JP2005300500A - Characteristic evaluating method and characteristic evaluating apparatus for electric double-layer capacitor - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a characteristic evaluating apparatus, capable of accurately evaluating a characteristic of an electric double-layer capacitor. <P>SOLUTION: A three-stage ladder-type equivalent circuit is set as an equivalent circuit of the electric double-layer capacitor 3, and the three-stage ladder-type equivalent circuit is expressed by using the model expression: y=ω<SP>T</SP>θ, wherein an adaptive digital filter can be applied. In an analyzing section 6, a parameter term θ is estimated by using the adaptive digital filter, based on values of capacitor inflow current measured by a current sensor 2 and capacitor terminal voltage measured by a voltage sensor 4 at a discharge timing of the electric double layer capacitor 3, and then the characteristic of the electric double-layer capacitor 3 is calculated, based on the estimated parameter term θ. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a characteristic evaluation method and a characteristic evaluation apparatus for evaluating characteristics of an electric double layer capacitor.

  An electric double layer capacitor is a large-capacity capacitor using an electric double layer generated at the interface between an electrode and an electrolyte, and is used as a backup power source such as a microcomputer, a memory, and a timer. Conventionally, when evaluating the characteristics of a capacitor, for example, the capacitance is obtained from a discharge curve of a capacitor terminal voltage when constant current discharge is performed (see, for example, Patent Document 1). When calculating the capacitance, the capacitor is regarded as a series circuit of the capacitance C and the resistor R, and the capacitance C is calculated from a predetermined voltage change and the time required for the change.

JP 2001-118753 A

  However, with regard to the electric double layer capacitor, there is a difference between the actually measured discharge curve and the discharge curve regarded as the CR series circuit, and for example, development of an electronic device using the electric double layer capacitor Sometimes, when a simulation is performed with such a CR series circuit, the simulation result and the actual measurement result are different, and the deviation becomes large particularly in a transient state. Therefore, the simulation cannot be used effectively, and the characteristics of the electric double layer capacitor cannot be evaluated with high accuracy.

ただし、ｓを微分パラメータ、次式（２）をローパスフィルタ特性を有する伝達関数、Ｖ_ｔ(t)をキャパシタ端子電圧、Ｉ_Ｃ(t)をキャパシタ流入電流値としたときに、ベクトルωの各要素は次式（３）で表される。

In the characteristic evaluation apparatus according to the present invention, a three-stage ladder-type equivalent circuit is set as an equivalent circuit of the electric double layer capacitor, and the three-stage ladder-type equivalent circuit is modeled as the following equation (1). Then, the computing means estimates the parameter term θ in the equation (1) by the adaptive digital filter based on the capacitor inflow current value and the capacitor terminal voltage measured by the measuring means when the electric double layer capacitor is discharged, and the estimated parameter The characteristics of the electric double layer capacitor are calculated based on the term θ.

However, when s is a differential parameter, the following equation (2) is a transfer function having a low-pass filter characteristic, V _t (t) is a capacitor terminal voltage, and I _C (t) is a capacitor inflow current value, each vector ω The element is expressed by the following equation (3).

  According to the present invention, the characteristics of the electric double layer capacitor can be accurately evaluated.

  Hereinafter, the best mode for carrying out the present invention will be described with reference to the drawings. FIG. 1 is a block diagram showing the configuration of a characteristic evaluation apparatus according to the present invention. In FIG. 1, an electric double layer capacitor 3 (hereinafter referred to as a capacitor 3) that is a characteristic evaluation target has a constant function having a charging function for the capacitor 3 and a constant current discharging function for discharging the capacitor 3 with a constant current. A current load device 1 is connected. Switching between the charging function and the constant current discharging function of the constant current load device 1 is performed by an instruction from the control unit 8. The control unit 8 is connected to an input unit 9 for starting processing and inputting various commands.

