JP4477185B2 - Characteristic evaluation method for lead acid battery and characteristic evaluation device for lead acid battery - Google Patents

Description

【０００６】
特開平４−１４１９６６号公報（特許第２５４６０５０号）は、鉛蓄電池の内部インピーダンスの測定のうち、位相が０になる周波数のインピーダンスと、周波数が０．１〜１０Ｈｚの間で、インピーダンスの虚数部の周波数に対する変化分をインピーダンスの実数部の周波数に対する変化分で除算した値が−１程度に最も近づく周波数でのインピーダンスから、鉛蓄電池の劣化状態を判定する方法を開示している。
【０００７】
特開平５−１３５８０６号公報（特許第２７９２７８４号）は、（ａ）０．００１〜１Ｈｚの間の２〜３点の周波数で、鉛蓄電池の内部インピーダンスを測定し、インピーダンスの虚数部を測定周波数の−０．５乗（ｆ^-1/2）に対してプロットし、そのＹ切片の値から、鉛蓄電池の残存容量を判定し、（ａ）さらに、０．０１〜０．０５Ｈｚの周波数で内部インピーダンスを測定し、その実部を虚数部に対してプロットし、その勾配の値から、鉛蓄電池の残存容量を判定する方法を開示している。
【０００８】
【発明が解決しようとする課題】
上記した方法はそれぞれ、下記に述べる問題点があり、鉛蓄電池、特に自動車などの車両に搭載される鉛蓄電池の特性評価には実用上、有効に使用することができなかった。下記に詳述する。
【０００９】
特開平４−９５７８８号公報に記載された方法は、鉛蓄電池の内部インピーダンスの測定結果から、式（１−１）に示した、インダクタンス成分（Ｌ），電解液抵抗値（Ｒｓ），電荷移動抵抗値（θ），電気二重層容量値（Ｃｄ），ワークブルグインピーダンス（Ｗ），ワークブルグ係数（σ）の６つのパラメータを求める必要がある。そのため、内部インピーダンスの測定は少なくとも６つの周波数で行うことが必要であり、６つのパラメータの最適解を求めるための演算が非常に煩雑になるという問題点があった。
すなわち、特開平４−９５７８８号公報に記載されている多数の周波数での測定、並びに煩雑な演算は、測定時間が長くなるだけでなく、測定装置の価格が高くなり、特に、車両に搭載した鉛蓄電池の評価には実用的でないという問題点があった。
【００１０】
特開平４−１４１９６６号公報に記載された方法は、内部インピーダンスの位相が０になる周波数を探し出して測定を行う必要があり、さらに、周波数が０．１〜１０Ｈｚの間でインピーダンスの虚部の周波数に対する変化分をインピーダンスの実部の周波数に対する変化分で除算した値が−１程度になる周波数を探し出して測定を行う必要がある。
すなわち、特開平４−１４１９６６号公報の方法は、内部インピーダンスの値が特定の条件を満たすような周波数を探し出す必要がある。そのため、周波数を変化させて測定を可能とする装置が必要となる他、上述した特定の条件を満たすことの判定を行う装置も必要になる。このような処理のためには複雑な測定装置が必要になり、装置価格が高くなり、特に、車両に搭載した鉛蓄電池の特性評価には実用的でないという問題点があった。
【００１１】
特開平５−１３５８０６号公報に記載された方法は、０．００１〜１Ｈｚでの内部インピーダンスの値を指標にしている。しかしながら、このような１Ｈｚ以下の低周波領域の測定は、１Ｈｚ以上の領域での測定と比較して、測定装置、特に周波数発振回路の構成が複雑化し、装置の価格が高騰する要因となり、また、測定時間が長くなるという問題点がある。
また、０．００１〜１Ｈｚでの内部インピーダンスは温度によって値が大きく変化する傾向にあるため、たとえば、車両に搭載した鉛蓄電池のように、温度が大きく変化する場所に設置された鉛蓄電池の測定にあっては、温度により補正が不可欠になるという問題点があった。
【００１２】
【課題を解決するための手段】
上記した課題を解決するために、本願発明者が、鋭意検討を重ねた結果、本発明の鉛蓄電池の特性評価方法を発明するに至った。本発明の鉛蓄電池の特性評価方法の要旨を図１〜図３を参照して、下記に述べる。
なお、本発明において、鉛蓄電池の残存容量、劣化状態などの検査を総称して、鉛蓄電池の特性評価と言う。
【００１３】
本発明の鉛蓄電池の特性評価方法は、まず、鉛蓄電池の等価回路を簡略化して、等価回路を、図１または図２に図解したように、少なくとも電荷移動抵抗値（Ｒｃｔ）と電気二重層容量値（Ｃｄ）との並列回路と電解液抵抗値（ＲΩ）との直列回路で構成し、インピーダンスが下記式で規定される等価回路として表す。等価回路の詳細について後述する。
【００１４】
〔ＲΩ＋（Ｒｃｔ／（１＋ｊωＣｄ））〕 ・・・（Ａ−１）
ただし、ω＝２πｆ
【００１５】
本発明の鉛蓄電池の評価特性方法においては、図３に図解したように、（１）鉛蓄電池の内部インピーダンスの実部をＸ軸に虚部に−１を乗じた値をＹ軸にプロットして規定される二次元座標におけるインピーダンス円を規定する、１〜１００Ｈｚの周波数の範囲で選ばれた、３点以上の複数の周波数について、鉛蓄電池の内部インピーダンスを測定する。
【００１６】
さらに本発明の鉛蓄電池の評価特性方法においては、図３に図解したように、（２）電荷移動抵抗値（Ｒｃｔ）と電気二重層容量値（Ｃｄ）との並列回路と、電解液抵抗値（ＲΩ）との直列回路で構成した等価回路から導出される電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）と、複数の周波数において測定した複数の鉛蓄電池の内部インピーダンスとの関係式に、複数の周波数において測定した複数の内部インピーダンスの値を参照して前記電解液抵抗値（ＲΩ），前記電荷移動抵抗値（Ｒｃｔ），前記電気二重層容量値（Ｃｄ）を求める。
【００１７】
最後に、本発明の鉛蓄電池の評価特性方法においては、図３に図解したように、（３）算出した電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）の全てまたは少なくとも１つから供試した鉛蓄電池の残存容量および／または劣化状態を判定する。
【００１８】
また、本発明の鉛蓄電池の評価装置は、上述した鉛蓄電池の評価方法を実施する装置であり、測定手段と、算出手段と、判定手段とを有する。
測定手段は上述した（１）の処理を行い、算出手段は上述した（２）の処理を行い、判定手段は上述した（３）の処理を行う。
【００１９】
【発明の実施の形態】
以下、本発明の鉛蓄電池の特性評価方法および鉛蓄電池の特性評価装置の実施の形態を添付図面を参照して述べる。
【００２０】
等価回路
図１および図２に本発明で適用した等価回路の回路例を示す。
図１は本発明で使用する第１の等価回路としての、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）からなる等価回路の構成図である。
図１の等価回路は、電荷移動抵抗値（Ｒｃｔ）と電気二重層容量値（Ｃｄ）とが並列に接続され、この並列回路に電解液抵抗値（ＲΩ）が直列に接続されている。したがって、その等価回路のインピーダンスは下記式で規定される。
【００２１】
〔ＲΩ＋（Ｒｃｔ／（１＋ｊωＣｄ））〕 ・・・（Ａ−２）
ただし、ω＝２πｆ
【００２２】
図２は本発明で使用する第２の等価回路としての、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ’とＲｃｔ’’），電気二重層容量値（Ｃｄ’とＣｄ’’）からなる等価回路の構成図である。
図２の等価回路は、図１の電気二重層容量値（Ｃｄ）を第１の電気二重層容量値（Ｃｄ’）と第２の電気二重層容量値（Ｃｄ’’）に置き換え、図１の電荷移動抵抗値（Ｒｃｔ）を第１の電荷移動抵抗値（Ｒｃｔ’）と第２の電荷移動抵抗値（Ｒｃｔ’’）に置き換えたものである。
図２の等価回路のインピーダンスは下記式で規定される。
【００２３】

