CN105891724A - On-line estimation method for state of charge of lithium ion battery based on extended single particle model - Google Patents

Abstract

The invention discloses an on-line estimation method for the state of charge (SOC) of a lithium ion battery based on an extended single particle model. The method comprises the following steps: 1) establishing a lithium ion battery single particle model; 2) solving the concentration distribution problem of liquid-phase lithium ions based on a BP (Back Propagation) neural network; 3) solving liquid-phase lithium ion concentration distribution of each area in the single particle model using the trained BP neural network to optimize the single particle model; and 4) implementing on-line estimation of the SOC of the lithium ion battery by adopting unscented Kalman filter based on the extended single particle model. The method considering the liquid-phase lithium ion concentration distribution of each area in the single particle model improves the simulation precision of the single particle model, and overcomes the defect of low precision of the single particle model under medium and high multiplying power conditions. The extended single particle model can better describe the nonlinear characteristic of the battery, and the SOC precision estimated by adopting unscented Kalman filter based on the extended single particle model is higher.

Description

Charge states of lithium ion battery On-line Estimation method based on extension individual-particle model

Technical field

The invention belongs to battery charge state estimation technique field, relate to the method for building up of the extension individual-particle model of lithium ion battery and charge states of lithium ion battery On-line Estimation method based on Unscented kalman filtering.

Background technology

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, have extended cycle life, self-discharge rate is low, free of contamination feature, lithium ion battery is widely used.

It is the important prerequisite realizing lithium ion battery state estimation that lithium ion battery carries out fuel cell modelling accurately.Electrochemical model based on inside lithium ion cell reaction, it is possible to relatively accurately reflect change and the change of outside batteries characteristic of inside battery microscopic quantity.Compared with empirical model, equivalent-circuit model and neural network model, the precision of electrochemical model is higher, and physical significance is definitely.

The most conventional electrochemical model has pseudo-two dimension P2D (pseudo 2D) model and single-particle SP (single particle) model.P2D model has the highest simulation accuracy, but calculating process is complicated, the longest, is therefore not suitable for On-line Estimation based on this model realization battery correlation behavior amount；SP model have ignored some internal procedures, calculates relatively simple, can realize the On-line Estimation of battery correlation behavior amount based on individual-particle model, but medium and compared with high magnification operating mode under poor to the simulation accuracy of battery.

The state-of-charge estimation of lithium ion battery is the critical function of battery management system, is presently mainly and sets up the equivalent-circuit model of battery, empirical model or neural network model based on battery external characteristics parameter, and the state-of-charge realizing battery on this basis is estimated.And these models are not analyzed outside batteries characteristic from mechanism and presented the basic reason of nonlinearity, thus can accurately not describe battery behavior, cause the estimation of battery SOC to there is certain error.Based on mechanism model, SOC is estimated, the estimated accuracy of battery SOC can be improved, prevent over-charging of battery from crossing and put, extend battery, make battery operated in normal state, reduce use cost.

Summary of the invention

In order to solve the problems referred to above, the present invention proposes charge states of lithium ion battery On-line Estimation method based on extension individual-particle model.

The present invention solves that its technical problem adopts the following technical scheme that

A kind of charge states of lithium ion battery On-line Estimation method based on extension individual-particle model, it is characterised in that comprise the following steps:

Step 1: set up the individual-particle model of lithium ion battery；

Step 2: solve liquid phase lithium concentration distribution problem based on BP neutral net, optimizes individual-particle model；

Step 3: based on the extension individual-particle model after optimizing, uses Unscented kalman filtering to realize the On-line Estimation of charge states of lithium ion battery.

The individual-particle model optimization method of described step 2, it specifically comprises the following steps that

For considering the impact on battery terminal voltage of the liquid phase electromotive force, increase on the basis of individual-particle model and inside battery liquid phase lithium concentration distribution is solved, thus improve individual-particle model simulation accuracy under middle high magnification operating mode.

(1) input quantity and the output quantity of BP neutral net are determined；

The input quantity of BP neutral net is the average lithium concentration of positive pole solid phase, the average lithium concentration of negative pole solid phase, positional information (x) and battery operated electric current, and output quantity is liquid phase lithium concentration.

