CN106383322A - Multi-time-scale double-UKF adaptive estimation method of SOC and battery capacity C - Google Patents

Abstract

The invention discloses a multi-time-scale double-UKF adaptive estimation method of an SOC and a battery capacity C. Firstly, a battery state space equation is established; the multi-time-scale double-UKF adaptive estimation method is used to estimate the SOC and the battery capacity C; the system parameters, state variables and system noise for a macro UKF and a micro UKF are initialized; the prediction equation of the macro UKF is updated; a suitable sigma point is selected to update the prediction equation of the micro UKF, and the process noise of the system is updated; the correction equation of the micro UKF is used, and the state variable of a micro Kalman filter is estimated; when a double-time scale approaches, the state estimation value of the micro Kalman filter is transmitted to a macro Kalman filter as a measurement value; the data of the micro Kalman filter is updated, the measurement of the macro Kalman filter is corrected, and a battery parameter is updated. According to the method, the estimation precision and the stability of a power battery SOC by a BMS can be improved.

Description

A kind of double UKF adaptive estimation SOC of Multiple Time Scales and the method for battery capacity C

Technical field

The present invention relates to the power battery management system field of new-energy automobile, the double UKF of specifically a kind of Multiple Time Scales Adaptive estimation SOC and the method for battery capacity C.

Background technology

Under the historical background of energy-conserving and environment-protective, new-energy automobile becomes the inexorable trend of China Automobile Industry.Electrokinetic cell There is provided power for New-energy electric vehicle, be one of core component of electric automobile, the performance of electrokinetic cell determines completely The performance of new energy electric motor vehicle.Battery management system (Battery Management System, abbreviation BMS) is exactly mainly In order to improve the utilization rate of battery, prevent battery from overcharge and overdischarge occurring, extend the service life of battery, monitoring electricity The state in pond.Wherein, the state-of-charge (State of Charge, abbreviation SOC, represented with z) of electrokinetic cell is important in BMS Parameter, its evaluation method is the key technology in BMS.

It is that the state-of-charge SOC of battery is set up as quantity of state based on the method for battery model estimated driving force battery SOC The state-space model of the standard of rising is thus realize electrokinetic cell SOC estimation.The method can directly be applied empty based on battery status Between model Kalman filter method.With respect to other SOC estimation method, the ratio of Kalman filter method application is wide, it It is a kind of time domain method of estimation, the state space thought in modern control theory is incorporated in optimal filter theory, can process Time-varying system, and Kalman filter adopts recursive calculation method, and amount of calculation data amount of storage is little, is easy to computer and counts online Calculate, and degree of accuracy, robustness are good.Wherein, lossless Kalman filter (Unscented Kalman Filter, abbreviation UKF) side Method is a kind of method more than the comparison of research in the estimation of electrokinetic cell SOC, is particularly well-suited to picture electrokinetic cell this non-by force Linear system, it is possible to obtain the higher SOC value of degree of accuracy.

Content of the invention

It is an object of the invention to provide a kind of raising BMS is to the estimation precision of electrokinetic cell SOC and estimation stability The double UKF adaptive estimation SOC of Multiple Time Scales and the method for battery capacity (being represented with C), to solve to carry in above-mentioned background technology The problem going out.

For achieving the above object, the present invention provides following technical scheme：

A kind of double UKF adaptive estimation SOC of Multiple Time Scales and the method for battery capacity C, comprise the steps：

Step one, sets up battery status space equation；Shown in battery status space equation such as formula (1)：

$\left\{\begin{array}{c}{x}_{k,l+1}=F(x_{k,l},{\mathrm{\θ}}_k,u_{k,l})+w_{k,l}\\ Y_{k,l}=g(x_k,u_k)+v_{k,l}\\ w_{k,l}~(0,Q_k)\\ v_{k,l}~(0,R_k)\end{array}\right.---\left(1\right)$

Wherein, x_k,lFor state vector, u_k,lFor deterministic input quantity, Y_k,lFor output vector；Nonlinear function F (x_k,l, θ_k,u_k,l) and g (x_k,u_k) with regard to state continuously differentiable；w_k,lAnd ν_k,lThe turbulent noise of the system of being respectively and observation noise, both It is white Gaussian noise；Q_kFor system disturbance covariance matrix, R_kFor observation noise covariance matrix；