ただし、ω＝２πｆ
【００２４】
特開平４−９５７８８号公報には、式１−１に示したように、６つのパラメータで構成される等価回路が示されている。鉛蓄電池の特性を正確に把握するには、特開平４−９５７８８号公報の等価回路による解析が望ましいが、たとえば、車両の搭載した鉛蓄電池の評価などのような場合には、本発明で適用する図１または図２で表現される等価回路での解析で十分である。むしろ、本発明の図１または図２に示した等価回路を適用して求めるパラメータの数を少なくすることで、測定周波数を少なくし、演算に係わる時間，コストを低減する方が実用的価値が高い。特に、自動車に搭載する鉛蓄電池の残存容量の判定を行う場合、有効数字２桁で十分であり、特開平４−９５７８８号公報の方法より、本発明の方法が実用的である。
【００２５】
３点の測定結果と円の関係
図８に例示として、３点の測定結果と円の関係を図解した。
すなわち、式Ａまたは式Ｂで規定したインピーダンスに対応させて、鉛蓄電池の内部インピーダンスの実部をＸ軸に虚部に−１を乗じた値をＹ軸にプロットして規定される二次元座標におけるインピーダンス円を規定する少なくとも３点以上の複数の周波数において、鉛蓄電池の内部インピーダンスを測定する。
【００２６】
測定周波数
本発明では、１〜１００Ｈｚの周波数の範囲で選ばれた任意の３〜５点（多くても６点）の周波数で測定を行う。
【００２７】
まず、１〜１００Ｈｚの周波数の範囲を選択した理由について述べる。上記した周波数の範囲が、鉛蓄電池の電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を求める上で特に効果的な周波数の範囲であることによる。すなわち、１Ｈｚ以上であれば、測定上かつ装置上、容易に実施できるし、１００Ｈｚ以内であるから、商用周波数の２倍程度の周波数であり、高周波ではないから、測定上かつ装置構成上から問題はない。
【００２８】
特開平５−１３５８０６号公報の方法では、０．００１〜１Ｈｚでの間の２〜３点の周波数における鉛蓄電池の内部インピーダンスから、鉛蓄電池の残存容量を判定している。しかしながら、発明者らの検討によれば、上記したように、０．００１〜１Ｈｚでの測定データを用いるより、本発明の実施の形態による１〜１００Ｈｚの測定データを用いる方が、鉛蓄電池の残留静電容量を判定する上で効果的であり、容易であった。
【００２９】
次いで、３〜５，６点の周波数で測定を行う理由について述べる。電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を求める上でインピーダンス円（図８参照）を規定するには最低３点の周波数で測定する必要がある。
異なる周波数での測定は多いほど、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を求める精度が高くなる。しかしながら、測定数が多くなると、測定時間がかかるし、可変周波数発振回路が複雑になり、測定後の演算が長くなる。したがって、実用的には、３〜５点の周波数、多くても６点の周波数で測定する。
【００３０】
次に、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）と、鉛蓄電池の残存容量および／または劣化状態との関係について考察する。
【００３１】
鉛蓄電池の残存容量および／または劣化状態との関係について第１の実施の形態
図４は電気二重層容量値（Ｃｄ）と鉛蓄電池の残存容量との関係を例示するグラフである。
本発明の検査方法における鉛蓄電池の残存容量の判定においては予め，図４に図解したように、電気二重層容量値（Ｃｄ）と鉛蓄電池の残存容量の関係式を求めておき、内部インピーダンスの複数の測定結果から求めた電気二重層容量値（Ｃｄ）を、上記関係式に照合することで鉛蓄電池の残存容量の判定を行うことができる。
【００３２】
なお、鉛蓄電池の残存容量は下記のごとく電気二重層容量値（Ｃｄ）との間に直線関係があることが判った。
【００３３】
残存容量（％）＝α×Ｃｄ＋β …（Ｃ）
【００３４】
なお、αおよびβは、鉛蓄電池の温度に依存して変化する。
【００３５】
鉛蓄電池の残存容量および／または劣化状態との関係について第２の実施の形態
図５は電荷移動抵抗値（Ｒｃｔ）と鉛蓄電池の残存容量との関係を例示するグラフである。
本発明の検査方法における鉛蓄電池の残存容量の判定においては予め，図５に図解したように、電荷移動抵抗値（Ｒｃｔ）と鉛蓄電池の残存容量の関係式を求めておき、内部インピーダンスの複数の測定結果から求めた電荷移動抵抗値（Ｒｃｔ）を上記関係式に照合することで鉛蓄電池の残存容量の判定を行うことができる。
【００３６】
なお、鉛蓄電池の残存容量は下記のごとく電荷移動抵抗値（Ｒｃｔ）との間に直線関係があることが判った。
【００３７】
残存容量（％）＝γ×Ｒｃｔ＋δ …（Ｄ）
【００３８】
なお、γおよびδは、鉛蓄電池の温度に依存して変化する。
【００３９】
鉛蓄電池の残存容量および／または劣化状態との関係について第３の実施の形態
本発明の鉛蓄電池の評価方法における鉛蓄電池の劣化状態の判定においてはさらに、予め、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）と、鉛蓄電池の劣化状態の関係式を求めておき、内部インピーダンスの測定結果から求めた電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を、上記関係式に照合することで鉛蓄電池の劣化状態の判定を行うことができる。
【００４０】
鉛蓄電池の残存容量は、電池の劣化状態並びに温度に影響を受けることがある。そこで、上記のように求めた鉛蓄電池の残存容量の値を、電池の劣化状態並びに温度の値で補正（補間）する必要が生じる場合がある。その際、電気二重層容量値（Ｃｄ）から求めた鉛蓄電池の残存容量を、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ）から求めた電池の劣化状態の判定結果によって補正を行うことができる。
【００４１】
残存容量に対する温度の影響
予め、鉛蓄電池の温度と、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ）の関係を求めておき、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ）の測定結果をその関係と照合することで、鉛蓄電池の温度を求めることが可能であるので、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ）から求めた鉛蓄電池の温度によって、残存容量に対する温度の影響を補正することも可能である。
【００４２】
上記した鉛蓄電池の残存容量、劣化状態の判定にあたっては、温度を本発明の方法とは別に測定し、その測定値を用いて、残存容量、劣化状態に対する温度の影響を補正することも可能である。
【００４３】
電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）の算出方法
図１および図２の等価回路から導出される、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）と、鉛蓄電池の内部インピーダンスの関係式に、上記複数の周波数において実測した複数の内部インピーダンスの値を参照することで、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を求めるための具体的方法例としては、統計的な手法、たとえば、最小二乗法により最適解を求める方法が好ましい。
【００４４】
しかしながら、車両に搭載した鉛蓄電池の特性評価に際しては、より簡便に最適解を求めることが望ましい。最小二乗法より簡便な方法として、以下に示す方法を挙げることができる。
【００４５】
第１の方法Ｍ
上述した１〜１００Ｈｚのうち、５〜１００Ｈｚの周波数の範囲で選ばれた任意の３〜４点の第１の周波数（Ｆａ）と、１〜５Ｈｚの周波数の範囲で選ばれた任意の１点の第２の周波数（Ｆｂ）で、鉛蓄電池の内部インピーダンスの測定を複数回行い、その測定値から電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を求める。
【００４６】
第１の方法Ｍでは、第１の周波数（Ｆａ）で測定された３〜４点の内部インピーダンスについて、図６に図解したように、内部インピーダンスの実数部をＸ軸に、内部インピーダンスの虚数部の値に−１を乗じた値をＹ軸にプロット（ｃｏｌｅ ｃｏｌｅ ｐｌｏｔ）した３〜４点を通過する円の軌道を求め、軌道のＸ軸切片Ｘａ，Ｘｂ（Ｘａ＜Ｘｂ）を求め、Ｘａを電解液抵抗値（ＲΩ）とし、Ｘｂ−Ｘａを電荷移動抵抗値（Ｒｃｔ）とし、（Ｘａ＋Ｘｂ）×０．５をＸ_m とし、さらに、内部インピーダンスの実数部をＹ軸に、周波数をＸ軸とした座標Ｃ_m に、第１の周波数Ｆａの内の最も低い周波数Ｆａ’と第２の周波数Ｆｂでの測定値をプロットし、両プロット点を結んだ直線上の、上記したＸ_m に相当する周波数をω_m とし、電気二重層容量値Ｃｄを（Ｒｃｔ×ω_m ）^-1とする。
【００４７】
図１および図２に示した等価回路から導出される、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）と内部インピーダンスの関係式のように、求めるべきパラメータが５点以下であっても、上記した関係式のパラメータを数学的に厳密に解くことは、演算が煩雑になり、演算装置の規模が増大し、価格が高騰することにつながる。そこで、本発明のように、簡単な演算で電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を求めることの実用的価値は極めて高い。
【００４８】
上述した簡便な第１の方法Ｍを行う場合にあっては、測定する周波数を、５〜１０Ｈｚの周波数の範囲で選ばれた任意の３〜４点の第１の周波数Ｆａと、１〜５Ｈｚの周波数の範囲で選ばれた任意の１点の第２の周波数Ｆｂとすることが特に好ましい。その理由は、上記したｃｏｌｅ ｃｏｌｅ ｐｌｏｔにおける円の軌跡を求める上で、５〜１００Ｈｚの周波数の範囲の測定値を用いることが好ましいためである。また、円の軌跡を求めるために、測定点は３点以上であることが必要である。円の軌跡を求める上で、さらに好ましくは、第１の測定周波数Ｆａの周波数が５〜１０Ｈｚの中の１点、１０〜３０Ｈｚの中の１点、５０〜１００Ｈｚの中の１点となることが挙げられる。
【００４９】
本願発明者は、座標Ｃ_m において、内部インピーダンスの実部と周波数に直線関係が得られる周波数の範囲は、およそ１〜１０Ｈｚの範囲であることを見いだした。そこで、第１の周波数Ｆｂの範囲は、およそ１〜５Ｈｚであることが好ましく、さらに、第１の周波数Ｆａの内、最も低い周波数Ｆａ’は、５〜１０Ｈｚの中の１点が選ばれることが好ましい。
【００５０】
特開平４−１４１９６６号公報の方法では、内部インピーダンスの値が特定の条件を満たすような周波数を探し出す必要があり、そのため、周波数を変化させた測定を可能とする装置が必要となり、特定の条件を満たすことの判定を行う装置が必要になる。そのため、測定装置が複雑になり、価格も高くなるという問題点があった。これに対して、本発明の方法では、測定する周波数を予め決めておくことが可能であるので、上記した問題点がなく、実用上好ましい。
【００５１】
また本発明の上述した実施の形態の方法は、本発明の実施の形態の方法による鉛蓄電池の特性評価（検査）を、適切な時間間隔をもって行い、前回までの検査で求められた電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）の値のうち少なくとも一つ以上の値を、当回の検査で求めた電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）の値のうち少なくとも一つ以上の値と比較し、その比較結果を、鉛蓄電池の残存容量と劣化状態の判定の補正に用いるという方法を併用することが可能である。
【００５２】
上記した方法を併用することにより、鉛蓄電池の残存容量と劣化状態の判定の精度を向上させること、および／または、判定のための演算をより簡便にすることが可能である。
【００５３】
自動車などの車両に搭載された鉛蓄電池の判定にあたっては、数秒から数十秒までの適切な時間間隔で検査を繰り返すことにより、温度などの周囲環境の影響を、簡単に補正できるので、特に有効である。
【００５４】
また、本発明の鉛蓄電池の評価方法を自動車などの車両に搭載された鉛蓄電池に対して用いる場合、運転者がエンジンを始動させる直前に本発明の検査方法を実施し、その検査結果をその検査以降の検査における判定の補正に用いることがさらに効果的である。その理由は、運転者が車両のエンジンを始動させる前の環境は、稼働している自動車の装置、機器が少ないため、それらの影響を受けず、本発明の検査の環境が良好なためである。
【００５５】
また、本発明の鉛蓄電池の評価方法を、自動車に搭載された鉛蓄電池に対して用いる場合、自動車のエンジンの停止中に行うことが効果的である。その理由は、エンジンが停止中で、オルタネータが停止している状況では、本発明の方法で測定が必要な周波数の範囲に、大きなノイズが発生する可能性が低いからである。
【００５６】
本発明の鉛蓄電池の評価方法を、自動車が停止した際のアイドリングストップの可否の判定に用いる場合には、上記した理由により、エンジンが停止した直後に、本発明の検査方法を実施することが好ましい。
【００５７】
【実施例】
上述した本発明の鉛蓄電池の評価方法の実施の形態についての具体的な実施例（実験例）を、添付図面を参照して述べる。
【００５８】
本発明の実施例において、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）によって構成される等価回路は、図１および図２に示したものである。
【００５９】
図４は、あらかじめ、７５Ａｈの鉛蓄電池の残存容量を調整して、鉛蓄電池の残存容量と電気二重層容量値（Ｃｄ）との関係を求めた結果を例示したグラフである。
電気二重層容量値（Ｃｄ）は、鉛蓄電池の内部インピーダンスの測定結果から後述する演算式から計算した。
鉛蓄電池の残存容量と電気二重層容量値（Ｃｄ）の関係は、温度依存性はあるが、ほぼ線形性（直線性）を示しており、電気二重層容量値（Ｃｄ）が判れば鉛蓄電池の残存容量を推定することが可能である。
劣化がない正常な鉛蓄電池の残存容量は、下記式（１）で規定される。
【００６０】
【数２】
残存容量（％）＝０．１８１×Ｃｄ＋０．０６４ …（１）
【００６１】
鉛蓄電池の測定条件および測定結果
（１）１００％充電状態の鉛蓄電池に、（ａ）１５Ａの電流で１時間放電させた後、または、（ｂ）３０Ａの電流で１０分間放電させた後、鉛蓄電池の残存容量を判定した。
（２）電池の周囲温度を２０°Ｃに設定しておいた。
（３）測定した内部インピーダンスを求めて計算した結果、電気二重層容量値（Ｃｄ）は３．６〔Ｆ〕となった。
（４）式（１）により残存容量を判定した結果、７２％となった。実際の残存容量は７３％であることから、本発明の鉛蓄電池の評価方法によりかなり精確に残量判定が可能であることが分かった。
【００６２】
以上のように、あらかじめ電気二重層容量値（Ｃｄ）と鉛蓄電池の残存容量の関係を求めておき、内部インピーダンスの測定結果から求めた電気二重層容量値（Ｃｄ）の値を、上記関係に照合することで、鉛蓄電池の残存容量を判定することが可能である。
【００６３】
また、式（１）は、周囲温度が２０°Ｃのものであるが、図３に図解したように、鉛蓄電池の温度を２０°Ｃ、４０°Ｃ、６０°Ｃと変化させた場合には、特性がシフトする傾向があり、鉛蓄電池の温度が分かれば残存容量を補間して算出することが可能である。従って、ある温度について特性を調べておき、任意の温度について鉛蓄電池に取り付けた温度センサー等によって検知し、その温度に応じて予め求めた特性（残存容量値）をシフトして（補間して）、その温度における特性（残存容量値）を算出することができる。
【００６４】
鉛蓄電池が劣化した場合には、正常な鉛蓄電池に対して残存容量が減少するものの、その特性は正常な鉛蓄電池と同様に線形性が見られることから、劣化の程度が分かれば残存容量を補正することが可能である。
【００６５】
判定の際の電池の劣化状態による補正と電池の温度のよる補正は、内部インピーダンスの測定結果から求めた電解液抵抗値（ＲΩ）を用いて行うこともできる。
【００６６】
図６は正常な鉛蓄電池および劣化した鉛蓄電池の温度による電解液抵抗値（ＲΩ）と鉛蓄電池の残存容量（ＳＯＣ）の関係を示すグラフである。
電解液抵抗値（ＲΩ）は残存容量（ＳＯＣ）によっては変化せず、温度および劣化度合いにより変化する。従って、内部インピーダンスの測定結果から求めた電解液抵抗値（ＲΩ）を用いて残存容量を補正することが可能である。
【００６７】
電荷移動抵抗値（Ｒｃｔ）と鉛蓄電池の残存容量との関係
なお、図５に図解した電荷移動抵抗値（Ｒｃｔ）と鉛蓄電池の残存容量との関係からも、上述した電気二重層容量値（Ｃｄ）と鉛蓄電池の残存容量との関係との関係から鉛蓄電池の残存容量を求めたように、鉛蓄電池の残存容量を求めることができた。
【００６８】
電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）の算出方法
次に、自動車用鉛蓄電池の残存容量を測定する際の電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）の導出方法についての具体例を述べる。
内部インピーダンスの測定周波数は、１００Ｈｚ、２０Ｈｚ、６Ｈｚ、２Ｈｚの４点とし、この４点の内部インピーダンスの測定結果から電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を演算した。
この４点の周波数を選んだ理由は下記による。
【００６９】
図７に図解したように、周波数を変化させて内部インピーダンスを測定し、内部インピーダンスの実部をＸ軸に、虚部に−１を乗じたＹ軸をプロットした（ｃｏｌｅ ｃｏｌｅ ｐｌｏｔ）。
図７に図解したように、特性は、円弧の特性を示す部分と直線状のような特性の２つの部分で示すことができる。ここで、円弧の特性は、図１に示す等価回路によって表すことが可能であるため、円弧の軌道を把握することにより、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を導出することが可能である。
【００７０】
例えば、３点を通過する円の軌道は一義的に決定されるため、非常に簡単に円の式を求めることができる。従って、３つの周波数１００Ｈｚ、２０Ｈｚ、６Ｈｚにより円の軌跡を把握した。
図７に示すように２Ｈｚ付近のプロットは、円の軌跡から外れており、円の式を精度良く求めるためには、測定する周波数を５〜１００Ｈｚの周波数の範囲とするのが好ましい。
【００７１】
測定周波数の数としては、円の式を求める上で、最低限３点の測定点が必要であり、測定点が増加することに伴う実用的価値の低下を考慮して、最大でも、５〜６点、できれば、３〜４点以下が望ましい。さらには、円の軌跡を求めるプロットが円周上に等間隔になっている場合が最も精度がよいため、第１の測定周波数Ｆａの周波数は、５〜１０Ｈｚの中の１点、１０〜３０Ｈｚの中の１点、５０〜１００Ｈｚの中の１点を使用することが最も望ましい。
【００７２】
図７は、後述する方法により求めた円の式から計算した円弧（破線）を示している。
円軌道のＸ軸切片をＸａ，Ｘｂ（Ｘａ＜Ｘｂ）とすると、Ｘａが電解液抵抗値（ＲΩ）に対応し、（Ｘｂ−Ｘａ）が電荷移動抵抗値（Ｒｃｔ）に対応する。３点を通過する円の式において、虚部を０とすることによりＸａとＸｂ（Ｘａ＜Ｘｂ）を求められ、Ｘａが電解液抵抗値（ＲΩ）、（Ｘｂ−Ｘａ）が電荷移動抵抗値（Ｒｃｔ）として計算される。
【００７３】
ここで、（Ｘａ＋Ｘｂ）×０．５をＸ_m として求めておく。Ｘ_m は、円の中心座標を示すインピーダンスの実部である。円の頂点を示す周波数をｆ_max とすると、電気二重層容量値（Ｃｄ）は、（Ｒｃｔ×２π×ｆ_max ）^-1で計算される。しかし、測定した周波数が必ずしも円周上の頂点とはならないため、近似的に次のような特性から円の頂点を示す周波数を求める。
【００７４】
周波数を変化させて内部インピーダンスを測定し、周波数をＸ軸、内部インピーダンスの実部をＹ軸として、プロットした結果を図８に示す。
内部インピーダンスの実部と周波数に直接関係が得られる周波数の範囲は、およそ１〜１０Ｈｚの範囲であることが判る。
図８中には、６Ｈｚと２Ｈｚの２点の周波数で求めた結果もプロットしている。２点間を結ぶ直線の式を求めることにより、この直線の式にＸ_m を代入して、円の頂点を近似的に示す周波数ｆ_m が求められる。電気二重層容量値（Ｃｄ）は、（Ｒｃｔ×２π×ｆ_m ）^-1で計算される。
【００７５】
周波数ｆ_m は、ほとんどの場合４〜５Ｈｚになるため、上記した方法を行う場合は、１〜５Ｈｚの周波数の範囲で選ばれた任意の１点の周波数と、５〜１０Ｈｚの中の１点から選ばれた周波数で測定することが好ましく、特に、円の軌跡を把握するために測定する周波数３〜４点の内、最も小さい周波数を使用するとより効率的である。
【００７６】
３点の周波数で測定した場合の電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を求める演算式について述べる。
４点の周波数で測定した場合は、任意の組合せの３点で電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を求め、それぞれの組合せで求めた判定結果の平均をとることができる。また、測定の安全サイドからそれぞれの組み合わせて求めた判定結果の最小値を使用しても良い。
いずれにしても、４点の周波数で測定した場合についても、３点で測定した場合と同様の計算を行う。まず、３点の周波数で測定した内部インピーダンスの測定結果から、任意の円の方程式を計算する。
【００７７】
図９は３点の周波数ｆ₁ ，ｆ₂ ，ｆ₃ で測定した内部インピーダンスをプロットした座標を示すグラフである。
下記のような３つの式が得られ、未知数が３つで、式が３つあることから、円の軌跡を定める係数ａ，ｂ，ｒを求めることができる。
【００７８】
【数３】
ｆ₁ で測定： （Ｘ₁ −ａ）² ＋（Ｙ₁ −ｂ）² ＝ｒ² …（２）
ｆ₂ で測定： （Ｘ₂ −ａ）² ＋（Ｙ₂ −ｂ）² ＝ｒ² …（３）
ｆ₃ で測定： （Ｘ₃ −ａ）² ＋（Ｙ₃ −ｂ）² ＝ｒ² …（４）
【００７９】
上記３つの式（２）〜（４）を解いた結果、係数ａ，ｂ，ｒはそれぞれ下記のようになる。
【００８０】
【数４】

