JP3550160B2 - Battery remaining capacity meter - Google Patents

Description

式（１）において、ａ₀ （θ）、ａ₁ （θ）、ａ₂ （θ）は電流ｉに対しては定数であるが、パラメ−タである残存容量θに対しては変化するものである。なお以下においては、定数に付けた（θ）は省略し、単にａ₀ 、ａ₁ 、ａ₂ と表記する。
【００１７】
定数ａ₀ は、放電電流ｉが０のときの端子電圧であるから、いわゆる無負荷開路電圧に相当するもので、電池の残存容量や、経年変化、周囲温度などに関係する。何故ならば、電池の反応が進むにつれて電解液の濃度が低下し、極板に反応物質が溜って実効的な極板面積が減少するので、残存容量は減少する傾向にあるからである。一方、周囲温度が上昇すれば、反応が活性化するので無負荷開路電圧は上昇する。本発明者らの考察によれば、定数ａ₀ は残存容量の減少に伴なって減少する。
【００１８】
定数ａ₁ は、電流ｉとの積が電圧降下を示すので、電池の内部電気抵抗に相当すると考えられる。残存容量の低下や経年変化にともなう電解液の濃度低下、極板中の不活性物質の蓄積、および極板の充填物質の脱落などによって、電圧降下は増加するので、電池の内部電気抵抗は増大する。したがって定数ａ₁ の極性は負であり、絶対値は残存容量の減少に伴なって増大する。また温度変化に対しては、定数ａ₀ と同様に、周囲温度が上昇すれば反応が活性化するので、電圧降下を減少させる方向に作用する。
【００１９】
定数ａ₂ は、電流ｉの２乗との積が電圧降下に影響するので、電池の分極作用に依存するものと解され、やはり残存容量に関係する。本発明者らの考察によれば、定数ａ₂ は、放電の初期と末期で比較的大きく、その中間では小さい。すなわち電池の残存容量が十分大きい時には定数ａ₂ は幾分大きく、残存容量の減少に伴なって徐々に小さくなり、残存容量がさらに少なくなると再び徐々に増加する傾向が見られた。
【００２０】
以上のような各係数と電池の物理的特性との関連性、ならびに各係数の変化傾向に関する考察に基づき、この実施例では、各係数ａ₀ 〜ａ₂ を残存容量θに関する２次曲線で代表させ、それぞれつぎの（２）〜（４）式で表わすことにした。
ａ₀ ＝ｂ₀₀＋ｂ₀₁・θ＋ｂ₀₂・θ² … （２）
ａ₁ ＝ｂ₁₀＋ｂ₁₁・θ＋ｂ₁₂・θ² … （３）
ａ₂ ＝ｂ₂₀＋ｂ₂₁・θ＋ｂ₂₂・θ² … （４）
そして、電池残存容量に対する各係数の具体的数値例を図２の（Ａ）〜（Ｃ）に示したようにした。もっとも、これは単なる１例であって適宜に変更可能であり、また明らかなように、特に電池の種類が変われば当然に変わるものである。またこれらの係数ａ₀ 〜ａ₂ は、測定対象の電池について残存容量をパラメ−タとした電圧電流特性曲線が分かれば実験的に求め得るものである。
【００２１】
上述のような電池モデルを用いて、図１の構成によって電池１の残存容量を計測または推定する。このために、ある時点（ｔ−Ｔ）から時点ｔまでの離散的サンプリングデ−タを用い、推定理論によって時点ｔにおける残存容量を求める方法を以下に説明する。
【００２２】
まず時点（ｔ−Ｔ）から時点ｔまでの間の時点τにおける電池１の実測端子電圧をｖ（τ）、この時の残存容量をθ、実測放電電流をｉ（τ）とし、これらを（１）式に代入して得られた端子電圧推定値をＶ_es（τ，θ）とする。さらに、前記時点（ｔ−Ｔ）から時点ｔまでのサンプリングデ−タを用い、非線形の最適化の方法を適用すると、つぎの（５）式の評価関数を最小にするθを求めることに帰する。この式は、非線形の最適化の方法としてガウス・ニュ−トン法を適用した例である。
【００２３】
【数５】

（５）式はθに関して非線形であるので、端子電圧推定値Ｖ_es（τ，θ）をある基準値θ₀ のまわりでテ−ラ−展開し、２次以上の項を省略して線形化すると（６）式になり、
【００２４】
【数６】

（６）式を（５）式に代入すると（７）式の線形評価関数が得られる。
【００２５】
【数７】

つぎに、θが変化したときに（７）式を最小にするようなδθ、すなわち（７）式のδθに関する偏微分係数を零にするδθを求める。このδθは、残存容量の基準値として先に仮定した初期値θ₀ に対する修正量であり、推定値として得られるので、以下ではδθ_esと表記する。修正量δθ_esは、つぎの（８）式で表わされる。
【００２６】
【数８】

修正量δθ_esが求められたならば、そのときのθ₀ をδθ_esだけ修正（加減算）して新たな残存容量を仮定し、（１）式によって再度推定端子電圧Ｖ_esを演算する。そして前記推定端子電圧Ｖ_es（τ、θ）と実測端子電圧ｖ（τ）との差が十分小さくなるまで、換言すれば、仮定残存容量θ₀ が収束するまで（８）式の演算を繰り返す。このとき（ｋ＋１）番目の仮定残存容量θ₀ （ｋ＋１）は、残存容量修正部８において、ｋ番目の仮定残存容量θ₀ （ｋ）をδθ_es（ｋ）だけ修正することによって得られるので、つぎの（９）式で表わすことができる。
θ₀ （ｋ＋１）＝θ₀ （ｋ）＋δθ_es（ｋ） … （９）
（９）式のθ₀ （ｋ＋１）が収束したこと（例えば、比｜δθ_es（ｋ）／θ₀ （ｋ＋１）｜の値が予め決めた閾値εよりも小さくなったこと）が収束判定部７で判定されると、出力制御部９が付勢され、そのときの仮定残存容量θ₀ （ｋ＋１）またはθ₀ （ｋ）が電池の残存容量を示す信号として出力される。
【００２７】
図３は、図１の電池モデルのハ−ド構成および上述した演算における信号の流れを示すブロック図である。その内容は上述の説明から自明であり、容易に理解できるので重複した説明は省略する。
【００２８】
図４の（Ａ）は、上記実施例の電池モデルを用いて推定した端子電圧Ｖ_es（点線）と実測した端子電圧ｖ（実線）との比較を示す図であり、両曲線の対比の便宜上、同図の（Ｂ）にその一部を拡大して示している。これらの図から、本発明によれば、電池の物理的特性に基づいたモデルを用いたので、良好な精度で電池の残存容量を推定できること、および実測値には観測ノイズが重畳しているが推定値はこのようなノイズの影響を受けていないことが分かる。また、（５）式の評価関数は常に単峰性となり、初期値θ₀ をどのような値に設定しても、必ず真値に収束することが、本発明者らのシミュレ−ションによっても確認された。
【００２９】
残存容量の温度補正
電池モデルに関して前述したように、電池の残存容量をパラメ−タとする放電電流対端子電圧の特性曲線は周囲温度に応じて変化する。すなわち、周囲温度が高いと電池反応が活性化するので、発生電圧が高くなり、曲線は全体として電圧軸の正方向に上昇する。また電池内部抵抗は温度が高いほど小さくなるので、内部抵抗に相当する曲線の傾斜は、温度が高いほど緩く、反対に温度が下がると急峻になり、したがって曲線は全体として立ってくる。
【００３０】
以上の考察から、ある電池の摂氏０度おける放電電流対端子電圧特性曲線が、例えば図５（Ａ）に示すようなものであると仮定すると、この特性曲線を電圧軸（縦軸）および電流軸（横軸）の方向に平行移動し、かつ反時計方向に回転すれば、より高い温度、例えば摂氏３０度における同電池の放電電流対端子電圧特性曲線に近似できることが分る。図５（Ｂ）は、図５（Ａ）の曲線を平行移動および反時計方向回転して得られたものであり、実質上摂氏３０度における同電池の放電電流対端子電圧特性曲線と見做すことができる。
【００３１】
明らかなように、上記のような特性曲線の平行移動および回転は座標軸変換操作に他ならないから、ある電池の標準温度（例えば、３０℃）における放電電流対端子電圧特性曲線（以下、標準曲線という）と、他の任意の温度での放電電流対端子電圧特性曲線を標準曲線に合致させるための座標変換の式とが知られてさえおれば、これと異なる周囲温度Ｔ℃での残存容量を上述した本発明の手法で容易に求めることができる。
【００３２】
すなわち、周囲温度Ｔ℃での実測によって得られた放電電流および端子電圧を、予め準備された座標変換の式またはテ−ブルに代入して標準温度での座標系の値に変換し、変換後の放電電流および端子電圧値を標準曲線に適用して残存容量θを求めれば、この値が周囲温度Ｔ℃での残存容量になる。
【００３３】
このための座標変換の式は、周知のように、周囲温度Ｔ℃で実測された放電電流値をＩ（Ｔ℃）、端子電圧値をＶ（Ｔ℃）とし、温度Ｔ℃での放電電流対端子電圧特性曲線を標準曲線に合致させるために必要な座標軸の回転角をα（ラジアン）、横軸（電流軸）および縦軸（電圧軸）方向の平行移動量をそれぞれｘ、ｙとし、さらに標準曲線の座標上での放電電流および端子電圧の実測値をそれぞれＩ（３０℃）、Ｖ（３０℃）とすれば、これらはつぎの（１０）および（１１）式で表わされる。
【００３４】