(2) training sample of BP neutral net is obtained；

Utilize COMSOL simulation software, relevant operating mode (including the constant-current discharge operating mode of each discharge-rate, cycle pulse electric discharge operating mode, constant-current constant-voltage charging operating mode and self-defined operating mode) is set, the pseudo-two-dimensional numerical model of lithium ion battery is solved, obtain the average lithium concentration of both positive and negative polarity solid phase under each operating mode and the distribution of liquid phase lithium concentration, as the training sample of BP neutral net.

(3) training sample normalized；

Input packet in training sample contains four, and order of magnitude difference is relatively big, for ensureing each factor par, accelerates convergence rate, is normalized data, is converted into scope value in [0,1] intervalNormalization formula is as shown in (1):

$\hat{x}=\frac{x-x_{min}}{x_{max}-x_{min}}---\left(1\right)$

In formula,Value after processing for input data normalization, x is input data, x_maxFor the maximum in input data, x_minFor the minimum of a value in input data.

(4) training BP neutral net, determines the input weights of BP neutral net, output weights and threshold value；

Utilize the training sample training BP neutral net that in step (3), normalized is crossed, and the liquid phase lithium concentration that BP neutral net exports is compared with the liquid phase lithium concentration in corresponding training sample, until the mean square deviation of BP neural metwork training reaches requirement, determine the input weights of BP neutral net, output weights and threshold value；

(5) the BP Neural Network Optimization individual-particle model trained is utilized；

The average lithium concentration of positive pole solid phase of current time, the average lithium concentration of negative pole solid phase, positional information (x) and battery operated electric current are first normalized, then input the BP neutral net trained, obtain the liquid phase lithium concentration of position required by current time.

Described step 3 based on the extension individual-particle model after optimizing, use Unscented kalman filtering to realize the On-line Estimation method of charge states of lithium ion battery, it specifically comprises the following steps that

(1) ampere-hour integration method formula is carried out sliding-model control, obtains Unscented kalman filtering and estimate the state equation of SOC, as shown in formula (2):

${\mathrm{SOC}}_k={\mathrm{SOC}}_{k-1}-\frac{I_{k-1}{T}_s}{C_N}---\left(2\right)$

In formula, T_sFor sampling time, C_NFor battery rated capacity, I is battery operated electric current, discharges for just, is charged as bearing.

Here SOC is defined as formula (3), (4):

$SOC=\frac{\frac{c_{n,avg}^s}{c_{n,\max }^s}-{\mathrm{\θ}}_{n,0\%}}{{\mathrm{\θ}}_{n,100\%}-{\mathrm{\θ}}_{n,0\%}}---\left(3\right)$

$SOC=\frac{\frac{c_{p,avg}^s}{c_{p,max}^s}-{\mathrm{\θ}}_{p,0\%}}{{\mathrm{\θ}}_{p,100\%}-{\mathrm{\θ}}_{p,0\%}}---\left(4\right)$

${\mathrm{\θ}}_i=\frac{c_{i,avg}^s}{c_{i,\max }^s},i=p,n---\left(5\right)$

In formula:For the average lithium concentration of both positive and negative polarity solid phase,For both positive and negative polarity solid phase maximum lithium concentration, θ_{100 %}It is stoichiometric proportion when 100% for state-of-charge, θ_{0 %}Being stoichiometric proportion when 0% for state-of-charge, n is negative pole, and p is positive pole.

(2) based on the individual-particle model after BP Neural Network Optimization, draw the relational expression of lithium ion battery terminal voltage and the average lithium concentration in both positive and negative polarity active particle, the observational equation of SOC will be estimated after its sliding-model control as Unscented kalman filtering.

(3) charge states of lithium ion battery On-line Estimation is realized based on Unscented kalman filtering.

Beneficial effects of the present invention is as follows:

1. individual-particle model assumes in battery that liquid phase lithium concentration everywhere is equal, have ignored the impact on battery terminal voltage of the liquid phase electromotive force, so that the simulation accuracy that individual-particle model is under middle high magnification operating mode is relatively low.The present invention considers that on the basis of individual-particle model inside battery liquid phase lithium concentration is distributed, thus improves individual-particle model simulation accuracy under middle high magnification operating mode；

2. use Unscented kalman filtering to carry out SOC estimation, there is compared with conventional Extension Kalman filtering less linearized stability, and extension individual-particle model can preferably describe the nonlinear characteristic of battery, SOC precision is higher therefore to use Unscented kalman filtering to estimate based on extension individual-particle model.

