Available input-output power estimating device for secondary battery

Abstract

An available input-output power estimating device for a secondary battery includes a parameter estimating section substituting a measured current value I and a measured voltage value V into an adaptive digital filter using an equivalent circuit model of the secondary battery for thereby collectively estimating values of parameters in the equivalent circuit model, an open circuit voltage calculator substituting I, V, and the estimated parameter values into the equivalent circuit model for calculating an open circuit voltage {circumflex over (V)}0, an available input power estimating section estimating an available input power Pin of the secondary battery using components (ân,{circumflex over (b)}n), associated with a direct term in the equivalent circuit model, in the estimated parameters, the open circuit voltage estimate value {circumflex over (V)}0 and an upper limit voltage Vmax of the terminal voltage, and an available output power estimating section estimating an available output power Pout for the secondary battery using (ân,{circumflex over (b)}n), {circumflex over (V)}0 and a lower limit voltage {circumflex over (V)}min of the terminal voltage.

Description

BACKGROUND OF THE INVENTION

The present invention relates to a technology of estimating power available to be inputted to and outputted from a secondary battery.

Such a technology is disclosed in the following literature: Daijiro Yumoto, Hideo Nakamura, Mayumi Hirota, and Norimasa Ochi, “Method of Estimating Internal State Quantity of Battery using Adaptive Digital Filter Theory”, Automobile Technology Association Spring-Autumn Academic Lecture Handout No. 20035031, May 21, 2003.

In the literature, measured values of current I and terminal voltage V, both of which are observable, are substituted into an adaptive digital filter using a battery model represented by $\begin{array}{cc}V=\frac{K\left(T_{2}s+1\right)}{T_{1}s+1}I+\frac{1}{T_{1}s+1}{V}_0& \left(1\right)\end{array}$ for estimating values of parameters (internal resistance K and open circuit voltage V₀). Then, substituting estimated values {circumflex over (K)} and {circumflex over (V)}₀ of the internal resistance K and the open circuit voltage V₀, and a lower limit value V_min of the terminal voltage V into a steady-state battery model given by V=KI+V₀  (2) allows a value (estimate value) of current I_out, at which a lower limit voltage value V_min is reached, to be calculated by $\begin{array}{cc}{\hat{I}}_{\mathrm{out}}=\frac{V_{\min }-{\hat{V}}_0}{\hat{K}}& \left(3\right)\end{array}$ This permits a value of available output power P_out to be estimated by $\begin{array}{cc}{\hat{P}}_{\mathrm{out}}=V_{\min }I_{\mathrm{out}}=\frac{{\hat{V}}_0-V_{\min }}{\hat{K}}{V}_{\min },& \left(4\right)\end{array}$ using the calculated current value Î_out and the lower limit value V_min.

Likewise, substituting the estimated values {circumflex over (K)}, {circumflex over (V)}₀ of the internal resistance K and the open circuit voltage V₀ and an upper limit value V_max of the terminal voltage V into Eq. (2) allows a value (estimate value) of current I_in, at which an upper limit value V_max is reached, to be calculated by $\begin{array}{cc}{\hat{I}}_{\mathrm{in}}=\frac{V_{\max }-{\hat{V}}_0}{\hat{K}}.& \left(5\right)\end{array}$

This permits a value of available input power P_in to be estimated by $\begin{array}{cc}{\hat{P}}_{\mathrm{in}}=V_{\max }{I}_{\mathrm{in}}=\frac{V_{\max }-{\hat{V}}_0}{\hat{K}}{V}_{\max },& \left(6\right)\end{array}$ using the calculated current value Î_in and the upper limit voltage value V_max.

Here, the term “open circuit voltage V₀” means a terminal voltage during current shutoff; the term “available input power P_in”, an instantaneous maximum input power in a range wherein a value of the terminal voltage V does not exceed the upper limit voltage value V_max that is predetermined for battery protection; and the term “available output power P_out” an instantaneous maximum output power in a range wherein a value of the terminal voltage V does not exceed the lower limit voltage value V_min that is predetermined for battery protection.

In general, since a value of the terminal voltage V of a secondary battery momentarily varies during a transitional period (that is, charging and discharging period) and a period until the terminal voltage V is stabilized after the charging and discharging, mere attempt to measure a value of the terminal voltage V results in an inability of accurately detecting the open circuit voltage V₀ as needed.

Also, throughout the following description, a symbol “{circumflex over ( )}” denotes an estimate value.

SUMMARY OF THE INVENTION

As will be understood from the fact that the steady-state battery model (2) is used to obtain the available input power P_in, the above-described technology is based on the assumption that a charging period is sufficiently long such that a value of the terminal voltage V reaches at the upper limit voltage value V_max under the steady state. In other words, this means that the charging period is longer than a time constant T₁ in the equation (7) described below, for example, approximately 2 or 3 seconds.

However, since only a direct term $\left(\frac{{\mathrm{KT}}_2}{T_1}I\right)$ in Eq. (7) affects a value of the terminal voltage V in the leading edge thereof, it does not reach at the upper limit voltage value V_max (with a reason described below) in cases where the charging period is short like that of pulsed charging.

Then, since an estimate value {circumflex over (K)} of internal resistance K contains a large error, an estimate value {circumflex over (P)}_in of the obtained available input power P_in inevitably contains an error, too. A similar issue arises in an estimate value {circumflex over (P)}_out of the available output power P_out.

The present invention has been completed with the above view in mind and has an object to provide an available input-output power estimating device for a secondary battery wherein an error of an estimate value is minimized even when charging and discharging are executed for a short time.

