JP4453464B2 - Method for estimating the shared voltage of a capacitor cell of an electric double layer capacitor, and withstand voltage setting / management method - Google Patents

Method for estimating the shared voltage of a capacitor cell of an electric double layer capacitor, and withstand voltage setting / management method Download PDF

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JP4453464B2
JP4453464B2 JP2004198811A JP2004198811A JP4453464B2 JP 4453464 B2 JP4453464 B2 JP 4453464B2 JP 2004198811 A JP2004198811 A JP 2004198811A JP 2004198811 A JP2004198811 A JP 2004198811A JP 4453464 B2 JP4453464 B2 JP 4453464B2
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論 堀越
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Meidensha Corp
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    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Description

本発明は、多数のキャパシタセルを直列接続した電気二重層キャパシタの各キャパシタセルの分担電圧推定方法、この推定方法を基に耐電圧を設定・管理する電気二重層キャパシタの耐電圧設定・管理方法に関する。 The present invention relates to a method for estimating a shared voltage of each capacitor cell of an electric double layer capacitor in which a large number of capacitor cells are connected in series, and a method for setting and managing a withstand voltage of an electric double layer capacitor based on this estimation method. About.

電気二重層キャパシタは分極性電極に電解質中のアニオン、カチオンを正極、負極表面に物理吸着させて竈気を蓄えることを原理としている。   An electric double layer capacitor is based on the principle that an anion and a cation in an electrolyte are physically adsorbed on a polarizable electrode on the surface of the positive electrode and the negative electrode to store air.

現在の電気二重層キャパシタ（以後キャパシタと呼称する）は、平板状の活性炭電極、集電極を用意し、イオンが通過可能なセパレータを挟んだ「積層型」である。活性炭電極、集電極の外周部には内部の電解質が漏れ出さないように、シールを行うためのパッキンを挟んでいる。このパッキンは同時に積層間での絶縁も兼ねている。キャパシタの組立を行う際には、必要な耐電圧分のセルをパッキンと交互に積み重ね（単セル耐電圧２.５Ｖ程度）、最後にエンドプレートで締め付けることにより密閉構造を保っている。   The current electric double layer capacitor (hereinafter referred to as a capacitor) is a “stacked type” in which a flat activated carbon electrode and a collecting electrode are prepared and a separator through which ions can pass is sandwiched. A packing for sealing is sandwiched between the outer periphery of the activated carbon electrode and the collecting electrode so that the internal electrolyte does not leak out. This packing also serves as insulation between the layers. When assembling the capacitor, cells having a required withstand voltage are alternately stacked with packing (single cell withstand voltage of about 2.5 V) and finally tightened with an end plate to maintain a sealed structure.

積層型キャパシタユニットは、金属電極端面の集電極にリード線を取り付ければユニット内で直列接続となり、（単セル耐電圧）×（積層数）だけの耐電圧を持つことになる。この積層型キャパシタユニットは、一般的な巻き取り方式を用いた同一容量のキャパシタと比較してケーブル等を必要とせず、コンパクトに耐電圧を高く設計できるため設置面積を小さくすることができる。   When a lead wire is attached to the collector electrode on the end face of the metal electrode, the multilayer capacitor unit is connected in series within the unit, and has a withstand voltage of (single cell withstand voltage) × (number of stacked layers). This multilayer capacitor unit does not require a cable or the like as compared with a capacitor of the same capacity using a general winding method, and can be designed compactly with a high withstand voltage, so that the installation area can be reduced.

現在のキャパシタの製造方法は、活性炭電極、セパレータ、集電極、パッキン等を交互に積み重ね、各セル間でシールをとった後にユニット内に電解液を導入し、活性炭電極、セパレータに電解質を含浸させている。電解液導入の際には、キャパシタユニットの一カ所に電解液導入口を設けこの一カ所から各セルを仕切る分極基材の孔を介して全てのセルに電解質が行き渡るようにしている。   The current method for manufacturing capacitors is to alternately stack activated carbon electrodes, separators, collector electrodes, packing, etc., seal each cell, introduce an electrolyte into the unit, and impregnate the activated carbon electrodes and separator with the electrolyte. ing. When introducing the electrolytic solution, an electrolytic solution introduction port is provided at one location of the capacitor unit, and the electrolyte is distributed to all the cells from the single location through the holes of the polarization base material that partitions the cells.

この種のキャパシタは、その等価回路が一般のコンデンサの等価回路と同様に、静電容量成分と内部抵抗成分の直列接続に、漏れ抵抗成分が並列接続された構成になることから、特性評価方法としては電圧を印加したときの漏れ抵抗を測定する方法がある。実際の測定方法は、キャパシタに電圧課電し、そのときに流れる電流（漏れ電流）から漏れ抵抗を求める方法が採用される（例えば、特許文献１参照）。   This type of capacitor has a configuration in which the equivalent circuit is a series connection of a capacitance component and an internal resistance component in the same way as an equivalent circuit of a general capacitor, and a leakage resistance component is connected in parallel. There is a method of measuring the leakage resistance when a voltage is applied. As an actual measurement method, a method is adopted in which voltage is applied to a capacitor and a leakage resistance is obtained from a current (leakage current) flowing at that time (see, for example, Patent Document 1).