ここで、回転角α、横軸（電流軸）および縦軸（電圧軸）方向の平行移動量ｘ、ｙは、もちろん予め種々の温度について実測して求めることもできる。
【００３５】
またはその代わりに、これらα、ｘおよびｙが実質上温度に比例することに基づき、例えば２つの相異なる温度０℃および３０℃における２種の特性曲線が既知であり、かつこれら両曲線がΔαの座標軸回転、Δｘ（３０・０）およびΔｙ（３０・０）の軸平行移動で重なると仮定すると、つぎの内挿式（１２）〜（１４）によって、Ｔ℃に対するα、ｘおよびｙの値を予め求めておいたり、その都度計算で求めたりすることができる。
回転角α＝｛Δα（３０・０）／３０｝（３０−Ｔ） … （１２）
平行移動量ｘ＝｛Δｘ（３０・０）／３０｝（３０−Ｔ） … （１３）
平行移動量ｙ＝｛Δｙ（３０・０）／３０｝（３０−Ｔ） … （１４）
以上のようにして、標準温度での放電電流対端子電圧特性曲線および座標変換の式を準備しておくだけで、任意の周囲温度における残存容量を容易に求めることができる。
【００３６】
残存容量の経時変化補正
以上においては、電池モデル５を代表する（１）式の各係数ａ₀ （θ）、ａ₁ （θ）、ａ₂ （θ）、したがって係数ｂ₀₀〜ｂ₂₂は電池の残存容量のみに依存し、電流ｉに対しては変化しないものと仮定した。しかし厳密には、これら係数は電池の充放電回数に応じて経時的にも変化するので、残存容量をより厳密に監視するためには、前記各係数ａ₀ 〜ａ₂ 、ｂ₀₀〜ｂ₂₂を経時的に（充放電回数に応じて）補正することが望ましい。
【００３７】
一般に知られているように、電池の残存容量は充電を完了して使用を開始した時の容量から、放電電流の時間積分値に大きく依存して減少する。既知の電流積算方式の残存容量計は、このことを利用したものである。
【００３８】
しかし厳密には、残存容量は放電電流のあり方によっても影響され、大電流による急放電の場合の方が小電流による緩放電の場合に較べて小さくなる。その主な原因は、放電電流によるジュ−ル熱損失Ｒｉ² に相当するエネルギ損失を生じるためと考えられる。したがって、残存容量θの減少速度は放電電流ｉに比例すると共に、その比例係数もまた放電電流に比例すると推測でき、
ｄθ／ｄｔ＝ｆ（ｉ）・ｉ
と表わすことができる。
【００３９】
ここで上記ｆ（ｉ）は、厳密には、一般的な多項式
ｆ（ｉ）＝Ｃ₁ ＋Ｃ₂ ・ｉ＋……＋Ｃ_n ・ｉⁿ ＋…
ただし、Ｃ₁ 、Ｃ₂ …Ｃ_n は定数
であるから、これを上式に代入すると、
ｄθ／ｄｔ＝Ｃ₁ ・ｉ＋Ｃ₂ ・ｉ² ＋……＋Ｃ_n ・^{ｉ n+1} ＋…
となる。
【００４０】
しかし、電池の物理的性質に対応させ易い最初の２項、すなわち電流積分値（アンペア時間）に対応するＣ₁ ・ｉの項および、電流の放電時の電流二乗損失に相当するエネルギ積分値（ワット時間）に対応するＣ₂ ・ｉ² を用いれば、実用上十分な精度で残存容量を把握できると考えられる。すなわち、
ｄθ／ｄｔ＝Ｃ₁ ・ｉ＋Ｃ₂ ・ｉ²
とすれば、実用上は十分である。上記の関係式を積分すると次の（１５）式が得られる。
【００４１】
【数９】

（１５）式において、定数項Ｃ₀ は使用（放電）開始時の残存容量であり、積分項はそれからの電池消費容量と見ることができる。（１５）式のθを前掲の（２）〜（４）式に代入し、得られた係数ａ₀ 〜ａ₂ をさらに（１）式に代入して離散形で表わすと、時点ｊでの推定端子電圧Ｖ_djを表わす式として下記の（１６）式が得られる。（１６）式による推定端子電圧Ｖ_djは、前掲（１）式で定義された電池モデルの各係数ａ₀ 〜ａ₂ が（２）〜（４）式で残存容量θの関数として定義されたのに対し、電流ｉのみの関数として定義される点で相違する。（１）式のθは、前述のように残存容量そのものであったが、（１５）式のθは、明らかなように、これと幾分その定義を異にするので、以下の説明ではこれを別の記号φで表わし、またその係数も（２）〜（４）式のｂ₀₀〜ｂ₂₂と区別してｄ₀₀〜ｄ₂₂で表わすことにする。
【００４２】
【数１０】

ここで、ｉ_k は時点ｋ（ただし、０≦ｋ≦ｊ）での実測電流値、またｉ_j は時点ｊでの実測電流値である。
【００４３】
前記（１６）式中の係数ｄ₀₀〜ｄ₂₂およびＣ₀ 〜Ｃ₂ は、前述の（１）式において係数ａ₀ 〜ａ₂ を既知として残存容量θを求めたときと同様に、時点ｊまでの実測電流値ｉ_j 、および時点ｊでの電圧値ｖ_j を用いて、上記（１６）式のＶ_djに推定理論を適用して求めることができる。具体的には、電圧の推定値Ｖ_djと実測値ｖ_j の差の二乗和をｎ個のデ−タ組について求め、これを評価関数Ｉ（ｄ₀₀〜ｄ₂₂、Ｃ₀ 〜Ｃ₂ ）とする。評価関数Ｉはつぎの（１７）式で表わされる。
【００４４】
【数１１】

