CN104573294A - Self-adaptive kalman filter estimation algorithm for power battery - Google Patents

Abstract

The invention discloses a self-adaptive kalman filter estimation algorithm for state of charger (SOC) for a power battery. According to the algorithm, the weighted sum of residual errors between output values measured each time and output values obtained by estimation and residual errors of the output values obtained by sigma points under various states can be obtained, then the weighted sum is regarded as an innovation to estimate the current noise covariance, the current noise covariance can be reduced along with the time, and the real-time feedback can be performed. Proved by theoretic and actual data validation, the algorithm can greatly improve the estimated accuracy of SOC.

Description

The adaptive Kalman filter algorithm for estimating of electrokinetic cell

Technical field

The present invention relates to a kind of adaptive Kalman filter algorithm for estimating of electrokinetic cell, particularly relate to adaptive noise covariance, the precision of error effect that the noise covariance being directed to the constant in the electrodeless Kalman filtering algorithm of square root brings estimation and propose the estimating algorithm in adaptive Kalman filter electricity pond dump energy (SOC).

Background technology

The state-of-charge (state of charge, SOC) of electrokinetic cell is estimated to have great importance to effective use of battery, is also one of gordian technique of battery management system.Because SOC not directly measures, and be amount of nonlinearity, also by the impact of other factors many, therefore very large to its difficulty estimated, improve estimated accuracy and be difficult to.At present conventional in engineering method is Current integrating method (ampere-hour method), but the method is responsive and easily produce cumulative errors to the initial value of SOC; The open-circuit voltage method experimentally adopted has good precision, but needs battery to leave standstill for a long time, is difficult to realize in vehicle condition; Neural network can be applied to any battery, but needs a large amount of training datas.Extended BHF approach (Extended Kalman Filter, EKF) algorithm needs calculating Jacobians matrix to make model linearization, thus introduce unnecessary linearized stability, electrodeless Kalman filtering (Unscented Kalman Filter, UKF) algorithm is a kind of new non-linear filtering method, relative EKF precision is improved, but there is the shortcoming of numerical instability, and the electrodeless Kalman filtering of square root (Square Root Unscented KalmanFilter, SR-UKF) algorithm not only has identical precision with UKF and adds the Positive of numerical stability and state covariance, but SR-UKF algorithm regards constant as noise covariance, the real-time update characteristic of noise can not be met, thus have impact on estimated accuracy.

Summary of the invention

The technical problem to be solved in the present invention is: in the electrodeless Kalman filtering algorithm of square root, constant noise covariance brings certain estimation error.In order to overcome this shortcoming, a kind of adaptive algorithm is proposed.Technical solution of the present invention is as follows:

1, the model of selected Ni-MH battery

The present invention has selected the electrochemical model of battery, and its discrete equation is as follows:

$S_{k+1}=S_k-\frac{\mathrm{\Δt}}{C_n}{I}_k+w_k---\left(1\right)$

$U_k=K_0-\frac{K_1}{S_k}-K_2{S}_k+K_3\ln \left(S_k\right)+K_4\ln (1-S_k)-{\mathrm{RI}}_k-\mathrm{hH}+v_k---\left(2\right)$

S wherein _krepresent the SOC in k moment; C _nfor the rated capacity of battery, the present invention gets 30Ah; Δ t is sampling time interval, and the present invention gets 0.5s; Subscript k represents a kth sampled point; U and I represents terminal voltage voltage and current respectively, and the present invention gathers gained by related sensor; R represents the internal resistance of cell, and the present invention needs identification, w and ν represents process noise and measurement noises respectively, is all white Gaussian noises, and lag parameter when H is charge/discharge transformation, the present invention needs identification.H is the coefficient of lag parameter, and its value is as follows:

K ₀, K ₁, K ₂, K ₃, K ₄describe battery open circuit voltage (U _{ocv, k}) and SOC(S _k) five unknown parameters of relation.