この特許文献１では、キャパシタを設定電圧まで充電した後、この設定電圧を保つよう充電電圧制御を行い、この状態で流れる定常電流を計測し、この定常電流に基づいた漏れ電流（漏れ抵抗）の大小で評価する。この評価方法は短時間で測定できる。
特開２００３−１３３１８９号公報 In Patent Document 1, after charging a capacitor to a set voltage, charge voltage control is performed so as to maintain the set voltage, a steady current flowing in this state is measured, and a leakage current (leakage resistance) based on the steady current is measured. Evaluate by size. This evaluation method can be measured in a short time.
JP 2003-133189 A

（１）キャパシタセルの電圧配分と漏れ抵抗の関係
キャパシタを長期課電したときの各セルの電圧配分は、一般的に個々のキャパシタセルの静電容量と漏れ抵抗比によって決まると言われている。キャパシタセルの分担電圧にバラツキが発生する要因を、図７に２キャパシタセル直列接続の等価回路図と、各成分（静電容量成分、内部抵抗成分、漏れ抵抗成分）の差異による電圧配分の違いを示す。２つのキャパシタセルでの電圧配分は、充放電時には、静電容量、内部抵抗の差異により電圧ばらつきが発生するが、長期課電時においては漏れ抵抗が最も大きな要因になると言われている。 (1) Relationship between voltage distribution of capacitor cell and leakage resistance It is said that the voltage distribution of each cell when a capacitor is charged for a long time is generally determined by the capacitance of each individual capacitor cell and the leakage resistance ratio. . Fig. 7 shows the equivalent circuit diagram of two capacitor cells connected in series and the difference in voltage distribution due to differences in each component (capacitance component, internal resistance component, leakage resistance component). Indicates. The voltage distribution between the two capacitor cells causes voltage variations due to differences in capacitance and internal resistance during charging and discharging, but leakage resistance is said to be the largest factor during long-term power application.

十分に緩和充電されたキャパシタのフロート状態（自己放電状態）は、図８で示した等価回路に見立てることができる。このときキャパシタ自体の内部抵抗は漏れ抵抗Ｒに対してほとんど無視できるほど小さいので単純なＲＣの並列接続回路と考えることができる。キャパシタの初期電圧をＥとした場合、放置時間ｔ秒後のキャパシタ電圧ｅc（ｔ）は下記の式（１）で示される。 The float state (self-discharge state) of the fully charged capacitor can be considered as the equivalent circuit shown in FIG. At this time, since the internal resistance of the capacitor itself is almost negligible with respect to the leakage resistance R, it can be considered as a simple RC parallel connection circuit. When the initial voltage of the capacitor is E, the capacitor voltage e c (t) after the standing time t seconds is expressed by the following equation (1).

ｅc（ｔ）＝Ｅ（１−ｅｘｐ（−ｔ／ＲＣ）） …（１）
この自己放電試験を行うことで放置時間に対する電圧低下の関係を測定することにより、式（１）の漏れ抵抗Ｒ以外のパラメータ（初期電圧Ｅ、静電容量Ｃ）が判明するので、漏れ抵抗Ｒを求めることができる。 e c (t) = E (1−exp (−t / RC)) (1)
By measuring the relationship between the voltage drop and the standing time by performing this self-discharge test, the parameters (initial voltage E, capacitance C) other than the leakage resistance R in Equation (1) are found. Can be requested.

（２）キャパシタの放電試験による漏れ抵抗測定
キャパシタの漏れ抵抗Ｒを推定するには、十分緩和充電されたキャパシタを自己放電させ、電圧変化を測定し、式（１）の時定数ＲＣを求めればよい。そこで、キャパシタセルを４４直列接続したキャパシタを２４ｈ以上充電後、そのまま自己放電させてみた。このときの各キャパシタセルの電圧保持率を図９に示す。 (2) Leakage resistance measurement by capacitor discharge test To estimate the leakage resistance R of a capacitor, self-discharge a sufficiently relaxed capacitor, measure the voltage change, and obtain the time constant RC of equation (1). Good. Therefore, after charging a capacitor in which 44 capacitor cells were connected in series for 24 hours or longer, it was self-discharged. FIG. 9 shows the voltage holding ratio of each capacitor cell at this time.