【００８１】
ここで、係数（因子）Ａ〜Ｆはそれぞれ下記で表される。
【００８２】
【数５】
Ａ＝Ｘ₁ −Ｘ₂ …（８）
Ｂ＝Ｘ₂ −Ｘ₃ …（９）
Ｃ＝Ｙ₁ −Ｙ₂ …（１０）
Ｄ＝Ｙ₂ −Ｙ₃ …（１１）
Ｅ＝Ｘ₁ ² −Ｘ₂ ² ＋Ｙ₁ ² −Ｙ₂ ² …（１２）
Ｆ＝Ｘ₂ ² −Ｘ₃ ² ＋Ｙ₂ ² −Ｙ₃ ² …（１３）
【００８３】
図９において、Ｒ_CTは実軸上の円の弦であることから、円の式からＹ＝０となる２点のＸを求め、この２点間の距離からＲ_CTを計算する。
【００８４】
【数６】
（Ｘ−ａ）² ＝ｒ² …（１４）
Ｘ＝ａ±ｒ …（１５）
Ｒ_CT ＝２・ｒ …（１６）
ＲΩ ＝ａ−ｒ …（１７）
【００８５】
図１０は４点目の周波数で測定した内部インピーダンスをプロットした座標を示すグラフである。
円の頂点を示す周波数ｆ_m については、ｆ_m を挟む周波数範囲における内部インピーダンスの実数部と周波数の関係は、図８に示すように、ある範囲について、ほぼ線形性があることから、直線近似により求めることができる。
第１の周波数ｆ₁ で測定した時の実数成分をＸ₁ 、第４の周波数ｆ₄ で測定したときの実数成分をＸ₄ とすると、ｆ_m は下式で表される。ここで、ｆ₁ ＞ｆ_m ＞ｆ₄ である。
【００８６】
【数７】