To achieve the above object, the present invention provides an available input-output power estimating device for a secondary battery, comprising: a current detector detecting a value I of a current of the secondary battery; a voltage detector detecting a value V of a terminal voltage of the secondary battery; a parameter estimating section substituting the measured current value I and voltage value V into an adaptive digital filter using a battery model represented by an equation (a) for thereby collectively estimating a value of a parameter vector, as a parameter vector estimate value, in the equation (a); an open circuit voltage calculator substituting the measured current value I , the voltage value V, and the parameter estimate value into the equation (a) for thereby calculating a value {circumflex over (V)}₀ of an open circuit voltage; an available input power estimating section substituting a set of components (â_n,{circumflex over (b)}_n) in the parameter vector estimate value, which is associated with a direct term in the equation (a); the open circuit voltage estimate value {circumflex over (V)}₀, and an upper limit voltage V_max, which is predetermined, of the terminal voltage into an equation (b) for thereby estimating an available input power P_in, of the secondary battery; and an available output power estimating section substituting the set of components (â_n,{circumflex over (b)}_n) in the parameter vector estimate value, which is associated with the direct term in the equation (a), the open circuit voltage estimate value {circumflex over (V)}₀, and a lower limit voltage V_min, which is predetermined, of the terminal voltage V into an equation (c) for thereby estimating an available output power P_out of the secondary battery, wherein the equations (a), (b) and (c) are described, respectively, as $\begin{array}{cc}V=\frac{B\left(s\right)}{A\left(s\right)}I+\frac{1}{C\left(s\right)}{V}_0,& \left(a\right)\\ P_{\mathrm{in}}=\frac{V_{\max }-{\hat{V}}_0}{{\hat{b}}_n}{\hat{a}}_n{V}_{\max },\mathrm{and}& \left(b\right)\\ P_{\mathrm{out}}=\frac{{\hat{V}}_0-V_{\min }}{{\hat{b}}_n}{\hat{a}}_n{V}_{\min }& \left(c\right)\end{array}$ where A(s) , B(s), and C(s) represent polynomials of a Laplace operator s, respectively, as follows: $\begin{array}{cc}A\left(s\right)=\sum _{k=0}^n{a}_k{s}^k,B\left(s\right)=\sum _{k=0}^n{b}_k{s}^k,\mathrm{and}C\left(s\right)=\sum _{k=0}^n{c}_k{s}^k& \left(d\right)\end{array}$ where the first order coefficients a₁, b₁, and c₁ of the polynomials take non-zero values, respectively.

Also, the present invention provides an estimating method of an available input-output power for a secondary battery, comprising: measuring a value I of a current of the secondary battery; measuring a value V of a terminal voltage of the secondary battery; substituting the measured current value I and the measured voltage value V into an adaptive digital filter using a battery model represented by an equation (a) for thereby collectively estimating a value of a parameter vector, as a parameter vector estimate value, in the equation (a); substituting the measured current value I , the measured voltage value V , and the parameter estimate value into the equation (a) for thereby calculating a value {circumflex over (V)}₀, as an open circuit voltage estimate value, of an open circuit voltage; substituting a set of components (â_n,{circumflex over (b)}_n), which is associated with a direct term in the equation (a), of the parameter vector estimate value, the open circuit voltage estimate value {circumflex over (V)}₀, and an upper limit voltage V_max, which is predetermined, of the terminal voltage V into an equation (b) for thereby estimating an available input power P_in of the secondary battery; and substituting the one set of components (â_n,{circumflex over (b)}_n), which is associated with the direct term in the equation (a), of the parameter vector estimate value, the open circuit voltage estimate value {circumflex over (V)}₀, and a lower limit voltage V_min, which is predetermined, of the terminal voltage V into an equation (c) for thereby estimating an available output power P_out of the secondary battery; wherein the equations (a), (b), and (c) are described, respectively, as $\begin{array}{cc}V=\frac{B\left(s\right)}{A\left(s\right)}I+\frac{1}{C\left(s\right)}{V}_0,& \left(a\right)\\ P_{\mathrm{in}}=\frac{V_{\max }-{\hat{V}}_0}{{\hat{b}}_n}{\hat{a}}_n{V}_{\max },\mathrm{and}& \left(b\right)\\ P_{\mathrm{out}}=\frac{{\hat{V}}_0-V_{\min }}{{\hat{b}}_n}{\hat{a}}_n{V}_{\min }& \left(c\right)\end{array}$ where A(s) , B(s), and C(s) represent polynomials of a Laplace operator s, respectively, as follows: $\begin{array}{cc}A\left(s\right)=\sum _{k=0}^n{a}_k{s}^k,B\left(s\right)=\sum _{k=0}^n{b}_k{s}^k,\mathrm{and}C\left(s\right)=\sum _{k=0}^n{c}_k{s}^k& \left(d\right)\end{array}$ where the first order coefficients a₁, b₁, and c₁ of the polynomials take non-zero values, respectively.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram of an available input-output power estimating device according to the present invention.

FIG. 2 is a block diagram showing a concrete structure of the available input-output power estimating device shown in FIG. 1.

FIG. 3 is a view showing an equivalent circuit model of a secondary battery of a first embodiment according to the present invention.

FIG. 4 is a view showing a correlation map between an open circuit voltage and a charging rate.

FIG. 5 is a flowchart of operation procedures to be executed by a battery controller 30.

FIG. 6 is a view for illustrating a direct term.

FIG. 7 is a view for illustrating an estimate value of available input power in the related art.

FIG. 8 is a view for illustrating an estimate value of available input power in the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 is a functional block diagram of an available input-output power estimating device according to the present invention.

The available input-output power estimating device 100 is comprised of a current detector 5 that detects a value of current I charged to and discharged from a secondary battery (which may be merely a battery), a terminal voltage detector 6 that detects a value of a terminal voltage V of the secondary voltage, a parameter estimating section 1 that collectively estimates a value (which will be described later in detail) of a parameter vector {right arrow over (θ)} in a battery model, with an open circuit voltage V₀ defined as an offset term, using the current value detected by the current detector 5 and the terminal voltage value detected by the terminal voltage detector 6, an open circuit voltage calculator 2 that calculates a value of the open circuit voltage V₀ based on the current value and the terminal voltage value, detected in the manner mentioned above, and the parameter vector value estimated in the manner described above, an available input power estimating section 3 that estimates a value P_in of an available input-output power of the secondary battery based on the parameter vector value, estimated in the manner described above, and the open circuit voltage calculated in the manner mentioned above, and an available output power estimating section 4 that estimates a value P_in of available input-output power of the secondary battery based on the parameter vector value estimated in the manner described above.

FIG. 2 is a block diagram showing a concrete structure of the available input-output power estimating device 100 shown in FIG. 1. Here, an exemplary structure is shown wherein the available input-output power estimating device 100 is applied to a system wherein a load 20, such as a motor, is driven with the secondary battery 10 and the secondary battery 10 is charged with regenerative power of the motor.

The available input-output power estimating device 100 includes a battery controller (electronic control unit) 30, an ammeter 40 that detects the current I charged to and discharged from the secondary battery 10, and a voltmeter 50 that detects the terminal voltage V of the secondary battery 10.

The battery controller 30 is structured of a microcomputer, composed of a CPU for calculating programs, a ROM storing the programs and a RAM that stores calculation results, and electronic circuitries, to which the ammeter 40, the voltmeter 50 and a temperature gauge (not shown), which detects temperatures of the battery, are connected.

The battery controller 30 corresponds to the parameter estimating section 1, the open circuit voltage calculator 2, the available input power estimating section 3 and the available output power estimating section 4, which are shown in FIG. 1; the ammeter 40 corresponds to the current detector 5; and the voltmeter 5 corresponds to the terminal voltage detector 6.