このときの放置時間と電圧保持率の関係を指数回帰し、係数の自然対数をマイナス逆数にすると図１０に示す各セルの時定数（ＲＣ）が求まる。ここで求めた時定数の単位を秒に直し、既知の静電容量で除すると、図１１に示す各キャパシタセルの漏れ抵抗Ｒが求まる。さらに、各キャパシタセルの漏れ抵抗Ｒについて全体の平均値を０％としたときの各キャパシタセルのバラツキを図１２に示す。   When the relationship between the standing time and the voltage holding ratio at this time is exponentially regressed and the natural logarithm of the coefficient is a negative reciprocal, the time constant (RC) of each cell shown in FIG. 10 is obtained. When the unit of the time constant obtained here is converted to seconds and divided by a known capacitance, the leakage resistance R of each capacitor cell shown in FIG. 11 is obtained. Further, FIG. 12 shows the variation of each capacitor cell when the overall average value of the leakage resistance R of each capacitor cell is 0%.

一般論で言えば、直列に接続したキャパシタセルの各電圧は、漏れ抵抗Ｒのバラツキ率でおおよそ分担するはずである。図１３にセル基準電圧を２.２７Ｖとした時の推定電圧分担を示す。この考え方によればセル最大電圧は２.７Ｖ近くに達し、最低では１.８Ｖ程度となるはずである。しかし、実際には図１４に示したように、長期課電を行って収束したセル電圧値と推定値の間には大きな隔たりがある。実際のセル電圧のバラツキは漏れ抵抗Ｒのバラツキ範囲よりも小さい範囲で収束し、同様の構成部品を用いたキャパシタの場合はほぼ例外なく同じ結果が得られ、何らかのパラメータ（要因）が他に存在することが分かる。   In general terms, each voltage of the capacitor cells connected in series should be roughly shared by the variation rate of the leakage resistance R. FIG. 13 shows the estimated voltage sharing when the cell reference voltage is 2.27V. According to this concept, the maximum cell voltage should be close to 2.7V, and should be at least about 1.8V. However, in actuality, as shown in FIG. 14, there is a large gap between the estimated cell voltage value and the estimated value converged by long-term power application. The actual cell voltage variation converges in a range smaller than the variation range of the leakage resistance R, and in the case of a capacitor using similar components, the same result is obtained almost without exception, and there are other parameters (factors). I understand that

以上のように、キャパシタセルを直列に接続した場合、直列接続キャパシタセル間の分担電圧は実際に長時間電圧印加を行わないとどのような範囲に収まるか分からず、短時間で電圧範囲を正確に推定することができないと言うのが現状である。   As described above, when capacitor cells are connected in series, the voltage sharing between the series-connected capacitor cells is not known in what range unless voltage is actually applied for a long time. The current situation is that it cannot be estimated.

前述した通り、キャパシタセルの耐電圧はおよそ２.５〜２.７Ｖ程度であり、漏れ抵抗のばらつき状態によってはこの電圧をオーバーすることも考えられる。このような理由から直列に接続したキャパシタセルは一部で分担電圧が大きくなり、急激な内部抵抗増加が生じ不良品となる可能性がある。   As described above, the withstand voltage of the capacitor cell is about 2.5 to 2.7 V, and this voltage may be exceeded depending on the variation state of the leakage resistance. For these reasons, a part of the capacitor cells connected in series has a large shared voltage, which may cause a sudden increase in internal resistance, resulting in a defective product.

本発明の目的は、多数のキャパシタセルを直列接続した電気二重層キャパシタの各セルの分担電圧を高い精度で推定できる電気二重層キャパシタセルの分担電圧推定方法、およびこの推定方法を基に耐電圧を設定・管理する電気二重層キャパシタの耐電圧設定・管理方法を提供することにある。 An object of the present invention is to provide a shared voltage estimation method for an electric double layer capacitor cell capable of estimating with high accuracy the shared voltage of each cell of an electric double layer capacitor in which a large number of capacitor cells are connected in series, and withstand voltage based on this estimation method An object of the present invention is to provide a method for setting and managing the withstand voltage of an electric double layer capacitor .

本発明は、直列接続キャパシタセルの分担電圧を収束させる要因として、キャパシタセルの課電履歴電圧によってその漏れ抵抗が変化することを見いだし、この漏れ抵抗の変化特性を基に各キャパシタセルのｎ時間後の漏れ抵抗を推定、さらには各キャパシタセルの漏れ抵抗比を基に各キャパシタセルの分担電圧を推定することにより、各キャパシタセルの漏れ抵抗を初期に１回だけ測定するのみで各キャパシタセルのｎ時間後の分担電圧を高い精度で推定できる分担電圧推定方法、およびこの分担電圧推定方法を基に耐電圧を設定および管理する電気二重層キャパシタの耐電圧設定・管理方法を提案するもので、以下の方法を特徴とする。 The present invention finds that the leakage resistance is changed by the applied voltage of the capacitor cell as a factor for converging the shared voltage of the series-connected capacitor cells, and n times of each capacitor cell based on the change characteristic of the leakage resistance. By estimating the leakage resistance later, and by estimating the shared voltage of each capacitor cell based on the leakage resistance ratio of each capacitor cell, each capacitor cell is measured only once at the initial stage. intended to propose the divided voltage estimation method the divided voltage after n time can be estimated with high accuracy, and an electric double layer withstand voltage setting and managing of the capacitor to set and manage the withstand voltage based on the divided voltage estimation method The following method is characterized.