Step 2, using Multiple Time Scales double UKF adaptive approach estimation SOC and battery capacity C；

(1) initialize to for the systematic parameter of grand UKF and micro- UKF and state variable and system noise；

(2) update the predictive equation of grand UKF；

(3) suitable sigma point is selected to update the predictive equation of micro- UKF, and the process noise w of more new system_k-1,l；

(4) utilize the correction equation of micro- UKF, estimate the state variable of micro- Kalman filter；

(5) when multiple time scale model convergence, the state estimation of micro- Kalman filter is passed to grand Kalman filter In, as measured value；

(6) data of micro- Kalman filter is updated, to carry out next circulation；

(7) the measurement correction of grand Kalman filter, updates battery parameter.

As the further scheme of the present invention：In step one, for single order RC battery model, electrokinetic cell state space Equation is：

$\left\{\begin{array}{c}{\stackrel{\·}{U}}_D=-\frac{U_D}{C_{Diff}{R}_{Diff}}+\frac{i_L}{C_{Diff}}\\ U_{cell}=U_{OCV}-U_D-i_L{R}_0\end{array}\right.---\left(2\right)$

Wherein, U_OCVFor battery open circuit voltage；

By Experimental Identification, determine U_OCV：

$U_{OCV}=K_0+\frac{K_l}{z_k}+K_2{z}_k+K_3\ln \left(z_k\right)+K_{4}ln(1-z_k)---\left(3\right).$

As the further scheme of the present invention：In step 2, UKF adaptive approach step is described as follows：

(1) select n+1 sigma point；

(2) predicted state value；

(3) predictive filtering varivance matrix；

(4) measure renewal equation；

(5) calculate Kalman gain；

(6) state and error update equation.

As the further scheme of the present invention：Place in step 2, in step 2, to process noise and observation noise Reason uses UKF adaptive approach, and computing formula is as follows：

${\mathrm{\μ}}_k=U_k^l-K_0+\frac{K_1}{z_k}+K_2{z}_k+K_3\ln \left(z_k\right)+K_4\ln (1-z_k)+U_K^D-R_0{i}_k---\left(4\right)$

$F_k=\frac{{\mathrm{\Σ}}_{n=k-l+1}^k{\mathrm{\μ}}_n{\mathrm{\μ}}_n^T}{M}---\left(5\right)$

$v_k=F_k+\underset{i=0}{\overset{2}{\Σ}}{W}^{\left(i\right)}(U_{k|k-1}^{\left(i\right)}-U_k^t+{\mathrm{\μ}}_k){(U_{k|k-1}^{\left(i\right)}-U_k^t+{\mathrm{\μ}}_k)}^T---\left(6\right)$

$Q_k=K_k{F}_k{K}_k^T---\left(7\right).$

As the further scheme of the present invention：In step 2, the estimation to battery capacity C is described as follows：

(1) battery capacity C is updated, and battery capacity renewal is divided into larger, accurate, less three kinds；

(2) battery capacity C is substituted into the estimation carrying out SOC in micro- UKF；

(3) input estimating SOC estimation as battery capacity C, thus obtain the value of accurate battery capacity C.

In view of battery capacity C with can measure terminal voltage U_iThere is no stronger relation, and load current i and C has direct pass System, but the impact very little to C for the accumulation of electric current in a short time, this make accurately to estimate C relatively difficult it is contemplated that two times The double UKF adaptive approach of yardstick, can amplify this effect by the accumulation of long period, and considers that SOC is held with battery The relation of amount C has

$d_k=z_{k,l}=z_{k,0}+\frac{T}{C_k^{-}}\underset{j=0}{\overset{L-1}{\Σ}}{n}_{k,j}{i}_{k,j}---\left(8\right)$

Here use the time scale difference of two wave filter, SOC is put to the effect of battery capacity C in other words by i Greatly, and using the output of micro- Kalman filter as measured value, the state variable of grand Kalman filter is modified, simultaneously UKF using also the required precision of the SOC value that micro- UKF estimates being decreased.

Compared with prior art, the invention has the beneficial effects as follows：

The adaptive estimation method of the double UKF of Multiple Time Scales proposed by the present invention, improves by using two UKF wave filter BMS is to the estimation precision of electrokinetic cell SOC and estimation stability.One of UKF wave filter is micro- Kalman filter, carries out The estimation of battery status parameter (as SOC)；Another UKF wave filter is grand Kalman filter, for estimating the parameter of battery (as battery capacity C).Intensity of variation speed additionally, due to institute's estimator is different, when between two Kalman filter with difference Between the yardstick cycle carry out exchange and the renewal of data, be simultaneously introduced self-adaptive link to process the problem of noise.