Accompanying drawing explanation

Fig. 1 is that charge states of lithium ion battery estimates flow chart

Fig. 2 is Li-ion battery model schematic diagram

Fig. 3 is governing equation and the boundary condition explanatory diagram in the pseudo-each region of two-dimensional numerical model

Fig. 4 is pseudo-correlated variables implication explanatory diagram involved by two-dimensional numerical model

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is described in further detail.

Fig. 2 is the schematic diagram of Li-ion battery model.Model is made up of three parts: negative regions, diaphragm area and positive pole zone.When electric discharge starts, electrochemical reaction is there is at negative electrode active particle surface and electrolyte interface, the lithium concentration causing active particle surface reduces, thus produce two kinds of phenomenons: lithium concentration difference occurs in (1) negative electrode active particle, causes lithium ion to be diffused to the surface by inside active particle；(2) lithium ion produced by the electrochemical reaction of interface enters in solution, causes local lithium concentration to raise, creates concentration difference inside cathode pole piece, causes lithium ion by negative pole to the diffusion of positive extreme direction and migration.Simultaneously, electrochemical reaction is there is at positive-active particle surface with electrolyte interface, the lithium concentration causing active particle surface raises, and the most also produces two kinds of phenomenons: lithium concentration difference occur in (1) positive-active particle, cause the diffusion of lithium ion ecto-entad；(2) interface occurs electrochemical reaction to consume the lithium ion in electrolyte, causes local lithium concentration to reduce, produces concentration difference inside anode pole piece, is more beneficial for lithium ion by negative pole to the diffusion of positive extreme direction and migration.Owing to whole battery need to ensure material balance, the abjection of negative pole district is how many lithium ions, and positive polar region will embed how many lithium ions.In whole reaction, for ensureing the charge balance of active particle, while producing a lithium ion, an electronics is also released, and under the effect of external current, electronics by negative regions arrival positive pole zone thus defines discharge current by external circuit.Charging process is contrary with said process.

Detailed description of the invention one: present embodiment is that the extension individual-particle model method for building up to lithium ion battery is described in detail.

The extension individual-particle model method for building up of lithium ion battery comprises the following steps:

Step 1: average lithium concentration and particle surface lithium concentration in solving both positive and negative polarity active particle；

Assuming that the active particle in both positive and negative polarity is the spheric granules that radius is equal, in electrode, reactive ion current density everywhere is the most equal.Then the reactive ion current density of both positive and negative polarity collector boundary is:

$j_n=\frac{{\mathrm{IR}}_n}{3AF(1-{\mathrm{\ϵ}}_n-{\mathrm{\ϵ}}_{f,n})l_n}---\left(6\right)$

$j_p=\frac{-{\mathrm{IR}}_p}{3AF(1-{\mathrm{\ϵ}}_p-{\mathrm{\ϵ}}_{f,p})l_p}---\left(7\right)$

In formula, I is battery operated electric current, discharges for just, is charged as bearing, and A is electrode effective area；R_p、R_nFor both positive and negative polarity active particle particle radius；l_p, l_nFor both positive and negative polarity electrode thickness；ε_p、ε_nFor positive and negative pole material porosity；ε_{f , p}、ε_{f , n}For both positive and negative polarity filler volume fraction；F is Faraday constant.

In view of the solid-state diffusion in active particle, average lithium concentration and particle surface lithium concentration in particle can approximate and be expressed from the next:

$c_{i,avg}^s=c_{i,0}^s-\underset{0}{\overset{t}{\∫}}3\frac{j_i}{R_i}dt,i=n,p---\left(8\right)$

$c_{j,surf}^s\left(t\right)=c_{i,avg}^s\left(t\right)+\frac{8D_{s,i}{q}_{i,avg}\left(t\right)-j_i}{35D_{s,i}}\·R_i,i=n,p---\left(9\right)$

In formulaFor lithium concentration average in both positive and negative polarity active particle,For the initial lithium concentration of solid phase, R_iFor both positive and negative polarity active particle particle radius, j_iFor both positive and negative polarity reactive ion current density,For both positive and negative polarity active particle surface lithium ion concentration, D_{s , i}For both positive and negative polarity solid phase diffusion welding, q_{i , avg}T (), for being lithium ion volume mean concentration flow in particle during solid-state diffusion, n is negative regions, and p is positive pole zone.