2, identification of Model Parameters

Carry out the experiment of intermittence (cycle 20min) constant-current discharge to battery at normal temperatures, integral method records battery open circuit voltage (U under calculating battery charge state (SOC) value and static condition _{ocv, k}), matching obtains SOC(S _k) and OCV relation

U _ocv,k＝F(S _k) (4)

Utilize this relation just can pick out parameter K in conjunction with least square method ₀, K ₁, K ₂, K ₃, K ₄.

Identification algorithm is as follows:

Make M _k=[1-(1/S _k)-S _kln (S _k) ln (1-S _k)], M=[M ₁m ₂l M _n] ^t

Then [K ₀k ₁k ₂k ₃k ₄] ^t=(M ^tm) ^-1u _ocv(5)

Here U _ocv=[U _ocv1u _ocv2l U _ocvN] be open-circuit voltage sequence, N represents sampling number.

The R of identification internal resistance below and discharge and recharge lag parameter H:

The voltage Y that each moment battery itself consumes can be obtained _k=F (S _k)-U _k(6)

Then [R H]=(T ^tt) ^-1t ^ty (7)

Here Y=[Y ₁y ₂l Y _n], T=[-I _k-h].(8)

3, initialization

Can initialization be: α, P ₀, wherein be the initial value of SOC, value of the present invention is 0.99; be respectively process noise covariance and measurement noises covariance initial value, the present invention gets 0.5 respectively.0.01; The value of α is by electrodeless Kalman Algorithm known 10 ^-4≤ α≤1, the present invention gets 0.001; P ₀for the initial value of the covariance of state estimation error, the present invention is taken as 0.001.

4, sigma point is calculated

{ W _ia power collection, be used for controlling the weight of each Sigma point, wherein w _i ^m=W _i ^c=1/{2 (L+ λ) }, the value of i is 1,2L2L.L is the dimension of state variable, λ=L (α ²-1) and it is scale parameter.Constant α determine Sigma point the scope of left and right, is normally placed in 10 ^-4in≤α≤1.When noise meets Gaussian distribution, the optimal value of β is 2.

By the known L=1 of model, so there are 3 sigma points.

First: second: 3rd:

Form a row vector ${\mathrm{\χ}}_{k-1}=\left[\begin{array}{ccc}{\hat{S}}_{k-1}& {\hat{S}}_{k-1}+\mathrm{\η}{P}_{k-1}& {\hat{S}}_{k-1}-\mathrm{\η}{P}_{k-1}\end{array}\right].$

5, the square root of the covariance of the state estimation error in k moment is calculated

Calculate the square root of the covariance of the state estimation error in k moment, i.e. the state estimation error covariance of electrodeless Kalman filtering (UKF, Unscented KalmanFilter) algorithm the subduplicate specific algorithm of each several part as follows:

${\mathrm{\χ}}_{k|k-1}={\mathrm{\χ}}_{k-1}-\frac{\mathrm{\Δt}}{C_n}{I}_k+w_k---\left(9\right)$

${\hat{S}}_k^{-}=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{{W_i}^m\mathrm{\χ}}_{i,k|k-1}---\left(10\right)$

χ _k|k-1represent the state value in the k moment released by the state in k-1 moment; χ _{i, k|k-1}represent the state value in i-th k moment obtained by the Sigma point estimation of the state estimation in k-1 moment, represent the weighted sum of each state estimation.

$P_k^{-}=\mathrm{qr}\left\{\left[\begin{array}{cc}\sqrt{{W_1}^c}({\mathrm{\χ}}_{1:2L,k|k-1}-{\hat{S}}_k^{-})& \sqrt{R_k^w}\end{array}\right]\right\}---\left(11\right)$