Brief description

Fig. 1 is electrokinetic cell single order RC illustraton of model；

Fig. 2 is the double UKF adaptive algorithm frame diagram of Multiple Time Scales；

Fig. 3 is self-adaptive link flow chart；

Fig. 4 is the estimation schematic diagram of battery capacity.

Specific embodiment

Below in conjunction with the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described, Obviously, described embodiment is only a part of embodiment of the present invention, rather than whole embodiments.Based in the present invention Embodiment, the every other embodiment that those of ordinary skill in the art are obtained under the premise of not making creative work, all Belong to the scope of protection of the invention.

Due to the uncertainty of battery model, the strong jamming of electrokinetic cell surrounding and very noisy, electrokinetic cell old Changing leads to battery parameter to have the factors such as changeableness, and the estimation precision of SOC and battery capacity can reduce it is therefore desirable to battery mould The parameter of type is updated.The adaptive estimation method of the double UKF of Multiple Time Scales proposed by the present invention is filtered by using two UKF Ripple device is solving these problems.One of UKF wave filter is micro- Kalman filter, carries out battery status parameter (as SOC) Estimation；Another UKF wave filter is grand Kalman filter, for estimating the parameter (as battery capacity C) of battery.In addition by Different in the intensity of variation speed of institute's estimator, between two Kalman filter, data is carried out with the different time scales cycle Exchange and update, be simultaneously introduced self-adaptive link to process the problem of noise.

Embodiment 1

Refer to Fig. 1-4, in the embodiment of the present invention, a kind of double UKF adaptive estimation SOC of Multiple Time Scales and battery capacity The method of C is described in detail.

Step one, sets up battery status space equation；

Step 2, using Multiple Time Scales double UKF adaptive approach estimation SOC and battery capacity C.

In step one, the electrokinetic cell state space equation of foundation is：

$\left\{\begin{array}{c}{x}_{k,l+1}=F(x_{k,l},{\mathrm{\θ}}_k,u_{k,l})+w_{k,l}\\ Y_{k,l}=g(x_k,u_k)+v_{k,l}\\ w_{k,l}~(0,Q_k)\\ v_{k,l}~(0,R_k)\end{array}\right.\mathrm{...}(1-1)$

Wherein, x_k,lFor state vector, u_k,lFor deterministic input quantity, Y_k,lFor output vector；Nonlinear function F (x_k,l, θ_k,u_k,l) and g (x_k,u_k) with regard to state continuously differentiable；w_k,lAnd ν_k,lThe turbulent noise of the system of being respectively and observation noise, both It is white Gaussian noise；Q_kFor system disturbance covariance matrix, R_kFor observation noise covariance matrix.

For single order RC battery model, can state as：

$\{\begin{array}{c}{\stackrel{\·}{U}}_D=-\frac{U_D}{C_{Diff}{R}_{Diff}}+\frac{i_L}{C_{Diff}}\\ U_{cell}=U_{OCV}-U_D-i_L{R}_0\end{array}\mathrm{...}(1-2)$

Wherein, U_OCVFor battery open circuit voltage.

By Experimental Identification it may be determined that U_OCV：

$U_{OCV}=K_0+\frac{K_l}{z_k}+K_2{z}_k+K_3\ln \left(z_k\right)+K_{4}ln(1-z_k)\mathrm{...}(1-3)$

Because model parameter change is slow and the sampling time is sufficiently small, and by U_DSolve and be expressed as discrete form simultaneously：

$U_{D\left(\right(k+1)T)}=\exp (-\frac{T}{C_{Diff}{R}_{Diff}})U_D\left(kT\right)+R_{Diff}{i}_L\left(kT\right)(1-\exp (-\frac{T}{C_{Diff}{R}_{Diff}}\left)\right)\mathrm{...}(1-4)$

Wherein C_DiffR_DiffValue typically can be regarded as constant, τ, by recognize τ=35.6, then formula (1-4) can be write as：

