Apparatus and method for estimating charge rate of secondary cell

• US 20040100227A1
• Filed: 10/30/2003
• Published: 05/27/2004
• Est. Priority Date: 11/25/2002
• Status: Active Grant

• Current Assignee: Nissan Motor Co., Ltd.
• Original Assignee: Nissan Motor Co., Ltd.
• Inventors: Nakamura, Hideo, Yumoto, Daijiro
• Granted Patent: US 7,098,625 B2
• Time in Patent Office: Days
• US Class Current: 320/151
• CPC Class Codes: G01R 31/3648 comprising digital calculation means, e.g. for performing an algorithm
• CPC Class Codes: G01R 31/3842 combining voltage and current measurements
• CPC Class Codes: H02J 7/0048 Detection of remaining charge capacity or state of charge [SOC]

Abstract

In charge rate estimating apparatus and method for a secondary cell, a current flowing through the secondary cell is measured, a voltage across terminals of the secondary cell is measured, an adaptive digital filtering is carried out using a cell model in a continuous time series shown in an equation (1), all of parameters at one time are estimated, the parameters corresponding to an open-circuit voltage which is an offset term of the equation (1) and coefficients of A(s), B(s), and C(s) which are transient terms, and, the charge rate is estimated from a relationship between a previously derived open-circuit voltage V₀ and the charge rate SOC using the open-circuit voltage V₀, $\begin{array}{cc}V=\frac{B\left(s\right)}{A\left(s\right)}·I+\frac{1}{C\left(s\right)}·V_0,& \left(1\right)\end{array}$

wherein s denotes a Laplace transform operator, A(s), B(s), and C(s) denote poly-nominal functions of s.

Claims

1. A charge rate estimating apparatus for a secondary cell, comprising:

a current detecting section capable of measuring a current flowing through the secondary cell;

a terminal voltage detecting section capable of measuring a voltage across terminals of the secondary cell;

a parameter estimating section that calculates an adaptive digital filtering using a cell model in a continuous time series shown in an equation (1) estimates all of parameters at one time, the parameters corresponding to an open-circuit voltage which is an offset term of the equation (1) and coefficients of A(s), B(s), and C(s) which are transient terms; and

a charge rate estimating section that estimates the charge rate from a relationship between a previously derived open-circuit voltage V₀ and the charge rate SOC using the open-circuit voltage V₀,

$\begin{array}{cc}V=\frac{B<br><br>\left(s\right)}{A<br><br>\left(s\right)}·<br><br>I+\frac{1}{C<br><br>\left(s\right)}·<br><br>V_0,& \left(1\right)\end{array}$

wherein s denotes a Laplace transform operator, A(s), B(s), and C(s) denote poly-nominal functions of s.

2. A charge rate estimating apparatus for a secondary cell as claimed in claim 1, wherein the open-circuit voltage V₀ of the cell model in the continuous time series shown in the equation (1) is approximated by means of an equation (2) to provide an equation (3) and the digital filter calculation is carried out using the equation (3) and equivalent equation (4), h is estimated in at least equation (4), the estimated h is substituted into equation (2) to derive an open-circuit voltage V₀, and the charge rate is estimated from a relationship between the previously derived open-circuit voltage V₀, and the charge rate is estimated from a relationship between the previously proposed open-circuit voltage V₀ and the charge rate (SOC).

3. A charge rate estimating apparatus for a secondary cell as claimed in claim 1, wherein the open-circuit voltage V₀ of the cell model in the time continuous time series is approximated in an equation (2) to calculate an equation (3), the adaptive digital filter calculation is carried out using an equation (4) which is equivalent to the equation (3), A(s), B(s), and C(s) are estimated from equation (4), the estimated A(s), B(s), and C(s) are substituted into equation (5) to determine V₀/G₂(s) and the charge rate is estimated from the relationship between the previously derived open-circuit voltage V₀ and the charge rate (SOC) using the derived V₀/G₂(s) in place of the open-circuit voltage V₀,

4. A charge rate estimating apparatus for a secondary cell as claimed in claim 1, wherein the cell model is calculated from an equation (6),

5. A charge rate estimating apparatus for a secondary cell as claimed in claim 4, wherein A(s)=T₁·

s+1, B(s)=K·

(T₂+1), C(s)=T₃·

s+1.