$P_{\mathrm{Sk}}^{-}=P_k^{-}\±\sqrt{\left|W_0^c\right|}({\mathrm{\χ}}_{0,k|k-1}-{\hat{S}}_k^{-}){({\mathrm{\χ}}_{0,k|k-1}-{\hat{S}}_k^{-})}^T---\left(12\right)$

be upper triangular matrix, the R factor namely in QR decomposition is also matrix $\left[\begin{array}{cc}\sqrt{{W_1}^c}({\mathrm{\χ}}_{1:2L,k|k-1}-\stackrel{W}{S_k^{-}})& \sqrt{R_k^w}\end{array}\right]$ The transposition of the Chlesky factor.It can thus be appreciated that be each several part square root.Due to may be negative value, so by $P_{\mathrm{Sk}}^{-}=P_k^{-}\±\sqrt{\left|W_0^c\right|}({\mathrm{\χ}}_{0,k|k-1}-{\hat{S}}_k^{-}){({\mathrm{\χ}}_{0,k|k-1}-{\hat{S}}_k^{-})}^T$ Overcome, in formula positive and negative by determine, for just just namely getting, for negative namely get negative.

6, the specific algorithm of time renewal and measurement updaue:

The first step: calculate the updated value exported

$U_k=K_0-\frac{K_1}{{\mathrm{\χ}}_{k|k-1}}-K_2{\mathrm{\χ}}_{k|k-1}+K_3\ln \left({\mathrm{\χ}}_{k|k-1}\right)+K_4\ln (1-{\mathrm{\χ}}_{k|k-1})-{\mathrm{RI}}_k-h_{k}H+v_k---\left(13\right)$

${\hat{U}}_k^{-}=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^m{U}_{i,k|k-1}---\left(14\right)$

U _k|k-1represent the output valve vector in the k moment calculated by each sigma point of quantity of state, U _{i, k|k-1}represent the output estimation value in the k moment that i-th sigma point calculates, i.e. U _k|k-1in element, represent the weighted sum of each estimated value, be used as the output estimation value in new moment.

Second step: measurement updaue:

1) the square root P of the covariance exporting residual error is calculated _uk, the cross covariance of state estimation error and output valve evaluated error

$P_{\mathrm{Uk}}=\mathrm{qr}\left\{\left[\begin{array}{cc}\sqrt{{W_1}^c}(U_{1:2L,k|k-1}-{\hat{U}}_k^{-})& \sqrt{R_k^v}\end{array}\right]\right\}---\left(15\right)$

$P_{\mathrm{Uk}}^{-}=P_{\mathrm{Uk}}\±\sqrt{\left|W_0^c\right|}(U_{0,k|k-1}-{\hat{U}}_k^{-}){(U_{0,k|k-1}-{\hat{U}}_k^{-})}^T---\left(16\right)$

$P_{S_k,U_k}=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^c[{\mathrm{\χ}}_{i,k|k-1}-{\hat{S}}_k^{-}]{[U_{i,k|k-1}-{\hat{U}}_k^{-}]}^T---\left(17\right)$

2) kalman gain κ is calculated _k

${\mathrm{\κ}}_k=(P_{S_k,U_k}/{P_{U_k}}^T/P_{U_k})---\left(18\right)$

3) state estimation:

${\hat{S}}_k={\hat{S}}_k^{-}+{\mathrm{\κ}}_k(U_k-{\hat{U}}_k^{-})---\left(19\right)$

4) state error covariance upgrades:

$H={\mathrm{\κ}}_k{P}_{\mathrm{Uk}}^{-}---\left(20\right)$

$P_k=P_{\mathrm{Sk}}^{-}-{\mathrm{HH}}^T---\left(21\right)$

H represent state estimation error covariance-weighted and.Be used for computing mode error covariance upgrade.

7, the real-time process of process noise covariance and measurement noises covariance

Calculate with

${\mathrm{\μ}}_k=U_k-(K_0-\frac{K_1}{S_k}-K_2{S}_k+K_3\ln \left(S_k\right)+K_4\ln (1-S_k)-{\mathrm{RI}}_k-h_{k}H+v_k)---\left(22\right)$

$F_k={\mathrm{\μ}}_k{{\mathrm{\μ}}_k}^T---\left(23\right)$

$R_k^v=F_k+\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^c(U_{i,k|k-1}-U_k){(U_{i,k|k-1}-U_k)}^T---\left(24\right)$

$R_k^w={\mathrm{\κ}}_k{F}_k{{\mathrm{\κ}}_k}^T---\left(25\right)$

μ _k(U _{i, k|k-1}-U _k) be the residual error that each Sigma point of residual sum of output quantity estimates the measurement output quantity obtained respectively.

