higher using Unscented kalman filtering estimation SOC precision based on extension individual-particle model.
Description
Technical field
The invention belongs to battery charge state estimation technique fields, are related to building for the extension individual-particle model of lithium ion battery
Cube method and charge states of lithium ion battery On-line Estimation method based on Unscented kalman filtering.
Background technique
Lithium ion battery is a kind of energy storage device that chemical energy can be converted to electric energy.Because its energy density is high, circulation
Service life is long, self-discharge rate is low, free of contamination feature, and lithium ion battery is widely used.
Carrying out accurate fuel cell modelling to lithium ion battery is an important prerequisite for realizing lithium ion battery state estimation.
Based on the electrochemical model of inside lithium ion cell reaction, it can relatively accurately reflect variation and the electricity of inside battery microscopic quantity
The variation of pond external behavior.Compared with empirical model, equivalent-circuit model and neural network model, the precision of electrochemical model is more
Height, physical significance is definitely.
Currently used electrochemical model has pseudo- two dimension P2D (pseudo 2D) model and single-particle SP (single
Particle) model.P2D model has very high simulation accuracy, but calculating process is complicated, time-consuming, therefore is not suitable for being based on
The On-line Estimation of the model realization battery correlated condition amount；SP model has ignored some internal procedures, calculate it is relatively simple, can be with
Based on individual-particle model realize battery correlated condition amount On-line Estimation, but it is medium and compared with high magnification operating condition under to battery
Simulation accuracy is poor.
The state-of-charge estimation of lithium ion battery is the critical function of battery management system, presently mainly based on outside battery
Characterisitic parameter establishes the equivalent-circuit model, empirical model or neural network model of battery, realizes battery on this basis
State-of-charge estimation.And these models analyze the basic reason that nonlinearity is presented in outside batteries characteristic not from mechanism,
Battery behavior thus can not accurately be described, leading to the estimation of battery SOC, there is a certain error.Based on mechanism model to SOC
Estimated, the estimated accuracy of battery SOC can be improved, prevent over-charging of battery over-discharge, extended battery, make battery work
Make in normal state, to reduce use cost.
Summary of the invention
To solve the above-mentioned problems, the invention proposes the charge states of lithium ion batteries based on extension individual-particle model to exist
Line estimation method.
The present invention is to solve its technical problem to adopt the following technical scheme that
A kind of charge states of lithium ion battery On-line Estimation method based on extension individual-particle model, which is characterized in that packet
Include following steps:
Step 1: establishing the individual-particle model of lithium ion battery；
Step 2: liquid phase lithium concentration distribution problem being solved based on BP neural network, optimizes individual-particle model；
Step 3: based on the extension individual-particle model after optimization, realizing that lithium ion battery is charged using Unscented kalman filtering
The On-line Estimation of state.
The individual-particle model optimization method of the step 2, the specific steps of which are as follows:
To consider influence of the liquid phase potential to battery terminal voltage, increase on the basis of individual-particle model to inside battery liquid phase
The solution of lithium concentration distribution, to improve simulation accuracy of the individual-particle model under middle high magnification operating condition.
(1) input quantity and output quantity of BP neural network are determined；
The input quantity of BP neural network is that be averaged lithium concentration, cathode solid phase of positive solid phase is averaged lithium concentration, position
Confidence ceases (x) and battery operating current, and output quantity is liquid phase lithium concentration.
(2) training sample of BP neural network is obtained；
Using COMSOL simulation software, related operating condition is set (including the constant-current discharge operating condition of each discharge-rate, cycle pulse
Electric discharge operating condition, constant-current constant-voltage charging operating condition and customized operating condition), the pseudo- two-dimensional numerical model of lithium ion battery is asked
Solution obtains be averaged lithium concentration and liquid phase lithium concentration of the positive and negative anodes solid phase under each operating condition and is distributed, as BP neural network
Training sample.
(3) training sample normalized；
Input data in training sample includes four, and order of magnitude difference is larger, to guarantee each factor par, is accelerated
Data are normalized in convergence rate, are converted into value of the range in [0,1] sectionNormalize formula such as (1) institute
Show:
In formula,For the value after input data normalized, x is input data, xmaxFor the maximum value in input data,
xminFor the minimum value in input data.
