CN105093129A - Method used for detecting residual capacities of energy storage cells - Google Patents

Abstract

The invention relates to a method used for detecting residual capacities of energy storage cells, relates to the cell management technology field and solves a problem that a residual cell capacity measurement method in the prior art is not applicable to on-line cell measurement. According to the method, a solid electrolyte film generation process of an energy storage cell is analyzed, corresponding relations between capacity loss amount of the energy storage cell caused during generation of the solid electrolyte film and internal resistance increase amount of the energy storage cell are established, an off-line test method is adopted to obtain the capacity loss amount of the energy storage cell and the ohm internal resistance increase amount at different aging stages, the least square method is adopted to calculate fitting coefficients alpha 1 and alpha 2, a cell ohm internal resistance on-line identification method is further adopted to calculate and obtain the ohm internal resistance increase amount of the energy storage cell at different aging stages, the acquired known quantities are respectively substituted into the relation, through the relation Q=Q0-deltaQloss, the residual capacity Q of the energy storage cell can be obtained. The method is further applicable to residual capacity detection on other cells.

Description

A kind of energy-storage battery residual capacity detection method

Technical field

The present invention relates to technical field of battery management.

Background technology

Along with the use of battery, the capacity of battery constantly reduces.Only in this capacity attenuation process, understand the current state of battery capacity in real time, and on this basis battery is reasonably used, the safety of guarantee battery and user of service, and the self-ability playing battery to greatest extent.

Detect accurately battery capacity is also the basis that battery electric quantity state (SOC) is estimated simultaneously.At present, main battery capacity means of testing mostly is off-line test method, and this method of testing needs to carry out full punching to battery and completely puts and obtain battery capacity, and this off-line test method is not suitable for the online workplace such as dynamic pure energy, electric automobile.Therefore, develop a kind of energy-storage battery capacity check method being applicable to work online to be of great significance.

Summary of the invention

The present invention is not suitable for the problem of the on-line measurement of battery in order to the measuring method solving existing battery remaining power, propose a kind of energy-storage battery residual capacity detection method.

A kind of energy-storage battery residual capacity detection method, this detection method comprises the steps:

Step one, based on the analysis to the solid electrolyte film generative process in energy-storage battery, set up the corresponding relation between the capacitance loss amount of the energy-storage battery caused when solid electrolyte film in energy-storage battery generates and the internal resistance recruitment of energy-storage battery:

${\mathrm{\ΔQ}}_{1oss}=\frac{-{\mathrm{\α}}_2+\sqrt{{\mathrm{\α}}_2^2+4{\mathrm{\α}}_1{\mathrm{\ΔR}}_{SEI}}}{2{\mathrm{\α}}_1}\≈\frac{-{\mathrm{\α}}_2+\sqrt{{\mathrm{\α}}_2^2+4{\mathrm{\α}}_1{\mathrm{\ΔR}}_o}}{2{\mathrm{\α}}_1},$

In formula, Δ Q _lossfor the capacitance loss amount of energy-storage battery, Δ R _sEIfor the internal resistance recruitment of energy-storage battery, Δ R _ofor the recruitment of the ohmic internal resistance of energy-storage battery, α ₁with α ₂be fitting coefficient;

Step 2, adopt off-line test method to obtain in the capacitance loss amount of the energy-storage battery of different ageing step and ohmic internal resistance recruitment, and adopt least square method to fitting coefficient α ₁with α ₂carry out matching, obtain fitting coefficient α ₁with α ₂value;

Step 3, employing battery ohmic internal resistance on-line identification method, calculate the recruitment Δ R obtaining the ohmic internal resistance of energy-storage battery in ageing process _o;

Step 4, the fitting coefficient α that step 2 is obtained ₁with α ₂value, the recruitment Δ R of the ohmic internal resistance of energy-storage battery that obtains in step 3 _osubstitute in the formula in step one, then obtain the capacitance loss amount △ Q of energy-storage battery _loss;

Step 5, again according to relational expression Q=Q ₀-△ Q _lossobtain the residual capacity Q of energy-storage battery; Wherein, Q ₀for the rated capacity of energy-storage battery.