（１７）式にｖ_j （ｊ時点での実測電圧値）および前記（１６）式の電圧推定値Ｖ_djを代入して得られる評価関数Ｉが最小になるような係数ｄ₀₀〜ｄ₂₂、Ｃ₀ 〜Ｃ₂ を求める。このためには、上記評価関数を各パラメ−タｄ₀₀〜ｄ₂₂、Ｃ₀ 〜Ｃ₂ について偏微分して得られる各式を０と置くと、パラメ−タ数と同数の連立方程式が得られるので、これを解いて各パラメ−タを求める。
【００４５】
具体的には、先に（１）ないし（８）式に関して行なったのと同じ手法を適用して各パラメ−タ（係数）の初期値からの修正量を求める。修正量が十分小さくなったとき、各パラメ−タが収束したと判断してそれぞれのパラメ−タすなわち係数ｄ₀₀〜ｄ₂₂、Ｃ₀ 〜Ｃ₂ を推定することができる。このようにして求めた係数Ｃ₀ 〜Ｃ₂ を（１５）式に代入すると、残存容量を表わす指標φを求めることもできる。
【００４６】
以下に、上述の係数ｄ₀₀〜ｄ₂₂、Ｃ₀ 〜Ｃ₂ を用いて前記定数ａ₀ 〜ａ₂ 、ｂ₀₀〜ｂ₂₂の経年変化を補正するための具体的手法を説明する。電池の使用に際し、充放電の各サイクルごとに、前述の方法で係数ｄ₀₀〜ｄ₂₂、Ｃ₀ 〜Ｃ₂ を求め、第ｉ回目（ただし、１≦ｉ≦ｎ）の充放電サイクルで得られた係数の推定値をｄ₀₀ ⁽ⁱ⁾ 〜ｄ₂₂ ⁽ⁱ⁾ 、Ｃ₀ ⁽ⁱ⁾ 〜Ｃ₂ ⁽ⁱ⁾ で表わす。１回目の充放電サイクルで得られた各係数ｄ₀₀ ⁽¹⁾ 〜ｄ₂₂ ⁽¹⁾ 、Ｃ₀ ⁽¹⁾ 〜Ｃ₂ ⁽¹⁾ に対する、ｎ回目の充放電サイクルでの各係数ｄ₀₀ ⁽ⁿ⁾ 〜ｄ₂₂ ⁽ⁿ⁾ 、Ｃ₀ ⁽ⁿ⁾ 〜Ｃ₂ ⁽ⁿ⁾ の比α₀₀ ⁽ⁿ⁾ 〜α₂₂ ⁽ⁿ⁾ 、α_c0 ⁽ⁿ⁾ 〜α_c2 ⁽ⁿ⁾ 、またはこれらの差、一般的には、ｎ回目と（ｎ−ｒ）回目との差または比などを演算して監視すれば、これらの値の変化状態（例えば、前記差あるいは比が予め定めた閾値を超えたこと）からパラメ−タすなわち電池モデルの経年変化を知ることができる。また変化状態が著しいとき（異常に早いか、大幅であるなどのとき）は、電池の異常と判定することもできる。
【００４７】
前記のような複数の係数の変化状態の判定のためには、例えば、株式会社日科技連出版社１９８９年４月１０日発行、奥野忠一他著『多変量解析法』第２７８頁（多変数による判別）、東京図書株式会社１９８９年１１月３０日発行，蓑谷千凰彦著『統計的仮説検定』１４５頁（推定と検定のはなし）、株式会社培風館昭和３６年９月３０日発行、浅井／村上訳『初等統計学』１５８頁（仮説の検定）などに詳述されている手法を利用することができる。
【００４８】
このような手法によって、ｎ回目の放電で電池モデルに修正を要するような経年変化が生じたと判定されたときは、前記（２）式のパラメ−タすなわち係数ｂ₀₀〜ｂ₂₂を修正し、電池モデル５を代表する（１）式の各係数ａ₀ （θ）、ａ₁ （θ）、ａ₂ （θ）を修正する。そのための具体的手法の１例は次の通りである。
【００４９】
新規に使用を開始する初期状態での電池モデルのパラメ−タは既知であるので、これらをｂ₀₀ ⁽¹⁾ 〜ｂ₂₂ ⁽¹⁾ で表わす。一方、ｉ回目（ただし、１≦ｉ≦ｎ）の充放電サイクルにおけるパラメ−タｄ₀₀ ⁽ⁱ⁾ 〜ｄ₂₂ ⁽ⁱ⁾ は上述のようにして求められる。まず初期状態でのパラメ−タｂに対する１回目の放電サイクルでのパラメ−タｄの比ｋを下記の（１８）式のように求めておくと共に、１回目とｎ回目の放電サイクルでの各パラメ−タｄの比αをつぎの（１９）式のように求める。
ｋ₀₀＝ｄ₀₀ ⁽¹⁾ ／ｂ₀₀ ⁽¹⁾ 〜ｋ₂₂＝ｄ₂₂ ⁽¹⁾ ／ｂ₂₂ ⁽¹⁾ … （１８）
α₀₀ ⁽ⁿ⁾ ＝ｄ₀₀ ⁽ⁿ⁾ ／ｄ₀₀ ⁽¹⁾ 〜α₂₂＝ｄ₂₂ ⁽ⁿ⁾ ／ｄ₂₂ ⁽¹⁾ …（１９）
（ｎ＋１）回目以降の放電サイクルの残存容量計測に用いるパラメ−タｂ₀₀ ^{(n )} 〜ｂ₂₂ ⁽ⁿ⁾ は次の（２０）式で得られる。
【００５０】
【数１２】

このようにして得られたパラメ−タｂ₀₀ ⁽ⁿ⁾ 〜ｂ₂₂ ⁽ⁿ⁾ を用いて電池モデルを修正し、これに基づいてその後の残存容量を演算すれば経年変化の影響のない、より正確な残存容量の監視が可能となる。
【００５１】
以上では、測定対象の電池の残存容量をパラメ−タとして、その放電電流および端子電圧の関係を数式化した電池モデルを用いる際に、前記放電電流の実測値を前記電池モデルの数式に代入してその端子電圧の推測値を演算し、前記推測端子電圧値の実測電圧に対する偏差に基づいて、前記偏差が小さくなるようにパラメ−タである残存容量を修正し、前記偏差が十分に小さくなってパラメ−タが収束した時、これを求める残存容量として出力するようにした。
【００５２】
しかし明らかなように、前記電池モデルの数式に、実測電流ではなくて、実測端子電圧の値を代入して放電電流の推測値を求め、推測放電電流値の実測値に対する偏差を０に近付けるようにして残存容量を求めることもできる。このために用いる数式は、前述の（１），（５）〜（８）式において、電圧と電流とを入れ替えれば良いことは自明であるので、その詳細説明は省略し、電流推定値Ｉ_esおよびパラメ−タ修正量δθ_esがそれぞれ次の（２１）、（２２）式で求められることを示すに止める。
Ｉ_es（ｔ，θ）＝ｐ₀ （θ）＋ｐ₁ （θ）・ｖ（ｔ） ＋ｐ₂ （θ）・ｖ² （ｔ） … （２１）
ここで、ｐ₀ 〜ｐ₂ はθの関数である。
【００５３】
【数１３】