(4) training BP neural network determines the input weight, output weight and threshold value of BP neural network；
The training sample training BP neural network crossed using normalized in step (3), and BP neural network is exported
Liquid phase lithium concentration be compared with the liquid phase lithium concentration in corresponding training sample, until BP neural network training
Mean square deviation reaches requirement, determines the input weight, output weight and threshold value of BP neural network；
(5) optimize individual-particle model using trained BP neural network；
Be averaged lithium concentration, cathode solid phase of the positive solid phase at current time is averaged lithium concentration, location information (x)
And battery operating current is first normalized, and then inputs trained BP neural network, obtains current time institute
Seek the liquid phase lithium concentration at position.
The step 3 based on the extension individual-particle model after optimization, lithium-ion electric is realized using Unscented kalman filtering
The On-line Estimation method of pond state-of-charge, the specific steps of which are as follows:
(1) current integration method formula is subjected to sliding-model control, obtains the state side of Unscented kalman filtering estimation SOC
Journey, as shown in formula (2):
In formula, TsFor sampling time, CNFor battery rated capacity, I is battery operating current, and electric discharge is positive, and charging is negative.
Here SOC is defined as formula (3), (4):
In formula:It is averaged lithium concentration for positive and negative anodes solid phase,For positive and negative anodes solid phase maximum lithium concentration,
θ100%Stoichiometric ratio when for state-of-charge being 100%, θ0%Stoichiometric ratio when for state-of-charge being 0%, n is cathode,
P is anode.
(2) based on the individual-particle model after BP neural network optimization, lithium ion battery end voltage and positive and negative anodes activity are obtained
The relational expression of average lithium concentration in particle, by the sight after its sliding-model control as Unscented kalman filtering estimation SOC
Survey equation.
(3) charge states of lithium ion battery On-line Estimation is realized based on Unscented kalman filtering.
Beneficial effects of the present invention are as follows:
1. individual-particle model assumes that the liquid phase lithium concentration in battery everywhere is equal, liquid phase potential is had ignored to battery-end
The influence of voltage, so that simulation accuracy of the individual-particle model under middle high magnification operating condition is lower.The present invention is in simple grain submodule
The distribution of inside battery liquid phase lithium concentration is considered on the basis of type, to improve individual-particle model under middle high magnification operating condition
Simulation accuracy；
2. carrying out SOC estimation using Unscented kalman filtering, there is smaller line compared with conventional Extension Kalman filtering
Property error, and extend individual-particle model and can better describe the nonlinear characteristic of battery, therefore based on extension simple grain submodule
Type is higher using Unscented kalman filtering estimation SOC precision.
Detailed description of the invention
Fig. 1 is charge states of lithium ion battery estimation flow chart
Fig. 2 is Li-ion battery model schematic diagram
Fig. 3 is the governing equation and boundary condition explanatory diagram in each region of pseudo- two-dimensional numerical model
Fig. 4 is correlated variables meaning explanatory diagram involved in pseudo- two-dimensional numerical model
Specific embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings.
Fig. 2 is the schematic diagram of Li-ion battery model.Model consists of three parts: negative regions, diaphragm area and anode
Region.When electric discharge starts, electrochemical reaction occurs at negative electrode active particle surface and electrolyte interface, leads to active particle surface
Lithium concentration reduce, thus generate two kinds of phenomenons: (1) there is lithium concentration difference in negative electrode active particle, cause
Lithium ion inside active particle by diffusing to the surface；(2) lithium ion caused by the electrochemical reaction of interface enters in solution, leads
It causes local lithium concentration to increase, concentration difference is produced inside cathode pole piece, cause lithium ion from cathode to positive extreme direction
Diffusion and migration.Meanwhile electrochemical reaction occurring at positive-active particle surface and electrolyte interface, lead to active particle
The lithium concentration on surface increases, and also generates two kinds of phenomenons in this way: (1) lithium concentration difference occurs in positive-active particle,
Lead to the diffusion of lithium ion ecto-entad；(2) generation electrochemical reaction in interface consumes the lithium ion in electrolyte, causes
Local lithium concentration reduces, and concentration difference is generated inside anode pole piece, is more advantageous to lithium ion from cathode to positive extreme direction
Diffusion and migration.Since entire battery need to guarantee material balance, how many lithium ion are deviate from cathode area, and positive polar region will be embedded in more
Few lithium ion.In entire reaction, for the charge balance for guaranteeing active particle, one electronics while generating a lithium ion
Also it is released, under the action of external current, electronics reaches positive pole zone by negative regions by external circuit to be formed
Discharge current.Charging process is opposite with the above process.