Adopt battery ohmic internal resistance on-line identification method in step 3, calculate the recruitment Δ R obtaining the ohmic internal resistance of energy-storage battery in ageing process _o, its computation process is as follows:

Steps A, set up discrete battery status spatial model according to the circuit structure of standard battery model; Wherein, U _land I _lrepresent the outer end voltage of battery respectively and flow through the total current of battery, and U _land I _lfor the known quantity measured in real time; V _oCbe used for representing the standard voltage source of this battery model inside, connect simultaneously and also have the ohmic internal resistance R of battery in the loop _o, and by polarization resistance R _pwith polarization capacity C _pthe polarized circuit network composed in parallel, I _pfor flowing through R _ppolarization current;

Steps A (one), according to equivalent-circuit model, list state equation needed for Kalman filter and observation equation respectively:

State equation is:

$x_k=\left[\begin{array}{c}{V}_{OC,k}\\ R_{O,k}\\ R_{P,k}\\ I_{P,k}\end{array}\right]=\left[\begin{array}{cccc}1& & & \\ & 1& & \\ & & 1& \\ & & & e^{-\mathrm{\Δ}t/\mathrm{\τ}}\end{array}\right]\left[\begin{array}{c}{V}_{OC,k-1}\\ R_{O,k-1}\\ R_{P,k-1}\\ I_{P,k-1}\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 0\\ \left(1-\left(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}}\right)/\left(\mathrm{\Δ}t/\mathrm{\τ}\right)\right)\×I_{L,k}+\left(\left(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}}\right)/\left(\mathrm{\Δ}t/\mathrm{\τ}\right)-e^{-\mathrm{\Δ}t/\mathrm{\τ}}\right)\×I_{L,k-1}\end{array}\right]+w_{k-1}$

Wherein:

X _k=[V _{oC, k}r _o,kr _p,ki _p,k] ^Τfor state vector; w _k-1for procedure activation noise;

τ=R _pc _pfor the time constant of the link that polarizes, Δ t is the time interval of double sampling, k=0,1,2 ..., n, represents at a kth sampled point;

Observation equation is:

z _k＝U _L,k＝h(x _k,u _k)+v _k＝V _OC,k+R _O,kI _L,k+R _P,kI _P,k+v _k

Wherein: z _k=U _l,kfor observational variable; v _kfor observation noise;

Steps A (two), according to above-mentioned state equation and observation equation, calculate respectively, arrange and write each equation requisite space matrix;

State equation gain matrix A _k:

$A_k=\left[\begin{array}{cccc}1& & & \\ & 1& & \\ & & 1& \\ & & & e^{-\mathrm{\Δ}t/\mathrm{\τ}}\end{array}\right]$

State equation control variable matrix B _k:

$B_k=\left[\begin{array}{c}0\\ 0\\ 0\\ \left(1-\left(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}}\right)/\left(\mathrm{\Δ}t/\mathrm{\τ}\right)\right)\×I_{L,k}+\left(\left(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}}\right)/\left(\mathrm{\Δ}t/\mathrm{\τ}\right)-e^{-\mathrm{\Δ}t/\mathrm{\τ}}\right)\×I_{L,k-1}\end{array}\right]$

Procedure activation noise gain matrix W _k:

$W_k=\left[\begin{array}{cccc}1& & & \\ & 1& & \\ & & 1& \\ & & & 1\end{array}\right]$

Observation equation gain matrix H _k:

$H_k=\frac{\∂h}{\∂x}({\tilde{x}}_k,u_k,0)=\left[\begin{array}{cccc}1& I_{L,k}& I_{P,k}& R_{P,k}\end{array}\right]$

Observation noise gain matrix V _k:

$V_k=\frac{\∂h}{\∂v}({\tilde{x}}_k,u_k,0)=1$

Step B, utilize extended Kalman filter estimated state vector:

First, the initial value x of the state vector that will estimate is set according to battery types ₀and timeconstantτ, make the initial value P of evaluated error covariance ₀=1, and choose procedure activation noise covariance matrix Q and observation noise covariance matrix R according to sensor accuracy;

Then, cycle calculations time update equation group and observation renewal equation group successively:

The computing formula of time update equation group is:

(1) state variable is calculated forward:

${\hat{x}}_{k|k-1}=A_k{\hat{x}}_{k-1}+B_k$

(2) reckon error covariance forward:

$P_{k|k-1}=A_k{P}_{k-1}{A}_k^T+Q$

The computing formula of observation renewal equation group is:

(1) spreading kalman gain is calculated:

K _k＝P _k|k-1H _k ^T(H _kP _k|k-1H _k ^T+R) ^-1

(2) by observational variable more new estimation:

$\begin{array}{c}{\hat{x}}_k={\hat{x}}_{k|k-1}+K_k\[z_k-(V_{OC,k}+{\hat{R}}_{O,k|k-1}{I}_{L,k}+{\hat{R}}_{P,k|k-1}{I}_{P,k|k-1})\]\\ ={\hat{x}}_{k|k-1}+K_k\[z_k-({\hat{x}}_{k|k-1}\left(1\right)+{\hat{x}}_{k|k-1}\left(2\right)I_{L,k}+{\hat{x}}_{k|k-1}\left(3\right){\hat{x}}_{k|k-1}\left(4\right))\]\end{array}$

Finally, error covariance is upgraded:

P _k＝(I ₄-K _kH _k)P _k|k-1

In formula, represent the prior estimate to x, represent the Posterior estimator to x;

R after step C, each iteration in output state vector _o,k, R _p,kas the estimated result of the ohmic internal resistance under current state and polarization resistance;

Step D, utilize formula Δ R _o=R _{o, 0}-R _o,kobtain the recruitment Δ R of the ohmic internal resistance of energy-storage battery _o, wherein, R _{o, 0}for the nominal ohm internal resistance of energy-storage battery.

Beneficial effect: this method is first according to the analysis of the stationary electrolysis plasma membrane generative process in energy-storage battery, corresponding relation formula between the capacitance loss amount of the energy-storage battery caused when the solid electrolyte film set up in energy-storage battery generates and the internal resistance recruitment of energy-storage battery, then adopt off-line test method to obtain in the capacitance loss amount of the energy-storage battery of different ageing step and ohmic internal resistance recruitment, and adopt least square method to the unknown parameter in relational expression and fitting coefficient α ₁with α ₂carry out matching, obtain fitting coefficient α ₁with α ₂value; Adopt battery ohmic internal resistance on-line identification method again, calculate the recruitment obtaining the ohmic internal resistance of energy-storage battery in ageing process; Now, the known quantity of aforementioned acquisition is all substituted in relational expression, according to relational expression Q=Q ₀-△ Q _lossobtain the residual capacity Q of energy-storage battery.

This method has easy to use and does not increase the remarkable advantage of system bulk and cost.This method make use of off-line measurement method and On-line Estimation method, and the measuring method solving existing battery remaining power is not suitable for the problem of the on-line measurement of battery.The present invention can be applicable to regenerative resource, extensive energy storage and electric automobile etc. using energy-storage battery as in the system of energy storage device.

Accompanying drawing explanation

Fig. 1 is a kind of process flow diagram of energy-storage battery residual capacity detection method;

Fig. 2 is for adopting least square method to factor alpha ₁with α ₂carry out the curve of matching acquisition;

The energy-storage battery equivalent-circuit model of Fig. 3 for using in embodiment two.

Embodiment

Embodiment one, see figures.1.and.2 explanation present embodiment, and a kind of energy-storage battery residual capacity detection method described in present embodiment, this detection method comprises the steps:

Step one, based on the analysis to the solid electrolyte film generative process in energy-storage battery, set up the corresponding relation between the capacitance loss amount of the energy-storage battery caused when solid electrolyte film in energy-storage battery generates and the internal resistance recruitment of energy-storage battery:

${\mathrm{\ΔQ}}_{1oss}=\frac{-{\mathrm{\α}}_2+\sqrt{{\mathrm{\α}}_2^2+4{\mathrm{\α}}_1{\mathrm{\ΔR}}_{SEI}}}{2{\mathrm{\α}}_1}=\frac{-{\mathrm{\α}}_2+\sqrt{{\mathrm{\α}}_2^2+4{\mathrm{\α}}_1{\mathrm{\ΔR}}_o}}{2{\mathrm{\α}}_1},$