【００８７】
よって、電気二重層容量値（Ｃｄ）は次式で表される。
【００８８】
【数８】

【００８９】
自動車に搭載された鉛蓄電池の判定にあっては、数秒から数十秒までの適切な間隔で検査を繰り返すことにより、温度などの周囲環境の影響を簡単に補正できるので、本発明の鉛蓄電池の評価方法は特に有効である。
【００９０】
残存容量判定はアイドリングストップ時に１分経過毎に測定し、過去の判定結果を参照する場合と、単独で判定した場合を比較した例を下記表１に示す。
【００９１】
【表１】

【００９２】
過去の判定結果の参照方法は、同じアイドルストップ期間中の残存容量判定において、１分経過毎に測定した判定結果を順次用いて平均値を使用した。
単独の場合の残存容量は、アイドルストップ直後から２分経過まで低下し、３分経過後の判定では逆に増加傾向を示している。対して、過去参照の残存容量は、３分経過後までは低下し、それ以降はほぼ一定値を示している。
アイドルストップ期間中においては、蓄電池からの放電が小さくなることはあっても、蓄電池が充電されることはない。
残存容量が上昇する要因は、主に温度などの周囲環境の影響が大きい。従って、単独で容量判定を行う場合より、過去の判定結果を参照して判定した場合の方が、温度などの周囲環境の影響を簡単に補正できるので特に有効である。
【００９３】
鉛蓄電池の評価装置
本発明の鉛蓄電池の特性評価装置は、上述した鉛蓄電池の評価方法を実施する装置である。
その鉛蓄電池の評価装置の構成を図１１に例示する。
鉛蓄電池の評価装置１０は、複数の周波数において鉛蓄電池の内部インピーダンスを測定する測定手段１２と、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を算出する算出手段１４と、算出した電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）から供試した鉛蓄電池の残存容量および／または劣化状態を判定する判定手段１６とを有する。
【００９４】
測定手段１２は、たとえば、可変周波数発振回路と、インピーダンス測定装置と、記憶回路を有するコンピュータ装置とで構成され、特性を評価すべき鉛蓄電池に可変周波数発振回路とインピーダンス測定回路とを接続し、インピーダンス測定回路にコンピュータ装置を接続する。
可変周波数発振回路は、１〜１００Ｈｚの周波数の範囲で選ばれた、内部インピーダンスの実部をＸ軸に虚部に−１を乗じた値をＹ軸にプロットして規定される二次元座標におけるインピーダンス円を規定する少なくとも３点以上の複数の周波数の信号を発振して鉛蓄電池に印加し、インピーダンス測定装置がそれぞれの周波数における鉛蓄電池の内部インピーダンスを測定する。コンピュータ装置はインピーダンス測定装置が測定した内部インピーダンスの特定値を入力して記憶回路に記憶する。
【００９５】
算出手段１４は、たとえば、上記記憶回路を有するコンピュータ装置で構成され、このコンピュータ装置により、上述した式（Ａ−１）または式（Ｂ−１）で規定される、少なくとも電荷移動抵抗値（Ｒｃｔ）と電気二重層容量値（Ｃｄ）との並列回路と電解液抵抗値（ＲΩ）との直列回路で構成した等価回路から導出される電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）と複数の周波数において測定した複数の鉛蓄電池の内部インピーダンスとの関係式に、複数の周波数において測定した複数の内部インピーダンスの値を参照して電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を求める。
【００９６】
判定手段１６は、たとえば、上記コンピュータ装置で構成され、算出手段１４で算出したした電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）から供試した鉛蓄電池の残存容量および／または劣化状態を判定する。
このような判定は、たとえば、上述した電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）と残存容量および／または劣化状態との関係をグラフとしてコンピュータ装置から表示装置に表示して、人間が目視で判定してもよいし、コンピュータ装置の判断処理で自動的に行ってもよい。
【００９７】
【発明の効果】
以上に述べたように、本発明によれば、１〜１００Ｈｚの周波数の範囲で選ばれた、任意の３〜５点の周波数で内部インピーダンスの測定を行い、測定結果を演算式に代入することにより鉛蓄電池の残存容量と劣化状態を判定できるため、短時間でしかも簡単に測定が可能である。また、測定周波数が３〜５点の固定周波数であるため、装置のコストを安くすることができる。
【００９８】
本発明によれば、鉛蓄電池の残存容量を精確に判定できるため、自動車が停車した際のアイドリングストップの可否の判定に用いると、とても有効である。
【図面の簡単な説明】
【図１】図１は本発明で使用する第１の等価回路としての、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）からなる等価回路の構成図である。
【図２】図２は本発明で使用する第２の等価回路としての、電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ’とＲｃｔ’’），電気二重層容量値（Ｃｄ’とＣｄ’’）からなる等価回路の構成図である。
【図３】図３は本発明の鉛蓄電池の評価特性方法の処理を示すフローチャートである。
【図４】図４は電気二重層容量値（Ｃｄ）と鉛蓄電池の残存容量との関係を例示するグラフである。
【図５】図５は電荷移動抵抗値（Ｒｃｔ）と鉛蓄電池の残存容量との関係を例示するグラフである。
【図６】図６は正常な鉛蓄電池および劣化した鉛蓄電池の温度による電解液抵抗値（ＲΩ）と鉛蓄電池の残存容量（ＳＯＣ）の関係を示すグラフである。
【図７】図７は電解液抵抗値（ＲΩ），電荷移動抵抗値（Ｒｃｔ），電気二重層容量値（Ｃｄ）を算出する方法を図解したグラフである。
【図８】図８は周波数とインピーダンスの実数成分との関係を図解したグラフである。
【図９】図９は３点の周波数で測定した内部インピーダンスをプロットした座標を示すグラフである。
【図１０】図１０は４点目の周波数で測定した内部インピーダンスをプロットした座標を示すグラフである。
【図１１】図１１は本発明の鉛蓄電池の評価装置の構成図である。
【符号の説明】
１０・・鉛蓄電池の評価装置
１２・・測定手段
１４・・算出手段
１６・・判定手段[0001]
BACKGROUND OF THE INVENTION
TECHNICAL FIELD The present invention relates to a method and apparatus for evaluating the characteristics of a lead storage battery, and in particular, a practical and effective characteristic evaluation method (inspection method) for a remaining capacity and a deteriorated state of a lead storage battery mounted on a vehicle such as an automobile, and its device. Relates to the device.
[0002]
[Prior art]
A lead-acid battery is mounted as a secondary battery in vehicles such as automobiles, and is used as a power source for engine starting and automobile equipment. In such a case, it is particularly necessary to accurately evaluate the remaining capacity and the deterioration state of the lead storage battery. For example, when stopping an automobile, the engine cannot be started after stopping if there is not enough remaining capacity in the lead-acid battery to start the engine next time.
Of course, in other cases, it is desired to accurately evaluate the remaining capacity and the deterioration state of a secondary storage battery such as a lead storage battery.
[0003]
Various methods have been proposed for inspecting the remaining capacity and deterioration state of such a lead storage battery.
For example, a method has been proposed in which a lead storage battery is completely discharged, its capacitance is measured, and a deterioration state is determined from the measured capacitance. However, since this method requires that the lead storage battery be completely discharged, there is a problem that the inspection method cannot be applied to the lead storage battery in use, in addition to waste of electric power due to the discharge. Furthermore, this inspection method is not a practical method because it takes time until the discharge is completed, and eventually the measurement time becomes long.
Accordingly, various methods have been developed that can inspect lead-acid batteries in a short time while preventing waste of power consumption.
[0004]
Japanese Laid-Open Patent Publication No. 4-95788 (Patent No. 2536257) describes the measurement results of the internal impedance of a lead storage battery, the inductance component (L) of the lead storage battery, the electrolyte resistance value (Rs), the charge transfer resistance value (θ), Applying to the equivalent circuit represented by the following formula (1-1) consisting of the electric double layer capacitance value (Cd), the workburg impedance (W), and the workburg coefficient (σ), the optimum solution is obtained, and the inductance component (L) , Electrolyte resistance value (Rs), charge transfer resistance value (θ), electric double layer capacitance value (Cd), workburg impedance (W), workburg coefficient (σ) are compared with the initial value Thus, a method for determining the life of a lead-acid battery is disclosed.
[0005]
[Expression 1]