（１）多数のキャパシタセルを直列接続した電気二重層キャパシタにおける各キャパシタセルの分担電圧推定方法であって、
キャパシタセルの課電履歴電圧によって変化する漏れ抵抗の変化特性を求めておく過程と、各キャパシタセルの漏れ抵抗を測定する過程と、前記測定した漏れ抵抗と前記漏れ抵抗の変化特性を基に各キャパシタセルのｎ時間後の漏れ抵抗をそれぞれ推定する過程と、この推定した各キャパシタセルの漏れ抵抗の比を基に各キャパシタセルの分担電圧を推定する過程とを有することを特徴とする。 (1) A shared voltage estimation method for each capacitor cell in an electric double layer capacitor in which a large number of capacitor cells are connected in series,
Based on the process of obtaining the change characteristics of the leakage resistance that changes depending on the voltage applied to the capacitor cell, the process of measuring the leakage resistance of each capacitor cell, and the measured leakage resistance and the change characteristics of the leakage resistance. The method includes a step of estimating the leakage resistance after n hours of the capacitor cell and a step of estimating a shared voltage of each capacitor cell based on the estimated ratio of the leakage resistance of each capacitor cell.

（２）多数のキャパシタセルを直列接続した電気二重層キャパシタの耐電圧設定・管理方法であって、
キャパシタセルの課電履歴電圧によって変化する漏れ抵抗の変化特性を求めておく過程と、各キャパシタセルの漏れ抵抗を測定する過程と、前記測定した漏れ抵抗と前記漏れ抵抗の変化特性を基に各キャパシタセルのｎ時間後の漏れ抵抗をそれぞれ推定する過程と、この推定した各キャパシタセルの漏れ抵抗の比を基に各キャパシタセルの分担電圧を推定する過程と、この推定した各キャパシタセルの分担電圧を基に電気二重層キャパシタの耐電圧を設定および管理する過程とを有することを特徴とする。 (2) A withstand voltage setting / management method for an electric double layer capacitor in which a large number of capacitor cells are connected in series,
Based on the process of obtaining the change characteristics of the leakage resistance that changes depending on the voltage applied to the capacitor cell, the process of measuring the leakage resistance of each capacitor cell, and the measured leakage resistance and the change characteristics of the leakage resistance. The process of estimating the leakage resistance of the capacitor cell after n hours, the process of estimating the shared voltage of each capacitor cell based on the ratio of the estimated leakage resistance of each capacitor cell, and the sharing of each estimated capacitor cell And setting and managing a withstand voltage of the electric double layer capacitor based on the voltage.

以上のとおり、本発明によれば、以下の効果がある。   As described above, the present invention has the following effects.

・課電履歴電圧に対する漏れ抵抗の変化特性を加味することで、直列接続キャパシタセルの漏れ抵抗を１回測定するだけで、各キャパシタセルの分担電圧を高い精度で推定することができる。   -By considering the change characteristic of the leakage resistance with respect to the applied voltage, the shared voltage of each capacitor cell can be estimated with high accuracy by measuring the leakage resistance of the series-connected capacitor cell only once.

・計算により分担電圧の推定が可能となることで、直列接続したキャパシタセルの耐電圧を越えない耐電圧設定および管理ができ、電気二重層キャパシタの信頼性を高めることができる。   -Since the shared voltage can be estimated by calculation, the withstand voltage can be set and managed not to exceed the withstand voltage of the capacitor cells connected in series, and the reliability of the electric double layer capacitor can be improved.

・キャパシタセルの組成構造として、課電履歴電圧が高くなるほど漏れ抵抗値が低下する度合いが大きくなる電解質塩を用いることで、直列接続キャパシタセルの分担電圧のバラツキを小さくすることができ、各キャパシタセルの耐電圧を越えることなく全体に印加する電圧を高く設定することができる。   ・ As the composition structure of the capacitor cell, by using an electrolyte salt that increases the degree of decrease in the leakage resistance value as the applied voltage is increased, the dispersion of the shared voltage of the series-connected capacitor cells can be reduced. The voltage applied to the whole can be set high without exceeding the withstand voltage of the cell.