In formula, Δ Q _lossfor the capacitance loss amount of energy-storage battery, Δ R _sEIfor the internal resistance recruitment of energy-storage battery, Δ R _ofor the recruitment of the ohmic internal resistance of energy-storage battery, α ₁with α ₂be fitting coefficient;

Step 2, adopt off-line test method to obtain in the capacitance loss amount of the energy-storage battery of different ageing step and ohmic internal resistance recruitment, and adopt least square method to fitting coefficient α ₁with α ₂carry out matching, obtain fitting coefficient α ₁with α ₂value;

Step 3, employing battery ohmic internal resistance on-line identification method, calculate the recruitment Δ R obtaining the ohmic internal resistance of energy-storage battery in ageing process _o;

Step 4, the fitting coefficient α that step 2 is obtained ₁with α ₂value, the recruitment Δ R of the ohmic internal resistance of energy-storage battery that obtains in step 3 _osubstitute in the formula in step one, then obtain the capacitance loss amount △ Q of energy-storage battery _loss;

Step 5, again according to relational expression Q=Q ₀-△ Q _lossobtain the residual capacity Q of energy-storage battery; Wherein, Q ₀for the rated capacity of energy-storage battery.

In present embodiment, for energy-storage battery (majority is lithium ion battery at present), in its vehicle-mounted (being such as arranged on electric automobile) operational phase (capacity is not less than 80% of new battery total capacity), the loss of energy-storage battery capacity grows primarily of the solid electrolyte film (SEI) in battery that the active lithium loss that causes causes.Along with the growth of SEI, the SEI resistance (R corresponding to it _sEI) also can increase thereupon.

Due to battery ohmic internal resistance (R _o) form primarily of the bulk resistor of battery, SEI resistance and charge transfer resistance three part, and at this one-phase, the bulk resistor of battery and charge transfer resistance change hardly, and so think in this ageing process, R _orecruitment just equal the recruitment of battery SEI resistance.

Detection method of the present invention, by setting up the corresponding relation between battery capacity loss amount and internal resistance of cell increase, in conjunction with corresponding battery ohmic internal resistance method of testing, completes the detection to battery capacity loss amount.

Compared with prior art, present invention achieves the on-line measurement of energy-storage battery capacity, and the calculated amount of this method is little, is suitable for online use, the measuring method solving existing battery capacity is not suitable for the problem of the on-line measurement of battery.

Embodiment two, reference Fig. 3 illustrate present embodiment, this embodiment is further illustrating a kind of energy-storage battery residual capacity detection method described in embodiment one, in present embodiment, adopt battery ohmic internal resistance on-line identification method in step 3, calculate the recruitment Δ R obtaining the ohmic internal resistance of energy-storage battery in ageing process _o, its computation process is as follows:

Steps A, set up discrete battery status spatial model according to the circuit structure of standard battery model; Wherein, U _land I _lrepresent the outer end voltage of battery respectively and flow through the total current of battery, and U _land I _lfor the known quantity measured in real time; V _oCbe used for representing the standard voltage source of this battery model inside, connect simultaneously and also have the ohmic internal resistance R of battery in the loop _o, and by polarization resistance R _pwith polarization capacity C _pthe polarized circuit network composed in parallel, I _pfor flowing through R _ppolarization current;

Steps A (one), according to equivalent-circuit model, list state equation needed for Kalman filter and observation equation respectively:

State equation is:

$x_k=\left[\begin{array}{c}{V}_{OC,k}\\ R_{O,k}\\ R_{P,k}\\ I_{P,k}\end{array}\right]=\left[\begin{array}{cccc}1& & & \\ & 1& & \\ & & 1& \\ & & & e^{-\mathrm{\Δ}t/\mathrm{\τ}}\end{array}\right]\left[\begin{array}{c}{V}_{OC,k-1}\\ R_{O,k-1}\\ R_{P,k-1}\\ I_{P,k-1}\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 0\\ \left(1-\left(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}}\right)/\left(\mathrm{\Δ}t/\mathrm{\τ}\right)\right)\×I_{L,k}+\left(\left(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}}\right)/\left(\mathrm{\Δ}t/\mathrm{\τ}\right)-e^{-\mathrm{\Δ}t/\mathrm{\τ}}\right)\×I_{L,k-1}\end{array}\right]+w_{k-1}$