Specific embodiment 1: to be that extension individual-particle model method for building up to lithium ion battery carries out detailed for present embodiment
It describes in detail bright.
The extension individual-particle model method for building up of lithium ion battery the following steps are included:
Step 1: solving average lithium concentration and particle surface lithium concentration in positive and negative anodes active particle；
Assuming that active particle in positive and negative anodes is the equal spheric granules of radius, the reactive ion current density in electrode everywhere
Also equal.The then reactive ion current density of positive and negative anodes collector boundary are as follows:
In formula, I is battery operating current, and electric discharge is positive, and charging is negative, and A is electrode effective area；Rp、RnIt is living for positive and negative anodes
Property particle granules radius；lp, lnThe negative plates that are positive thickness；εp、εnFor positive and negative pole material porosity；εF, p、εF, nIt is filled out for positive and negative anodes
Fill mass volume score；F is Faraday constant.
Average lithium concentration and particle surface lithium concentration in view of the solid-state diffusion in active particle, in particle
Can approximation be expressed from the next:
In formulaBe positive in negative electrode active particle averagely lithium concentration,For the initial lithium concentration of solid phase, RiFor
Positive and negative anodes active particle particle radius, jiBe positive negative reaction ion current density,Be positive negative electrode active particle surface lithium from
Sub- concentration, DS, iFor positive and negative anodes solid phase diffusion welding, qI, avg(t) to be that lithium ion volume is average in particle during solid-state diffusion
Concentration flux, n are negative regions, and p is positive pole zone.
Under constant-current discharge operating condition, qI, avg(t) calculating formula are as follows:
Under other any charge and discharge operating conditions, qI, avg(t) calculating formula are as follows:
Step 2: solving the liquid phase lithium concentration distribution in positive pole zone, negative regions and diaphragm area, optimization is single
Particle model；
Step 2.1: determining the input quantity and output quantity of BP neural network；
The input quantity of BP neural network is that be averaged lithium concentration, cathode solid phase of positive solid phase is averaged lithium concentration, position
Confidence ceases (x) and battery operating current, and output quantity is liquid phase lithium concentration.
Step 2.2: solving solid phase using pseudo- two-dimensional numerical model and be averaged lithium concentration and positive and negative anodes region and diaphragm
The liquid phase lithium concentration in region is distributed the training sample as BP neural network；
Pseudo- two-dimensional numerical model is that M.Doyle and T.Fuller is based on concentrated solution theory and porous electrode is theoretical, and considers
What the principle of electrochemical reaction such as charge conservation, kinetics and thermodynamics were established.
Pseudo- two-dimensional numerical model is specifically to be made of ten partial differential equation and 20 boundary conditions, pseudo- two-dimensional mathematics mould
The governing equation and boundary condition of type are as shown in table 1, and the meaning of each variable is shown in Table 2 in table 1.
Using COMSOL simulation software, related operating condition is set (including the constant-current discharge operating condition of each discharge-rate, cycle pulse
Electric discharge operating condition, constant-current constant-voltage charging operating condition and customized operating condition), the positive and negative anodes solid phase accurately solved under each operating condition is average
Lithium concentration and the distribution of liquid phase lithium concentration, the training sample as BP neural network.
Step 2.3: data normalization processing；
Input data in training sample includes four, and order of magnitude difference is larger, to guarantee each factor par, is accelerated
Data are normalized in convergence rate, are converted into value of the range in [0,1] sectionNormalize formula such as (12) institute
Show:
In formula,For the value after input data normalized, x is input data, xmaxFor the maximum value in input data,
xminFor the minimum value in input data.
Step 2.4: training BP neural network determines the input weight, output weight and threshold value of BP neural network；
The training sample training BP neural network crossed using normalized in step 2.3, and BP neural network is exported
Liquid phase lithium concentration be compared with the liquid phase lithium concentration in corresponding training sample, until BP neural network training
Mean square deviation reaches requirement, determines the input weight, output weight and threshold value of BP neural network；
Step 2.5: optimizing individual-particle model using trained BP neural network；
Be averaged lithium concentration, cathode solid phase of the positive solid phase at current time is averaged lithium concentration, location information (x)
And battery operating current is first normalized, and then inputs trained BP neural network, obtains current time institute
Seek the liquid phase lithium concentration at position.