6. A charge rate estimating apparatus for a secondary cell as claimed in claim 5, wherein

7. A charge rate estimating apparatus for a secondary cell as claimed in claim 6, wherein a=T₁·

T₃, b=T₁+T₃, c=K·

T₂·

T₃, d=K·

(T₂+T₃), e=K+A·

T₁, f=A . . . (11).

8. A charge rate estimating apparatus for a secondary cell as claimed in claim 7, wherein a stable low pass filter G₁(s) is introduced into both sides of the equation (10) to derive the following equation:

9. A charge rate estimating apparatus for a Secondary cell as claimed in claim 8, wherein actually measurable currents I and terminal voltages V which are processed by means of a low pass filter are as follows:

10. A charge rate estimating apparatus for a secondary cell as claimed in claim 9, wherein, using the equation (13), the equation of (12) is rewritten and rearranged as follows:

11. A charge rate estimating apparatus for a Secondary cell as claimed in claim 10, wherein a parameter estimating algorithm with the equation (16) as a prerequisite is defined as follows:

12. A charge rate estimating method for a secondary cell, comprising:

measuring a current flowing through the secondary cell;

measuring a voltage across terminals of the secondary cell;

calculating an adaptive digital filtering using a cell model in a continuous time series shown in an equation (1);

estimating all of parameters at one time, the parameters corresponding to an open-circuit voltage which is an offset term of the equation (1) and coefficients of A(s), B(s), and C(s) which are transient terms; and

estimating the charge rate from a relationship between a previously derived open-circuit voltage V₀ and the charge rate SOC using the open-circuit voltage V₀,

$\begin{array}{cc}V=\frac{B<br><br>\left(s\right)}{A<br><br>\left(s\right)}·<br><br>I+\frac{1}{C<br><br>\left(s\right)}·<br><br>V_0,& \left(1\right)\end{array}$

wherein s denotes a Laplace transform operator, A(s), B(s), and C(s) denote poly-nominal functions of s.

13. A charge rate estimating method for a secondary cell as claimed in claim 12, wherein the open-circuit voltage V₀ of the cell model in the continuous time series shown in the equation (1) is approximated by means of an equation (2) to provide an equation (3) and the digital filter calculation is carried out using the equation (3) and equivalent equation (4), h is estimated in at least equation (4), the estimated value of h is substituted into equation (2) to derive an open-circuit voltage V₀, and the charge rate is estimated from a relationship between the previously derived open-circuit voltage V₀, and the charge rate is estimated from a relationship between the previously proposed open-circuit voltage V₀ and the charge rate (SOC).

14. A charge rate estimating method for a secondary cell as claimed in claim 12, wherein the open-circuit voltage V₀ of the cell model in the continuous time series is approximated in an equation (2) to calculate an equation (3), the adaptive digital filter calculation is carried out using an equation (4) which is equivalent to the equation (3), A(s), B(s), and C(s) are estimated from the equation (4), the estimated A(s), B(s), and C(s) are substituted into equation (5) to determine V₀/G₂(s) and the charge rate is estimated from the relationship between the previously derived open-circuit voltage V₀ and the charge rate (SOC) using the derived V₀/G₂(s) in place of the open-circuit voltage V₀,

15. A charge rate estimating method for a secondary cell as claimed in claim 12, wherein the cell model is calculated from an equation (6),

16. A charge rate estimating method for a secondary cell, comprising:

measuring a current I(k) flowing through the secondary cell;

measuring a terminal voltage V(k) across the secondary cell;

storing the terminal voltage V(k) when a current is zeroed as an initial value of the terminal voltage Δ

V(k)=V(k)−

V_ini;

determining instantaneous current values I₀(k), I₁(k), and I₃(k) and instantaneous terminal voltages V₁(k), V₂(k), and V₃(k) from an equation (19),