$U_{k,l}^D\left(\right(k+1\left)T\right)=\exp (-\frac{T}{\mathrm{\τ}})U_{k,l-1}^D\left(kt\right)+R_{Diff}{i}_{k,l-1}\left(kT\right)(1-\exp (-\frac{T}{\mathrm{\τ}}\left)\right)\mathrm{...}(1-5)$

The theoretical calculation formula of SOC is：

$SOC=z_{k,l}=z_{0,0}-{\∫}_{t_{0,0}}^{t_{kj}}\frac{\mathrm{\η}\left(i_L\right(\mathrm{\τ}))i_L\left(\mathrm{\τ}\right)}{C}d\mathrm{\τ}\mathrm{...}(1-6)$

η(i_L(τ)) it is modifying factor under different discharge-rates；C is battery maximum available, is time temperature function. Then the discrete form of formula (1-6) is

$z_{k,l}=z_{k,l-1}-\frac{\mathrm{\η}\left(i_L\right(\mathrm{\τ}))i_L\left(\mathrm{\τ}\right)T}{C}\mathrm{...}(1-7)$

The form of formula (1-6), (1-7) state space of being write as is had：

$\left[\begin{array}{c}{U}_{k,l}^D\\ z_{k,l}\end{array}\right]=\left[\begin{array}{c}{U}_{k,l-1}^D\\ z_{k,l-1}\end{array}\right]+\left[\begin{array}{c}{R}_{Diff}(1-\exp (-\frac{T}{\mathrm{\τ}}\left)\right)\\ -\frac{\mathrm{\η}\left(i_L\right(\mathrm{\τ}))T}{C}\end{array}\right]i_{k,l-1}\mathrm{...}(1-8)$

State-space expression based on above-mentioned formula system is as follows：

$\left\{\begin{array}{c}{x}_{k,l+1}=F(x_{k,l},\mathrm{\θ},u_{k,l})=\left[\begin{array}{cc}\exp (-\frac{T}{\mathrm{\τ}})& 0\\ 0& 1\end{array}\right]x_{k,l}+\left[\begin{array}{c}{R}_{Diff}(1-\exp (-\frac{T}{\mathrm{\τ}}\left)\right)\\ -\frac{\mathrm{\η}\left(i_L\right(\mathrm{\τ}))T}{C}\end{array}\right]u_{k,l}\\ y_{k,l}=G(x_{k,l},\mathrm{\θ},u_{k,l})=U_{OCV}-U_{k,l}^D-R_0{u}_{k,l}\end{array}\right.\mathrm{...}(1-9)$

Wherein, parameter type is as follows：

$\left\{\begin{array}{c}{x}_{k,l}=\left[\begin{array}{c}{U}_{k,l}^D\\ z_{k,l}\end{array}\right]\\ {\mathrm{\θ}}_k=\[R_0,C\]\\ Y_{k,l}=U_{k,l}^t\\ u_{k,l}=i_{k,l}\end{array}\right.\mathrm{...}(1-10)$

In step 2, UKF adaptive approach step is described as follows：

(1) select n+1 sigma point；

$\left\{\begin{array}{c}{x}^{\left(0\right)}=\stackrel{\‾}{x}=E\left(x\right)\\ x^{\left(i\right)}=x^{\left(0\right)}+{\left(\sqrt{(n+k)P}\right)}_i^T,i=1,\mathrm{...},n\\ x^{(n+i)}=x^{\left(0\right)}-{\left(\sqrt{(n+k)P}\right)}_i^T,i=1,\mathrm{...},n\end{array}\right.\mathrm{...}(2-1)$

Symmetric sampling strategy is used to sigma point, then corresponding weighted value is：

$\left\{\begin{array}{c}{W}^{\left(0\right)}=\frac{k}{n+k}\\ W^{\left(i\right)}=\frac{1}{2(n+k)},i=1,\mathrm{...},2n\end{array}\right.\mathrm{...}(2-2)$

(2) predicted state value；

$\left\{\begin{array}{c}{x}_{k,k-1}^{\left(i\right)}=F(x_{k-1,k-1}^{\left(i\right)},u_k)+w_k\\ {\hat{x}}_{k,k-1}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}{x}_{k,k-1}^{\left(i\right)}\end{array}\right.\mathrm{...}(2-3)$