（実施形態１）
本実施形態は、直列接続キャパシタセルの分担電圧を収束させる要因として、課電履歴電圧に対する漏れ抵抗の変化について着目し、これを基に各キャパシタセルの分担電圧を高い精度で推定するもので、図１に推定手順を示すように、（Ｓ１）キャパシタセルの課電履歴電圧によって変化する漏れ抵抗の変化特性を求めておく過程と、（Ｓ２）各キャパシタセルの漏れ抵抗を測定する過程と、（Ｓ３）測定した漏れ抵抗と漏れ抵抗の変化特性を基に各キャパシタセルのｎ時間後の漏れ抵抗を推定する過程と、（Ｓ４）この推定した漏れ抵抗の比を基に各キャパシタセルの分担電圧を推定する過程とからなる分担電圧推定方法とする。 (Embodiment 1)
In the present embodiment, as a factor for converging the shared voltage of the series-connected capacitor cells, attention is paid to the change in leakage resistance with respect to the applied voltage history voltage, and based on this, the shared voltage of each capacitor cell is estimated with high accuracy. As shown in the estimation procedure in FIG. 1, (S1) a process of obtaining a change characteristic of the leakage resistance that varies depending on the applied voltage of the capacitor cell, (S2) a process of measuring the leakage resistance of each capacitor cell, (S3) The process of estimating the leakage resistance after n hours of each capacitor cell based on the measured leakage resistance and the variation characteristic of the leakage resistance, and (S4) sharing of each capacitor cell based on the ratio of the estimated leakage resistance. A shared voltage estimation method including a process of estimating a voltage.

本実施形態を立証する実験として、３つのキャパシタセルのサンプルに６０℃環境下で２.３Ｖ，２.５Ｖ，２.７Ｖの電圧を印加し、８００時間経過後に完全放電を行い、その後に２５℃環境下で各サンプルを２.３Ｖ／２時間充電を行い、そのときの各サンプルの漏れ抵抗を測定した。   As an experiment to verify this embodiment, 2.3 V, 2.5 V, and 2.7 V were applied to three capacitor cell samples in a 60 ° C. environment, and a complete discharge was performed after 800 hours. Each sample was charged by 2.3 V / 2 hours in an environment of ° C., and the leakage resistance of each sample at that time was measured.

当初は、課電履歴電圧が高ければ、自己放電は少なくなるものと考えていたが、実際には図２に示したように、課電履歴電圧が高かった順に自己放電が大きく、下記の表１に示した漏れ抵抗で比較すると、課電履歴電圧が２.５Ｖのサンプルでは課電履歴電圧が２.３Ｖのサンプルの７９％、課電履歴電圧が２.７Ｖのサンプルでは課電履歴電圧が２.３Ｖの５８％と、課電履歴電圧が高かったキャパシタセルは漏れ抵抗が大幅に小さくなり、これに伴い自己放電が大きくなることが判明した。   Initially, it was thought that the higher the applied voltage history voltage, the less the self-discharge, but in fact, as shown in FIG. Compared with the leakage resistance shown in Fig. 1, 79% of the sample with the applied voltage history voltage of 2.3V in the sample with the applied voltage history voltage of 79V, and the sampled voltage with the history of applied voltage of 2.7V. However, it was found that the capacitor cell having a high applied voltage history voltage of 2.3 V, which is 58%, has a significantly reduced leakage resistance, and the self-discharge increases accordingly.

Figure 0004453464
Figure 0004453464

この関係をグラフ化すると、図３に示すようになり、ほぼ直線（一次式）の関係が得られる。もっと広い電圧範囲で見た場合は、直線関係でなくなる可能性もあるが、通常の使用電圧範囲ではほぼリニアな関係であると捉えられ、課電履歴電圧が２.３Ｖのサンプルを基準とすると、各サンプルの漏れ抵抗比率には下記の式（２）の関係が得られる。   When this relationship is graphed, it is as shown in FIG. 3, and a substantially straight line (primary expression) relationship is obtained. When viewed in a wider voltage range, there is a possibility that it is no longer a linear relationship, but in the normal operating voltage range, it is considered that the relationship is almost linear, and if the voltage applied history voltage is 2.3V as a reference The relationship of the following formula (2) is obtained for the leakage resistance ratio of each sample.

漏れ抵抗比率＝−１.０５×課電履歴電圧（Ｖ）＋３.４１６ …（２）
次に、前項の試験結果から得られた漏れ抵抗の変異を加味して直列接続キャパシタセルの電圧分担の推定を試みた。 Leakage resistance ratio = −1.05 × history voltage (V) +3.416 (2)
Next, in consideration of the variation in leakage resistance obtained from the test results in the previous section, an attempt was made to estimate the voltage sharing of the series connected capacitor cells.

キャパシタセルの初期電位をＥ0とした場合、フロート時（自己放電時）ｔ秒後のセル電圧は、先に示した式（１）から推定できるが、この式中の漏れ抵抗Ｒについて、式（２）の要因を入れて漏れ抵抗値を補正する。５０時間後のｎ番目のセル電圧をＦ50(n)とした場合、式（１）の漏れ抵抗Ｒを式（２）の漏れ抵抗比率で補正した下記の式（３）で示される。 When the initial potential of the capacitor cell is E 0 , the cell voltage after t seconds at the time of float (at the time of self-discharge) can be estimated from the above equation (1). The leak resistance value is corrected by including the factor (2). When the n-th cell voltage after 50 hours is F 50 (n) , the following equation (3) is obtained by correcting the leakage resistance R of equation (1) with the leakage resistance ratio of equation (2).