Next, an essence of the present invention is described with a view to providing the ease of understanding the present specification.

In the present invention, a higher order model is assumed to be an equivalent circuit model of a secondary battery (hereinafter referred to as a battery model) that is described as $\begin{array}{cc}V=\frac{B\left(s\right)}{A\left(s\right)}I+\frac{1}{C\left(s\right)}{V}_0& \left(7\right)\end{array}$ where A(s), B(s) and C(s) represent polynomials of a Laplace operator (or Laplace variable) s given as $\begin{array}{cc}A\left(s\right)=\sum _{k=0}^n{a}_k{s}^k,B\left(s\right)=\sum _{k=0}^n{b}_k{s}^k,\mathrm{and}C\left(s\right)=\sum _{k=0}^n{c}_k{s}^k& \left(8\right)\end{array}$ where first order coefficients a₁, b₁, C₁ of the respective polynomials take non-zero values, respectively.

Substituting measured values of the current I and the terminal voltage V into an adaptive digital filter using the battery model (7) allows the calculation of estimate values (â_n,{circumflex over (b)}_n) of parameters (a_n, b_n) (that is, coefficients of the maximum order of polynomials A(s), B(s) of Eq. (8)), associated with the direct term in Eq. 7. Thus, substituting the estimate values (â_n, {circumflex over (b)}_m) of the parameters (a_n, b_n) and the measured value of the terminal voltage V into Eq. (7) allows the calculation of an estimate value {circumflex over (V)}₀ of the open circuit voltage V₀. Using the estimate values (â_n , {circumflex over (b)}_n) of the parameters, the estimate value {circumflex over (V)}₀ of the open circuit voltage V₀ and an upper limit voltage value V_max allows available input power P_in of the secondary battery to be estimated by $\begin{array}{cc}{P}_{\mathrm{in}}=\frac{V_{\max }-{\hat{V}}_0}{{\hat{b}}_n}{\hat{a}}_n{V}_{\max }.& \left(9\right)\end{array}$

At the same time, using the estimate values (â_n, {circumflex over (b)}_n) of the parameters, the estimate value {circumflex over (V)}₀ of the open circuit voltage V₀, and a lower limit voltage value V_min allows available output power {circumflex over (P)}_out of the secondary battery to be estimated by $\begin{array}{cc}{P}_{\mathrm{out}}=\frac{{\hat{V}}_0-V_{\min }}{{\hat{b}}_n}{\hat{a}}_n{V}_{\min }.& \left(10\right)\end{array}$

Hereinafter, the present invention is described in detail using concrete embodiments.

<First Embodiment>

FIG. 3 is a view showing a battery model of a secondary battery of a first embodiment.

Although this battery model is a reduction (primary) model without particular separation in positive and negative electrodes, this battery model is sufficient to illustrate charging and discharging characteristics of an actual secondary battery. In this figure, I represents current [A] (with a positive value representing a charging period while a negative value represents a discharging period); V a terminal voltage [V]; V₀ an open circuit voltage [V] (also called an electromotive force or an open circuit voltage); K internal resistance; T₁ and T₂ time constants; and s a Laplace operator (or Laplace variable).

This battery model is represented by $\begin{array}{cc}V=\frac{K\left(T_{2}s+1\right)}{T_{1}s+1}I+\frac{1}{T_{1}s+1}{V}_0.& \left(11\right)\end{array}$

Since Eq. (11) is a special case of Eq. (7) where both the denominators A(s) and C(s) of the first and second terms on the right side in Eq. (7) take A(s)=C(s)=T₁s+1, Eq. (11) well describes a battery such as a lithium battery in which an open circuit voltage converges at a relatively high speed.

First, a derivation process of an adaptive digital filter using the battery model (11) is described below.

Since it is considered that the open circuit voltage V₀ is equivalent to a value that the current I multiplied by variable efficiency h is integrated from an initial state, then the open circuit voltage V₀ can be described as $\begin{array}{cc}{V}_0=\frac{h}{s}I.& \left(12\right)\end{array}$ Then, substituting Eq. (12) into Eq. (11) gives $\begin{array}{cc}\begin{array}{c}V=\frac{K\left(T_{2}s+1\right)}{T_{1}s+1}I+\frac{1}{T_{1}s+1}\frac{h}{s}I\\ =\frac{{\mathrm{KT}}_2{s}^2+\mathrm{Ks}+h}{T_1{s}^2+s}I.\end{array}& \left(13\right)\end{array}$

Next, multiplying both sides of Eq. (13) by a lowpass filter (or band pass filter) operator G_lp (s) gives G_lp(s)(T s²+s)V=G_lp(s)(KT₂s²+Ks+h)I.   (14)

Also, the current I and the terminal voltage V multiplied by the lowpass filter operator G_lp(s) are defined as V₃=s²G_lp(s)V, V₂=sG_lp(s)V, V₁=G_lp(s)V, I₃=s²G_lp(s)I, I₂=sG_lp(s)I, I₁=G_lp(s)I.   (15) Here, the lowpass filter operator G_lp(s) is given as $\begin{array}{cc}{G}_{\mathrm{lp}}=\frac{1}{{\left(\mathrm{ps}+1\right)}^3}& \left(16\right)\end{array}$ wherein p represents a response time constant determining a response characteristic of the lowpass filter operator G_lp(s).

Substituting Eqs. (15) and (16) into Eq. (14) gives T₁V₃+V₂=KT₂I₃+KI₂+hI₁  (17) Eq. (17) can be further rewritten in a vector representation as $\begin{array}{cc}{V}_2=-T_1{V}_3+{\mathrm{KT}}_2{I}_3+{\mathrm{KI}}_2+{\mathrm{hI}}_1=\left(\begin{array}{cccc}{V}_3& I_3& I_2& I_1\end{array}\right)·\left(\begin{array}{c}-T_1\\ {\mathrm{KT}}_2\\ K\\ h\end{array}\right).& \left(18\right)\end{array}$

Since Eq. (18) is represented with an inner product between a known vector having components V₃, I₃, I₂, I₁ as observable quantities, and an unknown vector having components T₁, T₂, K, h as parameters, Eq. (18) can be reduced to a standard form of a general adaptive digital filter given as y={right arrow over (ω)}^T·{right arrow over (θ)}  (19) where y≡V₂,{right arrow over (ω)}^T≡(V₃,I₃, I₂,I₁), {right arrow over (θ)}^T≡(−T₁,KT₂,K,h)   (20)

Accordingly, using the current I and the terminal voltage V filtered by the adaptive digital filter enables a value of a parameter vector {right arrow over (θ)} to be estimated.