[0006]
JP-A-4-141966 (Patent No. 2546050) discloses an imaginary part of impedance between the impedance of the frequency at which the phase becomes 0 and the frequency of 0.1 to 10 Hz in the measurement of the internal impedance of the lead-acid battery. A method of determining the deterioration state of the lead-acid battery from the impedance at a frequency at which the value obtained by dividing the change with respect to the frequency of the current by the change with respect to the frequency of the real part of the impedance is about −1 is disclosed.
[0007]
JP-A-5-135806 (Patent No. 2792784) (a) measures the internal impedance of a lead-acid battery at a frequency of 2 to 3 points between 0.001 and 1 Hz, and measures the imaginary part of impedance. To the power of -0.5 (f^-1/2), The remaining capacity of the lead storage battery is determined from the value of the Y intercept, and (a) the internal impedance is measured at a frequency of 0.01 to 0.05 Hz, and the real part is changed to the imaginary part. In contrast, a method is disclosed in which the remaining capacity of a lead storage battery is determined based on the value of the slope plotted.
[0008]
[Problems to be solved by the invention]
Each of the above-described methods has the following problems, and cannot be effectively used practically for evaluating the characteristics of lead-acid batteries, particularly lead-acid batteries mounted on vehicles such as automobiles. Details are described below.
[0009]
The method described in Japanese Patent Laid-Open No. 4-95788 is based on the measurement result of the internal impedance of a lead storage battery, and the inductance component (L), electrolyte resistance value (Rs), and charge transfer shown in the equation (1-1). It is necessary to obtain six parameters: a resistance value (θ), an electric double layer capacitance value (Cd), a workburg impedance (W), and a workburg coefficient (σ). Therefore, it is necessary to measure the internal impedance at at least six frequencies, and there is a problem that the calculation for obtaining the optimal solution of the six parameters becomes very complicated.
That is, the measurement at a large number of frequencies and complicated calculations described in Japanese Patent Laid-Open No. 4-95788 not only increase the measurement time, but also increase the price of the measuring device. There was a problem that it was not practical for evaluating lead-acid batteries.
[0010]
In the method described in Japanese Patent Laid-Open No. 4-141966, it is necessary to find and measure the frequency at which the phase of the internal impedance is 0, and further, the imaginary part of the impedance is between 0.1 and 10 Hz. It is necessary to perform measurement by finding a frequency where the value obtained by dividing the change with respect to the frequency by the change with respect to the frequency of the real part of the impedance is about -1.
That is, the method disclosed in Japanese Patent Laid-Open No. 4-141966 needs to find a frequency whose internal impedance value satisfies a specific condition. Therefore, in addition to a device that enables measurement by changing the frequency, a device that determines that the above-described specific condition is satisfied is also required. Such a process requires a complicated measuring device, which increases the price of the device, and is problematic in that it is not practical for evaluating the characteristics of a lead storage battery mounted on a vehicle.
[0011]
The method described in Japanese Patent Laid-Open No. 5-135806 uses an internal impedance value at 0.001 to 1 Hz as an index. However, such a measurement in the low frequency region of 1 Hz or less is a factor that increases the price of the device because the configuration of the measurement device, particularly the frequency oscillation circuit, is complicated compared to the measurement in the region of 1 Hz or more. There is a problem that the measurement time becomes long.
In addition, since the internal impedance at 0.001 to 1 Hz tends to change greatly depending on the temperature, for example, measurement of a lead storage battery installed in a place where the temperature changes greatly, such as a lead storage battery mounted on a vehicle. However, there is a problem that correction is indispensable depending on the temperature.
[0012]
[Means for Solving the Problems]
In order to solve the above-described problems, the present inventors have intensively studied, and as a result, invented the method for evaluating the characteristics of the lead storage battery of the present invention. The summary of the method for evaluating the characteristics of the lead storage battery of the present invention will be described below with reference to FIGS.
In the present invention, the inspection of the remaining capacity and the deterioration state of the lead storage battery is collectively referred to as the characteristic evaluation of the lead storage battery.
[0013]
In the method for evaluating the characteristics of the lead storage battery of the present invention, first, the equivalent circuit of the lead storage battery is simplified, and as shown in FIG. 1 or FIG. 2, at least the charge transfer resistance value (Rct) and the electric double layer. It is constituted by a series circuit of a parallel circuit with a capacitance value (Cd) and an electrolyte resistance value (RΩ), and the impedance is represented as an equivalent circuit defined by the following equation. Details of the equivalent circuit will be described later.
[0014]
[RΩ + (Rct / (1 + jωCd))] (A-1)
However, ω = 2πf
[0015]
In the evaluation characteristic method of the lead storage battery of the present invention, as illustrated in FIG. 3, (1) the value obtained by multiplying the real part of the internal impedance of the lead storage battery by the X axis and the imaginary part by -1 is plotted on the Y axis. The internal impedance of the lead-acid battery is measured for a plurality of three or more frequencies selected in a frequency range of 1 to 100 Hz that defines an impedance circle in two-dimensional coordinates defined by
[0016]
Furthermore, in the evaluation characteristic method of the lead storage battery of the present invention, as illustrated in FIG. 3, (2) a parallel circuit of a charge transfer resistance value (Rct) and an electric double layer capacitance value (Cd), and an electrolyte resistance value The electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), the electric double layer capacitance value (Cd) derived from an equivalent circuit composed of a series circuit with (RΩ), and a plurality of measured values at a plurality of frequencies In relation to the internal impedance of the lead-acid battery, referring to the values of a plurality of internal impedances measured at a plurality of frequencies, the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacitance A value (Cd) is obtained.
[0017]
Finally, in the evaluation characteristics method of the lead storage battery of the present invention, as illustrated in FIG. 3, (3) the calculated electrolyte resistance value (RΩ), charge transfer resistance value (Rct), electric double layer capacity value ( The remaining capacity and / or deterioration state of the lead storage battery tested from all or at least one of Cd) is determined.
[0018]
Moreover, the evaluation apparatus for a lead storage battery according to the present invention is an apparatus that implements the above-described evaluation method for a lead storage battery, and includes a measurement unit, a calculation unit, and a determination unit.
The measurement means performs the process (1) described above, the calculation means performs the process (2) described above, and the determination means performs the process (3) described above.
[0019]
DETAILED DESCRIPTION OF THE INVENTION
DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of a lead storage battery characteristic evaluation method and a lead storage battery characteristic evaluation apparatus according to the present invention will be described below with reference to the accompanying drawings.
[0020]
Equivalent circuit
1 and 2 show circuit examples of equivalent circuits applied in the present invention.
FIG. 1 is a block diagram of an equivalent circuit comprising an electrolyte resistance value (RΩ), a charge transfer resistance value (Rct), and an electric double layer capacitance value (Cd) as a first equivalent circuit used in the present invention.
In the equivalent circuit of FIG. 1, the charge transfer resistance value (Rct) and the electric double layer capacitance value (Cd) are connected in parallel, and the electrolyte resistance value (RΩ) is connected in series to this parallel circuit. Therefore, the impedance of the equivalent circuit is defined by the following equation.
[0021]
[RΩ + (Rct / (1 + jωCd))] (A-2)
However, ω = 2πf
[0022]
FIG. 2 shows an electrolyte resistance value (RΩ), a charge transfer resistance value (Rct ′ and Rct ″), and an electric double layer capacitance value (Cd ′ and Cd ″) as a second equivalent circuit used in the present invention. It is a block diagram of the equivalent circuit which consists of.
The equivalent circuit of FIG. 2 replaces the electric double layer capacitance value (Cd) of FIG. 1 with a first electric double layer capacitance value (Cd ′) and a second electric double layer capacitance value (Cd ″). The charge transfer resistance value (Rct) is replaced with a first charge transfer resistance value (Rct ′) and a second charge transfer resistance value (Rct ″).
The impedance of the equivalent circuit in FIG. 2 is defined by the following equation.
[0023]