(3) predictive filtering varivance matrix；

$P_{k,k-1}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[x_{k,k-1}^{\left(i\right)}-{\hat{x}}_{k,k-1}\]\×{\[x_{k,k-1}^{\left(i\right)}-{\hat{x}}_{k,k-1}\]}^T+Q_k\mathrm{...}(2-4)$

(4) measure renewal equation；

$\left\{\begin{array}{c}{y}_{k,k-1}^{\left(i\right)}=g(x_{k,k-1}^{\left(i\right)},u_k)+w_k\\ {\hat{y}}_{k,k-1}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}{y}^{\left(i\right)}{y}_{k,k-1}^{\left(i\right)}\end{array}\right.\mathrm{...}(2-5)$

(5) calculate Kalman gain；

$\left\{\begin{array}{c}{P}_{k,k-1}^{xy}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[x_{k,k-1}^i-{\hat{x}}_{k,k-1}\]\×{\[x_{k,k-1}^i-{\hat{x}}_{k,k-1}\]}^T\\ P_{k,k-1}^{yy}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[y_{k,k-1}^i-{\hat{y}}_{k,k-1}\]\×{\[y_{k,k-1}^i-{\hat{y}}_{k,k-1}\]}^T+R_k\\ K_k=P_{k,k-1}^{xy}{P}_{k,k-1}^{yy-1}\end{array}\right.\mathrm{...}(2-6)$

(6) state and error update equation.

$\left\{\begin{array}{c}{\hat{x}}_{k,k}={\hat{x}}_{k,k-1}+K_k(y_k-{\hat{y}}_{k,k-1})\\ P_{k,k}=P_{k,k-1}+K_k{P}_{k,k-1}^{yy}{K}_k^T\end{array}\right.\mathrm{...}(2-7)$

In step 2, self-adaptive link is described as follows：

Process to process noise and observation noise uses adaptive algorithm, and adaptive algorithm is as shown in figure 3, calculate public Formula is as follows：

${\mathrm{\μ}}_k=U_k^l-K_0+\frac{K_1}{z_k}+K_2{z}_k+K_{3}ln\left(z_k\right)+K_{4}ln(1-z_k)+U_K^D-R_0{i}_k\mathrm{...}(2-8)$

$F_k=\frac{{\mathrm{\Σ}}_{n=k-l+1}^k{\mathrm{\μ}}_n{\mathrm{\μ}}_n^T}{M}\mathrm{...}(2-9)$

$v_k=F_k+\underset{i=0}{\overset{2}{\Σ}}{W}^{\left(i\right)}(U_{k|k-1}^{\left(i\right)}-U_k^t+{\mathrm{\μ}}_k){(U_{k|k-1}^{\left(i\right)}-U_k^t+{\mathrm{\μ}}_k)}^T\mathrm{...}(2-10)$

$Q_k=K_k{F}_k{K}_k^T\mathrm{...}(2-11)$

In step 2, the estimation to battery capacity C is as shown in figure 4, be described as follows：

(1) battery capacity C is updated, and capacity renewal is divided into larger, accurate, less three kinds；

(2) battery capacity C is substituted into the estimation carrying out SOC in micro- UKF, due to the difference of time scale, can carry out repeatedly The estimation of SOC；

(3) input estimating SOC estimation as battery capacity C, thus obtain the value of accurate battery capacity C.

In view of battery capacity C with can measure terminal voltage U_iThere is no stronger relation, and load current i and battery capacity C There is direct relation, but the impact very little to battery capacity C for the accumulation of electric current in a short time, and this makes accurately to estimate battery capacity C relatively difficult it is contemplated that the double UKF adaptive approachs of two time scales, can be amplified this by the accumulation of long period Effect, and consider that SOC and the relation of battery capacity C have

$d_k=z_{k,l}=z_{k,0}+\frac{T}{C_k^{-}}\underset{j=0}{\overset{L-1}{\Σ}}{n}_{k,j}{i}_{k,j}\mathrm{...}(2-12)$

Here use the time scale difference of two wave filter, SOC is put to the effect of battery capacity C in other words by i Greatly, and using the output of micro- Kalman filter as measured value, the state variable of grand Kalman filter is modified, simultaneously UKF using also the required precision of the SOC value that micro- UKF estimates being decreased.