Here it should be noted that the above derivation process of the adaptive digital filter using the battery model (11) is established for the more general first order battery model described as $\begin{array}{cc}V=\frac{K\left(T_{2}s+1\right)}{T_{1}s+1}I+\frac{1}{T_{3}s+1}{V}_0.& \left(11\text{-}a\right)\end{array}$ where T₃ is a time constant different from the time constant T₁ in general. In other words, an adaptive digital filter using the battery model (11-a) is reduced to the standard form (19), too.

In the presently filed embodiment, in order to estimate the parameter vector {right arrow over (θ)} , the both-limits trace gain method is used instead of the least square method because the least square method has a disadvantage such that once a value of the parameter vector {right arrow over (θ)} is converged to a local minimum value, subsequent variation in parameters make it difficult to converge a true minimum value of the parameter vector {right arrow over (θ)}. An algorithm of the both-limits trace gain method is described as follows: $\begin{array}{cc}\overrightarrow{\theta }\left(k\right)=\overrightarrow{\theta }\left(k-1\right)-\gamma \left(k\right)P\left(k-1\right)\overrightarrow{\omega }\left(k\right)·\left[{\overrightarrow{\omega }}^T\left(k\right)·\overrightarrow{\theta }\left(k-1\right)-y\left(k\right)\right],\gamma \left(k\right)=\frac{{\lambda }_3}{1+{\lambda }_3{\overrightarrow{\omega }}^T\left(k\right)·P\left(k-1\right)\overrightarrow{\omega }\left(k\right)},P\left(k\right)=\frac{1}{{\lambda }_1\left(k\right)}\left\{\begin{array}{c}P\left(k-1\right)-\\ \frac{{\lambda }_{3}P\left(k-1\right)\overrightarrow{\omega }\left(k\right)·{\overrightarrow{\omega }}^T\left(k\right)P\left(k-1\right)}{1+{\lambda }_3{\overrightarrow{\omega }}^T\left(k\right)·P\left(k-1\right)\overrightarrow{\omega }\left(k\right)}\end{array}\right\}=\frac{P^{\prime }\left(k\right)}{{\lambda }_1\left(k\right)},{\lambda }_1\left(k\right)=\{\begin{array}{cc}\frac{\mathrm{tr}\left\{P^{\prime }\left(k\right)\right\}}{{\gamma }_U}& \mathrm{for}{\lambda }_1\le \frac{\mathrm{tr}\left\{P^{\prime }\left(k\right)\right\}}{{\gamma }_U}\\ {\lambda }_1& \mathrm{for}\frac{\mathrm{tr}\left\{P^{\prime }\left(k\right)\right\}}{{\gamma }_U}\le {\lambda }_1\le \frac{\mathrm{tr}\left\{P^{\prime }\left(k\right)\right\}}{{\gamma }_L}\\ \frac{\mathrm{tr}\left\{P^{\prime }\left(k\right)\right\}}{{\gamma }_L}& \mathrm{for}\frac{\mathrm{tr}\left\{P^{\prime }\left(k\right)\right\}}{{\gamma }_L}\le {\lambda }_1\end{array}& \left(21\right)\end{array}$ where variable k represents a parameter of an iteration; and {right arrow over (θ)}(k) a value of a parameter vector {right arrow over (θ)} at a k-th time's iteration with an initial value {right arrow over (θ)}(0) being set to a sufficiently less value to be non-zero. Also, it is assumed that λ₁, λ₃, γ_U, γ_L represent initial values and further λ₁, λ₃ satisfy the conditions 0<λ₁<1 , 0<λ₃<∞, respectively. Furthermore, P(k) is a matrix with an initial value P(0) set to a sufficiently large value. The symbol tr{P′(k)} represents a trace of the matrix P′(k).

Now, description is made of operation procedures to be executed by the battery controller 30 using a flowchart of FIG. 5. In FIG. 5, the iteration is implemented for each fixed period T₀. Hereinafter, description is made of an operation process in the k-th time's iteration.

In step S10, the operation is executed to measure a value I(k) of current I and a value V(k) of a terminal voltage V.

In step S20, the operation is executed to discriminate whether a shutoff relay of the secondary battery is turned on or turned off. The battery controller 30 also executes control of the shutoff relay of the secondary battery and the operation goes to step S30 when the shutoff relay is turned off (with current I=0). When the relay is turned on, the operation goes to step S40.

In step S30, a value V(k) of the terminal voltage V is stored as a terminal voltage initial value V_int.

In step S40, a differential value ΔV(k) of the terminal voltage V is calculated by ΔV(k)=V(k)−V_int   (22) This calculation is conducted for avoiding divergence in a value of a parameter vector {right arrow over (θ)} during a start in estimating calculation because an initial value {right arrow over (θ)}(0) is set to a sufficiently less value to be non-zero.

During shutoff of the relay, since exactly I(k)=0 and ΔV(k)=0, the initial value {right arrow over (θ)}(0) of the parameter vector {right arrow over (θ)} remains the initial state.

In step S50, by using Eqs. (15) and (16), a value I(k) of current I and a differential value ΔV(k) of the terminal voltage V are filtered with a lowpass filter operator G_lp(s), thereby calculating values I₁(k)˜I₃(k) and V₁(k)˜V₃(k) of I₁˜I₃ and V₁˜V₃.

In this case, in order to increase an estimating accuracy of the algorithm in Eq. (21) (that is, for the purpose of minimizing noise), a time constant p of the lowpass filter operator G_lp(s) is set to have a value by which a response of a lowpass filter operator G_lp(s) is delayed.

However, this time constant p is set to provide a faster response than that of the secondary battery.

In step S60, substituting the values I₁(k)˜I₃(k) and V₁(k)˜V₃(k) into Eq. (21) allows the calculation of a value {right arrow over (θ)}(k) of the parameter vector {right arrow over (θ)}.

In step S70, components T₁(k), K(k)T₂(k), K(k) of the parameter vector {right arrow over (θ)}(k) calculated in step S60 and the values I₁(k)˜I₃(k) and V₁(k)˜V₃(k) calculated in step S50 are substituted into $\begin{array}{cc}\begin{array}{c}\Delta V_0\left(k\right)=G_{\mathrm{lp}}\left(s\right)·V_0\left(k\right)\\ =G_{\mathrm{lp}}\left(s\right)·\left\{\left(T_1\left(k\right)s+1\right)V\left(k\right)-K\left(k\right)\left(T_2\left(k\right)s+1\right)I\left(k\right)\right\}\\ =V_1\left(k\right)+T_1\left(k\right)V_2\left(k\right)-K\left(k\right)T_2\left(k\right)I_2\left(k\right)-K\left(k\right)I_1\left(k\right).\end{array}& \left(23\right)\end{array}$

Here, Eq. (23) is derived by multiplying both sides of an equation given as V₀(k)=(T₁(k)s+1)V(k)−K(k)(T₂(k)s+1)I(k),   (24) that is the modified Eq. (11), by the lowpass filter operator G_lp(S). Since the open circuit voltage V₀ slowly varies, ΔV₀(k)(=G_lp(s)·V₀(k)) represented by Eq. (23) can be used as a substitute for the value V₀(k) of the open circuit voltage V₀.