Prove

$R_k^v=F_k+\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^c(U_{i,k|k-1}-U_k){(U_{i,k|k-1}-U_k)}^T$

$R_k^w={\mathrm{\κ}}_k{F}_k{{\mathrm{\κ}}_k}^T$

Card:

Known:

$v_k=U_k-(K_0-\frac{K_1}{S_k}-K_2{S}_k+K_3\ln \left(S_k\right)+K_4\ln (1-S_k)-{\mathrm{RI}}_k-h_{k}H)$

${\stackrel{\‾}{v}}_k=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^c(U_{i,k|k-1}-U_k)$

be each sigma point output quantity residual weighted and, as v _kvaluation.

Obvious μ again _kthe residual values of output quantity, F _kit is the residual covariance of output quantity

So measurement noises covariance estimated value be the weighted sum of each each part mentioned above:

$R_k^v=F_k+\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^c(U_{i,k|k-1}-U_k){(U_{i,k|k-1}-U_k)}^T.$

Again from the equation of state in model:

$w_k=S_{k+1}-(S_k-\frac{\mathrm{\Δt}}{C_n}{I}_k)$

And

${\hat{w}}_k={\hat{S}}_k-{\hat{S}}_k^{-}={\mathrm{\κ}}_k(U_k-{\hat{U}}_k^{-})={\mathrm{\κ}}_k{\hat{v}}_k$

for w _kestimated value

Again because

${\mathrm{\κ}}_k{\hat{v}}_k\≈{\mathrm{\κ}}_k{\mathrm{\μ}}_k$

So

$R_k^w={\hat{w}}_k{\hat{w}}_k^T={\mathrm{\κ}}_k{F}_k{{\mathrm{\κ}}_k}^T$

Card is finished.

Accompanying drawing explanation

Fig. 1 is for being 1.2v for 10 joint rated voltages, and rated capacity is that the Ni-MH battery of 30Ah is composed in series SOC value that tested object algorithm estimates and the value that original algorithm is estimated and experiment value;

Fig. 2 is for being 1.2v for 10 joint rated voltages, and rated capacity is that the Ni-MH battery of 30Ah is composed in series SOC value that tested object algorithm estimates and the precision that original algorithm is estimated;

Embodiment

6, the model of selected Ni-MH battery

The present invention has selected the electrochemical model of battery, and its discrete equation is as follows:

$S_{k+1}=S_k-\frac{\mathrm{\Δt}}{C_n}{I}_k+w_k---\left(1\right)$

$U_k=K_0-\frac{K_1}{S_k}-K_2{S}_k+K_3\ln \left(S_k\right)+K_4\ln (1-S_k)-{\mathrm{RI}}_k-\mathrm{hH}+v_k---\left(2\right)$

S wherein _krepresent the SOC in k moment; C _nfor the rated capacity of battery, the present invention gets 30Ah; Δ t is sampling time interval, and the present invention gets 0.5s; Subscript k represents a kth sampled point; U and I represents terminal voltage voltage and current respectively, and the present invention gathers gained by related sensor; R represents the internal resistance of cell, and the present invention needs identification, w and ν represents process noise and measurement noises respectively, is all white Gaussian noises, and lag parameter when H is charge/discharge transformation, the present invention needs identification.H is the coefficient of lag parameter, and its value is as follows:

K ₀, K ₁, K ₂, K ₃, K ₄describe battery open circuit voltage (U _{ocv, k}) and SOC(S _k) five unknown parameters of relation.