さらに、温度変化や経時変化の影響を考慮した場合も、同様に類推して前述の補正手法を適用できることは明らかであろう。また以上では、電池モデルを数式化した例に付いて説明したが、その代りにテ−ブル（グラフ）化したモデルを用いても同様の残存容量計を構成できることは、容易に理解されるであろう。
【００５４】
【発明の効果】
本発明によれば、電池モデルをその物理的特性と関連付けたので、電池の残存容量をより正確にしかもリアルタイムで監視することができ、さらに温度変化や経年変化の影響を加味した残存容量の監視も可能となるのみならず、異常状態の検知も可能である。また、電池の残存容量がデジタル量として演算できるので、これを遠方の中央装置に伝送して集中管理することも容易になる。
【図面の簡単な説明】
【図１】本発明の原理的構成を示すブロックである。
【図２】本発明の１実施例におけるモデルの電池残存容量に対する各係数の具体的数値例を示す図である。
【図３】図１の電池モデルのハ−ド構成および信号の流れを示すブロック図である。
【図４】上記実施例の電池モデルを用いて推定した端子電圧端子電圧と実測した端子電圧との比較を示す図である。
【図５】電池の電圧電流特性の周囲温度による変化と、温度変化による座標軸変換の関係を示す図である。
【符号の説明】
１…電池 ２…負荷 ４…負荷制御部 ５…電池モデル ７…収束判定部 ８…残存容量修正部 ９…出力制御部[0001]
[Industrial applications]
The present invention relates to a remaining capacity meter of a battery, and more particularly to a remaining capacity meter of a battery that can be easily replaced in real time without interrupting a load, and can easily compensate for temperature and change over time.
[0002]
[Prior art]
Recently, electric vehicles have been receiving attention in connection with energy issues and environmental protection. Attention has also been focused on batteries for power storage for effective operation of the power system and utilization of natural energy, or batteries as emergency power sources for various control devices. In other fields, a distributed power source using a battery has come into practical use. In these cases, for efficient operation of the battery, it is necessary to control the charge and discharge of the battery accurately. Along with this, it is desired to constantly measure the remaining capacity of the battery as accurately as possible and without affecting the operation state.
[0003]
Conventionally, as a battery remaining capacity meter, (1) a specific gravity meter method utilizing the fact that the specific gravity of the electrolytic solution is proportional to the remaining capacity of the lead storage battery, and (2) the integrated value of the discharge current at the start of use (3) an open circuit voltage for estimating the remaining capacity based on the fact that the terminal voltage of the battery under no load, that is, the open circuit voltage is proportional to the remaining capacity of the lead storage battery, And (4) a voltage-current method utilizing the relationship between the discharge (load) current and the battery terminal voltage at that time.
[0004]
The hydrometer method can be used only for lead-acid batteries and is vulnerable to vibration, so it is not suitable especially for automobiles. The current integration method has a drawback that it is difficult to accurately measure the battery capacity at the start of use, and that the influence of secular change is large. The open-circuit voltage method utilizes the battery characteristic that the terminal voltage of the battery under no load, that is, the open-circuit voltage is a function of the remaining capacity, and measures the open-circuit voltage after a certain time after the load current is cut off. There are practical difficulties in having to do so.
[0005]
To solve this, a lead battery is represented by a model having parameters that vary with time, and the open circuit voltage at that time is determined from the measured values of the load current and terminal voltage and the current-voltage characteristics of the battery. It has been proposed to estimate the remaining capacity by applying the estimated open-circuit voltage to the relationship between the open-circuit voltage and the remaining capacity (see Journal of the Institute of Electrical Engineers of Japan, April 112, Vol. 112, No. 4). No. 259-267).
[0006]
The voltage-current method utilizes a battery characteristic that the remaining capacity of the battery is related to its voltage-current characteristic. Specifically, a voltage-current characteristic curve or a table at a standard temperature (30 degrees Celsius) of the battery to be measured is prepared as a parameter of the remaining battery capacity. After correcting the sample values of the current and voltage at the temperature at the time of measurement to the values at the standard temperature, the remaining capacity at the temperature at the time of measurement is obtained by applying the corrected value to the voltage-current characteristic curve or the table. If necessary, an interpolation operation can be performed.
[0007]
Thus, the voltage-current method is practical for many applications because the remaining capacity can be detected continuously and in real time without using the estimated value of the circuit voltage or interrupting the load current. In particular, it is considered to be preferable for use in an object having much vibration such as an electric vehicle. The details of the voltage-current method are described in, for example, Japanese Patent Application No. Hei 3-18430.
[0008]
[Problems to be solved by the invention]
In the above-described open-circuit voltage method, the open-circuit voltage is estimated using the battery model from the measured terminal voltage at the time of load, and the remaining capacity is further estimated using the open-circuit voltage estimated in this manner. Since the model is not associated with the physical characteristics of the battery, a problem is expected that it is not easy to correct for aging, temperature change, and the like, and high measurement accuracy cannot be expected.
[0009]
In the conventional voltage-current method, the voltage-current characteristic curve used as a standard or the table itself is made from the voltage and current obtained under a specific operating condition. If the voltage and current obtained below are applied to this characteristic curve or table, the true value of the remaining capacity cannot always be obtained, and a large error may occur. There is a problem that can not be enough. Further, when the noise superimposed on the measured current and the voltage is large, and thus the variation in the remaining capacity to be obtained is large, it is difficult to avoid an error due to the phase lag when trying to average with a moving average filter.
[0010]
SUMMARY OF THE INVENTION An object of the present invention is to provide a voltage / current type battery remaining capacity meter capable of solving the above-mentioned problems.
[0011]
[Means for Solving the Problems]
Using the remaining capacity as a parameter that matches the physical characteristics of the battery, prepare a battery model representative of the relationship between the discharge current and the terminal voltage, and measure one of the measured values of the discharge current and the terminal voltage. The other estimated value of the discharge current and the terminal voltage is calculated by substituting the estimated value into the battery model, and the parameter is corrected based on the deviation of the estimated value from the actually measured value so that the deviation is reduced. The parameter value when it becomes sufficiently small is output as the remaining capacity of the battery.
As a correction for a temperature change, a coordinate conversion formula between a voltage-current characteristic at a certain ambient temperature and a voltage-current characteristic using the remaining capacity as a parameter and a voltage-current characteristic at a standard temperature is stored, and measured at the certain ambient temperature. The converted discharge current and terminal voltage are converted into values at the standard temperature by the coordinate conversion formula, and the remaining capacity of the battery is calculated based on the measured discharge current and terminal voltage at the converted standard temperature. Further, when the amount of change or the rate of change of the value representing the battery model at the time of the n-th discharge with respect to the value at the time of the first charge / discharge exceeds a predetermined threshold value, the above-described coefficients are corrected and the battery model is corrected. Can be corrected over time.
[0012]
[Action]
The remaining capacity of the battery can be monitored more accurately and in real time, and the remaining capacity can be monitored in consideration of the influence of temperature change and aging, and an abnormal state can be detected. In addition, since the remaining capacity of the battery can be calculated as a digital amount, it can be easily transmitted to a remote central device for centralized management.
[0013]
【Example】
Hereinafter, the present invention will be described in detail with reference to the drawings. FIG. 1 is a block diagram showing the basic configuration of the present invention. A load 2 (for example, a motor for driving an electric vehicle) is connected to the battery 1 to be measured, and a load current, that is, a discharge current i of the battery 1 is detected by an ammeter 3. When the size of the load 2 is controlled by the load control unit 4 (for example, an accelerator pedal of an electric vehicle), the discharge current i changes, and the terminal voltage v of the battery 1 changes accordingly. The voltage v is measured by the voltmeter 10. As the battery model 5, an estimated terminal voltage V of the battery 1 as shown in the following equation (1) is used._esAnd a relational expression between the discharge current i at that time and the remaining capacity θ of the battery 1 (which is a parameter of the model). The value of the detected discharge current i is substituted into the equation of the model, and the estimated terminal voltage V_esIs calculated.
[0014]
Obtained estimated terminal voltage V_esIs supplied to the comparator 6 and compared with the measured terminal voltage v. The output of the comparator 6, that is, the estimated terminal voltage V_esAnd the measured terminal voltage v indicate the degree of approximation of the battery model 5 to the battery 1, that is, the degree of convergence. Therefore, the difference is supplied to the convergence judging unit 7 to judge whether or not the convergence has sufficiently converged below the threshold value. If not, the difference is fed back to the battery model and its parameters are determined. To correct. In the example of FIG. 1, the remaining capacity correction unit 8 corrects the parameter of the battery model 5, that is, the remaining capacity θ so as to reduce the difference. In the battery model 5, the estimated terminal voltage V is calculated using the corrected remaining capacity θ and the actually measured current value i._esIs calculated again.
[0015]
Measurement of current and voltage as described above, estimated terminal voltage V_esAnd the correction of the parameter θ are repeated to obtain the estimated terminal voltage V._esWhen the difference between the battery model 5 and the measured terminal voltage v becomes sufficiently small, it is considered that the battery model 5 is representative of the actual state of the battery 1, and the convergence determination unit 7 controls the output control unit 9 to The parameter of the battery model 5 is output as the remaining capacity θ. As described above, according to the present invention, the battery model 5 is modified so as to match the actual state of the battery 1 only by measuring the discharge current and the terminal voltage without interrupting the load of the battery 1. The remaining capacity θ can be detected.
[0016]
Next, the battery model 5 will be described in detail. In the present invention, as described above, the terminal voltage v of the battery 1 is a function of the discharge current i at that time and the remaining capacity θ of the battery 1 and the physical properties of the battery are taken into consideration. In the example, the battery model 5 at a certain time t is represented by the following quadratic equation (1).