In step S80, by adding the initial value (that is, the initial value V_int of the terminal voltage V(k)) of the open circuit voltage V₀ to the differential value ΔV(k) of the terminal voltage V calculated in step S70, a value V₀(k) of the open circuit voltage V₀ can be calculated as V₀(k)=ΔV₀(k)+V_int.   (25)

In step 90, a charging ratio SOC(k) is calculated based on the V₀(k) of the open circuit voltage V₀ calculated in step S80, by using a correlation map between the open circuit voltage V₀ and the charging ratio shown in FIG. 4. Here, in FIG. 4, V_L and V_H represent open circuit voltage values corresponding to SOC=0% and SOC=100%, respectively.

In step S100, values of allowable input and output powers P_in and P_out are calculated. For that purpose, there is a need to focus on the direct term in Eq. (11) because an instantaneous current value for a value of the terminal voltage V reaching at an upper voltage value V_max and a lower voltage value V_min. Therefore, the direct term is described below. Also, the upper voltage value V_max and the lower voltage value V_min represent predetermined upper and lower limits by which the secondary battery is protected and take fixed values, respectively.

First, Eq. (11-a), representing a general first battery model, is modified as follows: $\begin{array}{cc}\begin{array}{c}V=\frac{K\left(T_{2}s+1\right)}{T_{1}s+1}I+\frac{1}{T_{3}s+1}{V}_0\\ =\left\{\frac{{\mathrm{KT}}_2}{T_1}+\frac{K\left(1-\frac{T_2}{T_1}\right)}{T_{1}s+1}\right\}I+\frac{1}{T_{3}s+1}{V}_0\\ =\frac{{\mathrm{KT}}_2}{T_1}I+\left\{\frac{K\left(1-\frac{T_2}{T_1}\right)}{T_{1}s+1}I+\frac{1}{T_{3}s+1}{V}_0\right\}\end{array}& \left(26\right)\end{array}$ where a first term on a right side is called a direct term. Here it should be noted that this direct term necessary to calculate available input-output powers P_in and P_out is not affected by the time constant T₃. In Eq. (26), a voltage variation ΔV only for the direct term in terms of a current variation ΔI is given as $\begin{array}{cc}\Delta V=\frac{{\mathrm{KT}}_2}{T_1}\Delta I.& \left(27\right)\end{array}$FIG. 6 is a view for illustrating the direct term from another angle and shows a step response function in a real space corresponding to $\begin{array}{cc}y=\frac{T_{2}s+1}{T_{1}s+1}& \left(28\right)\end{array}$ in Eq. (26), where T₁>T₂. The step response function sharply rises to a value $\frac{T_2}{T_1}$ at time 0 and, thereafter, takes a waveform with a first-order lag. The direct term corresponds to the value $\frac{T_2}{T_1}$ during the rising period. In the presently filed embodiment, since the value $\frac{T_2}{T_1}$ is multiplied by an internal resistance K, the direct term has a coefficient $\frac{{\mathrm{KT}}_2}{T_1}.$ However, in the present invention, an estimate value of the parameter corresponding to this coefficient is generally represented as (â_n, {circumflex over (b)}_n).

In step S100, first, a difference between the upper limit voltage value V_max and the value V₀(k) of the open circuit voltage V₀ calculated in step S80 (in Eq. (25)) is calculated as ΔV(k)=V_max−V₀(k).   (29) Next, substituting components K(k)T₂(k), T₁(k) ΔV(k) of the value {right arrow over (θ)}(k) of the parameter vector {right arrow over (θ)} into Eq. (27) allows a current value ΔI to be calculated as $\begin{array}{cc}\Delta I\left(k\right)=\frac{\left(V_{\max }-V_0\left(k\right)\right)T_1\left(k\right)}{K\left(k\right)T_2\left(k\right)}.& \left(30\right)\end{array}$

Using the current variation ΔI(k) calculated in such a way allows the allowable input power P_in(k) in the k-th time's iteration to be calculated as $\begin{array}{cc}\begin{array}{c}{P}_{\mathrm{in}}\left(k\right)=V_{\max }\Delta I\left(k\right)\\ =\frac{\left(V_{\max }-V_0\left(k\right)\right)T_1\left(k\right)}{K\left(k\right)T_2\left(k\right)}{V}_{\max }.\end{array}& \left(31\right)\end{array}$

A value P_out(k) of the available output power P_out in the k-th time's iteration can be similarly derived by calculating a difference between the lower limit voltage value V_min and the value V₀(k) (in Eq. (25)) of the open circuit voltage V₀ calculated in step S80 as follows: ΔV(k)=V₀(k)−V_min.   (32)) Then, substituting components K(k)T₂(k) and T₁(k) of the value {right arrow over (θ)}(k) of the parameter vector {right arrow over (θ)} into Eq. (27) allows a current value ΔI to be calculated as $\begin{array}{cc}\Delta I\left(k\right)=\frac{\left(V_0\left(k\right)-V_{\min }\right)T_1\left(k\right)}{K\left(k\right)T_2\left(k\right)}.& \left(33\right)\end{array}$

Using the current variation ΔI(k) calculated in such a way allows the allowable output power P_out(k) in the k-th time's iteration to be calculated as $\begin{array}{cc}\begin{array}{c}{P}_{\mathrm{out}}\left(k\right)=V_{\min }\Delta I\left(k\right)\\ =\frac{\left(V_0\left(k\right)-V_{\min }\right)T_1\left(k\right)}{K\left(k\right)T_2\left(k\right)}{V}_{\min }.\end{array}& \left(34\right)\end{array}$

In step S110, values needed for subsequent iterations in the values calculated in such a way are stored and the calculation is terminated.