7, identification of Model Parameters

Carry out the experiment of intermittence (cycle 20min) constant-current discharge to battery at normal temperatures, integral method records battery open circuit voltage (U under calculating battery charge state (SOC) value and static condition _{ocv, k}), matching obtains SOC(S _k) and OCV relation

U _ocv,k＝F(S _k) (4)

Utilize this relation just can pick out parameter K in conjunction with least square method ₀, K ₁, K ₂, K ₃, K ₄.

Identification algorithm is as follows:

Make M _k=[1-(1/S _k)-S _kln (S _k) ln (1-S _k)], M=[M ₁m ₂l M _n] ^t

Then [K ₀k ₁k ₂k ₃k ₄] ^t=(M ^tm) ^-1u _ocv(5)

Here U _ocv=[U _ocv1u _ocv2l U _ocvN] be open-circuit voltage sequence, N represents sampling number.

The R of identification internal resistance below and discharge and recharge lag parameter H:

The voltage Y that each moment battery itself consumes can be obtained _k=F (S _k)-U _k(6)

Then [R H]=(T ^tt) ^-1t ^ty (7)

Here Y=[Y ₁y ₂l Y _n], T=[-I _k-h].(8)

8, initialization

Can initialization be: α, P ₀, wherein be the initial value of SOC, value of the present invention is 0.99; be respectively process noise covariance and measurement noises covariance initial value, the present invention gets 0.5 respectively.0.01; The value of α is by electrodeless Kalman Algorithm known 10 ^-4≤ α≤1, the present invention gets 0.001; P ₀for the initial value of the covariance of state estimation error, the present invention is taken as 0.001.

9, sigma point is calculated

{ W _ia power collection, be used for controlling the weight of each Sigma point, wherein w _i ^m=W _i ^c=1/{2 (L+ λ) }, the value of i is 1,2L2L.L is the dimension of state variable, λ=L(α ²-1) and it is scale parameter.Constant α determine Sigma point the scope of left and right, is normally placed in 10 ^-4in≤α≤1.When noise meets Gaussian distribution, the optimal value of β is 2.

By the known L=1 of model, so there are 3 sigma points.

First: second: 3rd:

Form a row vector ${\mathrm{\χ}}_{k-1}=\left[\begin{array}{ccc}{\hat{S}}_{k-1}& {\hat{S}}_{k-1}+\mathrm{\η}{P}_{k-1}& {\hat{S}}_{k-1}-\mathrm{\η}{P}_{k-1}\end{array}\right].$

10, the square root of the covariance of the state estimation error in k moment is calculated

Calculate the square root of the covariance of the state estimation error in k moment, i.e. the state estimation error covariance of electrodeless Kalman filtering (UKF, Unscented KalmanFilter) algorithm the subduplicate specific algorithm of each several part as follows:

${\mathrm{\χ}}_{k|k-1}={\mathrm{\χ}}_{k-1}-\frac{\mathrm{\Δt}}{C_n}{I}_k+w_k---\left(9\right)$

${\hat{S}}_k^{-}=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^m{\mathrm{\χ}}_{i,k|k-1}---\left(10\right)$

χ _k|k-1represent the state value in the k moment released by the state in k-1 moment; χ _{i, k|k-1}represent the state value in i-th k moment obtained by the Sigma point estimation of the state estimation in k-1 moment, represent the weighted sum of each state estimation.

$P_k^{-}=\mathrm{qr}\left\{\left[\begin{array}{cc}\sqrt{{W_1}^c}({\mathrm{\χ}}_{1:2L,k|k-1}-{\hat{S}}_k^{-})& \sqrt{R_k^w}\end{array}\right]\right\}---\left(11\right)$