  The current flowing through the capacitor 3 is measured by the current sensor 2, and the terminal voltage of the capacitor 3 is measured by the voltage sensor 4. The measurement values of the current sensor 2 and the voltage sensor 4 are input to the measurement / recording unit 5. The measurement / recording unit 5 performs sampling and A / D conversion at a predetermined sampling time based on an instruction from the control unit 8. The measurement value converted into the digital value is recorded in a recording medium (not shown) such as a semiconductor memory or a hard disk provided in the measurement / recording unit 5. The analysis unit 6 calculates a characteristic value necessary for evaluating the characteristics of the capacitor 3, for example, a resistance value or a capacitance value, based on the measurement value recorded in the measurement / recording unit 5. The display unit 7 is provided with a display monitor or the like, and can display measurement results and analysis results input from the analysis unit 6. The control unit 8 controls not only the constant current load device 1 described above but also the measurement / recording unit 5, the analysis unit 6, and the display unit 7.

《Derivation of model formula》
Next, model formulas used for analysis by the analysis unit 6 will be described. As a result of studying an equivalent circuit suitable for evaluating characteristics of the electric double layer capacitor, the inventor adopts a three-stage ladder type equivalent circuit as shown in FIG. When such a three-stage ladder equivalent circuit is used, the circuit equation is expressed as the following equation (4).

In this embodiment, an adaptive digital filter is applied to the circuit equation to estimate the unknown parameters (C, R) of the capacitor 3. First, the adaptive digital filter is derived from the circuit equation shown in equation (4). Derives the applicable model formula. In the adaptive digital filter theory, the capacitor 3 which is an unknown system is modeled by a system represented by the model standard form of the following equation (5).

ω ^T represents a transposed matrix of the matrix ω. In equation (5), y (t) is a measurable system output and corresponds to the output of the capacitor 3. ω (t) consists of a measurable system input and an output when the input and output y are passed through a filter of the model system. The vector θ is a parameter that cannot be measured, and is composed of unknown parameters (C, R) of the equivalent circuit of FIG. In the adaptive digital filter theory, the parameter estimation value θ ^* of the model system is estimated by an identification algorithm (adaptive algorithm) so that the estimated output y ^* of the model system approaches the measurable system output y. By using the parameter estimation value θ ^* estimated in this way, the output y of the model system represented by the equation (5) is a sufficiently approximate output of the unknown system.

ここで、ｓは微分オペレータであり、Ｋ_１〜Ｋ_６は以下に示す式（７）〜（１２）で表されるものである。

When the relationship between the terminal voltage V _t (t) and the capacitor inflow current I _C (t) of the equivalent circuit shown in FIG. 2 is obtained from the circuit equation (4) described above, the following equation (6) is obtained.

Here, s is a differential operator, and K _{1 to} K ₆ are represented by the following equations (7) to (12).

ここで、ローパスフィルタ１／Ｇｌｐ(s)は上述したモデルシステムのフィルタに対応するもであり、式（１３）の両辺が厳密にプロパーになるように次式（１４）のように選ぶ。なお、式（１４）においてτは時定数である。

Next, the equation (6) is rewritten as the following equation (13).

Here, the low-pass filter 1 / Glp (s) corresponds to the filter of the model system described above, and is selected as in the following equation (14) so that both sides of the equation (13) are strictly proper. In Equation (14), τ is a time constant.

When the filter outputs of the terminal voltage V _t (t) and the capacitor inflow current I _C (t) are defined as the following equation (15), the equation (13) can be transformed as the following equation (16).

θは未知のパラメータであり、式（１７）に示すｙ(t)およびω(t)の各要素は、計測可能な端子電圧Ｖ_ｔ(t)とキャパシタ流入電流Ｉ_Ｃ(t)とを式（１５）に基づきフィルタ処理して得られるフィルタ出力によって表される。 The model formula shown in Formula (16) is the same as the model standard form of Formula (5) described above, and this model system is a system to which an adaptive digital filter can be applied. Comparing equation (16) with equation (5), y (t), ω (t), and θ are expressed as the following equation (17).

θ is an unknown parameter, and each element of y (t) and ω (t) shown in the equation (17) represents a measurable terminal voltage V _t (t) and a capacitor inflow current I _C (t) as an equation. It is represented by the filter output obtained by filtering based on (15).

《Unknown parameter identification algorithm》
When the estimates of the unknown parameters theta and theta ^*, the output estimate y ^* corresponding to the estimated value theta ^* is denoted as "y ^{* =} ω ^T · θ ^*". Then, the unknown parameter θ is accurately estimated by sequentially updating the estimated value θ ^* based on the measurement data so that the difference between the output estimated value y ^* and the actually measured output value y approaches zero. . In the present embodiment, in order to improve the estimation accuracy, an “unlimited trace gain method” developed from the least square method is used, and an unknown parameter θ is obtained by an algorithm in a discrete time format described by the following equation (18). Identification.