In equation (1), a₀(Θ), a₁(Θ), a_Two(Θ) is a constant with respect to the current i, but changes with respect to the remaining capacity θ as a parameter. In the following, (θ) added to the constant is omitted, and simply a₀, A₁, A_TwoNotation.
[0017]
Constant a₀Is a terminal voltage when the discharge current i is 0, and corresponds to a so-called no-load open circuit voltage, and relates to the remaining capacity of the battery, aging, ambient temperature, and the like. This is because, as the reaction of the battery proceeds, the concentration of the electrolytic solution decreases, the reactant accumulates on the electrode plate, and the effective electrode plate area decreases, so that the remaining capacity tends to decrease. On the other hand, if the ambient temperature rises, the reaction is activated, so that the no-load open circuit voltage rises. According to our observations, the constant a₀Decreases as the remaining capacity decreases.
[0018]
Constant a₁Is considered to correspond to the internal electrical resistance of the battery because the product of the current i and the current i indicates a voltage drop. The voltage drop increases due to the decrease in the remaining capacity and the concentration of the electrolyte due to aging, the accumulation of inert substances in the electrode plate, and the dropout of the filling material of the electrode plate, so the internal electrical resistance of the battery increases. I do. Therefore the constant a₁Has a negative polarity, and its absolute value increases as the remaining capacity decreases. In addition, a constant a₀Similarly, when the ambient temperature rises, the reaction is activated, so that the voltage drop is reduced.
[0019]
Constant a_TwoSince the product of the current i and the square of the current i affects the voltage drop, it is understood that the current depends on the polarization action of the battery, and also relates to the remaining capacity. According to our observations, the constant a_TwoIs relatively large at the beginning and end of the discharge, and small at the middle. That is, when the remaining capacity of the battery is sufficiently large, the constant a_TwoWas somewhat larger, gradually decreased as the remaining capacity decreased, and gradually increased again when the remaining capacity was further reduced.
[0020]
Based on the above-described relationship between each coefficient and the physical characteristics of the battery and the change tendency of each coefficient, in this embodiment, each coefficient a₀~ A_TwoIs represented by a quadratic curve relating to the remaining capacity θ, and expressed by the following equations (2) to (4), respectively.
a₀= B₀₀+ B₀₁・ Θ + b₀₂・ Θ^Two    … (2)
a₁= B_Ten+ B₁₁・ Θ + b₁₂・ Θ^Two    … (3)
a_Two= B₂₀+ B_{twenty one}・ Θ + b_{twenty two}・ Θ^Two    … (4)
Specific numerical examples of each coefficient with respect to the remaining battery capacity are shown in FIGS. 2A to 2C. However, this is merely an example, and can be changed as appropriate. As is apparent, it naturally changes when the type of the battery changes. In addition, these coefficients a₀~ A_TwoCan be obtained experimentally if the voltage-current characteristic curve of the battery to be measured is obtained with the remaining capacity as a parameter.
[0021]
Using the battery model as described above, the remaining capacity of the battery 1 is measured or estimated by the configuration of FIG. For this purpose, a method of obtaining the remaining capacity at time t by estimation theory using discrete sampling data from a certain time (tT) to time t will be described below.
[0022]
First, the measured terminal voltage of battery 1 at time τ from time (t−T) to time t is v (τ), the remaining capacity at this time is θ, and the measured discharge current is i (τ). The terminal voltage estimated value obtained by substituting into the expression 1) is expressed as V_es(Τ, θ). Further, if the nonlinear optimization method is applied using the sampling data from the time point (tT) to the time point t, the result is to obtain θ that minimizes the evaluation function of the following equation (5). I do. This equation is an example in which the Gauss-Newton method is applied as a nonlinear optimization method.
[0023]
(Equation 5)

Since the equation (5) is nonlinear with respect to θ, the estimated terminal voltage V_es(Τ, θ) is a reference value θ₀And expand linearly by omitting terms of second and higher order to obtain equation (6).
[0024]
(Equation 6)

When the equation (6) is substituted into the equation (5), the linear evaluation function of the equation (7) is obtained.
[0025]
(Equation 7)

Next, δθ that minimizes the equation (7) when θ changes, that is, δθ that makes the partial differential coefficient relating to δθ in equation (7) zero, is obtained. This δθ is the initial value θ assumed earlier as the reference value of the remaining capacity.₀, Which is obtained as an estimated value._esNotation. Correction amount δθ_esIs represented by the following equation (8).
[0026]
(Equation 8)