Wherein:

X _k=[V _{oC, k}r _o,kr _p,ki _p,k] ^Τfor state vector; w _k-1for procedure activation noise;

τ=R _pc _pfor the time constant of the link that polarizes, Δ t is the time interval of double sampling, k=0,1,2 ..., n, represents at a kth sampled point;

Observation equation is:

z _k＝U _L,k＝h(x _k,u _k)+v _k＝V _OC,k+R _O,kI _L,k+R _P,kI _P,k+v _k

Wherein: z _k=U _l,kfor observational variable; v _kfor observation noise;

Steps A (two), according to above-mentioned state equation and observation equation, calculate respectively, arrange and write each equation requisite space matrix;

State equation gain matrix A _k:

$A_k=\left[\begin{array}{cccc}1& & & \\ & 1& & \\ & & 1& \\ & & & e^{-\mathrm{\Δ}t/\mathrm{\τ}}\end{array}\right]$

State equation control variable matrix B _k:

$B_k=\left[\begin{array}{c}0\\ 0\\ 0\\ (1-(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}})/(\mathrm{\Δ}t/\mathrm{\τ}))\×I_{L,k}+((1-e^{-\mathrm{\Δ}t/\mathrm{\τ}})/(\mathrm{\Δ}t/\mathrm{\τ})-e^{-\mathrm{\Δ}t/\mathrm{\τ}})\×I_{L,k-1}\end{array}\right]$

Procedure activation noise gain matrix W _k:

$W_k=\left[\begin{array}{cccc}1& & & \\ & 1& & \\ & & 1& \\ & & & 1\end{array}\right]$

Observation equation gain matrix H _k:

$H_k=\frac{\∂h}{\∂x}({\tilde{x}}_k,u_k,0)=\left[\begin{array}{cccc}1& I_{L,k}& I_{P,k}& R_{P,k}\end{array}\right]$

Observation noise gain matrix V _k:

$V_k=\frac{\∂h}{\∂v}({\tilde{x}}_k,u_k,0)=1$

Step B, utilize extended Kalman filter estimated state vector:

First, the initial value x of the state vector that will estimate is set according to battery types ₀and timeconstantτ, make the initial value P of evaluated error covariance ₀=1, and choose procedure activation noise covariance matrix Q and observation noise covariance matrix R according to sensor accuracy;

Then, cycle calculations time update equation group and observation renewal equation group successively:

The computing formula of time update equation group is:

(1) state variable is calculated forward:

${\hat{x}}_{k|k-1}=A_k{\hat{x}}_{k-1}+B_k$

(2) reckon error covariance forward:

$P_{k|k-1}=A_k{P}_{k-1}{A}_k^T+Q$

The computing formula of observation renewal equation group is:

(1) spreading kalman gain is calculated:

K _k＝P _k|k-1H _k ^T(H _kP _k|k-1H _k ^T+R) ^-1

(2) by observational variable more new estimation:

$\begin{array}{c}{\hat{x}}_k={\hat{x}}_{k|k-1}+K_k\[z_k-(V_{OC,k}+{\hat{R}}_{O,k|k-1}{I}_{L,k}+{\hat{R}}_{P,k|k-1}{I}_{P,k|k-1})\]\\ ={\hat{x}}_{k|k-1}+K_k\[z_k-({\hat{x}}_{k|k-1}\left(1\right)+{\hat{x}}_{k|k-1}\left(2\right)I_{L,k}+{\hat{x}}_{k|k-1}\left(3\right){\hat{x}}_{k|k-1}\left(4\right))\]\end{array}$

Finally, error covariance is upgraded:

P _k＝(I ₄-K _kH _k)P _k|k-1

In formula, represent the prior estimate to x, represent the Posterior estimator to x;

R after step C, each iteration in output state vector _o,k, R _p,kas the estimated result of the ohmic internal resistance under current state and polarization resistance;

Step D, utilize formula Δ R _o=R _{o, 0}-R _o,kobtain the recruitment Δ R of the ohmic internal resistance of energy-storage battery _o, wherein, R _{o, 0}for the nominal ohm internal resistance of energy-storage battery.

In present embodiment, R _{o, 0}for the nominal ohm internal resistance of energy-storage battery, nominal ohm internal resistance refers to the ohmic internal resistance of battery when Default Value.