By repeatedly executing the iteration processes in the algorithm (21) of the both-limits trace gain method in such a manner, the estimate value {circumflex over (P)}_in of the available input power P_in(k) and the estimate value {circumflex over (P)}_out of the available output power P_out can be finally obtained as $\begin{array}{cc}{\hat{P}}_{\mathrm{in}}=V_{\max }\Delta \hat{I}& \left(35\right)\\ =\frac{\left(V_{\max }-{\hat{V}}_0\right){\hat{T}}_1}{\hat{K}{\hat{T}}_2}{V}_{\max }& \\ =\frac{{\hat{T}}_1}{{\hat{T}}_2}\left\{\frac{\left(V_{\max }-{\hat{V}}_0\right)}{\hat{K}}{V}_{\max }\right\},& \\ {\hat{P}}_{\mathrm{out}}=V_{\min }\Delta \hat{I}& \left(36\right)\\ =\frac{\left({\hat{V}}_0-V_{\min }\right){\hat{T}}_1}{\hat{K}{\hat{T}}_2}{V}_{\min }& \\ =\frac{{\hat{T}}_1}{{\hat{T}}_2}\left\{\frac{\left({\hat{V}}_0-V_{\min }\right)}{\hat{K}}{V}_{\min }\right\}.& \end{array}$

Applying the method described above to the general battery model (7) provides results as represented by Eq. (9) and Eq. (10).

Lastly, a difference between the related art and the present invention is described below.

FIG. 7 is a view for illustrating the estimate value of the available input power in the related art described above, and FIG. 8 is a view for illustrating the estimate value of the available input power in the first embodiment according to the present invention.

As shown in FIG. 7, in the related art, a current variation ΔI was calculated by using the steady-state battery module (2). That is, it was assumed that, in the related art, a charging time interval was sufficiently long such that a value of the terminal voltage V reaches at the upper limit voltage value V_max under the steady state. Accordingly, since the variation value in the leading edge of the terminal voltage V is affected by only the direct term in cases where the charging time interval is short like that of the pulsed charging, the voltage variation ΔV is described as Eq. (27). Accordingly, since the value of the terminal voltage V does not reach at the voltage value of ΔV=KΔI (that is, the upper limit voltage value V_max) under the steady state, large error is observed in the estimate value {circumflex over (P)}_in of the allowable input power P_in. This similarly applies to the estimate value {circumflex over (P)}_out of the available output power P_out under a situation where rapid discharging takes place.

On the contrary, in the presently filed embodiment, since the current variation ΔI is calculated from Eq. (30) based on the direct term, as shown in FIG. 8, the voltage variation ΔV in the leading edge of the terminal voltage V is given as $\begin{array}{cc}\Delta V=\frac{\hat{K}{\hat{T}}_2}{{\hat{T}}_1}\Delta I.& \left(37\right)\end{array}$ More generally, in the battery model (7) of the secondary battery, the voltage variation ΔV of the terminal voltage V is given as $\begin{array}{cc}\Delta V=\frac{{\hat{a}}_n}{{\hat{b}}_n}\Delta I.& \left(38\right)\end{array}$

From this, it is easily understood that, in the present invention, the voltage variation ΔV in the leading edge of the terminal voltage V reaches at a value fairly close to the voltage value of ΔV=KΔI (that is, the upper limit voltage value V_max) under the steady state.

Accordingly, in the present invention, even in cases where the charging time interval is short like that of the pulsed charging, only the voltage variation ΔV (direct term) in the leading edge of the terminal voltage V is able to nearly reach the upper limit voltage value V_max.

As a result, an error of the estimate value {circumflex over (P)}_in of the allowable input power P_in is reduced. A similar effect results in the estimate value {circumflex over (P)}_out of the available output power P_out under the situation where rapid discharging takes place.

<Second Embodiment>

A second embodiment is configured such that the lowpass filter treatment is executed on the components K(k)T₂(k), T₁(k) of the value {right arrow over (θ)}(k) of the parameter vector {right arrow over (θ)}(or components ({circumflex over (a )}_n, {circumflex over (b)}_n,) in the battery model shown in FIG. 7), which are associated with the direct term, obtained in the first embodiment.

The second embodiment differs from the first embodiment in respect of step S100 in the flowchart of operations in the first embodiment shown in FIG. 5 and is similar thereto in other respect. Therefore, description of the other respect is herein omitted.

Since the components K(k)T₂(k) and T₁(k) of the value {right arrow over (θ)}(k) of the parameter vector {circumflex over (θ)} are easily affected by noise, the presently filed embodiment is configured to execute filter treatment on these components K(k)T₂(k) and T₁(k) by using a lowpass filter operator given as $\begin{array}{cc}G\left(s\right)=\frac{1}{\tau s+1}.& \left(39\right)\end{array}$

Then, Eq. (30) is corrected in step S100 like $\begin{array}{cc}\Delta I\left(k\right)=\left(V_{\max }-V_0\left(k\right)\right)G\left(s\right)\left\{\frac{T_1\left(k\right)}{K\left(k\right)T_2\left(k\right)}\right\}.& \left(40\right)\end{array}$

Using the current variation ΔI calculated in such a manner allows the value P_in(k) in the k-th time's iteration for the available input power P_in to be calculated as $\begin{array}{cc}\begin{array}{c}{P}_{\mathrm{in}}\left(k\right)=V_{\max }\Delta I\left(k\right)\\ =\left(V_{\max }-V_0\left(k\right)\right)G\left(s\right)\left\{\frac{T_1\left(k\right)}{K\left(k\right)T_2\left(k\right)}\right\}{V}_{\max }.\end{array}& \left(41\right)\end{array}$

As for the value P_out(k) of the available output power P_out, Eq. (33) is similarly corrected as $\begin{array}{cc}\Delta I\left(k\right)=\left(V_0\left(k\right)-V_{\min }\right)G\left(s\right)\left\{\frac{T_1\left(k\right)}{K\left(k\right)T_2\left(k\right)}\right\}.& \left(42\right)\end{array}$

By using the current variation ΔI calculated in such a way, the value P_out(k) of the available output power P_out in the k-th time's iteration is calculated as $\begin{array}{cc}\begin{array}{c}{P}_{\mathrm{out}}\left(k\right)=V_{\min }\Delta I\left(k\right)\\ =\left(V_0\left(k\right)-V_{\min }\right)G\left(s\right)\left\{\frac{T_1\left(k\right)}{K\left(k\right)T_2\left(k\right)}\right\}{V}_{\min }.\end{array}& \left(43\right)\end{array}$

Thus, in consideration of the fact that the components K(k)T₂(k) and T₁(k), which are associated with the direct term, in the value {right arrow over (θ)}(k) of the parameter vector {right arrow over (θ)} are easily affected by noise, the second embodiment executes the lowpass filter treatment on these components K(k)T₂(k) and T₁(k) (or components (â_n, {circumflex over (b)}_n)) in the battery model shown in FIG. 7). Therefore, there is an advantage in that errors of the estimate value {circumflex over (P)}_in of the available input power P_in and the estimate value {circumflex over (P)}_out of the available output power P_out are further reduced because noise is less than that occurring when using the components K(k)T₂(k), T₁(k) (or (â_n, {circumflex over (b)}_n))in the battery model shown in FIG. 7) of the value {right arrow over (θ)}(k) of the parameter vector {right arrow over (θ)} calculated in the first embodiment.