$P_{\mathrm{Sk}}^{-}=P_k^{-}\±\sqrt{\left|W_0^c\right|}({\mathrm{\χ}}_{0,k|k-1}-{\hat{S}}_k^{-}){({\mathrm{\χ}}_{0,k|k-1}-{\hat{S}}_k^{-})}^T---\left(12\right)$

be upper triangular matrix, the R factor namely in QR decomposition is also matrix $\left[\begin{array}{cc}\sqrt{{W_1}^c}({\mathrm{\χ}}_{1:2L,k|k-1}-\stackrel{W}{S_k^{-}})& \sqrt{R_k^w}\end{array}\right]$ The transposition of the Chlesky factor.It can thus be appreciated that be each several part square root.Due to may be negative value, so by $P_{\mathrm{Sk}}^{-}=P_k^{-}\±\sqrt{\left|W_0^c\right|}({\mathrm{\χ}}_{0,k|k-1}-{\hat{S}}_k^{-}){\left({\mathrm{\χ}}_{0,k|k-1}{\hat{S}}_k^{-}\right)}^T$ Overcome, in formula positive and negative by determine, for just just namely getting, for negative namely get negative.

6, the specific algorithm of time renewal and measurement updaue:

The first step: calculate the updated value exported

$U_k=K_0-\frac{K_1}{{\mathrm{\χ}}_{k|k-1}}-K_2{\mathrm{\χ}}_{k|k-1}+K_3\ln \left({\mathrm{\χ}}_{k|k-1}\right)+K_4\ln (1-{\mathrm{\χ}}_{k|k-1})-{\mathrm{RI}}_k-h_{k}H+v_k---\left(13\right)$

${\hat{U}}_k^{-}=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^m{U}_{i,k|k-1}---\left(14\right)$

U _k|k-1represent the output valve vector in the k moment calculated by each sigma point of quantity of state, U _{i, k|k-1}represent the output estimation value in the k moment that i-th sigma point calculates, i.e. U _k|k-1in element, represent the weighted sum of each estimated value, be used as the output estimation value in new moment.

Second step: measurement updaue:

1) the square root P of the covariance exporting residual error is calculated _uk, the cross covariance of state estimation error and output valve evaluated error

$P_{\mathrm{Uk}}=\mathrm{qr}\left\{\left[\begin{array}{cc}\sqrt{{W_1}^c}(U_{1:2L,k|k-1}-{\hat{U}}_k^{-})& \sqrt{R_k^v}\end{array}\right]\right\}---\left(15\right)$

$P_{\mathrm{Uk}}^{-}=P_{\mathrm{Uk}}\±\sqrt{\left|W_0^c\right|}(U_{0,k|k-1}-{\hat{U}}_k^{-}){(U_{0,k|k-1}-{\hat{U}}_k^{-})}^T---\left(16\right)$

$P_{S_k,U_k}=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^c[{\mathrm{\χ}}_{i,k|k-1}-{\hat{S}}_k^{-}][U_{i,k|k-1}-{\hat{U}}_k^{-}{]}^T---\left(17\right)$

2) kalman gain κ is calculated _k

${\mathrm{\κ}}_k=(P_{S_k,U_k}/{P_{U_k}}^T/P_{U_k})---\left(18\right)$

3) state estimation:

${\hat{S}}_k={\hat{S}}_k^{-}+{\mathrm{\κ}}_k(U_k-{\hat{U}}_k^{-})---\left(19\right)$

4) state error covariance upgrades:

$H={\mathrm{\κ}}_k{P}_{\mathrm{Uk}}^{-}---\left(20\right)$

$P_k=P_{\mathrm{Sk}}^{-}-{\mathrm{HH}}^T---\left(21\right)$

H represent state estimation error covariance-weighted and.Be used for computing mode error covariance upgrade.

8, the real-time process of process noise covariance and measurement noises covariance

Calculate with

${\mathrm{\μ}}_k=U_k-(K_0-\frac{K_1}{S_k}-K_2{S}_k+K_3\ln \left(S_k\right)+K_4\ln (1-S_k)-{\mathrm{RI}}_k-h_{k}H+v_k)---\left(22\right)$

$F_k={\mathrm{\μ}}_k{{\mathrm{\μ}}_k}^T---\left(23\right)$

$R_k^v=F_k+\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^c(U_{i,k|k-1}-U_k){(U_{i,k|k-1}-U_k)}^T---\left(24\right)$

$R_k^w={\mathrm{\κ}}_k{F}_k{{\mathrm{\κ}}_k}^T---\left(25\right)$

μ _k(U _{i, k|k-1}-U _k) be the residual error that each Sigma point of residual sum of output quantity estimates the measurement output quantity obtained respectively.