Ｆ50(n)＝Ｅ0×（１−ｅｘｐ（−５０×３６００／Ｒ（ｎ）×（−１.０５×Ｅ0＋３．４１６）×Ｃ …（３）
式（３）を用い、ｎ個の直列キャパシタセルの５０時間後の電圧を全て推定する。５０時間後の全直列セル電圧総和（ΣＦ50）を初期電圧の総和（ｎ×Ｅ0）から差し引いた平均電圧低下分をＶP50とすると、下記の式（４）になる。 F 50 (n) = E 0 × (1-exp (-50 × 3600 / R (n) × (-1.05 × E 0 +3.416) × C ... (3)
Using Equation (3), all the voltages after 50 hours of the n series capacitor cells are estimated. When an average voltage drop obtained by subtracting the total series cell voltage sum (ΣF 50 ) after 50 hours from the sum of initial voltages (n × E 0 ) is V P50 , the following equation (4) is obtained.

ＶP50＝（ｎ×Ｅ0−ΣＦ50(n)）／ｎ …（４）
５０時間後のキャパシタセル電圧をＥ50(n)とすると、下記の式（５）で示すことができる。 V P50 = (n × E 0 −ΣF 50 (n) ) / n (4)
If the capacitor cell voltage after 50 hours is E 50 (n) , it can be expressed by the following equation (5).

Ｅ50(n)＝Ｆ50(n)＋ＶP50 …（５）
式（３）、（４）、（５）の要領で１００時間後のセル電圧Ｅ100を推定すると以下の式に従って求めることができる。 E 50 (n) = F 50 (n) + V P50 (5)
When the cell voltage E 100 after 100 hours is estimated in the manner of the equations (3), (4), and (5), it can be obtained according to the following equation.

Ｆ100(n)＝Ｅ50(n)×（１−ｅｘｐ（−５０×３６００／Ｒ（ｎ）×（−１.０５×Ｅ50(n)＋３．４１６）×Ｃ
ＶP100＝（ｎ×Ｅ50(n)−ΣＦ100(n)）／ｎ
Ｅ100(n)＝Ｆ100(n)＋ＶP100
これを反復計算させ、課電時間に対するセル電圧を推定した結果を図４に示す。今回の試験では５０時間毎に反復計算を行ったが、時間区分をより狭くすればより精度は向上すると考えられる。図４の結果から、キャパシタセル電圧は２.３７Ｖ〜２.１０Ｖの間で約２０００時間後に拡散が止まり、一定の範囲で推移することが分かる。 F 100 (n) = E 50 (n) × (1-exp (-50 × 3600 / R (n) × (-1.05 × E 50 (n) +3.416) × C
V P100 = (n × E 50 (n) −ΣF 100 (n) ) / n
E 100 (n) = F 100 (n) + V P100
FIG. 4 shows the result of repeatedly calculating this and estimating the cell voltage with respect to the charging time. In this test, iterative calculation was performed every 50 hours, but it seems that the accuracy will be improved if the time interval is narrowed. From the results of FIG. 4, it can be seen that the diffusion of the capacitor cell voltage between 2.37 V and 2.10 V stops after about 2000 hours and changes within a certain range.

無限大時間後の各セル平均分担電圧逸脱率と、平均漏れ抵抗逸脱率を比較して図５に推定分担電圧と実測の分担電圧として示した。平均分担電圧の逸脱率のバラツキは非常に小さくなり、漏れ抵抗のバラツキの１／３〜１／４程度に収束する結果を得た。これは実測値と極めて近い結果である。セル電圧の絶対値、バラツキ範囲とも推定値と良く一致していることが分かる。他のキャパシタでも同様の推定を行ったが全て計算結果と実測値は極めてよく一致することが確認できた。   The average share voltage deviation rate of each cell after infinite time and the average leakage resistance deviation rate were compared and shown as an estimated share voltage and an actually measured share voltage in FIG. The variation of the deviation rate of the average shared voltage was very small, and the result of convergence to about 1/3 to 1/4 of the variation of the leakage resistance was obtained. This is a result very close to the actually measured value. It can be seen that the absolute value and variation range of the cell voltage agree well with the estimated value. Although the same estimation was performed for other capacitors, it was confirmed that the calculation results and the measured values all agreed well.