Using the double UKF adaptive approach of Multiple Time Scales, step 2, estimates that SOC and the step of battery capacity C are described as follows：

(1) initialize to for the systematic parameter of grand UKF and micro- UKF and state variable and system noise；

$\left\{\begin{array}{c}{\mathrm{\θ}}_0=E\[{\mathrm{\θ}}_0\],P_{{\mathrm{\θ}}_0}=E\[({\mathrm{\θ}}_0-{\widehat{\mathrm{\θ}}}_0){({\mathrm{\θ}}_0-{\widehat{\mathrm{\θ}}}_0)}^T\]\\ x_{0,0}=E\[x_{0,0}\],P_{x_{0,0}}=E\[(x_{0,0}-{\hat{x}}_{0,0}){(x_{0,0}-{\hat{x}}_{0,0})}^T\]\\ {\mathrm{\ω}}_{0,0}=E\[{\mathrm{\ω}}_{0,0}\]\\ v_{0,0}=E\[v_{0,0}\]\\ {\mathrm{\ρ}}_0=E\[{\mathrm{\ρ}}_0\]\end{array}\right.\mathrm{...}(2-13)$

Wherein, k ∈ { 1 ..., ∞ }

(2) update the predictive equation of grand UKF；

$\{\begin{array}{c}{\widehat{\mathrm{\θ}}}_k^{-}={\widehat{\mathrm{\θ}}}_{k-1}^{-}\\ P_{{\mathrm{\θ}}_k}=P_{{\mathrm{\θ}}_{k-1}}+{\mathrm{\ρ}}_{k-1}\end{array}\mathrm{...}(2-14)$

(3) suitable sigma point is selected to update the predictive equation of micro- UKF according to formula (2-1) (2-2), and according to formula (2-8) the process noise w of (2-9) (2-10) (2-11) more new system_k-1,l, using initialized noise during first time；

$\left\{\begin{array}{c}{\hat{x}}_{k,l}^{-}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}{x}_{k,l-1}^{\left(i\right)}\\ {\hat{P}}_{x_{k,l-1}}^{-}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[x_{k,l-1}^{\left(i\right)}-{\hat{x}}_{k-1,l}^{-}\]\×{\[x_{k,l-1}^{\left(i\right)}-{\hat{x}}_{k-1,l}^{-}\]}^T+Q_{k,l-1}\\ y_{k,l-1}^i=g(x_{k,l-1}^{\left(i\right)},u_{k,l-1})+w_{k,l-1}\end{array}\right.\mathrm{...}(2-15)$

(4) utilize the correction equation of micro- UKF, estimate the state variable of micro- Kalman filter.

$\left\{\begin{array}{c}{y}_{k,l-1}^i=g(x_{k,l-1}^{\left(i\right)},u_{k,l-1})+w_{k,l-1}\\ {\hat{y}}_{k,l-1}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}{y}_{k,l-1}^i\\ P_{k,l}^{yy}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[y_{k,l-1}^i-{\hat{y}}_{k,l-1}\]\×{\[y_{k,l-1}^i-{\hat{y}}_{k,l-1}\]}^T+R_{k,l-1}\\ P_{k,l}^{xy}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[x_{k,l-1}^i-{\hat{x}}_{k,l-1}^{-}\]\×{\[x_{k,l-1}^i-{\hat{x}}_{k,l-1}^{-}\]}^T\\ K_{k,l}=P_{k,l}^{xy}{P}_{k,l}^{yy-1}\\ {\hat{x}}_{k,l}={\hat{x}}_{k,l-1}^{-}+K_{k,l}(y_k-{\hat{y}}_{k,l-1})\\ P_{k,l}={\hat{P}}_{x_{k,l-1}}^{-}+K_{k,l}{P}_{k,l}^{yy}{K}_{k,l}^T\end{array}\right.\mathrm{...}(2-16)$

(5) when multiple time scale model convergence, the state estimation of micro- Kalman filter is passed to grand Kalman filter In, as measured value.