Under constant-current discharge operating mode, q_{i , avg}T the calculating formula of () is:

$q_{i,avg}\left(t\right)=\frac{3j_i}{4D_{s,i}}\[\exp (-t/{\mathrm{\τ}}_i^s)-1\],{\mathrm{\τ}}_i^s=\frac{R_i^2}{30D_{s,i}},i=n,p---\left(10\right)$

Under other any discharge and recharge operating modes, q_{i , avg}T the calculating formula of () is:

$q_{i,avg}\left(t_{k+1}\right)=q_{i,avg}\left(t_k\right)-\[\frac{45j_i}{2R_i^2}+30\frac{D_{s,i}}{R_i^2}{q}_{i,avg}\left(t_k\right)\]\·(t_{k+1}-t_k)---\left(11\right)$

Step 2: solve the liquid phase lithium concentration distribution in positive pole zone, negative regions and diaphragm area, optimize individual-particle model；

Step 2.1: determine input quantity and the output quantity of BP neutral net；

The input quantity of BP neutral net is the average lithium concentration of positive pole solid phase, the average lithium concentration of negative pole solid phase, positional information (x) and battery operated electric current, and output quantity is liquid phase lithium concentration.

Step 2.2: utilize pseudo-two-dimensional numerical model to solve the liquid phase lithium concentration distribution training sample as BP neutral net of the average lithium concentration of solid phase and both positive and negative polarity region and diaphragm area；

Pseudo-two-dimensional numerical model is that M.Doyle and T.Fuller is theoretical based on concentrated solution and porous electrode is theoretical, and considers what the principle of electrochemical reaction such as charge conservation, kinetics and thermodynamics were set up.

Pseudo-two-dimensional numerical model is specifically made up of ten partial differential equation and 20 boundary conditions, and governing equation and the boundary condition of pseudo-two-dimensional numerical model are as shown in table 1, and in table 1, the implication of each variable is shown in Table 2.

Utilize COMSOL simulation software, relevant operating mode (including the constant-current discharge operating mode of each discharge-rate, cycle pulse electric discharge operating mode, constant-current constant-voltage charging operating mode and self-defined operating mode) is set, solve the average lithium concentration of both positive and negative polarity solid phase under each operating mode and the distribution of liquid phase lithium concentration exactly, as the training sample of BP neutral net.

Step 2.3: data normalization processes；

Input packet in training sample contains four, and order of magnitude difference is relatively big, for ensureing each factor par, accelerates convergence rate, is normalized data, is converted into scope value in [0,1] intervalNormalization formula is as shown in (12):

$\hat{x}=\frac{x-x_{min}}{x_{max}-x_{min}}---\left(12\right)$

In formula,Value after processing for input data normalization, x is input data, x_maxFor the maximum in input data, x_minFor the minimum of a value in input data.

Step 2.4: training BP neutral net, determines the input weights of BP neutral net, output weights and threshold value；

Utilize the training sample training BP neutral net that normalized in step 2.3 is crossed, and the liquid phase lithium concentration that BP neutral net exports is compared with the liquid phase lithium concentration in corresponding training sample, until the mean square deviation of BP neural metwork training reaches requirement, determine the input weights of BP neutral net, output weights and threshold value；

Step 2.5: utilize the BP Neural Network Optimization individual-particle model trained；

The average lithium concentration of positive pole solid phase of current time, the average lithium concentration of negative pole solid phase, positional information (x) and battery operated electric current are first normalized, then input the BP neutral net trained, obtain the liquid phase lithium concentration of position required by current time.

Step 3: solve liquid phase concentration difference overpotential:

Solve negative pole-collector boundary (x=L) and the liquid phase lithium concentration of positive pole-collector boundary (x=0) by step 2, then pass through formula (13) thus obtain liquid phase concentration difference overpotential.

