Secondary battery control unit

Abstract

A secondary battery control unit has a calculating portion identifying a parameter of an equivalent circuit based on an estimation error that is obtained by a comparison between an actual output value of a secondary battery and an equivalent output value of the equivalent circuit. Based on a predetermined amount of an infinitesimal change in the parameter and an evaluation function that is obtained using a result of the comparison, the calculating portion numerically calculates a slope of the evaluation function and renews the parameter based on the slope. As a result, the secondary battery control unit has the calculating portion capable of identifying the parameter of the equivalent circuit while reflecting effects of deterioration of the secondary battery and capable of being integrated to a vehicle-mounted microcomputer.

Claims

1. A secondary battery control unit for controlling a secondary battery that is equipped to a vehicle driven by at least a motor, the secondary battery control unit comprising: an equivalent circuit expressing the secondary battery; and a calculating portion identifying a parameter of the equivalent circuit based on an estimation error that is obtained by a comparison between an actual output value of the secondary battery and an equivalent output value of the equivalent circuit, numerically calculating, based on a predetermined amount of an infinitesimal change in the parameter and an evaluation function that is obtained using a result of the comparison, a slope of the evaluation function, and renewing the parameter based on the slope.

2. The secondary battery control unit according to claim 1, wherein the equivalent circuit includes a direct current resistance, a reaction resistance having a nonlinear characteristic derived from Butler-Volmer equation, and a diffusion resistance having a plurality of parallel circuits each including a resistance and a capacitance, the plurality of parallel circuits being connected in series, and the parameter of the equivalent circuit includes a parameter of the diffusion resistance.

3. The secondary battery control unit according to claim 1, wherein at every sampling point, the calculating portion calculates a before-change estimation error and an after-change estimation error, the before-change estimation error being obtained by a comparison between an actual output value and an equivalent output value before an infinitesimal change in the parameter, the after-change estimation error being obtained by a comparison between an actual output value and an equivalent output value after the infinitesimal change in the parameter, calculates a before-change sum of squared errors before the infinitesimal change in the parameter using the before-change estimation error, and calculates an after-change sum of squared errors after the infinitesimal change in the parameter using the after-change estimation error.

4. The secondary battery control unit according to claim 3, wherein at an identifying point of every N times of the sampling points, the N being an integer equal to or larger than 2, the calculating portion determines a renewing amount of the parameter by subtracting a quotient of the before-change sum of square errors divided by the N from a quotient of the after-change sum of square errors divided by the N and dividing a subtracted difference by the predetermined amount of the infinitesimal change in the parameter, and renews the parameter.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above and other objects, features and advantages of the present disclosure will become more apparent from the following detailed description made with reference to the accompanying drawings, in which like parts are designated by like reference numbers and in which:

(2) FIG. 1 is a configuration diagram of a system to which an electronic control unit according to an embodiment of the present disclosure is employed;

(3) FIG. 2 is a diagram illustrating an example of an equivalent circuit model of a secondary battery;

(4) FIG. 3 is a diagram illustrating a basic form of an adaptive filter;

(5) FIG. 4 is a block diagram to calculate an estimation error;

(6) FIG. 5 is a flowchart in a case where the equivalent circuit model shown in FIG. 2 is a primary circuit; and

(7) FIG. 6 is a diagram illustrating effects of the present embodiment.

DETAILED DESCRIPTION

(8) Embodiment of the present disclosure will be described hereinafter with reference to the drawings. To make the description easier to understand, same elements of the drawings will be designated with the same symbols as far as possible and descriptions thereof will not be repeated.

(9) As shown in FIG. 1, a system to which an electronic control unit 10 (secondary battery control unit) is employed includes a current value measuring portion 20, a voltage value measuring portion 22, a load 30 and a secondary battery 32 in addition to the electronic control unit 10.

(10) The secondary battery 2 of the electronic control unit 10 is a secondary battery such as a lithium ion battery whose state of charge (SOC) is to be monitored. The current value measuring portion 20 measures a current value of the secondary battery 32 and outputs the current value to the electronic control unit 10. The voltage value measuring portion 22 measures a voltage value (actual output value) of the secondary battery 32 and outputs the voltage value to the electronic control unit 10. The load 30 of the electronic control unit 10 is a load such as a main motor that is connected to the secondary battery 32.

(11) The electronic control unit 10 has a calculating portion 12. The calculating portion 12 identifies parameters of an equivalent circuit of the secondary battery 32 based on the current value outputted from the current value measuring portion 20 and the voltage value outputted from the voltage value measuring portion 22, and estimates the SOC. The calculating portion 12 is integrated as a microcontroller to the electronic control unit 10.