$\left\{\begin{array}{c}{y}_{k,l}^i=g(x_{k,L-1}^{\left(i\right)},u_{k,l-1})+w_{k,L-1}\\ {\hat{y}}_{k,L-1}=\underset{0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}{y}_{k,L-1}^i\\ P_{k,L}^{yy}=\underset{0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[y_{k,L-1}^i-{\hat{y}}_{k,L-1}\]\×{\[y_{k,L-1}^i-{\hat{y}}_{k,L-1}\]}^T+R_{k,L-1}\\ P_{k,L}^{xy}=\underset{0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[x_{k,L-1}^{\left(i\right)}-{\hat{x}}_{k,L}^{-}\]\×{\[x_{k,L-1}^{\left(i\right)}-{\hat{x}}_{k,L}^{-}\]}^T\\ K_{k,L}=P_{k,L-1}^{xy}{P}_{k,L-1}^{yy-1}\\ {\hat{x}}_{k,l}={\hat{x}}_{k-1,l}^{-}+K_{k,L}(y_k-{\hat{y}}_{k,L-1})\\ P_{k,L}={\hat{P}}_{x_{k,l-1}}^{-}+K_{k,L}{P}_{k,l}^{yy}{K_{k,L}}^T\end{array}\right.\mathrm{...}(2-17)$

(6) data of micro- Kalman filter is updated, to carry out next circulation；

$\left\{\begin{array}{c}{\hat{x}}_{k+1,0}={\hat{x}}_{k,L}\\ P_{k+1,0}=P_{k,L}\\ y_{k+1,0}=y_{k,L}\\ u_{k+1,0}=u_{k,L}\end{array}\right.---(2-18)$

(7) the measurement correction of grand Kalman filter, updates battery parameter.

$\left\{\begin{array}{c}{\mathrm{\θ}}_k^{\left(i\right)}={\widehat{\mathrm{\θ}}}_{k-1}+e_k\\ {\widehat{\mathrm{\θ}}}_k^{-}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}{\mathrm{\θ}}_k^i\\ {\hat{P}}_{{\mathrm{\θ}}_k}^{-}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[{\mathrm{\θ}}_k^{\left(i\right)}-{\widehat{\mathrm{\θ}}}_k^{-}\]\×{\[{\mathrm{\θ}}_k^{\left(i\right)}-{\widehat{\mathrm{\θ}}}_k^{-}\]}^T+{\mathrm{\ρ}}_k\\ d_k^{\left(i\right)}=h({\mathrm{\θ}}_k^{\left(i\right)},u_k)\\ {\hat{d}}_k=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}{d}_k^{\left(i\right)}\\ P_{{\mathrm{\θ}}_k}^{yy}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[d_k^{\left(i\right)}-{\hat{d}}_k\]\×{\[d_k^{\left(i\right)}-{\hat{d}}_k\]}^T\\ P_{{\mathrm{\θ}}_k}^{xy}=\underset{i=0}{\overset{2n}{\Σ}}{W}^{\left(i\right)}\[{\mathrm{\θ}}_k^{\left(i\right)}-{\widehat{\mathrm{\θ}}}_k^{-}\]\×{\[{\mathrm{\θ}}_k^{\left(i\right)}-{\widehat{\mathrm{\θ}}}_k^{-}\]}^T\\ K_{k+1}=P_{{\mathrm{\θ}}_k}^{xy}{P}_{{\mathrm{\θ}}_k}^{yy-1}\\ {\widehat{\mathrm{\θ}}}_{k+1}={\widehat{\mathrm{\θ}}}_k^{-}+K_{k+1}(d_k-{\hat{d}}_k)\\ P_{{\mathrm{\θ}}_k}=P_{{\mathrm{\θ}}_k}^{-}+K_{k+1}{P}_{{\mathrm{\θ}}_k}^{yy}{K_{k+1}}^T\end{array}\right.\mathrm{...}(2-19).$

It is obvious to a person skilled in the art that the invention is not restricted to the details of above-mentioned one exemplary embodiment, Er Qie In the case of the spirit or essential attributes of the present invention, the present invention can be realized in other specific forms.Therefore, no matter From the point of view of which point, embodiment all should be regarded as exemplary, and be nonrestrictive, the scope of the present invention is by appended power Profit requires rather than described above limits, it is intended that all in the implication and scope of the equivalency of claim by falling Change is included in the present invention.

Moreover, it will be appreciated that although this specification is been described by according to embodiment, not each embodiment only wraps Containing an independent technical scheme, only for clarity, those skilled in the art should for this narrating mode of description Using description as an entirety, the technical scheme in each embodiment can also form those skilled in the art through appropriately combined Understandable other embodiment.