${\mathrm{\η}}_{Electrolyte\_Concentration}=(1-t_{+})\frac{2RT}{F}\ln \frac{c_e\left(L\right)}{c_e\left(0\right)}---\left(13\right)$

In formula, t₊For lithium ionic mobility；R is gas constant；T is temperature, and unit is K；c_eFor liquid phase lithium concentration；L is the overall width of positive pole zone, diaphragm area, negative regions.

Step 4: solve liquid phase ohmic polarization overpotential；

${\mathrm{\η}}_{liquid\_ohm}=-\frac{I}{2A}(\frac{l_n}{{\mathrm{\κ}}_{eff,n}}+2\frac{l_{sep}}{{\mathrm{\κ}}_{eff,sep}}+\frac{l_p}{{\mathrm{\κ}}_{eff,p}})---\left(14\right)$

In formula, K_{eff , i}For liquid phase effective conductivity, l_iFor peak width, n is negative regions, and p is positive pole zone, and sep is diaphragm area.

Step 5: solve reaction polarization overpotential；

${\mathrm{\η}}_{act\_polarization}=\frac{2RT}{F}\[\ln (\sqrt{m_p^2+1}+m_p)-\ln (\sqrt{m_n^2+1}+m_n)\]---\left(15\right)$

In formula, a_sFor specific surface area, α_a、α_cIt it is apparent exchange coefficient.

$m_p=\frac{j_p}{2k_p{(c_{p,max}^s-c_{p,surf}^s)}^{0.5}{\left(c_{p,surf}^s\right)}^{0.5}{\left(c_e\right)}^{0.5}}---\left(16\right)$

$m_n=\frac{j_n}{2k_n{(c_{n,max}^s-c_{n,surf}^S)}^{0.5}{\left(c_{n,surf}^s\right)}^{0.5}{\left(c_e\right)}^{0.5}}---\left(17\right)$

In formula, k_iFor both positive and negative polarity reaction rate constant, c_eFor liquid phase lithium concentration.

Step 6, solves SEI film ohmic polarization overpotential；

η_SEI=R_{SEI , p}Fj_p-R_{SEI , n}Fj_n (18)

In formula, R_{SEI , p}、R_{SEI , n}For both positive and negative polarity SEI film ohmic internal resistance.

Step 7: solve terminal voltage；

$V\left(t\right)=U_p\left(\frac{c_{p,surf}^s}{c_{p,\max }^s}\right)-U_n\left(\frac{c_{n,surf}^s}{c_{n,\max }^s}\right)+{\mathrm{\η}}_{liquid\_ohm}+{\mathrm{\η}}_{act\_polarization}+{\mathrm{\η}}_{Electrolyte\_Concentration}+{\mathrm{\η}}_{SEI}---\left(19\right)$

In formula, U_pFor positive pole open-circuit voltage, U_nFor negative pole open-circuit voltage.

Correlative required by step 3-step 6 is substituted into,

$\begin{array}{c}V=U_p\left(\frac{c_{p,surf}^s}{c_{p,max}^s}\right)-U_n\left(\frac{c_{n,surf}^s}{c_{n,max}^s}\right)+\frac{2RT}{F}\[\ln (\sqrt{m_p^2+1}+m_p)-\ln (\sqrt{m_n^2+1}+m_n)\]\\ -\frac{I}{2A}(\frac{l_n}{{\mathrm{\κ}}_{eff,n}}+2\frac{l_{sep}}{{\mathrm{\κ}}_{eff,sep}}+\frac{l_p}{{\mathrm{\κ}}_{eff,p}})+(1-t_{+})\frac{2RT}{F}\ln \frac{c_e\left(L\right)}{c_e\left(0\right)}+R_{SEI,p}{\mathrm{Fj}}_p-R_{SEI,n}{\mathrm{Fj}}_n\end{array}---\left(20\right)$

SOC definition is as shown in (21), (22).