<Third Embodiment>

A third embodiment is configured such that the lowpass filter treatment is executed on a ratio $\frac{T_1\left(k\right)}{T_2\left(k\right)}$ of the components K(k)T₂(k) and T₁(k) of the value {right arrow over (θ)}(k) of the parameter vector {right arrow over (θ)} (or (â_n, {circumflex over (b)}_n)) in the battery model shown in FIG. 7), which are associated with the direct term obtained in the first embodiment.

The third embodiment differs from the first embodiment in respect of step S100 in the flowchart of the operations in the first embodiment, shown in FIG. 5, and is similar thereto in other respect. Therefore, description of the other respect is herein omitted.

Although the components K(k)T₂(k) and T₁(k) in the value {circumflex over (θ)}(k) of the parameter vector {right arrow over (θ)} calculated in step SS60 are easily affected by noise, variation of the value K(k) of internal resistance K, a steady state gain, is small. Therefore, in the presently filed embodiment, the filter treatment is executed on the ratio $\frac{T_1\left(k\right)}{T_2\left(k\right)}$ by using the lowpass filter operator G(s) represented by Eq. (39). Ten, Eq. (30) is corrected in step S100 like $\begin{array}{cc}\Delta I\left(k\right)=\frac{\left(V_{\max }-V_0\left(k\right)\right)}{K\left(k\right)}G\left(s\right)\left\{\frac{T_1\left(k\right)}{T_2\left(k\right)}\right\}.& \left(44\right)\end{array}$

Using the current variation ΔI calculated in such a way, the value P_in(k) of the available input power P_in is calculated as $\begin{array}{cc}\begin{array}{c}{P}_{\mathrm{in}}\left(k\right)=V_{\max }\Delta I\left(k\right)\\ =\frac{\left(V_{\max }-V_0\left(k\right)\right)V_{\max }}{K\left(k\right)}G\left(s\right)\left\{\frac{T_1\left(k\right)}{T_2\left(k\right)}\right\}.\end{array}& \left(45\right)\end{array}$

For the value P_out(k) of the available output power P_out in the k-th time's iteration is similarly corrected like $\begin{array}{cc}\Delta I\left(k\right)=\frac{\left(V_0\left(k\right)-V_{\min }\right)}{K\left(k\right)}G\left(s\right)\left\{\frac{T_1\left(k\right)}{T_2\left(k\right)}\right\}.& \left(46\right)\end{array}$

By using the current variation ΔI calculated in such a way, the value P_out(k) of the available output power P_out is calculated as $\begin{array}{cc}\begin{array}{c}{P}_{\mathrm{out}}\left(k\right)=V_{\max }\Delta I\left(k\right)\\ =\frac{\left(V_0\left(k\right)-V_{\min }\right)V_{\min }}{K\left(k\right)}G\left(s\right)\left\{\frac{T_1\left(k\right)}{T_2\left(k\right)}\right\}.\end{array}& \left(47\right)\end{array}$

Thus, in consideration of the fact that the components K(k)T₂(k) and T₁(k), which are associated with the direct term, of the value {right arrow over (θ)}(k) of the parameter vector {right arrow over (θ)} are easily affected by noise while variation of the value K(k) of internal resistance K is small, the second embodiment executes the lowpass filter treatment on the ratio $\frac{T_1\left(k\right)}{T_2\left(k\right)}.$ By using the ratio $\frac{T_1\left(k\right)}{T_2\left(k\right)}$ filtered by the lowpass filter G(s) in combination with the value K(k) of the internal resistance K with less variation, there is advantage in that errors of the estimate value {circumflex over (P)}_in of the available input power P_in and the estimate value {circumflex over (P)}_out of the available output power P_out are further reduced because noise is less than that using only the components K(k)T₂(k) and T₁(k) of the value {right arrow over (θ)}(k) of the parameter vector {right arrow over (θ)} in the second embodiment, resulting from fluctuation in these components, is further eliminated.

As will be easily understood from the foregoing description, the present invention allows the estimation of available input power P_in and available output power P_out by using the estimate values (â_n, {circumflex over (b)}_n) of the parameter vector associated with the direct term whereby even in cases where the charging time interval is short like the pulsed charging, it becomes possible to calculate the current value ΔI by which the terminal voltage V reaches at the upper limit voltage V_max of the terminal voltage V in the leading edge of the terminal voltage V. Accordingly, the estimate value {circumflex over (P)}_in of the available input power P_in can be precisely aligned with the actual value, enabling reduction in error. Similar advantageous effect also results in the estimate value {circumflex over (P)}_out of the available output power P_out under a situation where rapid charging takes place.

The entire content of Japanese Patent Application No. P2004-173448 with a filing data of Jun. 11, 2004 is herein incorporated by reference.

Although the present invention has been described above by reference to certain embodiments of the invention, the invention is not limited to the embodiments described above and modifications will occur to those skilled in the art, in light of the teachings. The scope of the invention is defined with reference to the following claims.

Claims

1. An available input-output power estimating device for a secondary battery, comprising: a current detector measuring a value I of a current of the secondary battery; a voltage detector measuring a value V of a terminal voltage of the secondary battery; a parameter estimating section substituting the measured current value I and the measured voltage value V into an adaptive digital filter using a battery model represented by an equation (a) for thereby collectively estimating a value of a parameter vector, as a parameter vector estimate value, in the equation (a); an open circuit voltage calculator substituting the measured current value I, the measured voltage value V, and the parameter estimate value into the equation (a) for thereby calculating a value {circumflex over (V)}0, as an open circuit voltage estimate value, of an open circuit voltage; an available input power estimating section substituting a set of components (ân, {circumflex over (b)}n), which is associated with a direct term in the equation (a), of the parameter vector estimate value, the open circuit voltage estimate value {circumflex over (V)}0, and an upper limit voltage Vmax, which is predetermined, of the terminal voltage V into an equation (b) for thereby estimating an available input power Pin of the secondary battery; and an available output power estimating section substituting the one set of components (ân, {circumflex over (b)}n), which is associated with the direct term in the equation (a), of the parameter vector estimate value, the open circuit voltage estimate value {circumflex over (V)}0, and a lower limit voltage Vmin, which is predetermined, of the terminal voltage V into an equation (c) for thereby estimating an available output power Pout of the secondary battery; wherein the equations (a), (b), and (c) are described, respectively, as V=B⁡(s)A⁡(s)⁢I+1C⁡(s)⁢V0,(a)Pin=Vmax-V^0b^n⁢ ⁢a^n⁢Vmax,(b)and Pout=V^0-Vminb^n⁢ ⁢a^n⁢Vmin(c)where A(s) , B(s) , and C(s) represent polynomials of a Laplace operator s, respectively, as follows: A⁡(s)=∑k=0n⁢ak⁢sk,B⁡(s)=∑k=0n⁢bk⁢sk,and⁢ ⁢C⁡(s)=∑k=0n⁢ck⁢sk(d)where the first order coefficients a1, b1, and c1 of the polynomials take non-zero values, respectively.