Claims (5)

1. the method for a kind of double UKF adaptive estimation SOC of Multiple Time Scales and battery capacity C is it is characterised in that include following walking Suddenly：

Step one, sets up battery status space equation；Shown in battery status space equation such as formula (1)：

$\left\{\begin{array}{c}{x}_{k,l+1}=F(x_{k,l},{\mathrm{\θ}}_k,u_{k,l})+w_{k,l}\\ Y_{k,l}=g(x_k,u_k)+v_{k,l}\\ w_{k,l}~(0,Q_k)\\ v_{k,l}~(0,R_k)\end{array}\right.---\left(1\right)$

Wherein, x_k,lFor state vector, u_k,lFor deterministic input quantity, Y_k,lFor output vector；Nonlinear function F (x_k,l,θ_k, u_k,l) and g (x_k,u_k) with regard to state continuously differentiable；w_k,lAnd ν_k,lThe turbulent noise of the system of being respectively and observation noise, both are White Gaussian noise；Q_kFor system disturbance covariance matrix, R_kFor observation noise covariance matrix；

Step 2, using Multiple Time Scales double UKF adaptive approach estimation SOC and battery capacity C；

(1) initialize to for the systematic parameter of grand UKF and micro- UKF and state variable and system noise；

(2) update the predictive equation of grand UKF；

(3) suitable sigma point is selected to update the predictive equation of micro- UKF, and the process noise w of more new system_k-1,l；

(4) utilize the correction equation of micro- UKF, estimate the state variable of micro- Kalman filter；

(5) when multiple time scale model convergence, the state estimation of micro- Kalman filter is passed in grand Kalman filter, make For measured value；

(6) data of micro- Kalman filter is updated, to carry out next circulation；

(7) the measurement correction of grand Kalman filter, updates battery parameter.

2. the method for the double UKF adaptive estimation SOC of Multiple Time Scales according to claim 1 and battery capacity C, its feature It is, in step one, for single order RC battery model, electrokinetic cell state space equation is：

$\left\{\begin{array}{c}{\stackrel{\·}{U}}_D=-\frac{U_D}{C_{Diff}{R}_{Diff}}+\frac{i_L}{C_{Diff}}\\ U_{cell}=U_{OCV}-U_D-i_L{R}_0\end{array}\right.---\left(2\right)$

Wherein, U_OCVFor battery open circuit voltage；

By Experimental Identification, determine U_OCV：

$U_{OCV}=K_0+\frac{K_l}{z_k}+K_2{z}_k+K_{3}ln\left(z_k\right)+K_{4}ln(1-z_k)---\left(3\right).$

3. the method for the double UKF adaptive estimation SOC of Multiple Time Scales according to claim 1 and battery capacity C, its feature It is, in step 2, UKF adaptive approach step is described as follows：

(1) select n+1 sigma point；

(2) predicted state value；

(3) predictive filtering varivance matrix；

(4) measure renewal equation；

(5) calculate Kalman gain；

(6) state and error update equation.

4. the method for the double UKF adaptive estimation SOC of Multiple Time Scales according to claim 1 and battery capacity C, its feature It is, in step 2, the process to process noise and observation noise uses UKF adaptive approach, and computing formula is as follows：

${\mathrm{\μ}}_k=U_k^l-K_0+\frac{K_1}{z_k}+K_2{z}_k+K_{3}ln\left(z_k\right)+K_{4}ln(1-z_k)+U_K^D-R_0{i}_k---\left(4\right)$

$F_k=\frac{{\mathrm{\Σ}}_{n=k-l+1}^k{\mathrm{\μ}}_n{\mathrm{\μ}}_n^T}{M}---\left(5\right)$

$v_k=F_k+\underset{i=0}{\overset{2}{\Σ}}{W}^{\left(i\right)}(U_{k|k-1}^{\left(i\right)}-U_k^t+{\mathrm{\μ}}_k){(U_{k|k-1}^{\left(i\right)}-U_k^t+{\mathrm{\μ}}_k)}^T---\left(6\right)$

$Q_k=K_k{F}_k{K}_k^T---\left(7\right).$

5. the method for the double UKF adaptive estimation SOC of Multiple Time Scales according to claim 1 and battery capacity C, its feature It is, in step 2, estimation to battery capacity C, comprise the following steps that：

(1) battery capacity C is updated, and battery capacity renewal is divided into larger, accurate, less three kinds；

(2) battery capacity C is substituted into the estimation carrying out SOC in micro- UKF；

(3) input estimating SOC estimation as battery capacity C, thus obtain the value of accurate battery capacity C.