(12) Next, a processing of the calculating portion 12 will be described with reference to FIG. 2 and FIG. 3. As shown in FIG. 2, an equivalent circuit model includes a DC resistance Rs, a reaction resistance R and a diffusion resistance. The reaction resistance R has a nonlinear characteristic that is derived from Butler-Volmer equation. The diffusion resistance includes a parallel circuit of a resistance Rw1 and a capacitance Cw1 and a parallel circuit of a resistance Rw2 and a capacitance Cw2, and these parallel circuits are connected in series.

(13) Generally, a basic form of the adaptive filter shown in FIG. 3 is expressed by a formula (f1)) and a formula (f2).

(14) $\begin{array}{cc}\left[\text{Eq}.1\right]& \\ W\left(k+1\right)=W\left(k\right)-\mu .Math.\nabla \left(k\right)& \left(\mathrm{f1}\right)\\ \nabla \left(k\right)=\frac{\partial J}{\partial W\left(k\right)}& \left(\mathrm{f2}\right)\end{array}$

(15) Terms in the formula (f1) and the formula (f2) are as follows. In the present embodiment, bold letters in the formulas represent vector quantity and normal letters in the formulas represent scalar quantity. That is, in the formula (f1) and the formula (f2). W and ∇ are vector quantity, and k, μ and J are scalar quantity. W(k) represents a parameter vector of the filter. k represents the number of samplings. μ represents a step size. J represents an evaluation function.

(16) In such a case, W is a parameter of the diffusion resistance of the equivalent circuit model (see FIG. 2) and is expressed as follows.
W=[Rw1 Rw2 . . . Rwn Cw1 Cw2 . . . Cwn]

(17) n represents a degree of a RC parallel circuit.

(18) Hereinafter, to simplify the description, cases where n=1 will be described. Also, in the following description, a portion corresponding to W in FIG. 2 will be only considered. The DC resistance Rs and the reaction resistance R, which is derived from Butler-Valmer equation and has the nonlinear characteristic, can be calculated by another method. By considering the DC resistance Rs, the reaction resistance R and an open circuit voltage (OCV) together, a voltage applied to the diffusion resistance can be calculated from the voltage value (actual output value) of the secondary battery 32 measured by the voltage value measuring portion 22.

(19) An error e and the evaluation function J are defined as a formula (f3) and a formula (f4). When the formula (f3) is substituted in the formula (f4), and the resulting formula (f4) is further substituted in the formula (f2), a formula (f5) can be obtained. d(k) is the voltage value of the secondary battery 32 measured by the voltage value measuring portion 22. y(k) is an output value of a digital filter (the voltage value of the equivalent circuit model) that corresponds to the current value of the secondary battery 2 measured by the current value measuring portion 20.

(20) $\begin{array}{cc}\left[\mathrm{Eq}.2\right]& \\ e\left(k\right)=d\left(k\right)-y\left(k\right)& \left(\mathrm{f3}\right)\\ J\left(k\right)=E\left[e^2\left(k\right)\right]& \left(\mathrm{f4}\right)\\ \nabla \left(k\right)=\frac{\partial J}{\partial W\left(k\right)}=\frac{\partial \frac{.Math.{\left\{d\left(k\right)-y\left(k\right)\right\}}^2}{N}}{\partial W\left(k\right)}& \left(\mathrm{f5}\right)\end{array}$

(21) Hereinafter, y (=V: voltage) in the case of n=1 will be calculated specifically. An impedance of the RC parallel circuit can be calculated as expressed by a formula (f6).

(22) $\begin{array}{cc}\left[\mathrm{Eq}.3\right]& \\ Z\left(s\right)=\frac{R}{\mathrm{RCs}+1}& \left(\mathrm{f6}\right)\end{array}$

(23) When a formula (f7) is discretized using Backward-Euler method, a formula (f8) can be obtained.

(24) $\begin{array}{cc}\left[\mathrm{Eq}.4\right]& \\ s=\frac{1-z^{-1}}{T}& \left(\mathrm{f7}\right)\\ \left[\mathrm{Eq}.5\right]& \\ V\left(k\right)=\frac{\mathrm{RC}}{T+\mathrm{RC}}V\left(k-1\right)+\frac{\mathrm{RT}}{T+\mathrm{RC}}I\left(k\right)& \left(\mathrm{f8}\right)\end{array}$

(25) When V(k+1) is calculated from the formula (f8), a formula (f9) can be obtained.