$SOC=\frac{\frac{c_{n,avg}^s}{c_{n,\max }^s}-{\mathrm{\θ}}_{n,0\%}}{{\mathrm{\θ}}_{n,100\%}-{\mathrm{\θ}}_{n,0\%}}---\left(21\right)$

$SOC=\frac{\frac{c_{p,avg}^s}{c_{p,\max }^s}-{\mathrm{\θ}}_{p,0\%}}{{\mathrm{\θ}}_{p,100\%}-{\mathrm{\θ}}_{p,0\%}}---\left(22\right)$

${\mathrm{\θ}}_i=\frac{c_{i,avg}^s}{c_{i,\max }^s},i=p,n---\left(23\right)$

In formula:For the average lithium concentration of both positive and negative polarity solid phase,For both positive and negative polarity solid phase maximum lithium concentration, θ_{100 %}It is stoichiometric proportion when 100% for state-of-charge, θ_{0 %}Being stoichiometric proportion when 0% for state-of-charge, n is negative pole, and p is positive pole.

Then formula (20) can be to be converted into following form, as shown in formula (24)；

V=U_p(SOC)-U_n(SOC)+f(I) (24)

By formula (24) sliding-model control, can be used as Unscented kalman filtering and estimate the observational equation of SOC, as shown in formula (25).

V=U_{p , k}(SOC_k)-U_{n , k}(SOC_k)+f(I_k)+ν_k (25)

In formula, v_kBe average be zero, covariance be the white Gaussian noise of R.

Detailed description of the invention two: Unscented kalman filtering device is a kind of non-linear gauss' condition estimator based on minimum variance estimate criterion, non-linear optimum Gaussian filter as basic theories framework, is used Unscented transform to approach the Posterior Mean after nonlinear system is propagated and posteriority covariance by it simultaneously.

Present embodiment is to based on extension individual-particle model of the present invention, uses Unscented kalman filtering to realize charge states of lithium ion battery On-line Estimation and illustrates.

Known n ties up Discrete time Nonlinear Systems, n=1 knowable to bonding state space equation:

$\left\{\begin{array}{c}{X}_{k+1}=f(X_k,u_k)+w_k\\ Y_k=h(X_k,u_k)+v_k\end{array}\right.---\left(26\right)$

In formula (26), f () and h () is Unscented kalman filtering spatial model state equation and the nonlinear mapping function of observational equation.X_kIt is state variable (SOC), u_kIt is input controlled quentity controlled variable (electric current), Y_kIt is output observed quantity (terminal voltage), w_kWith v_kBe average be zero, covariance be the white Gaussian noise of Q and R.

Step 1: set up state space equation；

Using the ampere-hour integration method formula after discrete as state space equation, as shown in formula (27):

${\mathrm{SOC}}_{k+1}={\mathrm{SOC}}_k-\frac{I_k}{C_N}{T}_s+w_k---\left(27\right)$

In formula, C_NFor battery rated capacity, T_sFor sampling time, I_sFor battery operated electric current, w_kBe average be zero, covariance be the white Gaussian noise of Q.

Step 2: set up observational equation；

V=U_{p , k}(SOC_k)-U_{n , k}(SOC_k)+f(I_k)+ν_k (28)

In formula, v_kBe average be zero, covariance be the white Gaussian noise of R.

Step 3: average and covariance initialize:

X₀=E [x (0)] (29)

P₀=E [(x (0)-X₀)(x(0)-X₀)] (30)

Step 4: produce 2 × n+1 sigma point, calculating respective weights:

$\left\{\begin{array}{c}{\hat{X}}_{k-1,i}^{+}={\hat{X}}_{k-1}^{+},i=0\\ {\hat{X}}_{k-1,i}^{+}={\hat{X}}_{k-1}^{+}+\sqrt{(n+\mathrm{\λ})P_{k-1}^{+}},i=1:n\\ {\hat{X}}_{k-1,i}^{+}={\hat{X}}_{k-1}^{+}-\sqrt{(n+\mathrm{\λ})P_{k-1}^{+}},i=n+1:2n\end{array}\right.---\left(31\right)$

$W_{\left(i\right)}^m=W_{\left(i\right)}^c=\{\begin{array}{cc}\mathrm{\λ}/(\mathrm{\λ}+n)& i=0\\ 1/\[2*(\mathrm{\λ}+n)\]& i\≠0\end{array}---\left(32\right)$

For electrochemical model, n represents state variable dimension, and λ is proportionality coefficient, for regulating Sigma point and the interval of reset condition point, meets λ+n=3 under normal circumstances, it is also possible to finely tune according to actual conditions.