Correction amount δθ_esIs obtained, then θ at that time₀To δθ_esIs corrected (addition / subtraction) and a new remaining capacity is assumed, and the estimated terminal voltage V_esIs calculated. And the estimated terminal voltage V_esUntil the difference between (τ, θ) and the measured terminal voltage v (τ) becomes sufficiently small, in other words, the assumed remaining capacity θ₀Is repeated until converges. At this time, the (k + 1) th assumed remaining capacity θ₀(K + 1) is the k-th assumed remaining capacity θ in the remaining capacity correction unit 8.₀(K) is δθ_esSince it is obtained by correcting only (k), it can be expressed by the following equation (9).
θ₀(K + 1) = θ₀(K) + δθ_es(K) ... (9)
Θ in equation (9)₀(K + 1) has converged (for example, the ratio | δθ_es(K) / θ₀(The value of (k + 1) | becomes smaller than a predetermined threshold value ε) is determined by the convergence determining unit 7, the output control unit 9 is activated, and the assumed remaining capacity θ at that time is determined.₀(K + 1) or θ₀(K) is output as a signal indicating the remaining capacity of the battery.
[0027]
FIG. 3 is a block diagram showing a hardware configuration of the battery model of FIG. 1 and a signal flow in the above-described calculation. The contents are obvious from the above description, and can be easily understood, so that duplicate description will be omitted.
[0028]
FIG. 4A shows the terminal voltage V estimated using the battery model of the above embodiment._esIt is a figure which shows the comparison of the terminal voltage v (solid line) with the (dotted line) and the actually measured, and for convenience of comparison of both curves, (B) of the same figure has expanded and shown a part. From these figures, according to the present invention, since the model based on the physical characteristics of the battery was used, it is possible to estimate the remaining capacity of the battery with good accuracy, and observation noise is superimposed on the measured value. It can be seen that the estimated value is not affected by such noise. Further, the evaluation function of the equation (5) is always unimodal, and the initial value θ₀It has been confirmed by the simulations of the present inventors that no matter what value is set, the value always converges to the true value.
[0029]
Temperature compensation of remaining capacity
As described above for the battery model, the characteristic curve of the discharge current versus the terminal voltage with the remaining capacity of the battery as a parameter changes according to the ambient temperature. That is, when the ambient temperature is high, the battery reaction is activated, so that the generated voltage increases and the curve as a whole increases in the positive direction of the voltage axis. Also, since the internal resistance of the battery decreases as the temperature increases, the slope of the curve corresponding to the internal resistance becomes gentler as the temperature increases, and on the contrary, becomes steeper as the temperature decreases, and thus the curve rises as a whole.
[0030]
From the above considerations, assuming that a discharge current-terminal voltage characteristic curve at 0 degree Celsius of a certain battery is, for example, as shown in FIG. 5A, this characteristic curve is represented by a voltage axis (vertical axis) and a current axis. It can be seen that the parallel displacement in the direction of the axis (horizontal axis) and the rotation in the counterclockwise direction can approximate the discharge current-terminal voltage characteristic curve of the battery at a higher temperature, for example, 30 degrees Celsius. FIG. 5 (B) is obtained by translating and rotating the curve of FIG. 5 (A) in a counterclockwise direction, and is regarded as a discharge current-terminal voltage characteristic curve of the battery at substantially 30 degrees Celsius. Can be
[0031]
As is apparent, since the parallel movement and rotation of the characteristic curve as described above are nothing but a coordinate axis conversion operation, a discharge current vs. terminal voltage characteristic curve (hereinafter, referred to as a standard curve) at a standard temperature (for example, 30 ° C.) of a certain battery. ) And a coordinate conversion equation for matching the discharge current vs. terminal voltage characteristic curve at any other temperature to the standard curve, the remaining capacity at an ambient temperature T ° C different from this is known. It can be easily obtained by the method of the present invention described above.
[0032]
That is, the discharge current and the terminal voltage obtained by the actual measurement at the ambient temperature T ° C. are substituted into a coordinate conversion equation or a table prepared in advance to convert the values into a coordinate system value at a standard temperature. Is applied to the standard curve to obtain the remaining capacity θ, this value becomes the remaining capacity at the ambient temperature T ° C.
[0033]
As is well known, the coordinate conversion equation for this is such that the discharge current value measured at an ambient temperature T ° C. is I (T ° C.), the terminal voltage value is V (T ° C.), and the discharge current value at a temperature T ° C. Α (radian) is the rotation angle of the coordinate axis required to match the terminal voltage characteristic curve to the standard curve, and x and y are the parallel movement amounts in the horizontal axis (current axis) and vertical axis (voltage axis) directions, Further, assuming that the actually measured values of the discharge current and the terminal voltage on the coordinates of the standard curve are I (30 ° C.) and V (30 ° C.), these are expressed by the following equations (10) and (11).
[0034]

Here, the rotation angle α, the parallel movement amounts x and y in the horizontal axis (current axis) and vertical axis (voltage axis) directions can be naturally measured and measured in advance at various temperatures.
[0035]
Alternatively, based on the fact that α, x and y are substantially proportional to temperature, for example, two characteristic curves at two different temperatures 0 ° C. and 30 ° C. are known and both curves are Δα Assuming that the coordinate axis rotation and the axis translation of Δx (3 • 0) and Δy (3 • 0) overlap, the following interpolation equations (12) to (14) show that α, x and y with respect to T ° C. The value can be obtained in advance or calculated each time.
Rotation angle α = {Δα (30.0) / 30} (30−T) (12)
Translation amount x = {Δx (30.0) / 30} (30−T) (13)
Translation amount y = {Δy (30.0) / 30} (30−T) (14)
As described above, the remaining capacity at an arbitrary ambient temperature can be easily obtained only by preparing the discharge current-terminal voltage characteristic curve at the standard temperature and the equation for coordinate conversion.
[0036]
Time-dependent correction of remaining capacity
In the above, each coefficient a of the equation (1) representing the battery model 5₀(Θ), a₁(Θ), a_Two(Θ) and therefore the coefficient b₀₀~ B_{twenty two}Depends only on the remaining capacity of the battery, and does not change with respect to the current i. However, strictly speaking, these coefficients change over time in accordance with the number of times of charging and discharging of the battery.₀~ A_Two, B₀₀~ B_{twenty two}Is preferably corrected over time (according to the number of times of charge / discharge).
[0037]
As is generally known, the remaining capacity of the battery decreases from the capacity at the start of use after charging is completed, largely depending on the time integral value of the discharge current. A known current integration type remaining capacity meter utilizes this fact.
[0038]
However, strictly speaking, the remaining capacity is also affected by the state of the discharge current, and the state of rapid discharge with a large current is smaller than the case of gentle discharge with a small current. The main cause is Joule heat loss Ri due to discharge current.^TwoIt is considered that an energy loss corresponding to Therefore, it can be estimated that the rate of decrease of the remaining capacity θ is proportional to the discharge current i, and that the proportional coefficient is also proportional to the discharge current.
dθ / dt = f (i) · i
Can be expressed as
[0039]
Here, f (i) is strictly a general polynomial.
f (i) = C₁+ C_Two・ I + ... + C_n・ Iⁿ+ ...
Where C₁, C_Two... C_nIs a constant
Therefore, substituting this into the above equation gives
dθ / dt = C₁・ I + C_Two・ I^Two+ ... + C_n・^{i n + 1}+ ...
It becomes.
[0040]
However, the first two terms that are easy to correspond to the physical properties of the battery, that is, C corresponding to the current integrated value (ampere hours)₁C corresponding to the term i and the energy integral value (watt time) corresponding to the current squared loss at the time of discharging the current_Two・ I^TwoIt is considered that the remaining capacity can be grasped with sufficient accuracy for practical use. That is,
dθ / dt = C₁・ I + C_Two・ I^Two
If so, it is sufficient for practical use. By integrating the above relational expression, the following expression (15) is obtained.
[0041]
(Equation 9)

In equation (15), the constant term C₀Is the remaining capacity at the start of use (discharge), and the integral term can be regarded as the battery consumption capacity therefrom. Substituting θ in equation (15) into equations (2) to (4) above, the obtained coefficient a₀~ A_TwoIs further substituted into equation (1) and expressed in discrete form, the estimated terminal voltage V at time j_djThe following equation (16) is obtained as an equation representing. Estimated terminal voltage V by equation (16)_djIs the coefficient a of the battery model defined by the above equation (1).₀~ A_TwoIs defined as a function of the remaining capacity θ in the equations (2) to (4), but is defined as a function of only the current i. Although θ in the expression (1) is the remaining capacity itself as described above, θ in the expression (15) has a slightly different definition, as is apparent. Is represented by another symbol φ, and the coefficient is also represented by b in Equations (2) to (4).₀₀~ B_{twenty two}Distinguished from d₀₀~ D_{twenty two}Will be represented by
[0042]
(Equation 10)