(26) $\begin{array}{cc}\left[\mathrm{Eq}.6\right]& \\ \begin{array}{c}V\left(k+1\right)=\frac{\mathrm{RC}}{T+\mathrm{RC}}\underset{\_}{V\left(k\right)}+\frac{\mathrm{RT}}{T+\mathrm{RC}}I\left(k+1\right)\\ =\frac{\mathrm{RC}}{T+\mathrm{RC}}\left\{\frac{\mathrm{RC}}{T+\mathrm{RC}}\underset{\_}{V\left(k-1\right)}+\frac{\mathrm{RT}}{T+\mathrm{RC}}I\left(k\right)\right\}+\\ \frac{\mathrm{RT}}{T+\mathrm{RC}}I\left(k+1\right)\\ =\mathrm{.Math.}\end{array}& \left(\mathrm{f9}\right)\end{array}$

(27) According to the formula (f9), since previous values of ∇ (underlined portion in the formula (f9)) are required to calculate present values of V, that is, V is nested, recursion is necessary. Therefore, as a value of k increases, the formula (f9) is more complicated. Hence, it will be difficult to calculate the partial derivative using the formulas, that is, it will be difficult to substitute the formula (f9) in y(k) of a formula (f10), which is surrounded by a broken-line frame. Also, as the number of samplings increases, larger RAM capacity will be required to store the data.

(28) $\begin{array}{cc}\left[\mathrm{Eq}.7\right]& \\ \nabla \left(k\right)=\frac{\partial J}{\partial W\left(k\right)}=\frac{\partial \frac{.Math.{\left\{d\left(k\right)-\right\}}^2}{N}}{\partial W\left(k\right)}& \left(\mathrm{f10}\right)\end{array}$

(29) In the present embodiment, an infinitesimal change dW in the parameter is fixed (constant) and the slope is calculated numerically. Specifically, a multiply-accumulation of errors (sum of squared errors) using a parameter W and a multiply-accumulation of errors (sum of squared errors) using a parameter W+dW are calculated simultaneously at every sampling point, the parameter W+dW being obtained by shifting the parameter W by the infinitesimal change dW, which is determined beforehand. ∇ is obtained by subtracting a quotient of the sum of square errors using the parameter W divided by N from a quotient of the sum of square errors using the parameter W+dW divided by N, and dividing the subtracted difference by dW. As such, R and C do not remain as variables and a situation where ∇ is nested as described above can be avoided. Therefore, the calculation can be simplified. Specifically, as expressed by a formula (f11), dJ is obtained by determining dW beforehand, and the slope is obtained by dividing the dJ by the dW.

(30) $\begin{array}{cc}\left[\mathrm{Eq}.8\right]& \\ \begin{array}{c}\nabla \left(k\right)=\frac{\partial J}{\partial W\left(k\right)}->\frac{{J\left(k\right).Math.}_{W=W+\mathrm{dW}}-J\left(k\right){|}_{W=W}}{\mathrm{dW}\left(k\right)}\\ =\frac{E\left[e^2\left(k\right){|}_{W=W+\mathrm{dW}}\right]-{E[e^2\left(k\right).Math.}_{W=W}]}{\mathrm{dW}\left(k\right)}\\ =\frac{\frac{\underset{i=1}{\overset{k}{.Math.}}{\left\{d\left(i\right)-y\left(i\right){|}_{W=W+\mathrm{dW}}\right\}}^2}{N}-\frac{\underset{i=1}{\overset{k}{.Math.}}{\left\{d\left(i\right)-y\left(i\right){|}_{W=W}\right\}}^2}{N}}{\mathrm{dW}\left(k\right)}\end{array}& \left(\mathrm{f11}\right)\end{array}$

(31) Accordingly, since the R and the C need not to be remained as variables and the calculation can be made in a state where specific values are substituted, the situation where ∇ is nested as described above can be avoided.

(32) Furthermore, to decrease the RAM capacity for storing the data, calculations expressed by a formula (f12), a formula (f13), a formula (f14) and a formula (f15) are made at every sampling point. Specifically, in the case where the calculation of the formula (f11) is made at once, the RAM needs to store all data that are required in the calculation. Conversely, in the case where the calculations of the formulas (f12), (f13), (f14) and (f15) are made at every sampling point, the RAM needs not to store all data and the RAM capacity can be decreased compared to the case where the calculation is made at once.