However, ω = 2πf
[0024]
Japanese Patent Laid-Open No. 4-95788 discloses an equivalent circuit composed of six parameters as shown in Expression 1-1. In order to accurately grasp the characteristics of the lead storage battery, analysis using an equivalent circuit described in Japanese Patent Laid-Open No. 4-95788 is desirable. For example, in the case of evaluation of a lead storage battery mounted on a vehicle, the present invention is applied. The analysis with the equivalent circuit expressed in FIG. 1 or 2 is sufficient. Rather, it is more practical to reduce the number of parameters to be obtained by applying the equivalent circuit shown in FIG. 1 or FIG. 2 of the present invention, thereby reducing the measurement frequency and reducing the time and cost for calculation. high. In particular, when determining the remaining capacity of a lead storage battery mounted on an automobile, two significant figures are sufficient, and the method of the present invention is more practical than the method of Japanese Patent Laid-Open No. 4-95788.
[0025]
Relationship between 3 points measurement result and circle
As an example, FIG. 8 illustrates the relationship between the measurement results at three points and the circle.
That is, two-dimensional coordinates defined by plotting on the Y-axis the value obtained by multiplying the real part of the internal impedance of the lead-acid battery by the X-axis and the imaginary part by -1 corresponding to the impedance defined by the expression A or B The internal impedance of the lead-acid battery is measured at a plurality of frequencies of at least three points that define the impedance circle.
[0026]
Measurement frequency
In the present invention, measurement is performed at an arbitrary frequency of 3 to 5 points (at most 6 points) selected in a frequency range of 1 to 100 Hz.
[0027]
First, the reason for selecting the frequency range of 1 to 100 Hz will be described. This is because the above-described frequency range is a particularly effective frequency range for obtaining the electrolytic solution resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacitance value (Cd) of the lead storage battery. That is, if it is 1 Hz or more, it can be easily carried out on the measurement and on the apparatus, and since it is within 100 Hz, the frequency is about twice the commercial frequency and is not a high frequency. There is no.
[0028]
In the method disclosed in Japanese Patent Laid-Open No. 5-135806, the remaining capacity of the lead storage battery is determined from the internal impedance of the lead storage battery at two to three frequencies between 0.001 and 1 Hz. However, according to the study of the inventors, as described above, it is more preferable to use the measurement data of 1 to 100 Hz according to the embodiment of the present invention than to use the measurement data of 0.001 to 1 Hz. It was effective and easy to determine the residual capacitance.
[0029]
Next, the reason for measuring at 3 to 5 and 6 frequencies will be described. In order to define the impedance circle (see FIG. 8) in determining the electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacitance value (Cd), it is necessary to measure at least three frequencies. is there.
The more measurements are made at different frequencies, the higher is the accuracy with which the electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacitance value (Cd) are determined. However, as the number of measurements increases, the measurement time increases, the variable frequency oscillation circuit becomes complicated, and the computation after measurement becomes longer. Therefore, practically, the measurement is performed at 3 to 5 frequencies, and at most 6 frequencies.
[0030]
Next, the relationship between the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), the electric double layer capacity value (Cd), and the remaining capacity and / or deterioration state of the lead storage battery will be considered.
[0031]
First Embodiment Regarding Relationship between Remaining Capacity and / or Deterioration State of Lead Storage Battery
FIG. 4 is a graph illustrating the relationship between the electric double layer capacity value (Cd) and the remaining capacity of the lead storage battery.
In the determination of the remaining capacity of the lead storage battery in the inspection method of the present invention, as illustrated in FIG. 4, a relational expression between the electric double layer capacity value (Cd) and the remaining capacity of the lead storage battery is obtained in advance, and the internal impedance of The remaining capacity of the lead storage battery can be determined by comparing the electric double layer capacity value (Cd) obtained from a plurality of measurement results with the above relational expression.
[0032]
It has been found that the remaining capacity of the lead storage battery has a linear relationship with the electric double layer capacity value (Cd) as follows.
[0033]
Remaining capacity (%) = α × Cd + β (C)
[0034]
Α and β vary depending on the temperature of the lead storage battery.
[0035]
Second embodiment regarding relationship between remaining capacity and / or deterioration state of lead-acid battery
FIG. 5 is a graph illustrating the relationship between the charge transfer resistance value (Rct) and the remaining capacity of the lead storage battery.
In the determination of the remaining capacity of the lead storage battery in the inspection method of the present invention, as illustrated in FIG. 5, a relational expression between the charge transfer resistance value (Rct) and the remaining capacity of the lead storage battery is obtained in advance. The remaining capacity of the lead storage battery can be determined by comparing the charge transfer resistance value (Rct) obtained from the measurement results with the above relational expression.
[0036]
It has been found that the remaining capacity of the lead storage battery has a linear relationship with the charge transfer resistance value (Rct) as follows.
[0037]
Remaining capacity (%) = γ × Rct + δ (D)
[0038]
Note that γ and δ vary depending on the temperature of the lead storage battery.
[0039]
Third Embodiment Regarding Relationship between Remaining Capacity and / or Degradation State of Lead Acid Battery
In the determination of the deterioration state of the lead storage battery in the lead battery evaluation method of the present invention, the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), the electric double layer capacity value (Cd), and the lead storage battery The relational expression of the deterioration state is obtained, and the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacitance value (Cd) obtained from the measurement result of the internal impedance are collated with the above relational expression. By doing so, the deterioration state of the lead storage battery can be determined.
[0040]
The remaining capacity of the lead storage battery may be affected by the deterioration state and temperature of the battery. Therefore, it may be necessary to correct (interpolate) the value of the remaining capacity of the lead storage battery obtained as described above with the deterioration state and temperature value of the battery. At that time, the remaining capacity of the lead storage battery obtained from the electric double layer capacity value (Cd) is corrected by the determination result of the deterioration state of the battery obtained from the electrolyte resistance value (RΩ) and the charge transfer resistance value (Rct). be able to.
[0041]
Effect of temperature on remaining capacity
The relationship between the temperature of the lead storage battery, the electrolyte resistance value (RΩ), and the charge transfer resistance value (Rct) is obtained in advance, and the measurement results of the electrolyte resistance value (RΩ) and the charge transfer resistance value (Rct) Since the temperature of the lead storage battery can be obtained by checking with the relationship, the influence of the temperature on the remaining capacity depends on the temperature of the lead storage battery obtained from the electrolyte resistance value (RΩ) and the charge transfer resistance value (Rct). It is also possible to correct.
[0042]
In determining the remaining capacity and deterioration state of the lead storage battery described above, it is also possible to measure the temperature separately from the method of the present invention and use the measured value to correct the influence of the temperature on the remaining capacity and deterioration state. is there.
[0043]
Method for calculating electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacitance value (Cd)
The relationship between the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), the electric double layer capacity value (Cd), and the internal impedance of the lead storage battery, derived from the equivalent circuit of FIGS. Example of specific method for obtaining electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacitance value (Cd) by referring to a plurality of internal impedance values measured at a plurality of frequencies Is preferably a statistical method, for example, a method for obtaining an optimal solution by a least square method.
[0044]
However, when evaluating the characteristics of a lead storage battery mounted on a vehicle, it is desirable to obtain an optimal solution more easily. As a simpler method than the least square method, the following methods can be exemplified.
[0045]
First method M
Among the above-mentioned 1 to 100 Hz, an arbitrary 3 to 4 point first frequency (Fa) selected within a frequency range of 5 to 100 Hz and an arbitrary one point selected within a frequency range of 1 to 5 Hz In the second frequency (Fb), the internal impedance of the lead-acid battery is measured several times, and from the measured values, the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacity value (Cd) Ask for.
[0046]
In the first method M, as illustrated in FIG. 6, with respect to the internal impedances of 3 to 4 points measured at the first frequency (Fa), the real part of the internal impedance is set on the X axis, and the imaginary part of the internal impedance is obtained. A value obtained by multiplying the value of -1 by -1 is plotted on the Y axis (coll call plot), a trajectory of a circle passing through 3 to 4 points is obtained, and X-axis intercepts Xa and Xb (Xa <Xb) of the trajectory are obtained. Is the electrolyte resistance value (RΩ), Xb−Xa is the charge transfer resistance value (Rct), and (Xa + Xb) × 0.5 is X_mFurthermore, the coordinate C with the real part of the internal impedance on the Y axis and the frequency on the X axis_mThe measured values at the lowest frequency Fa ′ and the second frequency Fb among the first frequencies Fa are plotted, and the above-mentioned X on the straight line connecting both plot points is plotted._mThe frequency corresponding to_mAnd the electric double layer capacitance value Cd is (Rct × ω_m)^-1And
[0047]
As shown in the relational expression of the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), the electric double layer capacitance value (Cd), and the internal impedance, which is derived from the equivalent circuit shown in FIGS. Even if the power parameter is 5 points or less, mathematically rigorously solving the parameters of the relational expression described above makes the calculation complicated, increases the scale of the arithmetic device, and increases the price. Therefore, as in the present invention, the practical value of obtaining the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacitance value (Cd) by a simple calculation is extremely high.
[0048]
In the case where the simple first method M described above is performed, the frequency to be measured is set to an arbitrary 3 to 4 points of the first frequency Fa selected within a frequency range of 5 to 10 Hz, and 1 to 5 Hz. It is particularly preferable that the second frequency Fb is an arbitrary one point selected in the frequency range. The reason is that it is preferable to use a measured value in the frequency range of 5 to 100 Hz in obtaining the locus of the circle in the above-described coll coll plot. In addition, in order to obtain the locus of a circle, it is necessary that there are three or more measurement points. In obtaining the locus of the circle, more preferably, the frequency of the first measurement frequency Fa is one point in 5 to 10 Hz, one point in 10 to 30 Hz, and one point in 50 to 100 Hz. Is mentioned.
[0049]
The inventor of the present application uses coordinates C_mThe frequency range in which a linear relationship between the real part of the internal impedance and the frequency is obtained is found to be approximately 1 to 10 Hz. Therefore, it is preferable that the range of the first frequency Fb is approximately 1 to 5 Hz, and furthermore, the lowest frequency Fa ′ among the first frequencies Fa is selected from one point of 5 to 10 Hz. Is preferred.
[0050]
In the method disclosed in Japanese Patent Laid-Open No. 4-141966, it is necessary to find a frequency at which the value of the internal impedance satisfies a specific condition. Therefore, an apparatus that enables measurement with the frequency changed is required. An apparatus for determining whether to satisfy the condition is required. As a result, the measuring apparatus becomes complicated and the price is high. On the other hand, in the method of the present invention, since the frequency to be measured can be determined in advance, there is no above-mentioned problem and it is practically preferable.
[0051]
Further, the method of the above-described embodiment of the present invention performs the characteristic evaluation (inspection) of the lead storage battery by the method of the embodiment of the present invention at an appropriate time interval, and the electrolytic solution resistance obtained by the previous inspection. At least one of the value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacitance value (Cd), the electrolyte resistance value (RΩ) obtained by the current inspection, and the charge transfer A method of comparing at least one value of the resistance value (Rct) and the electric double layer capacity value (Cd) and using the comparison result to correct the determination of the remaining capacity and the deterioration state of the lead storage battery. It is possible to use together.
[0052]
By using the above-described method in combination, it is possible to improve the accuracy of determination of the remaining capacity and the deterioration state of the lead storage battery and / or to make the calculation for the determination easier.
[0053]
When determining lead-acid batteries mounted on vehicles such as automobiles, it is particularly effective because the effects of the surrounding environment such as temperature can be easily corrected by repeating the inspection at appropriate time intervals from several seconds to several tens of seconds. It is.
[0054]
Further, when the lead storage battery evaluation method of the present invention is used for a lead storage battery mounted on a vehicle such as an automobile, the inspection method of the present invention is performed immediately before the driver starts the engine, and the inspection result is It is more effective to use for correction of determination in the inspection after the inspection. The reason for this is that the environment before the driver starts the engine of the vehicle is not affected by the number of operating automobile devices and equipment, and the environment for inspection of the present invention is favorable. .
[0055]
Moreover, when using the evaluation method of the lead storage battery of this invention with respect to the lead storage battery mounted in the motor vehicle, it is effective to carry out while the engine of a motor vehicle is stopped. The reason is that in a situation where the engine is stopped and the alternator is stopped, there is a low possibility that large noise will be generated in the frequency range that requires measurement by the method of the present invention.
[0056]
When the lead storage battery evaluation method of the present invention is used to determine whether or not idling can be stopped when the vehicle is stopped, the inspection method of the present invention can be carried out immediately after the engine is stopped for the reason described above. preferable.
[0057]
【Example】
Specific examples (experimental examples) of the above-described embodiment of the method for evaluating a lead storage battery of the present invention will be described with reference to the accompanying drawings.
[0058]
In an embodiment of the present invention, an equivalent circuit constituted by an electrolyte resistance value (RΩ), a charge transfer resistance value (Rct), and an electric double layer capacitance value (Cd) is as shown in FIGS. .
[0059]
FIG. 4 is a graph illustrating a result of adjusting the remaining capacity of a 75 Ah lead storage battery in advance and determining the relationship between the remaining capacity of the lead storage battery and the electric double layer capacity value (Cd).
The electric double layer capacity value (Cd) was calculated from an arithmetic expression described later from the measurement result of the internal impedance of the lead storage battery.
The relationship between the remaining capacity of the lead-acid battery and the electric double layer capacity value (Cd) is temperature-dependent, but shows almost linearity (linearity). If the electric double layer capacity value (Cd) is known, the lead-acid battery It is possible to estimate the remaining capacity.
The remaining capacity of a normal lead-acid battery without deterioration is defined by the following formula (1).
[0060]
[Expression 2]
Remaining capacity (%) = 0.181 × Cd + 0.064 (1)
[0061]
Measurement conditions and measurement results for lead-acid batteries
(1) A lead-acid battery in a 100% charged state was discharged for 1 hour at a current of (a) 15A, or (b) discharged for 10 minutes at a current of 30A, and then the remaining capacity of the lead-acid battery was determined. .
(2) The ambient temperature of the battery was set to 20 ° C.
(3) As a result of calculating | requiring and calculating the measured internal impedance, the electrical double layer capacitance value (Cd) was 3.6 [F].
(4) As a result of judging the remaining capacity by the equation (1), it was 72%. Since the actual remaining capacity is 73%, it has been found that the remaining amount can be determined fairly accurately by the evaluation method of the lead storage battery of the present invention.
[0062]
As described above, the relationship between the electric double layer capacity value (Cd) and the remaining capacity of the lead storage battery is obtained in advance, and the value of the electric double layer capacity value (Cd) obtained from the measurement result of the internal impedance is expressed by the above relationship. By comparing, it is possible to determine the remaining capacity of the lead storage battery.
[0063]
In addition, although the equation (1) is for an ambient temperature of 20 ° C., as illustrated in FIG. 3, when the temperature of the lead storage battery is changed to 20 ° C., 40 ° C., and 60 ° C. The characteristic tends to shift, and if the temperature of the lead storage battery is known, the remaining capacity can be calculated by interpolation. Therefore, the characteristic is investigated for a certain temperature, and an arbitrary temperature is detected by a temperature sensor or the like attached to the lead storage battery, and the characteristic (remaining capacity value) obtained in advance is shifted (interpolated) according to the temperature. The characteristic (remaining capacity value) at that temperature can be calculated.
[0064]
When a lead acid battery deteriorates, the remaining capacity decreases compared to a normal lead acid battery, but its characteristics are linear as in a normal lead acid battery. It is possible to correct.
[0065]
The correction due to the deterioration state of the battery at the time of determination and the correction due to the temperature of the battery can also be performed using the electrolyte resistance value (RΩ) obtained from the measurement result of the internal impedance.
[0066]
FIG. 6 is a graph showing the relationship between the electrolyte resistance value (RΩ) and the remaining capacity (SOC) of the lead storage battery depending on the temperatures of the normal lead storage battery and the deteriorated lead storage battery.
The electrolyte resistance value (RΩ) does not change depending on the remaining capacity (SOC) but changes depending on the temperature and the degree of deterioration. Therefore, it is possible to correct the remaining capacity using the electrolyte resistance value (RΩ) obtained from the measurement result of the internal impedance.
[0067]
Relationship between charge transfer resistance (Rct) and lead-acid battery remaining capacity
In addition, from the relationship between the charge transfer resistance value (Rct) illustrated in FIG. 5 and the remaining capacity of the lead storage battery, the relationship between the electric double layer capacity value (Cd) and the remaining capacity of the lead storage battery described above leads to Just as the remaining capacity of the storage battery was determined, the remaining capacity of the lead storage battery could be determined.
[0068]
Method for calculating electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacitance value (Cd)
Next, a specific example of a method for deriving the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacity value (Cd) when measuring the remaining capacity of the lead acid battery for automobiles will be described.
The measurement frequency of internal impedance is 100 Hz, 20 Hz, 6 Hz, and 2 Hz. From the measurement results of internal impedance at these four points, the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacitance value (Cd) was calculated.
The reason for selecting these four frequencies is as follows.
[0069]
As illustrated in FIG. 7, the internal impedance was measured by changing the frequency, and the real part of the internal impedance was plotted on the X-axis and the Y-axis obtained by multiplying the imaginary part by −1 (core call plot).
As illustrated in FIG. 7, the characteristic can be represented by two parts, a part indicating the characteristic of the arc and a characteristic like a straight line. Here, since the characteristics of the arc can be expressed by the equivalent circuit shown in FIG. 1, the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), It is possible to derive the multilayer capacitance value (Cd).
[0070]
For example, since the trajectory of a circle passing through three points is uniquely determined, the formula of the circle can be obtained very easily. Therefore, the locus of the circle was grasped at three frequencies of 100 Hz, 20 Hz, and 6 Hz.
As shown in FIG. 7, the plot in the vicinity of 2 Hz is out of the locus of the circle, and in order to obtain the circle equation with high accuracy, it is preferable that the frequency to be measured is in the frequency range of 5 to 100 Hz.
[0071]
As the number of measurement frequencies, at least three measurement points are required to obtain the circle formula, and in consideration of a decrease in practical value accompanying an increase in measurement points, a maximum of 5 measurement points is required. 6 points, preferably 3 to 4 points or less are desirable. Furthermore, since the accuracy is best when the plot for obtaining the locus of the circle is equally spaced on the circumference, the frequency of the first measurement frequency Fa is one point in the range of 5 to 10 Hz, 10 to 30 Hz. It is most desirable to use one of the points, one of 50-100 Hz.
[0072]
FIG. 7 shows an arc (broken line) calculated from a circle formula obtained by a method described later.
Assuming that the X-axis intercept of the circular orbit is Xa, Xb (Xa <Xb), Xa corresponds to the electrolyte resistance value (RΩ), and (Xb−Xa) corresponds to the charge transfer resistance value (Rct). In a circle equation passing through three points, Xa and Xb (Xa <Xb) can be obtained by setting the imaginary part to 0, where Xa is the electrolyte resistance value (RΩ) and (Xb−Xa) is the charge transfer resistance value. Calculated as (Rct).
[0073]
Where (Xa + Xb) × 0.5 is X_mI ask for it. X_mIs the real part of the impedance indicating the center coordinates of the circle. The frequency indicating the top of the circle is f_maxThen, the electric double layer capacitance value (Cd) is (Rct × 2π × f_max)^-1Calculated by However, since the measured frequency does not necessarily become the apex on the circumference, the frequency indicating the apex of the circle is approximately obtained from the following characteristics.
[0074]
FIG. 8 shows the results of plotting the internal impedance measured while changing the frequency, with the frequency as the X axis and the real part of the internal impedance as the Y axis.
It can be seen that the frequency range in which a direct relationship is obtained between the real part of the internal impedance and the frequency is approximately 1 to 10 Hz.
In FIG. 8, the results obtained at two frequencies of 6 Hz and 2 Hz are also plotted. By calculating the straight line connecting the two points, the straight line_m, And the frequency f approximately representing the vertex of the circle_mIs required. The electric double layer capacitance value (Cd) is (Rct × 2π × f_m)^-1Calculated by
[0075]
Frequency f_mIs 4 to 5 Hz in most cases, so when performing the above method, it is selected from one arbitrary frequency selected in the frequency range of 1 to 5 Hz and one of 5 to 10 Hz. In particular, it is preferable to use the smallest frequency among 3 to 4 points to be measured for grasping the locus of the circle.
[0076]
An arithmetic expression for obtaining the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacitance value (Cd) when measured at three frequencies will be described.
When measured at the frequency of 4 points, the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacitance value (Cd) were obtained at 3 points in any combination, and were obtained for each combination. An average of the determination results can be taken. Moreover, you may use the minimum value of the determination result calculated | required combining each from the safe side of a measurement.
In any case, even when measurement is performed at four frequencies, the same calculation as that performed when measurement is performed at three points is performed. First, an equation of an arbitrary circle is calculated from the measurement results of internal impedance measured at three frequencies.
[0077]
FIG. 9 shows three frequencies f.₁, F₂, F_ThreeIt is a graph which shows the coordinate which plotted the internal impedance measured by.
The following three equations are obtained, and since there are three unknowns and three equations, the coefficients a, b, and r that determine the locus of the circle can be obtained.
[0078]
[Equation 3]
f₁Measured with: (X₁-A)²+ (Y₁-B)²= R²  ... (2)
f₂Measured with: (X₂-A)²+ (Y₂-B)²= R²  ... (3)
f_ThreeMeasured with: (X_Three-A)²+ (Y_Three-B)²= R²  (4)
[0079]
As a result of solving the above three formulas (2) to (4), the coefficients a, b and r are as follows.
[0080]
[Expression 4]