Step 3: solve liquid phase concentration difference overpotential:
Cathode-collector boundary (x=L) and anode-collector boundary (x=0) liquid phase are solved by step 2
Lithium concentration, then by formula (13) so as to find out liquid phase concentration difference overpotential.
In formula, t+For lithium ionic mobility；R is gas constant；T is temperature, unit K；ceFor liquid phase lithium concentration；L
For positive pole zone, diaphragm area, negative regions overall width.
Step 4: solving liquid phase ohmic polarization overpotential；
In formula, KEff, iFor liquid phase effective conductivity, liFor peak width, n is negative regions, and p is positive pole zone, and sep is
Diaphragm area.
Step 5: solving reaction polarization overpotential；
In formula, asFor specific surface area, αa、αcIt is apparent exchange coefficient.
In formula, kiBe positive negative reaction rate constant, ceFor liquid phase lithium concentration.
Step 6, SEI film ohmic polarization overpotential is solved；
ηSEI=RSEI, pFjp-RSEI, nFjn (18)
In formula, RSEI, p、RSEI, nFor positive and negative anodes SEI film ohmic internal resistance.
Step 7: solving end voltage；
In formula, UpFor positive open-circuit voltage, UnFor cathode open-circuit voltage.
Correlative required by step 3- step 6 is substituted into, is obtained
SOC definition is such as shown in (21), (22).
In formula:It is averaged lithium concentration for positive and negative anodes solid phase,For positive and negative anodes solid phase maximum lithium concentration,
θ100%Stoichiometric ratio when for state-of-charge being 100%, θ0%Stoichiometric ratio when for state-of-charge being 0%, n is cathode,
P is anode.
Then formula (20) can be converted following form, as shown in formula (24)；
V=Up(SOC)-Un(SOC)+f(I) (24)
By formula (24) sliding-model control, the observational equation of Unscented kalman filtering estimation SOC can be used as, such as formula (25) institute
Show.
V=UP, k(SOCk)-UN, k(SOCk)+f(Ik)+νk (25)
In formula, vkIt is the white Gaussian noise that mean value is zero, covariance is R.
Specific embodiment 2: Unscented kalman filtering device is a kind of non-linear Gauss based on minimum variance estimate criterion
State estimator, it using non-linear optimal Gaussian filter as basic theories frame, while approached using Unscented transform through
Posterior Mean and posteriority covariance after nonlinear system propagation.
Present embodiment is to realize lithium using Unscented kalman filtering to based on extension individual-particle model of the present invention
Ion battery state-of-charge On-line Estimation is illustrated.
Known n ties up Discrete time Nonlinear Systems, n=1 known to bonding state space equation:
F () and h () is that Unscented kalman filtering spatial model state equation and the non-linear of observational equation reflect in formula (26)
Penetrate function.XkIt is state variable (SOC), ukIt is input control quantity (electric current), YkIt is output observed quantity (end voltage), wkWith vkIt is equal
Value is zero, covariance is Q and the white Gaussian noise of R.
Step 1: establishing state space equation；
Current integration method formula after will be discrete is as state space equation, as shown in formula (27):
In formula, CNFor battery rated capacity, TsFor sampling time, IsFor battery operating current, wkIt is mean value is zero, association side
Difference is the white Gaussian noise of Q.
Step 2: establishing observational equation；
V=UP, k(SOCk)-UN, k(SOCk)+f(Ik)+νk (28)
In formula, vkIt is the white Gaussian noise that mean value is zero, covariance is R.
Step 3: mean value and covariance initialization:
X0=E [x (0)] (29)
P0=E [(x (0)-X0)(x(0)-X0)] (30)
Step 4: 2 × n+1 sigma point is generated, respective weights are calculated:
For electrochemical model, n represents state variable dimension, and λ is proportionality coefficient, for adjusting Sigma point and original
The interval of beginning state point meets λ+n=3 under normal conditions, can also finely tune according to the actual situation.
Step 5: calculate result of the Sigma point Jing Guo nonlinear transformation:
Step 6: previous step result is weighted, mean value and covariance are sought:
Step 7: quantity of state is by needing to correct Sigma point before measurement equation:
Step 8: ask the observation predicted value and covariance of amendment Sigma point:
Step 9: seek kalman gain:
K=Pxy(Py)-1 (41)
Step 10: ask the measurement of state variable mean value and covariance to update:
Unscented kalman filtering is loop iteration process,For the latest estimated value at current time, as current time SOC
Estimated value,It is state space for the estimated value of observed quantity, analysis modeling error can be used to.