Prove

$R_k^v=F_k+\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^c(U_{i,k|k-1}-U_k){(U_{i,k|k-1}-U_k)}^T$

$R_k^w={\mathrm{\κ}}_k{F}_k{{\mathrm{\κ}}_k}^T$

Card:

Known:

$v_k=U_k-(K_0-\frac{K_1}{S_k}-K_2{S}_k+K_3\ln \left(S_k\right)+K_4\ln (1-S_k)-{\mathrm{RI}}_k-h_{k}H)$

${\stackrel{\‾}{v}}_k=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^c(U_{i,k|k-1}-U_k)$

be each sigma point output quantity residual weighted and, as v _kvaluation.

Obvious μ again _kthe residual values of output quantity, F _kit is the residual covariance of output quantity

So measurement noises covariance estimated value be the weighted sum of each each part mentioned above:

$R_k^v=F_k+\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{W_i}^c(U_{i,k|k-1}-U_k){(U_{i,k|k-1}-U_k)}^T.$

Again from the equation of state in model:

$w_k=S_{k+1}-(S_k-\frac{\mathrm{\Δt}}{C_n}{I}_k)$

And

${\hat{w}}_k={\hat{S}}_k-{\hat{S}}_k^{-}={\mathrm{\κ}}_k(U_k-{\hat{U}}_k^{-})={\mathrm{\κ}}_k{\hat{v}}_k$

for w _kestimated value

Again because

${\mathrm{\κ}}_k{\hat{v}}_k\≈{\mathrm{\κ}}_k{\mathrm{\μ}}_k$

So

$R_k^w={\hat{w}}_k{\hat{w}}_k^T={\mathrm{\κ}}_k{F}_k{{\mathrm{\κ}}_k}^T$

Card is finished.

Experimental verification of the present invention:

By being 1.2v by 10 joint rated voltages, rated capacity is that the Ni-MH battery of 30Ah is composed in series tested object.The value that the SOC value of algorithm estimation and original algorithm are estimated and experiment value are as shown in Figure of description 1, and the curve of wherein estimation of the present invention is ASR-UKF, and the estimation curve of former algorithm is SR-UKF.Experiment show relatively former algorithm, precision is improved generally, error in 1.5%, as shown in Figure of description 2.

Claims (3)

1. electrokinetic cell adaptive Kalman filter algorithm for estimating choosing battery model be simplify a battery electrochemical model, its discrete state equations and output equation as follows:

S wherein _krepresent the SOC in k moment, C _nfor the rated capacity of battery, value of the present invention is 30Ah, and Δ t is sampling time interval, value of the present invention is 0.5s, subscript k represents a kth sampled point, U and I represents terminal voltage voltage and current respectively, can obtain by related sensor sampling, R represents the internal resistance of cell, the present invention needs identification, w and ν represents process noise and measurement noises respectively, is all white Gaussian noises, lag parameter when H is charge/discharge transformation, the present invention needs identification.H is the coefficient of lag parameter, and its value is as follows:

K ₀, K ₁, K ₂, K ₃, K ₄describe battery open circuit voltage U _ocvwith S _kfive unknown parameters of relation.

Comprise the following steps:

1) preparation of model: parameter identification, setting initial value, the square root calculating sigma point, calculate the covariance of the state estimation error in k moment

2) Kalman filtering: the time upgrades, measurement updaue.

2. as described in right 1, it is characterized in that, the preparation of model in step 1, the concrete grammar of parameter identification is as follows:

Carry out the experiment of intermittence (cycle 20min) constant-current discharge to battery at normal temperatures, integral method records battery open circuit voltage (U under calculating battery charge state (SOC) value and static condition _ocv), obtain S _kwith U _{ocv, k}relation

Utilize this relation just can pick out parameter K in conjunction with least square method ₀, K ₁, K ₂, K ₃, K ₄.