[0081]
Here, the coefficients (factors) A to F are respectively expressed as follows.
[0082]
[Equation 5]
A = X₁-X₂                                        ... (8)
B = X₂-X_Three                                        ... (9)
C = Y₁-Y₂                                        (10)
D = Y₂-Y_Three                                        ... (11)
E = X₁ ²-X₂ ²+ Y₁ ²-Y₂ ²                    (12)
F = X₂ ²-X_Three ²+ Y₂ ²-Y_Three ²                    ... (13)
[0083]
In FIG. 9, R_CTIs a circular chord on the real axis, and X of two points where Y = 0 is obtained from the equation of the circle, and R is calculated from the distance between the two points._CTCalculate
[0084]
[Formula 6]
(X-a)²= R²                                    ... (14)
X = a ± r (15)
R_CT  = 2 · r (16)
RΩ = ar− (17)
[0085]
FIG. 10 is a graph showing coordinates in which the internal impedance measured at the fourth frequency is plotted.
Frequency f indicating the top of the circle_mFor f_mAs shown in FIG. 8, the relationship between the real part of the internal impedance and the frequency in the frequency range sandwiching the frequency range can be obtained by linear approximation since there is almost linearity in a certain range.
First frequency f₁The real component when measured with X₁, The fourth frequency f_FourThe real component when measured with X_FourThen f_mIs represented by the following equation. Where f₁> F_m> F_FourIt is.
[0086]
[Expression 7]

[0087]
Therefore, the electric double layer capacitance value (Cd) is expressed by the following equation.
[0088]
[Equation 8]

[0089]
In the determination of a lead storage battery mounted on an automobile, the influence of the ambient environment such as temperature can be easily corrected by repeating the inspection at appropriate intervals from several seconds to several tens of seconds. This evaluation method is particularly effective.
[0090]
Table 1 below shows an example in which the remaining capacity determination is measured every 1 minute when idling is stopped, and the case where the past determination result is referred to the case where the determination is made independently is compared.
[0091]
[Table 1]