This method utilizes nominal ohm internal resistance and the ohmic internal resistance R adopting battery ohmic internal resistance on-line identification method to calculate the battery (energy-storage battery) obtained _o,kdo difference, obtain the recruitment Δ R of the ohmic internal resistance of energy-storage battery _o.Steps A in this method can be also CN102680795A see application publication number to the acquisition process of step C, and name is called " a kind of real-time online method of estimation of internal resistance of rechargeable battery ".This method changes secondary cell into energy-storage battery.This method utilizes the ohmic internal resistance of the battery under the enforcement On-line Estimation method acquisition current state of internal resistance of rechargeable battery, then utilizes formula △ R _o=R _{o, 0}-R _o,kobtain the recruitment Δ R of the ohmic internal resistance of energy-storage battery _o.The method is the improvement done in prior art.

Method of the present invention can not only realize the internal resistance detection battery under duty being carried out to real-time online, and in whole estimation process, only needs the terminal voltage and the load current that provide battery, and without the need to separately increasing other ancillary hardware circuit.

Claims (2)

1. an energy-storage battery residual capacity detection method, is characterized in that, this detection method comprises the steps:

Step one, based on the analysis to the solid electrolyte film generative process in energy-storage battery, set up the corresponding relation between the capacitance loss amount of the energy-storage battery caused when solid electrolyte film in energy-storage battery generates and the internal resistance recruitment of energy-storage battery:

${\mathrm{\ΔQ}}_{\mathrm{lo}ss}=\frac{-{\mathrm{\α}}_2+\sqrt{{\mathrm{\α}}_2^2+4{\mathrm{\α}}_1{\mathrm{\ΔR}}_{SEI}}}{2{\mathrm{\α}}_1}\≈\frac{-{\mathrm{\α}}_2+\sqrt{{\mathrm{\α}}_2^2+4{\mathrm{\α}}_1{\mathrm{\ΔR}}_o}}{2{\mathrm{\α}}_1},$

In formula, Δ Q _lossfor the capacitance loss amount of energy-storage battery, Δ R _sEIfor the internal resistance recruitment of energy-storage battery, Δ R _ofor the recruitment of the ohmic internal resistance of energy-storage battery, α ₁with α ₂be fitting coefficient;

Step 2, adopt off-line test method to obtain in the capacitance loss amount of the energy-storage battery of different ageing step and ohmic internal resistance recruitment, and adopt least square method to fitting coefficient α ₁with α ₂carry out matching, obtain fitting coefficient α ₁with α ₂value;

Step 3, employing battery ohmic internal resistance on-line identification method, calculate the recruitment Δ R obtaining the ohmic internal resistance of energy-storage battery in ageing process _o;

Step 4, the fitting coefficient α that step 2 is obtained ₁with α ₂value, the recruitment Δ R of the ohmic internal resistance of energy-storage battery that obtains in step 3 _osubstitute in the formula in step one, then obtain the capacitance loss amount △ Q of energy-storage battery _loss;

Step 5, according to relational expression Q=Q ₀-△ Q _lossobtain the residual capacity Q of energy-storage battery; Wherein, Q ₀for the rated capacity of energy-storage battery.

2. a kind of energy-storage battery residual capacity detection method according to claim 1, is characterized in that, adopts battery ohmic internal resistance on-line identification method in step 3, calculates the recruitment Δ R obtaining the ohmic internal resistance of energy-storage battery in ageing process _o, its computation process is as follows:

Steps A, set up discrete battery status spatial model according to the circuit structure of standard battery model; Wherein, U _land I _lrepresent the outer end voltage of battery respectively and flow through the total current of battery, and U _land I _lfor the known quantity measured in real time; V _oCbe used for representing the standard voltage source of this battery model inside, connect simultaneously and also have the ohmic internal resistance R of battery in the loop _o, and by polarization resistance R _pwith polarization capacity C _pthe polarized circuit network composed in parallel, I _pfor flowing through R _ppolarization current;

Steps A (one), according to equivalent-circuit model, list state equation needed for Kalman filter and observation equation respectively:

State equation is:

$x_k=\left[\begin{array}{c}{V}_{OC,k}\\ R_{O,k}\\ R_{P,k}\\ I_{P,k}\end{array}\right]=\left[\begin{array}{cccc}1& & & \\ & 1& & \\ & & 1& \\ & & & e^{-\mathrm{\Δ}t/\mathrm{\τ}}\end{array}\right]\left[\begin{array}{c}{V}_{OC,k-1}\\ R_{O,k-1}\\ R_{P,k-1}\\ I_{P,k-1}\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 0\\ (1-(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}})/(\mathrm{\Δ}t/\mathrm{\τ}\left)\right)\×I_{L,k}\left(\right(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}})/(\mathrm{\Δ}t/\mathrm{\τ})-e^{-\mathrm{\Δ}t/\mathrm{\τ}})\×I_{L,k-1}\end{array}\right]+w_{k-1}$

Wherein:

X _k=[V _{oC, k}r _o,kr _p,ki _p,k] ^Τfor state vector; w _k-1for procedure activation noise;

τ=R _pc _pfor the time constant of the link that polarizes, Δ t is the time interval of double sampling, k=0,1,2 ..., n, represents at a kth sampled point;

Observation equation is:

z _k＝U _L,k＝h(x _k,u _k)+v _k＝V _OC,k+R _O,kI _L,k+R _P,kI _P,k+v _k

Wherein: z _k=U _l,kfor observational variable; v _kfor observation noise;

Steps A (two), according to above-mentioned state equation and observation equation, calculate respectively, arrange and write each equation requisite space matrix;

State equation gain matrix A _k:

$A_k=\left[\begin{array}{cccc}1& & & \\ & 1& & \\ & & 1& \\ & & & e^{-\mathrm{\Δ}t/\mathrm{\τ}}\end{array}\right]$

State equation control variable matrix B _k:

$B_k=\left[\begin{array}{c}0\\ 0\\ 0\\ (1-(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}})/(\mathrm{\Δ}t/\mathrm{\τ}\left)\right)\×I_{L,k}+\left(\right(1-e^{-\mathrm{\Δ}t/\mathrm{\τ}})/(\mathrm{\Δ}t/\mathrm{\τ})-e^{-\mathrm{\Δ}t/\mathrm{\τ}})\×I_{L,k-1}\end{array}\right]$

Procedure activation noise gain matrix W _k:

$W_k=\left[\begin{array}{cccc}1& & & \\ & 1& & \\ & & 1& \\ & & & 1\end{array}\right]$

Observation equation gain matrix H _k:

$H_k=\frac{\∂h}{\∂x}({\tilde{x}}_k,u_k,0)=\left[\begin{array}{cccc}1& I_{L,k}& I_{P,k}& R_{P,k}\end{array}\right]$

Observation noise gain matrix V _k:

$V_k=\frac{\∂h}{\∂v}({\tilde{x}}_k,u_k,0)=1$

Step B, utilize extended Kalman filter estimated state vector:

First, the initial value x of the state vector that will estimate is set according to battery types ₀and timeconstantτ, make the initial value P of evaluated error covariance ₀=1, and choose procedure activation noise covariance matrix Q and observation noise covariance matrix R according to sensor accuracy;

Then, cycle calculations time update equation group and observation renewal equation group successively:

The computing formula of time update equation group is:

(1) state variable is calculated forward:

(2) reckon error covariance forward:

$P_{k|k-1}=A_k{P}_{k-1}{A}_k^T+Q$

The computing formula of observation renewal equation group is:

(1) spreading kalman gain is calculated:

K _k＝P _k|k-1H _k ^T(H _kP _k|k-1H _k ^T+R) ^-1

(2) by observational variable more new estimation:

Finally, error covariance is upgraded:

P _k＝(I ₄-K _kH _k)P _k|k-1

In formula, represent the prior estimate to x, represent the Posterior estimator to x;

R after step C, each iteration in output state vector _o,k, R _p,kas the estimated result of the ohmic internal resistance under current state and polarization resistance;

Step D, utilize formula Δ R _o=R _{o, 0}-R _o,kobtain the recruitment Δ R of the ohmic internal resistance of energy-storage battery _o, wherein, R _{o, 0}for the nominal ohm internal resistance of energy-storage battery.