In Expression (18), λ ₃ and α ₁ are “0 <λ ₃ <1”. The weights of adaptive estimation set in the range of “0 <α ₁ <∞”, and γ _U and γ _L are values that set the upper and lower limits of adaptive estimation. trace (Q (k)) represents the sum of the diagonal elements of the matrix Q (k). K represents the data order of the sampled measurement data, and if the sampling period is T, kT represents time. Equation (18) sequentially calculates the parameter estimation value θ ^* of k = 1, 2, 3,... From the data of k = 0, and θ ^* (− 1), P (−1), λ ₃ , α ₁ , γ _U and γ _L are given.

Next, the operation procedure of the characteristic evaluation apparatus of this embodiment will be described. First, a discharge test is performed according to the flowchart of FIG. 3, and measurement data is acquired and recorded. Next, analysis is performed according to the flowchart of FIG. 4 based on the acquired data, and R _{1 to} R ₃ and C _{1 to} C ₃ of the equivalent circuit representing the unknown parameter θ, that is, the capacitor ₃ are determined.

<< Explanation of discharge test procedure >>
FIG. 3 is a flowchart showing the procedure of the discharge test. In step S1, the capacitor 3 is charged to a predetermined level. Normally, charging is performed until full charge. In that case, charging is performed at a constant current up to the rated voltage, and then constant voltage charging is performed at the rated voltage. In step S2, a constant sampling time, that is, starts measuring the current I _C and the terminal voltage V _t of the capacitor 3 at a sampling period T as described above, it starts the constant current discharge of the capacitor 3 in the subsequent step S3.

When starting the constant current discharge, the terminal voltage V _t of the capacitor 3 drops with the discharge as shown in FIG. Figure 5 is a graph showing changes in the capacitor terminal voltage V _t and the capacitor inflow current I _C at the time of the discharge, the curve L1 represents the change in the capacitor terminal voltage V _t, the curve L2 is a change in the capacitor inrush current I _C Show. For example, a graph as shown in FIG. In step S4, when the terminal voltage V _t reaches a predetermined value V _S (for example, 0.5 V or 0 V), the discharge current is set to zero and the discharge is stopped.

Stopping the discharge in step S4, the terminal voltage V _t approaches a constant value increased for reasons such as the voltage drop due to the internal resistance component is eliminated (see FIG. 5). In step S5, the measurement is continued for a predetermined time even after the discharge is stopped, and these voltage changes are recorded. When the predetermined time has elapsed, the measurement is stopped. In step S6, the measurement data is recorded on a recording medium provided in the measurement / recording unit 5 (see FIG. 1), and a series of discharge test procedures is completed.

<< Explanation of analysis procedure >>
FIG. 4 is a flowchart showing an analysis procedure, which is processed by the analysis unit 6 of FIG. In step S 11, a pair of data (V _t , I _C ) to be analyzed is read from the measurement data recorded on the recording medium of the measurement / recording unit 5 and sent to the analysis unit 6. In step S12, filter components V _t2 , V _t3 , and V _t4 for the data V _t are obtained based on the equation (15) described above.

ただし、ｋ＝０〜ｎ−１であり、ｎはサンプリングされたデータの数である。上述したようにサンプリング周期Ｔを用いるとｋＴはサンプリング時刻を表すので、データ順番を表すｋは時刻に対応している。 For example, regarding V _t4 , the filter processing is “V _t4 (t) = {s ³ / (τ · s + 1) ⁴ } · V _t (t)”. By converting this into a discrete function, V _t4 (k) can be obtained by (19).

However, k = 0 to n−1, and n is the number of sampled data. As described above, when the sampling period T is used, kT represents the sampling time, and therefore k representing the data order corresponds to the time.

In step S13, I _C1 , I _C2 , I _C3 , and I _C4 are obtained from the measurement data I _C based on the equation (15), considering the filter components V _t2 , V _t3 , and V _t4 in step S12. The processing from step S11 to step S13 is executed for all acquired measurement data pairs (V _t (k), I _C (k)). As a result, n sets of y (k) = I _C1 (k), ω (k) = (V _t4 (k), V _t3 (k), V _t2 (k), I _C4 (k), I _C3 ( k), I _C2 (k)).