[0092]
As a method for referring to past determination results, an average value was used by sequentially using determination results measured every 1 minute in remaining capacity determination during the same idle stop period.
The remaining capacity in the case of the single unit decreases until 2 minutes have elapsed immediately after the idle stop, and on the contrary, the determination after 3 minutes has shown an increasing tendency. On the other hand, the remaining capacity of the past reference decreases until after 3 minutes, and after that, shows a substantially constant value.
During the idle stop period, even if the discharge from the storage battery is reduced, the storage battery is not charged.
The cause of the increase in the remaining capacity is largely the influence of the surrounding environment such as temperature. Therefore, the case where the determination is made with reference to the past determination result is more effective than the case where the capacity determination is performed alone because the influence of the surrounding environment such as the temperature can be easily corrected.
[0093]
Lead storage battery evaluation system
The lead acid battery characteristic evaluation apparatus of the present invention is an apparatus that implements the lead acid battery evaluation method described above.
The structure of the evaluation apparatus for the lead storage battery is illustrated in FIG.
The lead-acid battery evaluation apparatus 10 includes a measuring means 12 for measuring the internal impedance of the lead-acid battery at a plurality of frequencies, an electrolyte resistance value (RΩ), a charge transfer resistance value (Rct), and an electric double layer capacity value (Cd). The remaining capacity and / or the deterioration state of the tested lead storage battery are determined from the calculating means 14 for calculating, and the calculated electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacity value (Cd). Determination means 16.
[0094]
The measuring means 12 is composed of, for example, a variable frequency oscillation circuit, an impedance measurement device, and a computer device having a memory circuit, and connects the variable frequency oscillation circuit and the impedance measurement circuit to a lead storage battery whose characteristics are to be evaluated. A computer device is connected to the impedance measurement circuit.
The variable frequency oscillation circuit is selected in a frequency range of 1 to 100 Hz in a two-dimensional coordinate system defined by plotting a value obtained by multiplying the real part of the internal impedance by the X axis and the imaginary part by −1 on the Y axis. A signal having a plurality of frequencies of at least three points defining the impedance circle is oscillated and applied to the lead storage battery, and the impedance measuring device measures the internal impedance of the lead storage battery at each frequency. The computer device inputs a specific value of the internal impedance measured by the impedance measuring device and stores it in the storage circuit.
[0095]
The calculating means 14 is constituted by, for example, a computer device having the storage circuit, and at least the charge transfer resistance value (Rct) defined by the above formula (A-1) or (B-1) by the computer device. ) And electric double layer capacitance value (Cd) and an equivalent circuit composed of a series circuit of an electrolyte resistance value (RΩ), an electrolyte resistance value (RΩ), and a charge transfer resistance value (Rct) , The relation between the electric double layer capacity value (Cd) and the internal impedances of the lead acid batteries measured at a plurality of frequencies is referred to the values of a plurality of internal impedances measured at a plurality of frequencies, and the electrolyte resistance value ( RΩ), charge transfer resistance value (Rct), and electric double layer capacitance value (Cd).
[0096]
The determination means 16 is composed of, for example, the above-described computer device, and the lead used in the test from the electrolytic solution resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacitance value (Cd) calculated by the calculation means 14 The remaining capacity and / or deterioration state of the storage battery is determined.
Such a determination is made, for example, by using a graph representing the relationship between the above-described electrolyte resistance value (RΩ), charge transfer resistance value (Rct), electric double layer capacitance value (Cd) and the remaining capacity and / or the deterioration state. The image may be displayed on the display device, and may be determined visually by a human, or automatically by a determination process of a computer device.
[0097]
【The invention's effect】
As described above, according to the present invention, the internal impedance is measured at an arbitrary frequency of 3 to 5 points selected in the frequency range of 1 to 100 Hz, and the measurement result is substituted into the arithmetic expression. Can determine the remaining capacity and the deterioration state of the lead-acid battery, so that the measurement can be performed easily in a short time. Moreover, since the measurement frequency is a fixed frequency of 3 to 5 points, the cost of the apparatus can be reduced.
[0098]
According to the present invention, since the remaining capacity of the lead-acid battery can be accurately determined, it is very effective when used for determining whether or not an idling stop is possible when the automobile stops.
[Brief description of the drawings]
FIG. 1 shows the configuration of an equivalent circuit comprising an electrolyte resistance value (RΩ), a charge transfer resistance value (Rct), and an electric double layer capacitance value (Cd) as a first equivalent circuit used in the present invention. FIG.
FIG. 2 shows an electrolyte resistance value (RΩ), a charge transfer resistance value (Rct ′ and Rct ″), and an electric double layer capacitance value (Cd ′) as a second equivalent circuit used in the present invention. It is a block diagram of an equivalent circuit consisting of Cd ″).
FIG. 3 is a flowchart showing processing of the evaluation characteristic method for a lead storage battery of the present invention.
FIG. 4 is a graph illustrating the relationship between the electric double layer capacity value (Cd) and the remaining capacity of the lead storage battery.
FIG. 5 is a graph illustrating the relationship between the charge transfer resistance value (Rct) and the remaining capacity of the lead storage battery.
FIG. 6 is a graph showing a relationship between an electrolyte resistance value (RΩ) and a remaining capacity (SOC) of a lead storage battery according to temperatures of a normal lead storage battery and a deteriorated lead storage battery.
FIG. 7 is a graph illustrating a method for calculating an electrolyte resistance value (RΩ), a charge transfer resistance value (Rct), and an electric double layer capacitance value (Cd).
FIG. 8 is a graph illustrating the relationship between the frequency and the real component of the impedance.
FIG. 9 is a graph showing coordinates in which internal impedances measured at three frequencies are plotted.
FIG. 10 is a graph showing coordinates in which internal impedance measured at a fourth frequency is plotted.
FIG. 11 is a block diagram of a lead-acid battery evaluation apparatus according to the present invention.
[Explanation of symbols]
10. ・ Evaluation device for lead acid battery
12. ・ Measuring means
14. Calculation means
16 .. Judgment means

Claims (13)

The impedance is represented by an equivalent circuit defined by the following equation, which is composed of a series circuit of at least a parallel circuit of a charge transfer resistance value (Rct) and an electric double layer capacitance value (Cd) and an electrolyte resistance value (RΩ). An evaluation characteristic method of a lead storage battery of a lead storage battery,
[RΩ + (Rct / (1 + jωCd))] (A)
However, ω = 2πf
A frequency range of 1 to 100 Hz that defines an impedance circle in a two-dimensional coordinate defined by plotting a real part of the internal impedance of the lead-acid battery by multiplying an imaginary part by -1 on an X axis and a Y axis. Measure the internal impedance of the lead-acid battery for a plurality of selected three or more frequencies,
Electrolyte resistance value (RΩ) derived from an equivalent circuit composed of a parallel circuit of the charge transfer resistance value (Rct) and electric double layer capacitance value (Cd) and a series circuit of the electrolyte resistance value (RΩ) ), Charge transfer resistance value (Rct), electric double layer capacitance value (Cd) and internal impedances of the lead acid batteries measured at the plurality of frequencies, and a plurality of internals measured at the plurality of frequencies. With reference to the impedance value, the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacitance value (Cd) are obtained,
Determining the remaining capacity and / or deterioration state of the lead storage battery tested from all or at least one of the calculated electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacity value (Cd) A characteristic evaluation method for a lead-acid battery. Obtain a relational expression between the electric double layer capacity value (Cd) and the remaining capacity of the lead storage battery in advance,
The value of the electric double layer capacity value (Cd) obtained from a plurality of measurement results for the internal impedance is compared with the relational expression of the remaining capacity of the lead storage battery to determine the remaining capacity of the lead storage battery,
The correction by the deterioration state of the lead storage battery at the time of this determination, and the correction by the temperature of the lead storage battery,
The evaluation method of the lead acid battery of Claim 1. The electric double layer capacity value (Cd) and the remaining capacity of the lead storage battery are defined as a straight line having a temperature-dependent gradient.
The evaluation characteristic method of the lead acid battery of Claim 2. For a plurality of predetermined temperatures in advance, create a plurality of relational expressions between the electric double layer capacity value (Cd) and the remaining capacity of the lead storage battery,
Measuring the temperature of the lead storage battery, interpolating using a relational expression of two approximate temperatures among the plurality of relational expressions, and evaluating the characteristics of the lead storage battery according to the temperature of the lead storage battery;
The evaluation characteristic method of the lead acid battery of Claim 3. The electrolytic solution resistance value (RΩ), the charge transfer resistance value (Rct), and the electric two-dimensional correction obtained from a plurality of measurement results of the internal impedance are corrected by the deterioration state of the lead storage battery and the correction by temperature at the time of the determination. It is performed using the multilayer capacitance value (Cd),
The evaluation characteristic method of the lead acid battery of Claim 2. Obtain a relational expression between the charge transfer resistance value (Rct) of the lead storage battery and the remaining capacity of the lead storage battery in advance,
The charge transfer resistance value (Rct) obtained from a plurality of measurement results of the internal impedance is compared with the relational expression of the remaining capacity of the lead storage battery to determine the remaining capacity of the lead storage battery,
The evaluation characteristic method for a lead storage battery according to claim 1, wherein the correction based on the deterioration state of the lead storage battery in the determination and the correction based on the temperature of the lead storage battery are performed. The electrolyte resistance value (RΩ) and the electric double layer capacity value (Cd) obtained from a plurality of measurement results of the internal impedance are corrected according to the deterioration state of the battery at the time of the determination and the correction based on the temperature of the lead storage battery. The evaluation characteristic method for a lead storage battery according to claim 6, wherein the evaluation characteristic method is used. The plurality of measurement frequencies are
An arbitrary 3 to 4 first frequency (Fa) selected in the range of 5 to 100 Hz;
The evaluation characteristic method for a lead-acid battery according to claim 1, wherein the second frequency (Fb) is an arbitrary one point selected in a frequency range of 1 to 5 Hz. Derivation of the electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacitance value (Cd),
(A) The real part of the measured internal impedance is plotted on the X axis, and the value obtained by multiplying the imaginary part by -1 is plotted on the Y axis.
(B) Among these, the trajectory of a circle passing through a 3-4 point plot measured at the first frequency (Fa) is obtained,
(C) Obtain X-axis intercepts Xa and Xb (where Xa <Xb) of the orbit,
(D) The intercept Xa is the electrolyte resistance value (RΩ), (Xb−Xa) is the charge transfer resistance value (Rct), (Xa + Xb) × 0.5 is X _m ,
(E) The measured values at the lowest frequency (Fa ') and the second frequency (Fb) of the first frequency (Fa) are plotted on the coordinates where the real part of the internal impedance is the Y axis and the frequency is the X axis. And the frequency corresponding to the above X _m on the straight line connecting both plots is ω _m ,
(F) The electric double layer capacitance value (Cd) is calculated as (Rct × ω _m ) ⁻¹ ,
The evaluation characteristic method of the lead acid battery according to claim 1. The first measurement frequency (Fa) is
1 point in 5-10Hz,
1 point in 10-30Hz,
The method for evaluating a lead storage battery according to claim 6, comprising one point in the range of 50 to 100 Hz. Characteristic evaluation of the lead storage battery is performed at predetermined time intervals,
At least one of the values of the electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacitance value (Cd) obtained in the previous characteristic evaluation is determined in this inspection. Compared with at least one of the obtained electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacitance value (Cd),
2. The evaluation characteristic method for a lead storage battery according to claim 1, wherein the comparison result is used for correcting determination of the remaining capacity and the deterioration state of the lead storage battery. The lead storage battery evaluation characteristic method according to any one of claims 1 to 11, wherein the processing is performed on the lead storage battery mounted on the vehicle during an engine stop period of the vehicle. The impedance is represented by an equivalent circuit defined by the following equation, which is composed of a series circuit of at least a parallel circuit of a charge transfer resistance value (Rct) and an electric double layer capacitance value (Cd) and an electrolyte resistance value (RΩ). A lead-acid battery evaluation characteristic device for a lead-acid battery,
[RΩ + (Rct / (1 + jωCd))] (B)
However, ω = 2πf
At least the impedance circle in the two-dimensional coordinates defined by plotting the real part of the internal impedance selected from the frequency range of 1 to 100 Hz and the imaginary part multiplied by -1 on the Y axis is plotted on the Y axis Measuring means for measuring the internal impedance of the lead-acid battery at a plurality of three or more frequencies;
Electrolyte resistance value (RΩ) derived from an equivalent circuit composed of a parallel circuit of the charge transfer resistance value (Rct) and electric double layer capacitance value (Cd) and a series circuit of the electrolyte resistance value (RΩ) , Charge transfer resistance value (Rct), electric double layer capacitance value (Cd) and the internal impedance of the plurality of lead storage batteries measured at the plurality of frequencies, and a plurality of internal impedances measured at the plurality of frequencies. Calculating means for obtaining the electrolyte resistance value (RΩ), the charge transfer resistance value (Rct), and the electric double layer capacitance value (Cd) by referring to values;
Lead storage battery having a determination means for determining the remaining capacity and / or deterioration state of the lead storage battery tested from the calculated electrolyte resistance value (RΩ), charge transfer resistance value (Rct), and electric double layer capacity value (Cd) Characterization equipment.

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