2. The available input-output power estimating device for the secondary battery according to claim 1, wherein: the set of components (ân, {circumflex over (b)}n) of the parameter vector estimate value is filtered with a lowpass function.

3. The available input-output power estimating device for the secondary battery according to claim 1, wherein: in case of A(s)=K(T2s+1) , B(s)=T1s+1, and C(s)=T3s+1 in the equation (a), components {circumflex over (T)}1 and {circumflex over (K)}{circumflex over (T)}2 of the parameter vector estimate value are filtered with a lowpass transfer function G(s) and then, in place of the equation (b) and the equation (c), an equation (e) and an equation (f) are used, wherein the equations (e) and (f) are described, respectively, as Pin=(Vmax-V^0)⁢G⁡(s)⁢{T^1K^⁢T^2}⁢Vmax,⁢and(e)P^out=(V^0-Vmin)⁢G⁡(s)⁢{T^1K^⁢T^2}⁢Vmin(f)where T1, T2, and T3 are time constants, respectively; K is an internal resistance of the secondary battery.

4. The available input-output power estimating device for the secondary battery according to claim 1, wherein: in case of A(s)=K(T2s+1) , B(s)=T1+1 , and C(s)=T3s+1 in the equation (d), a filter treatment is executed on a ratio T^1T^1calculated from the parameter vector estimate value is filtered with a lowpass transfer function G(s) and then, in place of the equation (b) and the equation (c), an equation (g) and an equation (h) are used, wherein the equations (g) and (h) are described as Pin=Vmax-V^0K^⁢G⁡(s)⁢{T^1T^2}⁢Vmax,⁢and(g)Pout=V^0-VminK^⁢G⁡(s)⁢{T^1T^2}·Vmin,(h)where T1, T2 , and T3 are time constants, respectively; K is an internal resistance of the secondary battery.

5. An available input-output power estimating device for a secondary battery, comprising: a current detecting means measuring a value I of a current of the secondary battery; a voltage detecting means measuring a value V of a terminal voltage of the secondary battery; a parameter estimating means substituting the measured current value I and the measured voltage value V into an adaptive digital filter using a battery model represented by an equation (a) for thereby collectively estimating a value of a parameter vector, as a parameter vector estimate value, in the equation (a); an open circuit voltage calculating means substituting the measured current value I, the measured voltage value V, and the parameter estimate value into the equation (a) for thereby calculating a value {circumflex over (V)}0, as an open circuit voltage estimate value, of an open circuit voltage; an available input power estimating means substituting a set of components (ân, {circumflex over (b)}n), which is associated with a direct term in the equation (a), of the parameter vector estimate value, the open circuit voltage estimate value {circumflex over (V)}0, and an upper limit voltage Vmax, which is predetermined, of the terminal voltage V into an equation (b) for thereby estimating an available input power Pin of the secondary battery; and an available output power estimating means substituting the one set of components (ân, {circumflex over (b)}n), which is associated with the direct term in the equation (a), of the parameter vector estimate value, the open circuit voltage estimate value {circumflex over (V)}0, and a lower limit voltage Vmin, which is predetermined, of the terminal voltage V into an equation (c) for thereby estimating an available output power Pout of the secondary battery; wherein the equations (a) , (b), and (c) are described, respectively, as V=B⁡(s)A⁡(s)⁢I+1C⁡(s)⁢V0,(a)Pin=Vmax-V^0b^n⁢a^n⁢Vmax,⁢and(b)Pout=V^0-Vminb^n⁢a^n⁢Vmin(c)where A(s) , B(s) , and C(s) represent polynomials of a Laplace operator s, respectively, as follows: A⁡(s)=∑k=0n⁢ak⁢sk,B⁡(s)=∑k=0n⁢bk⁢sk,and⁢ ⁢C⁡(s)=∑k=0n⁢ck⁢sk(d)where the first order coefficients a1, b1, and c1 of the polynomials take non-zero values, respectively.

6. An estimating method of an available input-output power for a secondary battery, comprising: measuring a value I of a current of the secondary battery; measuring a value V of a terminal voltage of the secondary battery; substituting the measured current value I and the measured voltage value V into an adaptive digital filter using a battery model represented by an equation (a) for thereby collectively estimating a value of a parameter vector, as a parameter vector estimate value, in the equation (a); substituting the measured current value I , the measured voltage value V, and the parameter estimate value into the equation (a) for thereby calculating a value {circumflex over (V)}0, as an open circuit voltage estimate value, of an open circuit voltage; substituting a set of components (ân, {circumflex over (b)}n), which is associated with a direct term in the equation (a), of the parameter vector estimate value, the open circuit voltage estimate value {circumflex over (V)}0, and an upper limit voltage Vmax, which is predetermined, of the terminal voltage V into an equation (b) for thereby estimating an available input power Pin of the secondary battery; and substituting the one set of components (ân, {circumflex over (b)}n), which is associated with the direct term in the equation (a), of the parameter vector estimate value, the open circuit voltage estimate value {circumflex over (V)}0, and a lower limit voltage Vmin, which is predetermined, of the terminal voltage V into an equation (c) for thereby estimating an available output power Pout of the secondary battery; wherein the equations (a), (b), and (c) are described, respectively, as V=B⁡(s)A⁡(s)⁢I+1C⁡(s)⁢V0,(a)Pin=Vmax-V^0b^n⁢a^n⁢Vmax,⁢and(b)Pout=V^0-Vminb^n⁢a^n⁢Vmin(c)where A(s), B(s), and C(s) represent polynomials of a Laplace operator s, respectively, as follows: A⁡(s)=∑k=0n⁢ak⁢sk,B⁡(s)=∑k=0n⁢bk⁢sk,and⁢ ⁢C⁡(s)=∑k=0n⁢ck⁢sk(d)where the first order coefficients a1, b1, and c1 , of the polynomials take non-zero values, respectively.