In step S14, initial values θ ^* (− 1), P (−1), λ ₃ , α ₁ , γ _U and γ _L necessary for parameter identification are set. In step S15, the unknown parameter θ ^* (k), that is, K ₁ (k) to K ₆ (k) is estimated based on the parameter identification algorithm expressed by the equation (18). In step S16, the unknown parameters K ₁ (k) to K ₆ (k) obtained in step S15 and the relations of the equations (7) to (12) described above are the unknown parameters of the capacitor 3 R ₁ (k). , R ₂ (k), R ₃ (k), C ₁ (k), C ₂ (k), C ₃ (k) are obtained.

6A and 6B are diagrams showing measurement data obtained by the charge / discharge test. FIG. 6A shows a change in the capacitor terminal voltage V _t (k), and FIG. 6B shows a change in the capacitor inflow current I _C (k). The horizontal axis of the graph is indicated by k corresponding to the sampling time. On the other hand, (a) to (d) in FIG. 7 show changes in K _{1 to} K ₄ estimated by calculation, and (a) and (b) in FIG. 8 show changes in K ₅ and K ₆ . Is shown. Further, in FIG. 9 (a) ~ (c) is a diagram showing the _R 1 to R ₃ which is calculated from _K 1 ~K _6, in FIG. 10 (a) ~ (c) is from _K 1 ~K ₆ The calculated C _{1 to} C ₃ are shown.

As can be seen from FIGS. 7 to 10, since the estimated K _{1 to} K ₆ , R _{1 to} R ₃ and C _{1 to} C ₃ vary depending on k, the operator selects k1 which seems to be appropriate in step S17. , R ₁ (k1) to R ₃ (k1) and C ₁ (k1) to C ₃ (k1) are determined for k1. In step S18, the circuit equation of equation (4) is solved using the parameters R ₁ (k1) to R ₃ (k1) and C ₁ (k1) to C ₃ (k1) determined in step S17, and the terminal voltage V _t Is calculated and compared with the actual measurement data.

Steps S17 and S18 are processed in an interactive manner with the operator. For example, the graphs R _{1 to} R ₃ and C _{1 to} C ₃ shown in FIGS. 9 and 10 are displayed on the display unit 7. When the operator inputs k = k1 from the input unit 9, the display unit 7 displays a graph of the terminal voltage V _t (see FIG. 11) as the calculation result in the case of k1. The operator refers to the graph displayed on the display unit 7 and determines whether or not to calculate another k. If it is desired to confirm a different k, another k is input and the processes in steps S17 and S18 are repeated. Steps S17 and S18 are repeatedly executed in accordance with an operator instruction until a desired calculation result is obtained.

As described above, since the parameter varies depending on k, the terminal voltage V _t finally calculated also varies depending on k. Figure 11 is a graph showing in comparison the measurement value the terminal voltage _{V t} that is calculated for different k, (a) is k = 2000, (b) is k = 4000, (c) is k = Each case of 6000 is shown. The horizontal axis is expressed in time (s), and 20 (s), 40 (s), and 60 (s) correspond to k = 2000, 4000, and 6000, respectively, as compared with FIG. 6 where the horizontal axis is k. doing.

  The calculated value at k = 2000 agrees well with the measured value when the time is less than 30 (s), and when k = 4000, it agrees well near 10 (s) and 40 (s). In the case of = 6000, the values agree well at 10 (s) or less and around 50 (s). As described above, since the range that better matches the measured value differs depending on the value of k when determining the parameter, it is only necessary to select the optimum k that matches the intended use of the measurement result.

FIG. 12 shows a simulation result (a) in the CR series circuit which has been conventionally considered with respect to the capacitor inflow current I _C and a simulation result (b) in the three-stage ladder equivalent circuit of the present embodiment. Is. As can be seen from FIG. 12, it is understood that it is better to calculate the coincidence between the calculated value and the actually measured value using a three-stage ladder equivalent circuit.