以上のことから、本実施形態では、直列接続したキャパシタセルの課電履歴電圧による漏れ抵抗の変化に着目し、この漏れ抵抗の変化を加味して各キャパシタセルのｎ時間後の漏れ抵抗の変化を推定し、この推定値を基に各キャパシタセルのｎ時間後の分担電圧を求めることにより、各キャパシタセルの漏れ抵抗を初期に１回だけ測定するのみで各キャパシタセルのｎ時間後の分担電圧を高い精度で推定する。   From the above, in this embodiment, paying attention to the change in leakage resistance due to the voltage applied history voltage of the capacitor cells connected in series, taking into account this change in leakage resistance, the change in leakage resistance after n hours of each capacitor cell. And the share voltage after n hours of each capacitor cell is obtained based on the estimated value, and the share of the capacitor cell after n hours is measured only once at the initial stage. Estimate voltage with high accuracy.

この分担電圧の推定方法を採用することにより、電気二重層キャパシタを構成する各キャパシタセルの一部の分担電圧が大きくなり、急激な内部抵抗増加が生じ、電気二重層キャパシタの製品自体が不良品となる可能性を回避することができる。換言すれば、信頼性の高い電気二重層キャパシタの製造に寄与できる。   By adopting this shared voltage estimation method, the shared voltage of a part of each capacitor cell constituting the electric double layer capacitor is increased, causing a sudden increase in internal resistance, and the electric double layer capacitor product itself is defective. The possibility of becoming can be avoided. In other words, it can contribute to the manufacture of a highly reliable electric double layer capacitor.

また、本実施形態による分担電圧推定方法を基にして電気二重層キャパシタの耐電圧設定および管理を行うことにより、信頼性の高い電気二重層キャパシタを提供することができる。   In addition, a highly reliable electric double layer capacitor can be provided by setting and managing the withstand voltage of the electric double layer capacitor based on the shared voltage estimation method according to the present embodiment.

（実施形態２）
本実施形態では、キャパシタセルに印加される電圧（課電履歴電圧）と自己放電特性の変化についてキャパシタセルを構成する部品の何に依存しているのかを調べた。その結果、電解液中の電解質塩の種類により、前記の図３における課電履歴電圧に対する漏れ抵抗比の傾きが大きく現れることが判明した。 (Embodiment 2)
In the present embodiment, it was investigated what depends on the components constituting the capacitor cell with respect to changes in voltage (voltage applied history voltage) applied to the capacitor cell and self-discharge characteristics. As a result, it has been found that the slope of the leakage resistance ratio with respect to the applied voltage hysteresis voltage in FIG. 3 appears greatly depending on the type of electrolyte salt in the electrolytic solution.

図６ではＰＣ溶媒にＥＭＩ（イミダゾウリウム塩）を２.５ｍｏｌ／Ｌ配合した電解液での関係図を示した。４級アンモニウム塩では２.５Ｖ課電時の漏れ抵抗が２.３Ｖ課電時の７９％であったのに対して、ＥＭＩでは５６％であり、下記の式（６）で示すように漏れ抵抗比の傾きが２倍程度大きくなる。   FIG. 6 shows a relationship diagram in an electrolytic solution in which EMI (imidazolium salt) is mixed with 2.5 mol / L in a PC solvent. With quaternary ammonium salt, the leakage resistance when applying 2.5V was 79% of when applying 2.3V, whereas EMI was 56%. As shown by the following formula (6), The slope of the resistance ratio becomes about twice as large.

漏れ抵抗比率＝−１.８×キャパシタ電圧（Ｖ）＋５.１２ …（６）
実施形態１による実験と計算によれば、電圧の分担範囲は４級アンモニウム塩を使用した場合の約１／６で収束し、キャパシタを直列接続で構成するには好適であることが分かった。 Leakage resistance ratio = −1.8 × capacitor voltage (V) +5.12 (6)
According to the experiment and calculation according to the first embodiment, it was found that the voltage sharing range converges to about 1/6 of the case where a quaternary ammonium salt is used, which is suitable for configuring the capacitors in series connection.

このように、課電履歴電圧が高くなると急激に漏れ抵抗比が大きくなるような電解質塩を用いることで、直列接続したキャパシタセルの電圧分担のバラツキ範囲はより小さくなり、特定のキャパシタセルが耐電圧を越える危険性が小さくなり、信頼性が向上する。又、直列接続キャパシタセル全体に印加する電圧を高めて各キャパシタセルの基準電圧自体も向上させることができる。   In this way, by using an electrolyte salt whose leakage resistance ratio suddenly increases as the applied voltage is increased, the voltage sharing variation range of the capacitor cells connected in series becomes smaller, and the specific capacitor cell has a higher resistance. The risk of exceeding the voltage is reduced and the reliability is improved. Further, the voltage applied to the entire series-connected capacitor cells can be increased to improve the reference voltage itself of each capacitor cell.