$\begin{array}{cc}\begin{array}{cccc}{I}_0=\frac{1}{G_1<br><br>\left(s\right)}·<br><br>I,& \text{\hspace{1em}<br><br>}& \text{\hspace{1em}<br><br>}& \text{\hspace{1em}<br><br>}\\ I_1=\frac{s}{G_1<br><br>\left(s\right)}·<br><br>I,& \text{\hspace{1em}<br><br>}& \text{\hspace{1em}<br><br>}& V_1=\frac{s}{G_1<br><br>\left(s\right)}·<br><br>V,\\ I_2=\frac{s^2}{G_1<br><br>\left(s\right)}·<br><br>I,& \text{\hspace{1em}<br><br>}& \text{\hspace{1em}<br><br>}& V_2=\frac{s^2}{G_1<br><br>\left(s\right)}·<br><br>V,\\ I_3=\frac{s^3}{G_1<br><br>\left(s\right)}·<br><br>I,& \text{\hspace{1em}<br><br>}& \text{\hspace{1em}<br><br>}& V_3=\frac{s^3}{G_1<br><br>\left(s\right)}·<br><br>V,\mathrm{and}\\ \frac{1}{G_1<br><br>\left(s\right)}=\frac{1}{{\left(p<br><br>\text{\hspace{1em}<br><br>}<br><br>1·<br><br>s+1\right)}^3},& \text{\hspace{1em}<br><br>}& \text{\hspace{1em}<br><br>}& \text{\hspace{1em}<br><br>}\end{array}& \left(19\right)\end{array}$

wherein p1 denotes a constant determining a responsive characteristic of G₁(s);

substituting the instantaneous current values I₀(k), I₁(k), and I₃(k ) and the instantaneous terminal voltages V₁(k) , V₂(k) , and V₃(k) into an equation (18),

$\begin{array}{cc}\mathrm{\gamma <br><br>}<br><br>\left(k\right)=\frac{{\mathrm{\lambda <br><br>}}_3<br><br>\left(k\right)}{1+{\mathrm{\lambda <br><br>}}_3<br><br>\left(k\right)·<br><br>{\mathrm{\omega <br><br>}}^T<br><br>\left(k\right)·<br><br>P<br><br>\left(k-1\right)·<br><br>\mathrm{\omega <br><br>}<br><br>\left(k\right)}& \left(18\right)\\ \mathrm{\theta <br><br>}<br><br>\left(k\right)=\mathrm{\theta <br><br>}<br><br>\left(k-1\right)-\mathrm{\gamma <br><br>}<br><br>\left(k\right)·<br><br>P<br><br>\left(k-1\right)·<br><br>\mathrm{\omega <br><br>}<br><br>\left(k\right)·<br><br>\left[{\mathrm{\omega <br><br>}}^T<br><br>\left(k\right)·<br><br>\mathrm{\theta <br><br>}(k-1〉<br><br>-y<br><br>\left(k\right)\right]& \text{\hspace{1em}<br><br>}\\ P<br><br>\left(k\right)=\frac{1}{{\mathrm{\lambda <br><br>}}_1<br><br>\left(k\right)}<br><br>\left\{P<br><br>\left(k-1\right)-\frac{{\mathrm{\lambda <br><br>}}_3<br><br>\left(k\right)·<br><br>P<br><br>\left(k-1\right)·<br><br>\mathrm{\omega <br><br>}<br><br>\left(k\right)·<br><br>{\mathrm{\omega <br><br>}}^T<br><br>\left(k\right)·<br><br>P<br><br>\left(k-1\right)}{1+{\mathrm{\lambda <br><br>}}_3<br><br>\left(k\right)·<br><br>{\mathrm{\omega <br><br>}}^T<br><br>\left(k\right)·<br><br>P<br><br>\left(k-1\right)·<br><br>\mathrm{\omega <br><br>}<br><br>\left(k\right)}\right\}& \text{\hspace{1em}<br><br>}\\ \text{\hspace{1em}<br><br>}<br><br>=\frac{P^{\mathrm{\prime <br><br>}}<br><br>\left(k\right)}{{\mathrm{\lambda <br><br>}}_1<br><br>\left(k\right)}& \text{\hspace{1em}<br><br>}\\ {\mathrm{\lambda <br><br>}}_1<br><br>\left(k\right)=\{\frac{\mathrm{trace}<br><br>\left\{P^{\mathrm{\prime <br><br>}}<br><br>\left(k\right)\right\}}{{\mathrm{\gamma <br><br>}}_U};<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\lambda <br><br>}}_1\le <br><br>\frac{\mathrm{trace}<br><br>\left\{P^{\mathrm{\prime <br><br>}}<br><br>\left(k\right)\right\}}{{\mathrm{\gamma <br><br>}}_U}& \text{\hspace{1em}<br><br>}\\ \text{\hspace{1em}<br><br>}<br><br>\{{\mathrm{\lambda <br><br>}}_1;<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{\mathrm{trace}<br><br>\left\{P^{\mathrm{\prime <br><br>}}<br><br>\left(k\right)\right\}}{{\mathrm{\gamma <br><br>}}_U}\le <br><br>{\mathrm{\lambda <br><br>}}_1\le <br><br>\frac{\mathrm{trace}<br><br>\left\{P^{\mathrm{\prime <br><br>}}<br><br>\left(k\right)\right\}}{{\mathrm{\gamma <br><br>}}_L}& \text{\hspace{1em}<br><br>}\\ \text{\hspace{1em}<br><br>}<br><br>\{\frac{\mathrm{trace}<br><br>\left\{P^{\mathrm{\prime <br><br>}}<br><br>\left(k\right)\right\}}{{\mathrm{\gamma <br><br>}}_L};<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{\mathrm{trace}<br><br>\left\{P^{\mathrm{\prime <br><br>}}<br><br>\left(k\right)\right\}}{{\mathrm{\gamma <br><br>}}_L}\le <br><br>{\mathrm{\lambda <br><br>}}_1,& \text{\hspace{1em}<br><br>}\end{array}$