As described above, in this embodiment, a three-stage ladder equivalent circuit as shown in FIG. 2 is used as the equivalent circuit of the capacitor 3, so that a simulation result that closely matches the actual measurement value can be obtained and the simulation is used. Thus, the characteristics of the capacitor 3 can be obtained with high accuracy. Furthermore, by applying the concept of the adaptive digital filter to the estimation of the unknown parameters R _{1 to} R ₃ and C _{1 to} C ₃ of the equivalent circuit, it is possible to easily obtain the optimum parameters. Further, since the apparatus shown in FIG. 1 can be used just by changing the analysis part of the conventional characteristic evaluation apparatus, it has an advantage that the apparatus can be easily developed and manufactured.

  In the correspondence between the embodiment described above and the elements of the claims, the current sensor 2, the voltage sensor 4 and the measurement / recording unit 5 constitute a measurement means, and the analysis unit 6 constitutes an arithmetic means. In addition, the present invention is not limited to the above embodiment as long as the characteristics of the present invention are not impaired.

It is a block diagram which shows schematic structure of the characteristic evaluation apparatus by this invention. It is a figure which shows the equivalent circuit of a capacitor used in the characteristic evaluation method in this Embodiment, and a circuit equation. It is a flowchart which shows the procedure of a discharge test. It is a flowchart which shows the procedure of an analysis. Is a graph showing changes in the capacitor terminal voltage V _t and the capacitor inflow current I _C during discharge. Is a diagram showing the measurement data by charge and discharge test, showing a change of (a) a change in the capacitor terminal voltage V _{t (k),} the (b) is a capacitor inflow current I _{C (k).} Is a diagram illustrating a _K 1 ~K ₄ estimated by calculation, showing a variation of the _K 1 ~K ₄ in (a) ~ (d). A diagram illustrating a _K 5, _{K 6} estimated by calculation, (a) shows the change in _{K 5,} showing the (b) change in _{K 6.} Is a diagram showing the R ₁ to R _3, showing (a) shows _{R 1,} (b) is a _{R 2,} (c) a is _{R 3} respectively. Is a diagram illustrating a C ₁ -C _3, showing (a) shows _{C 1,} (b) is a _{C 2,} the (c) is _{C 3} respectively. It is a diagram showing the terminal voltage _{V t} for different k, (a) is k = 2000, (b) is k = 4000, respectively in the case of (c) is k = 6000. It is a comparison figure of a simulation result, (a) is a simulation result in CR series circuit, (b) shows the simulation result in a three-stage ladder type equivalent circuit, respectively.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Constant current load apparatus 2 Current sensor 3 Electric double layer capacitor 4 Voltage sensor 5 Measurement / recording part 6 Analysis part 7 Display part 8 Control part 9 Input part

Claims (2)

Measure the capacitor inflow current value and the capacitor terminal voltage when discharging the electric double layer capacitor,
A three-stage ladder equivalent circuit is set as an equivalent circuit of the electric double layer capacitor,
The three-stage ladder equivalent circuit is modeled as the following equation (Equation 1), and the parameter term θ of the equation (Equation 1) is applied to the adaptive digital filter based on the measured capacitor inflow current value and the capacitor terminal voltage. Estimated using
A characteristic evaluation method comprising calculating the characteristic of the electric double layer capacitor based on the estimated parameter term θ.

However, when s is a differential parameter, the following equation (Equation 2) is a transfer function having a low-pass filter characteristic, V _t (t) is a capacitor terminal voltage, and I _C (t) is a capacitor inflow current value, Each element is expressed by the following equation (Equation 3).

A measuring means for measuring a capacitor inflow current value and a capacitor terminal voltage when discharging the electric double layer capacitor;
A three-stage ladder type equivalent circuit is set as an equivalent circuit of the electric double layer capacitor, the three-stage ladder type equivalent circuit is modeled as the following equation (Equation 4), and the measured capacitor inflow current value and the capacitor And calculating means for estimating the parameter term θ of the formula (Equation 4) using an adaptive digital filter based on the terminal voltage and calculating the characteristics of the electric double layer capacitor based on the estimated parameter term θ. Characteristic evaluation device characterized by

However, when s is a differential parameter, the following equation (Equation 5) is a transfer function having a low-pass filter characteristic, V _t (t) is a capacitor terminal voltage, and I _C (t) is a capacitor inflow current value, the vector ω Each element is expressed by the following formula (Formula 6).

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