Where i_kIs the measured current value at time k (where 0 ≦ k ≦ j), and i_jIs the measured current value at time j.
[0043]
The coefficient d in the equation (16)₀₀~ D_{twenty two}And C₀~ C_TwoIs the coefficient a in the above equation (1).₀~ A_TwoIs known, and the measured current value i up to time j is the same as when the remaining capacity θ was obtained._j, And the voltage value v at time j_jBy using the above equation, V_djCan be obtained by applying estimation theory. Specifically, the estimated value V of the voltage_djAnd the measured value v_jIs obtained for n data sets, and the sum of squares is calculated as an evaluation function I (d₀₀~ D_{twenty two}, C₀~ C_Two). The evaluation function I is expressed by the following equation (17).
[0044]
(Equation 11)

In equation (17),_j(Measured voltage value at time j) and the estimated voltage value V in equation (16)._djIs a coefficient d such that the evaluation function I obtained by substituting₀₀~ D_{twenty two}, C₀~ C_TwoAsk for. For this purpose, the above-mentioned evaluation function is set to each parameter d.₀₀~ D_{twenty two}, C₀~ C_TwoIf each equation obtained by partial differentiation of is set to 0, simultaneous equations having the same number as the number of parameters can be obtained. This is solved to obtain each parameter.
[0045]
More specifically, the amount of correction from the initial value of each parameter (coefficient) is obtained by applying the same method as previously performed with respect to the expressions (1) to (8). When the correction amount becomes sufficiently small, it is determined that each parameter has converged, and each parameter, that is, the coefficient d is determined.₀₀~ D_{twenty two}, C₀~ C_TwoCan be estimated. The coefficient C thus obtained₀~ C_TwoIs substituted into Expression (15), an index φ representing the remaining capacity can be obtained.
[0046]
Below, the above-mentioned coefficient d₀₀~ D_{twenty two}, C₀~ C_TwoUsing the constant a₀~ A_Two, B₀₀~ B_{twenty two}The following describes a specific method for correcting the secular change of the above. In using the battery, the coefficient d is calculated by the method described above for each charge / discharge cycle.₀₀~ D_{twenty two}, C₀~ C_TwoAnd the estimated value of the coefficient obtained in the ith (where 1 ≦ i ≦ n) charge / discharge cycle is calculated as d₀₀ ⁽ⁱ⁾~ D_{twenty two} ⁽ⁱ⁾, C₀ ⁽ⁱ⁾~ C_Two ⁽ⁱ⁾Expressed by Each coefficient d obtained in the first charge / discharge cycle₀₀ ⁽¹⁾~ D_{twenty two} ⁽¹⁾, C₀ ⁽¹⁾~ C_Two ⁽¹⁾For each coefficient d in the nth charge / discharge cycle₀₀ ⁽ⁿ⁾~ D_{twenty two} ⁽ⁿ⁾, C₀ ⁽ⁿ⁾~ C_Two ⁽ⁿ⁾Ratio α₀₀ ⁽ⁿ⁾~ Α_{twenty two} ⁽ⁿ⁾, Α_c0 ⁽ⁿ⁾~ Α_c2 ⁽ⁿ⁾Or the difference between them, generally, the difference or ratio between the n-th and (n−r) -th operations is calculated and monitored. ), It is possible to know the parameter, that is, the aging of the battery model. Further, when the change state is remarkable (when it is abnormally early or large), it can be determined that the battery is abnormal.
[0047]
In order to determine the change state of the plurality of coefficients as described above, for example, Nikka Giren Publishing Co., Ltd., published on April 10, 1989, Chuichi Okuno et al., “Multivariate Analysis Method”, p. 278 (multivariable analysis) , Tokyo Book Co., Ltd., November 30, 1989, Chiho Minoya, Statistical Hypothesis Test, p. 145 (without estimation and test), Baifukan Co., Ltd., September 30, 1961, Asai / A method described in detail in Murakami's "Elementary Statistics", p. 158 (test of a hypothesis) can be used.
[0048]
If it is determined that the battery model has undergone an aging change that requires correction in the n-th discharge, the parameter of the equation (2), that is, the coefficient b₀₀~ B_{twenty two}Is corrected, and each coefficient a of the equation (1) representing the battery model 5 is corrected.₀(Θ), a₁(Θ), a_TwoModify (θ). One example of a specific method for that is as follows.
[0049]
Since the parameters of the battery model in the initial state of starting new use are known,₀₀ ⁽¹⁾~ B_{twenty two} ⁽¹⁾Expressed by On the other hand, the parameter d in the i-th (1 ≦ i ≦ n) charge / discharge cycle₀₀ ⁽ⁱ⁾~ D_{twenty two} ⁽ⁱ⁾Is determined as described above. First, the ratio k of the parameter d in the first discharge cycle to the parameter b in the initial state is obtained as shown in the following equation (18), and each of the ratios in the first and nth discharge cycles is calculated. The ratio α of the parameter d is obtained as in the following equation (19).
k₀₀= D₀₀ ⁽¹⁾/ B₀₀ ⁽¹⁾~ K_{twenty two}= D_{twenty two} ⁽¹⁾/ B_{twenty two} ⁽¹⁾  … (18)
α₀₀ ⁽ⁿ⁾= D₀₀ ⁽ⁿ⁾/ D₀₀ ⁽¹⁾~ Α_{twenty two}= D_{twenty two} ⁽ⁿ⁾/ D_{twenty two} ⁽¹⁾… (19)
Parameter b used for measuring the remaining capacity of the (n + 1) th and subsequent discharge cycles₀₀ ^{(n )}~ B_{twenty two} ⁽ⁿ⁾Is obtained by the following equation (20).
[0050]
(Equation 12)

Parameter b thus obtained₀₀ ⁽ⁿ⁾~ B_{twenty two} ⁽ⁿ⁾If the remaining battery capacity is calculated based on the corrected remaining battery capacity, the remaining battery capacity can be monitored more accurately without being affected by aging.
[0051]
In the above description, when using the battery model in which the relationship between the discharge current and the terminal voltage is expressed as a mathematical expression using the remaining capacity of the battery to be measured as a parameter, the measured value of the discharge current is substituted into the mathematical expression of the battery model. Then, the estimated value of the terminal voltage is calculated, and based on the deviation of the estimated terminal voltage value from the actually measured voltage, the remaining capacity, which is a parameter, is corrected so as to reduce the deviation, and the deviation becomes sufficiently small. Thus, when the parameters converge, this is output as the required remaining capacity.
[0052]
However, as is apparent, the estimated value of the discharge current is obtained by substituting the value of the actually measured terminal voltage, not the actually measured current, into the formula of the battery model, and the deviation of the estimated value of the estimated discharge current from the actually measured value approaches zero. Then, the remaining capacity can be determined. It is obvious that the equations used for this purpose can be obtained by exchanging the voltage and the current in the above-described equations (1), (5) to (8)._esAnd parameter correction amount δθ_esIs obtained by the following equations (21) and (22), respectively.
I_es(T, θ) = p₀(Θ) + p₁(Θ) · v (t) + p_Two(Θ) · v^Two(T) ... (21)
Where p₀~ P_TwoIs a function of θ.
[0053]
(Equation 13)