(33) $\begin{array}{cc}\left[\mathrm{Eq}.9\right]& \\ e\left(k\right){|}_{W=W+\mathrm{dW}}=d\left(k\right)-y\left(k\right){|}_{W=W+\mathrm{dW}}& \left(\mathrm{f12}\right)\\ e\left(k\right){|}_{W=W}=d\left(k\right)-y\left(k\right){|}_{W=W}& \left(\mathrm{f13}\right)\\ \left[\mathrm{Eq}.10\right]& \\ \underset{i=1}{\overset{k}{.Math.}}{e}^2\left(i\right){|}_{W=W+\mathrm{dW}}=\underset{\_}{\underset{i=1}{\overset{k-1}{.Math.}}{e}^2\left(i\right){|}_{W=W+\mathrm{dW}}}+e^2\left(k\right){|}_{W=W+\mathrm{dW}}& \left(\mathrm{f14}\right)\\ \underset{i=1}{\overset{k}{.Math.}}{e}^2\left(i\right){|}_{W=W}=\underset{\_}{\underset{i=1}{\overset{k-1}{.Math.}}{e}^2\left(i\right){|}_{W=W}}+e^2\left(k\right){|}_{W=W}& \left(\mathrm{f15}\right)\end{array}$

(34) FIG. 4 is a block diagram illustrating a calculation to obtain the error e as expressed by the formula (f12) and the formula (f13). The formula (f12) is a formula to calculate an after-change estimation error. The after-change estimation error is obtained by a comparison between an actual output value d(k) after the infinitesimal change in the parameter W and an equivalent output value y(k) after the infinitesimal change in the parameter W. The formula (f13) is a formula to calculate a before-change estimation error. The before-change estimation error is obtained by a comparison between an actual output value d(k) before the infinitesimal change in the parameter W and an equivalent output value y(k) before the infinitesimal change in the parameter W.

(35) Next, a method for identifying the parameters will be described with reference to FIG. 5, which is a flowchart in a case where the equivalent circuit model is a primary circuit (n=1). In the flowchart shown in FIG. 5, default values of k and p are 1. The infinitesimal change dW is determined before the processing of the flowchart shown in FIG. 5 is started

(36) At S01, data are sampled based on the output values of the current value measuring portion 20 and the voltage value measuring portion 22. At S02, a difference between the actual output value and the equivalent output value is calculated using the above-described formulas (f12) and (f13).

(37) At S03, the sum of squared errors is calculated using the calculated result of S02 and the formulas (f14) and (f15). At S04, it is determined whether the subjective sampling point accords with an identifying point, that is, k=N. When the subjective sampling point accords with the identifying point (k=N), the processing proceeds to S05. When the subjective sampling point does not accord with the identifying point, the processing proceeds to S10. At S10, k is set to k+1 and the processing is finished.

(38) At S05, by using the formula), the sum of squared errors is divided by N to obtain e and then ∇ is obtained.

(39) At S06, W(p+1)=W(p)−μ.Math.∇(k) is calculated and the parameters are identified.

(40) At S07, k is set to 1. At S08, p is set to p+1 and the processing is finished.

(41) Effects of reducing the RAM capacity will be described with reference to FIG. 6. FIG. 6 illustrates a sampling condition of the present embodiment and a sampling condition of a comparative example. Each arrow represents a sampling interval. FIG. 6 illustrates an example in which the sampling number N is 3. When N pieces of the data are sampled and calculated at once, all of the N pieces of the data need to be stored. On the other hand, in the present embodiment, since the sums of the squared errors are calculated one after another, all of the N pieces of the data need not to be stored. Also, it is advantageous that the sums of the squared errors are calculated one after another and a calculation amount at one-time can be reduced. That is, the present embodiment can achieve an effect that the calculation can be simplified in addition to an effect that the RAM capacity can be reduced.

(42) However, since the N pieces of the data are not calculated at once and the past data are not stored and are discarded in the present embodiment, the identifying of the parameters cannot be processed in pipeline as described in the comparative example of FIG. 6. That is, the parameters cannot be identified at every sampling point. However, since the rate of the parameter changing is low in the diffusion resistance of the present embodiment, the calculating method described in FIG. 6 does not have any negative effect.

(43) The embodiment described above is not limited to the hybrid vehicle and can be employed to a control unit of a secondary battery that is equipped to a vehicle driven by at least a motor, such as an electric vehicle. The present disclosure is not limited to the above embodiment. That is, it will be apparent for those skilled in the art from this disclosure to make various changes and modifications in the present disclosure. For example, each element and an arrangement or a condition thereof are not limited to the above embodiment and can be suitably modified. Furthermore, each element of the above embodiment can be suitably combined in the present disclosure.