Step 5: calculating Sigma point is through the result of nonlinear transformation:

${\hat{X}}_{k,i}^{-}=f({\hat{X}}_{k-1,j}^{+},u_{k-1}),i=0:2n---\left(33\right)$

Step 6: previous step result is weighted, asks for average and covariance:

${\hat{X}}_k^{-}=\underset{i=0}{\overset{2n}{\Σ}}{\mathrm{\ω}}_{\left(i\right)}^m{\hat{X}}_{k,i}^{-}---\left(34\right)$

$P_k^{-}=\underset{i=0}{\overset{2n}{\Σ}}{\mathrm{\ω}}_{\left(i\right)}^c\[({\hat{X}}_{k,i}^{-}-{\hat{X}}_k^{-}){({\hat{X}}_{k,i}^{-}-{\hat{X}}_k^{-})}^T\]+Q---\left(35\right)$

Step 7: quantity of state needed before measurement equation revise Sigma point:

$\left\{\begin{array}{c}s{\hat{X}}_{k,i}^{-}={\hat{X}}_k^{-}\\ s{\hat{X}}_{k,i}^{-}={\hat{X}}_k^{-}+\sqrt{(n+\mathrm{\λ})P_k^{-}},i=1:n\\ s{\hat{X}}_{k,i}^{-}={\hat{X}}_k^{-}-\sqrt{(n+\mathrm{\λ})P_k^{-}},i=n+1:2n\end{array}\right.---\left(36\right)$

Step 8: ask and revise the observation predicted value of Sigma point and covariance:

${\hat{Y}}_{k,i}=h(s{\hat{X}}_{k,i}^{-},u_k)---\left(37\right)$

${\hat{Y}}_k=\underset{i=0}{\overset{2n}{\Σ}}{\mathrm{\ω}}_{\left(i\right)}^c{\hat{Y}}_{k,i}---\left(38\right)$

$P_y=\underset{i=0}{\overset{2n}{\Σ}}{\mathrm{\ω}}_{\left(i\right)}^c\[({\hat{Y}}_{k,i}-{\hat{Y}}_k){({\hat{Y}}_{k,i}-{\hat{Y}}_k)}^T\]+R---\left(39\right)$

$P_{xy}=\underset{i=0}{\overset{2n}{\Σ}}{\mathrm{\ω}}_{\left(i\right)}^c\[(s{\hat{X}}_{k,i}^{-}-{\hat{X}}_k^{-}){({\hat{Y}}_{k,i}-\hat{Y})}^T\]---\left(40\right)$

Step 9: seek kalman gain:

K=P_xy(P_y)^-1 (41)

Step 10: ask the measurement of state variable average and covariance to update:

${\hat{X}}_k^{+}={\hat{X}}_k^{-}+K\left(y\right(k)-{\hat{Y}}_k)---\left(42\right)$

$P_k^{+}=P_k^{-}-{\mathrm{KP}}_y{K}^T---\left(43\right)$

Unscented kalman filtering is loop iteration process,For the latest estimated value of current time, it is current time SOC estimation,For state space for the estimate of observed quantity, can be used to analysis modeling error.

Claims (3)

1. charge states of lithium ion battery On-line Estimation method based on extension individual-particle model, it is characterised in that comprise the following steps:

Step 1: set up the individual-particle model of lithium ion battery；

Step 2: solve liquid phase lithium concentration distribution problem based on BP neutral net, optimizes individual-particle model；

Step 3: based on the individual-particle model after optimizing, uses Unscented kalman filtering to realize the On-line Estimation of charge states of lithium ion battery.