Further, it is clear that the above-described correction method can be applied by analogy in a case where the influence of a temperature change or a temporal change is considered. In the above description, an example in which the battery model is expressed as a mathematical expression has been described. However, it is easily understood that a similar remaining capacity meter can be configured by using a table (graph) model instead. There will be.
[0054]
【The invention's effect】
According to the present invention, since the battery model is associated with its physical characteristics, the remaining capacity of the battery can be monitored more accurately and in real time, and furthermore, the monitoring of the remaining capacity taking into account the effects of temperature changes and aging changes Not only is possible, but also an abnormal state can be detected. In addition, since the remaining capacity of the battery can be calculated as a digital amount, it can be easily transmitted to a remote central device for centralized management.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a basic configuration of the present invention.
FIG. 2 is a diagram showing specific numerical examples of respective coefficients with respect to the remaining battery capacity of the model in one embodiment of the present invention.
FIG. 3 is a block diagram showing a hardware configuration and a signal flow of the battery model of FIG. 1;
FIG. 4 is a diagram showing a comparison between a terminal voltage terminal voltage estimated using the battery model of the embodiment and an actually measured terminal voltage.
FIG. 5 is a diagram showing a relationship between a change in a voltage-current characteristic of a battery due to an ambient temperature and a coordinate axis conversion due to the temperature change.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... Battery 2 ... Load 4 ... Load control part 5 ... Battery model 7 ... Convergence judgment part 8 ... Remaining capacity correction part 9 ... Output control part

Claims (8)

Means for measuring the charge / discharge current of the battery and the terminal voltage at that time,
A battery model representing the relationship between the charge / discharge current and the terminal voltage with the remaining capacity of the battery as a parameter;
Calculating means for substituting one measured value of the charge / discharge current and the terminal voltage into the battery model and calculating the other estimated value of the charge / discharge current and the terminal voltage;
Means for correcting parameters based on the deviation of the estimated value from the actually measured value so that the deviation is reduced;
Convergence determining means for determining that the deviation has become sufficiently small and the parameters have converged;
Means for outputting a parameter value at the time of convergence as the remaining capacity of the battery,
The charge / discharge current is a measured current value, and the measured current value at a certain time t is i (t), the remaining capacity of the battery at that time is θ, and the estimated terminal voltage is V _es (t, θ). A battery residual capacity meter characterized in that the model is represented by the following quadratic equation.
V _es (t, θ) = a ₀ (Θ) + a ₁ (Θ) · i (t) + a ₂ (Θ) · i ² (t)
Where a ₀ ~ A ₂ Is a function of θ. Capacity meter of a battery of claim 1, wherein said a ₀ ~a _2, characterized in that the formula below.
a ₀ = b ₀₀ + b ₀₁ · θ + b ₀₂ · θ ²
a ₁ = b ₁₀ + b ₁₁ · θ + b ₁₂ · θ ²
a ₂ = b ₂₀ + b ₂₁ · θ + b ₂₂ · θ ²
Here, b _{00 to} b ₂₂ are constants. The actual measured voltage at a certain time τ between (t−T) and t is v (τ), and the estimated terminal voltage calculated based on the actual measured current i (τ) is V _es (τ, θ ₀ ). The correction amount δθ _es of the parameter θ when

Capacity meter of a battery according to claim 1 or 2, characterized in that it is computed in. The measured current value at a certain time point j is i _j , the measured current value at a time point k (where 0 ≦ k ≦ j) is i _k , C ₁ and C ₂ are constants, and the estimated terminal voltage at the time point j is V _dj , a second battery model represented by the following equation:

Means for determining coefficients d _{00 to} d ₂₂ in the above equation for each charge / discharge cycle of the battery;
When each coefficient obtained in the i-th (where 1 ≦ i ≦ n) charge / discharge cycle is d ₀₀ ⁽ⁱ⁾ to d ₂₂ ⁽ⁱ⁾ , at least some of the coefficients are (n−r) times. means for monitoring the change state up to the n-th time;
Means for modifying the coefficients b _{00 to} b ₂₂ based on the coefficients d ₀₀ ^{(i) to} d ₂₂ ⁽ⁱ⁾ when the change state of the coefficient exceeds a predetermined amount. A battery remaining capacity meter according to claim 2 or 3 . In the initial state of use, the coefficients b _{00 to} b ₂₂ are b ₀₀ ^{(1) to} b ₂₂ ⁽¹⁾ , and the coefficients in the i-th (1 ≦ i ≦ n) charge / discharge cycle are d ₀₀ ⁽ⁱ⁾ to d ₀₀ ⁽ⁱ⁾ . d ₂₂ ⁽ⁱ⁾ , the ratio k of the coefficient d in the first discharge cycle to the coefficient b in the initial state, and the ratio α of each parameter d in the first and nth discharge cycles, respectively:
k ₀₀ = d ₀₀ ⁽¹⁾ / b ₀₀ ^{(1) to} k ₂₂ = d ₂₂ ⁽¹⁾ / b ₂₂ ⁽¹⁾
α ₀₀ ⁽ⁿ⁾ = d ₀₀ ⁿ⁾ / d ₀₀ ^{(1) to} α ₂₂ = d ₂₂ ⁿ⁾ / d ₂₂ ⁽¹⁾
5. The remaining capacity meter for a battery according to claim 4, wherein the parameters b ₀₀ ^{(n) to} b ₂₂ ⁽ⁿ⁾ after time-dependent change correction are calculated by the following equations.

Means for measuring the charge / discharge current of the battery and the terminal voltage at that time,
A battery model representing the relationship between the charge / discharge current and the terminal voltage with the remaining capacity of the battery as a parameter;
Calculating means for substituting one measured value of the charge / discharge current and the terminal voltage into the battery model and calculating the other estimated value of the charge / discharge current and the terminal voltage;
Means for correcting parameters based on the deviation of the estimated value from the actually measured value so that the deviation is reduced ;
Convergence determining means for determining that the deviation has become sufficiently small and the parameters have converged;
Means for outputting a parameter value at the time of convergence as the remaining capacity of the battery,
The terminal voltage is a measured voltage value, and the measured voltage value at a certain time t is represented by v (t).
The remaining capacity of the battery is represented by the following quadratic equation when the remaining capacity of the battery at that time is θ and the estimated charge / discharge current is I _es (t, θ).
I _es (t, θ) = p ₀ (θ) + p ₁ (θ) · v (t) + p ₂ (θ) · v ² (t)
Here, p _{0 to} p ₂ are functions of θ. The actual measured current value at a certain time τ between (t−T) and t is i (τ), and the estimated current value calculated based on the actually measured voltage value v (τ) is I _es (τ, θ ₀ ). The correction amount δθ _es of the parameter θ when

The remaining capacity meter of a battery according to claim 6 , wherein the calculation is performed by: The battery model representing the relationship between the charge / discharge current and the terminal voltage with the remaining capacity of the battery as a parameter is based on the battery characteristics at a standard temperature.
A means for storing a coordinate conversion equation between a voltage-current characteristic at a certain ambient temperature and a voltage-current characteristic having a remaining capacity as a parameter and a voltage-current characteristic at a standard temperature;
Means for converting the charge / discharge current and the terminal voltage actually measured at the certain ambient temperature into a value at a standard temperature by the coordinate conversion formula,
The battery remaining capacity meter according to any one of claims 1 to 7 , wherein the remaining capacity of the battery is calculated based on the converted charge / discharge current and the measured terminal voltage value at the standard temperature.

Images