したがって、本実施形態は、イミダゾリウム塩など、課電履歴電圧が高くなるほど漏れ抵抗値が低下する度合いが大きくなる電解質塩を用いた組成構造のキャパシタセルを直列接続した電気二重層キャパシタを提案するものであり、この構成により直列接続キャパシタセルの分担電圧バラツキを小さくした電気二重層キャパシタを得ることができる。   Therefore, the present embodiment proposes an electric double layer capacitor in which capacitor cells having a composition structure using an electrolyte salt, such as an imidazolium salt, whose degree of decrease in leakage resistance value increases as the applied voltage is increased, are connected in series. With this configuration, it is possible to obtain an electric double layer capacitor in which the variation in the shared voltage of the series connected capacitor cells is reduced.

本発明の実施形態を示す分担電圧推定手順図。The shared voltage estimation procedure figure which shows embodiment of this invention. キャパシタセルの課電電圧履歴の差異による自己放電カーブ。Self-discharge curve due to differences in applied voltage history of capacitor cells. キャパシタセルの漏れ抵抗比率の差異。Difference in leakage resistance ratio of capacitor cell. キャパシタセルの漏れ抵抗変更を加味した分担電圧推定。Estimated shared voltage taking into account changes in leakage resistance of capacitor cells. 実測値と推定値の分担電圧比較。Comparison of shared voltage between measured value and estimated value. ＥＭＩ電解質での課電履歴と漏れ抵抗比率。Electricity history and leakage resistance ratio in EMI electrolyte. 直列接続キャパシタセルの電圧分担要因の説明図。Explanatory drawing of the voltage sharing factor of a series connection capacitor cell. キャパシタセルの自己放電の等価回路。Capacitor cell self-discharge equivalent circuit. キャパシタセルの自己放電状態における電圧保持率。Voltage holding ratio in the self-discharge state of the capacitor cell. キャパシタセルの自己放電カーブからの時定数推定値。Estimated time constant from the self-discharge curve of the capacitor cell. キャパシタセルの時定数からの漏れ抵抗推定値。Estimated leakage resistance from the capacitor cell time constant. キャパシタセルの漏れ抵抗平均逸脱率。Leakage resistance average deviation rate of capacitor cell. キャパシタセルの漏れ抵抗比からの分担電圧推定値。Estimated shared voltage from the leakage resistance ratio of the capacitor cell. キャパシタセルの実測値と推定値の電圧分担比較。Comparison of voltage sharing between measured value and estimated value of capacitor cell.

Claims (2)

多数のキャパシタセルを直列接続した電気二重層キャパシタにおける各キャパシタセルの分担電圧推定方法であって、
キャパシタセルの課電履歴電圧によって変化する漏れ抵抗の変化特性を求めておく過程と、各キャパシタセルの漏れ抵抗を測定する過程と、前記測定した漏れ抵抗と前記漏れ抵抗の変化特性を基に各キャパシタセルのｎ時間後の漏れ抵抗をそれぞれ推定する過程と、この推定した各キャパシタセルの漏れ抵抗の比を基に各キャパシタセルの分担電圧を推定する過程とを有することを特徴とする電気二重層キャパシタのキャパシタセルの分担電圧推定方法。 A shared voltage estimation method for each capacitor cell in an electric double layer capacitor in which a large number of capacitor cells are connected in series,
Based on the process of obtaining the change characteristics of the leakage resistance that changes depending on the voltage applied to the capacitor cell, the process of measuring the leakage resistance of each capacitor cell, and the measured leakage resistance and the change characteristics of the leakage resistance. And a process of estimating the leakage resistance after n hours of the capacitor cell, and a process of estimating a shared voltage of each capacitor cell based on the ratio of the estimated leakage resistance of each capacitor cell. A shared voltage estimation method for a capacitor cell of a multilayer capacitor. 多数のキャパシタセルを直列接続した電気二重層キャパシタの耐電圧設定・管理方法であって、
キャパシタセルの課電履歴電圧によって変化する漏れ抵抗の変化特性を求めておく過程と、各キャパシタセルの漏れ抵抗を測定する過程と、前記測定した漏れ抵抗と前記漏れ抵抗の変化特性を基に各キャパシタセルのｎ時間後の漏れ抵抗をそれぞれ推定する過程と、この推定した各キャパシタセルの漏れ抵抗の比を基に各キャパシタセルの分担電圧を推定する過程と、この推定した各キャパシタセルの分担電圧を基に電気二重層キャパシタの耐電圧を設定および管理する過程とを有することを特徴とする電気二重層キャパシタの耐電圧設定・管理方法。 A method for setting and managing a withstand voltage of an electric double layer capacitor in which a large number of capacitor cells are connected in series,
Based on the process of obtaining the change characteristics of the leakage resistance that changes depending on the voltage applied to the capacitor cell, the process of measuring the leakage resistance of each capacitor cell, and the measured leakage resistance and the change characteristics of the leakage resistance. The process of estimating the leakage resistance of the capacitor cell after n hours, the process of estimating the shared voltage of each capacitor cell based on the ratio of the estimated leakage resistance of each capacitor cell, and the sharing of each estimated capacitor cell And a method for setting and managing a withstand voltage of the electric double layer capacitor based on the voltage.
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