Identification algorithm is as follows:

Make M _k=[1-(1/S _k)-S _kln (S _k) ln (1-S _k)], M=[M ₁m ₂l M _n] ^t

Then [K ₀k ₁k ₂k ₃k ₄] ^t=(M ^tm) ^-1u _ocv(5)

Here U _ocv=[U _{ocv, 1}u _{ocv, 2}l U _{ocv, N}] be open-circuit voltage sequence, N represents sampling number.

The R of identification internal resistance below and discharge and recharge lag parameter H:

Can be obtained by (1) and (4): the voltage Y that each moment battery itself consumes _k=F (S _k)-U _k(6)

Then [R H]=(T ^tt) ^-1t ^ty (7)

Here Y=[Y ₁y ₂l Y _n], T=[-I _k-h].（8）

Initialization, its concrete grammar is as follows:

Can initialization be: α, P ₀, wherein be the initial value of SOC, value of the present invention is 0.99; be respectively process noise covariance and measurement noises covariance initial value, the present invention gets 0.5 respectively.0.01; The value of α is by electrodeless Kalman Algorithm known 10 ^-4≤ α≤1, the present invention gets 0.001; P ₀for the initial value of the covariance of state estimation error, the present invention is taken as 0.001, and its square root just directly can be asked for evolution,

The state vector χ in the k moment utilizing the estimation of the Sigma of the state estimation in k-1 moment point to obtain _k|k-1.

Because { W _ia power collection, be used for controlling the weight of each Sigma point, wherein w _i ^m=W _i ^c=1/{2 (L+ λ) }, the value of i is 1,2L2L.L is the dimension of state variable, λ=L(α ²-1) and it is scale parameter.Constant α determine Sigma point the scope of left and right, is normally placed in 10 ^-4in≤α≤1.When noise meets Gaussian distribution, the optimal value of β is 2.By the known L=1 of model, so there are 3 sigma points.

First: second: 3rd:

They form a row vector

(9) χ in _k|k-1represent by the state value seeing the k+1 moment that the state in moment is released, χ in formula (10) _{i, k|k-1}represent the state value in i-th k moment obtained by the Sigma point estimation of the state estimation in k-1 moment, represent the weighted sum of each state estimation.Calculate the square root of covariance and the state estimation error covariance of electrodeless Kalman filtering (UKF, Unscented Kalman Filter) algorithm of the state estimation error in k moment the subduplicate specific algorithm of each several part as follows:

(11) in formula be upper triangular matrix, the R factor namely in QR decomposition is also matrix the transposition of the Chlesky factor.It can thus be appreciated that be each several part square root.Due to may be negative value, so by overcome, in formula positive and negative by determine, for just just namely getting, for negative namely get negative, here with process noise covariance and the measurement noises covariance in k moment respectively.

3. as described in right 1, it is characterized in that, the time that step 2 Kalman filtering comprises upgrades, measurement updaue, and the specific algorithm of time renewal and measurement updaue is as follows:

Calculate the updated value exported:

U _k|k-1represent the output valve vector in the k moment calculated by each sigma point of quantity of state, U _{i, k|k-1}represent the output estimation value in the k moment that i-th sigma point calculates, i.e. U _k|k-1in element, represent the weighted sum of each estimated value, be used as the output estimation value in new moment.

Measurement updaue:

The first step: the square root P calculating the covariance exporting residual error _uk, the cross covariance of state estimation error and output valve evaluated error

Second step: calculate kalman gain κ _k

State estimation:

By and κ _kcan obtain:

State error covariance upgrades:

H represent state estimation error covariance-weighted and.Be used for computing mode error covariance upgrade.

Calculate with

μ _k(U _{i, k|k-1}-U _k) be measure the residual error that each Sigma point of residual sum of output quantity estimates the measurement output quantity obtained respectively.