wherein θ

(k) denotes a parameter estimated value at a time point of k (k=0, 1, 2, 3 . . . ), λ

₁, λ

₃(k), γ

u, and γ

L denote initial set value, b<

λ

₁<

1, 0<

λ

₃(k)<

∞

. P(0) is a sufficiently large value, θ

(0) provides an initial value which is non-zero but very sufficiently small value, trace{P} means a trace of matrix P, wherein y(k)=V₁(k)

$\begin{array}{cc}\begin{array}{c}{\mathrm{\omega <br><br>}}^T<br><br>\left(k\right)=\left[\begin{array}{cccccc}{V}_3<br><br>\left(k\right)& V_2<br><br>\left(k\right)& I_3<br><br>\left(k\right)& I_2<br><br>\left(k\right)& I_1<br><br>\left(k\right)& I_0<br><br>\left(k\right)\end{array}\right]\\ \mathrm{\theta <br><br>}<br><br>\left(k\right)=\left[\begin{array}{c}-a<br><br>\left(k\right)\\ -b<br><br>\left(k\right)\\ c<br><br>\left(k\right)\\ d<br><br>\left(k\right)\\ e<br><br>\left(k\right)\\ f<br><br>\left(k\right)\end{array}\right];<br><br>\end{array}& \left(20\right)\end{array}$

substituting a, b, c, d, e, and f in the parameter estimated value θ

(k) into and equation (22) to calculate V₀′

which is an alternate of V₀ which corresponds to a variation Δ

V₀(k) of the open-circuit voltage estimated value from a time at which the estimated calculation start is carried out;

$\begin{array}{cc}\begin{array}{c}{V}_0^{\mathrm{\prime <br><br>}}=\frac{\left(T_1·<br><br>s+1\right)}{G_2<br><br>\left(s\right)}·<br><br>V_0=a·<br><br>V_6+b·<br><br>V_5+V_4-c·<br><br>I_6-d·<br><br>I_5-e·<br><br>I_4;<br><br>\\ \mathrm{and}\end{array}& \left(22\right)\end{array}$

calculating an open-circuit voltage estimated value V₀(k) according the variation Δ

V₀(k) of the open-circuit voltage estimated value and the terminal voltage initial value V_ini.

17. A charge rate estimating method for a secondary cell as claimed in claim 16, which further comprises:

calculating a charge rate (SOC) from the open-circuit voltage estimated value Δ

V₀(k).

18. A charge rate estimating method for a secondary cell as claimed in claim 17, wherein the charge rate (SOC) is calculated using a correlation map between the open-circuit voltage V₀ and the charge rate of the secondary cell from the open-circuit voltage estimated value Δ

V₀(k).