Claims (3)
1. the charge states of lithium ion battery On-line Estimation method based on extension individual-particle model, which is characterized in that including following
Step:
Step 1: establishing the individual-particle model of lithium ion battery；
Step 2: liquid phase lithium concentration distribution problem being solved based on BP neural network, optimizes individual-particle model；
Step 3: based on the individual-particle model after optimization, using Unscented kalman filtering realize charge states of lithium ion battery
Line estimation.
2. the charge states of lithium ion battery On-line Estimation method according to claim 1 based on extension individual-particle model,
It is characterized in that the specific implementation method of the step 2 are as follows:
Consider influence of the liquid phase potential to battery terminal voltage, increases on the basis of individual-particle model to inside battery liquid phase lithium ion
The solution of concentration distribution, to improve simulation accuracy of the individual-particle model under middle high magnification operating condition, specific step is as follows in detail:
(1) input quantity and output quantity of BP neural network are determined；
The input quantity of BP neural network is that be averaged lithium concentration, cathode solid phase of positive solid phase is averaged lithium concentration, upper a period of time
Liquid phase lithium concentration, location information (x) and the battery operating current at quarter, output quantity are that the liquid phase lithium ion at current time is dense
Degree；
(2) training sample of BP neural network is obtained；
Using COMSOL simulation software, the constant-current discharge operating condition, cycle pulse electric discharge operating condition, constant current that different discharge-rates are arranged are permanent
Pressure charging operating condition and customized operating condition, solve the pseudo- two-dimensional numerical model of lithium ion battery, obtain under each operating condition
Positive and negative anodes solid phase be averaged lithium concentration and liquid phase lithium concentration distribution, the training sample as BP neural network；
(3) training sample normalized；
Input data in training sample includes five, and order of magnitude difference is larger, to guarantee each factor par, accelerates convergence
Data are normalized in speed, are converted into value of the range in [0,1] sectionIt is shown to normalize formula such as (1):
In formula,For the value after input data normalized, x is input data, xmaxFor the maximum value in input data, xmin
For the minimum value in input data；
(4) training BP neural network determines the input weight, output weight and threshold value of BP neural network；
The training sample training BP neural network crossed using normalized in step (3), and the liquid that BP neural network is exported
Phase lithium concentration is compared with the liquid phase lithium concentration in corresponding training sample, square until BP neural network training
Difference reaches requirement, determines the input weight, output weight and threshold value of BP neural network；
(5) optimize individual-particle model using trained BP neural network；
Be averaged lithium concentration, cathode solid phase of the positive solid phase at current time is averaged lithium concentration, the liquid phase of last moment
Lithium concentration, location information (x) and battery operating current are first normalized, and then input trained BP mind
Through network, the liquid phase lithium concentration at position required by current time is obtained.
3. the charge states of lithium ion battery On-line Estimation method according to claim 1 based on extension individual-particle model,
It is characterized in that the specific implementation method of the step 3 are as follows:
(1) current integration method formula is subjected to sliding-model control, obtains the state equation of Unscented kalman filtering estimation SOC, such as
Shown in formula (2):
In formula, TsFor sampling time, CNFor battery rated capacity, I is battery operating current, and electric discharge is positive, and charging is negative；
Here SOC is defined as formula (3), (4):
In formula:It is averaged lithium concentration for positive and negative anodes solid phase,For positive and negative anodes solid phase maximum lithium concentration, θ100%For
Stoichiometric ratio when state-of-charge is 100%, θ0%Stoichiometric ratio when for state-of-charge being 0%, n is cathode, and p is positive
Pole；
(2) based on the individual-particle model after BP neural network optimization, lithium ion battery end voltage and positive and negative anodes active particle are obtained
The relational expression of interior average lithium concentration, by the observation side after its sliding-model control as Unscented kalman filtering estimation SOC
Journey；
(3) charge states of lithium ion battery On-line Estimation is realized based on Unscented kalman filtering.
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| CN114879073A (en) * | 2022-04-22 | 2022-08-09 | 清华大学 | Charge state updating method based on power characteristics of electrochemical model of lithium ion battery |
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