The most according to claim 1 based on extension individual-particle model, use Unscented kalman filtering to realize the online of charge states of lithium ion battery Method of estimation, it is characterised in that the specific implementation method of described step 2 is:

Consider the impact on battery terminal voltage of the liquid phase electromotive force, increase on the basis of individual-particle model and inside battery liquid phase lithium concentration distribution is asked Solve, thus improve individual-particle model simulation accuracy under middle high magnification operating mode.Specifically comprise the following steps that in detail

(1) input quantity and the output quantity of BP neutral net are determined；

The input quantity of BP neutral net is the average lithium concentration of positive pole solid phase, the average lithium concentration of negative pole solid phase, positional information (x) and battery Operating current, output quantity is liquid phase lithium concentration.

(2) training sample of BP neutral net is obtained；

Utilize COMSOL simulation software, relevant operating mode is set and (includes the constant-current discharge operating mode of each discharge-rate, cycle pulse electric discharge operating mode, perseverance Stream constant-voltage charge operating mode and self-defined operating mode), the pseudo-two-dimensional numerical model of lithium ion battery is solved, obtains the both positive and negative polarity under each operating mode solid Phase average lithium concentration and the distribution of liquid phase lithium concentration, as the training sample of BP neutral net.

(3) training sample normalized；

Input packet in training sample contains four, and order of magnitude difference is relatively big, for ensureing each factor par, accelerates convergence rate, to data It is normalized, is converted into scope value in [0,1] intervalNormalization formula is as shown in (1):

$\hat{x}=\frac{x-x_{min}}{x_{max}-x_{min}}---\left(1\right)$

In formula,Value after processing for input data normalization, x is input data, x_maxFor the maximum in input data, x_minFor input data In minimum of a value.

(4) training BP neutral net, determines the input weights of BP neutral net, output weights and threshold value；

Utilize the training sample training BP neutral net that in step (3), normalized is crossed, and liquid phase lithium ion BP neutral net exported is dense Degree compares with the liquid phase lithium concentration in corresponding training sample, until the mean square deviation of BP neural metwork training reaches requirement, determines BP god Input weights, output weights and threshold value through network；

(5) the BP Neural Network Optimization individual-particle model trained is utilized；

By the average lithium concentration of positive pole solid phase of current time, the average lithium concentration of negative pole solid phase, positional information (x) and battery operated electric current first It is normalized, then inputs the BP neutral net trained, obtain the liquid phase lithium concentration of position required by current time.

The most according to claim 1 based on extension individual-particle model, use Unscented kalman filtering to realize the online of charge states of lithium ion battery Method of estimation, it is characterised in that the specific implementation method of described step 3 is:

(1) ampere-hour integration method formula is carried out sliding-model control, obtains Unscented kalman filtering and estimate the state equation of SOC, as shown in formula (2):

${\mathrm{SOC}}_k={\mathrm{SOC}}_{k-1}-\frac{I_{k-1}{T}_s}{C_N}---\left(2\right)$

In formula, T_sFor sampling time, C_NFor battery rated capacity, I is battery operated electric current, discharges for just, is charged as bearing.

Here SOC is defined as formula (3), (4):

$SOC=\frac{\frac{c_{n,\mathrm{\α}vg}^s}{c_{n,\max }^s}-{\mathrm{\θ}}_{n,0\%}}{{\mathrm{\θ}}_{n,100\%}-{\mathrm{\θ}}_{n,0\%}}---\left(3\right)$

$SOC=\frac{\frac{c_{p,avg}^s}{c_{p,max}^s}-{\mathrm{\θ}}_{p,0\%}}{{\mathrm{\θ}}_{p,100\%}-{\mathrm{\θ}}_{p,0\%}}---\left(4\right)$

${\mathrm{\θ}}_i=\frac{c_{i,avg}^s}{c_{i,\max }^s},i=p,n---\left(5\right)$

In formula:For the average lithium concentration of both positive and negative polarity solid phase,For both positive and negative polarity solid phase maximum lithium concentration, θ_100%For state-of-charge It is stoichiometric proportion when 100%, θ_0%Being stoichiometric proportion when 0% for state-of-charge, n is negative pole, and p is positive pole.

(2) based on the individual-particle model after BP Neural Network Optimization, draw average lithium in lithium ion battery terminal voltage and both positive and negative polarity active particle from The relational expression of sub-concentration, will estimate the observational equation of SOC as Unscented kalman filtering after its sliding-model control.

(3) charge states of lithium ion battery On-line Estimation is realized based on Unscented kalman filtering.