JP3976633B2

JP3976633B2 - Discharge voltage drop component calculation method in battery, and discharge voltage drop component separation calculation method and apparatus

Info

Publication number: JP3976633B2
Application number: JP2002223340A
Authority: JP
Inventors: 洋一荒井
Original assignee: Yazaki Corp
Current assignee: Yazaki Corp
Priority date: 2001-08-03
Filing date: 2002-07-31
Publication date: 2007-09-19
Anticipated expiration: 2022-07-31
Also published as: JP2003177163A

Description

【０００１】
【発明の属する技術分野】
本発明はバッテリにおける放電電流−端子電圧（Ｉ−Ｖ）特性における電圧降下成分を算出する方法、並びに、算出した電圧降下成分によって電圧降下成分を分離して算出する放電時電圧降下成分分離算出方法及び装置に係り、より詳細には、バッテリから負荷に電力を供給したときバッテリから放電される放電電流とこれに伴って変化する端子電圧との関係を示す放電電流−端子電圧（Ｉ−Ｖ）特性において、放電電流の大きさに応じて降下する端子電圧中の電圧降下成分を算出するバッテリにおける放電時電圧降下成分算出方法、並びに、電圧降下成分を分離して算出するバッテリにおける放電時電圧降下成分分離算出方法及び装置に関するものである。
【０００２】
【従来の技術】
一般に、バッテリは放電電流をカバーする充電を行うことによって、その充電容量の範囲内において繰り返し使用できることになっているが、過放電や電解液不足などの不測の事態を招いた場合は勿論のこと、これらの事態を招かなくても、長期間にわたって使用し経年変化が起こると、放電によって負荷に供給できる電力量である放電可能容量が急激に低下するようになる。このため、経年変化によって放電可能容量の低下している状態においては、充電を上回る放電がわずかな期間発生しても、例えば車両に搭載したバッテリの場合には、エンジン停止後にスタータモータを起動してエンジンを再始動できなくなる事態を招きかねない。
【０００３】
因みに、新品と経年変化の生じているバッテリとを比較した場合、新品に比べて経年変化の生じているバッテリでは、その純抵抗が大きくなることが知られている。そのため、定期点検時などに、バッテリ交換の目安としてバッテリの純抵抗を測定することが考えられている。これは、純抵抗を知ることによって、純抵抗と分極抵抗成分との割合などを考慮し、劣化度を定めることができるからである。また、純抵抗が分かると、バッテリの開回路電圧を推定するためにも利用できるからである。
【０００４】
一般に、バッテリから電流が放電されるとバッテリの端子電圧に降下を生じる。この電圧降下は、バッテリの内部インピーダンス（合成抵抗）によるものであるが、バッテリの構造などに基因するＩＲ損（純抵抗、すなわち、オーミック抵抗による電圧降下）と、化学的な反応に基因する分極抵抗成分（活性化分極、濃度分極）による電圧降下に分けることができる。バッテリの放電電流−端子電圧（Ｉ−Ｖ）特性を求めた場合、図１１に示すように、ＩＲ損による電圧降下は、バッテリの状態が同じであれば純抵抗が一定値を保つため、放電電流の大きさに応じて直線的に増加する変化を示すことが知られている。
【０００５】
【発明が解決しようとする課題】
しかし、分極抵抗成分による電圧降下は、分極が一定値を保たず、放電電流の大きさと放電時間によって変化する。このため、分極抵抗成分を含んだＩ−Ｖ特性からは、バッテリの様々な状態を直接推定することは実質的にできないことがわかっている。そこで、従来、分極抵抗成分を算出した純抵抗のみを測定するなど、Ｉ−Ｖ特性において、放電電流の大きさに応じて降下する端子電圧中の電圧降下成分を算出するとともに、分離して算出する技術が必要とされている。
【０００６】
しかも、バッテリを対象として、使用状態にあるときに適用して有効に活用できるものが求められている。
【０００７】
よって、本発明は上述した状況に鑑み、使用中のバッテリから負荷に電力を供給したときバッテリから放電される放電電流とこれに伴って変化する端子電圧との関係を示すＩ−Ｖ特性において、放電電流の大きさに応じて降下する端子電圧中の電圧降下成分を算出するバッテリにおける放電時電圧降下成分算出方法を提供することを課題としている。
【０００８】
発明はまた、上記Ｉ−Ｖ特性において、放電電流の大きさに応じて降下する端子電圧中の濃度分極による電圧降下成分を分離して算出するバッテリにおける放電時電圧降下成分分離算出方法及び装置を提供することを課題としている。
【０００９】
【課題を解決するための手段】
上記課題を解決するため本発明によって成された請求項１はバッテリにおける放電時電圧降下成分算出方法に関するもの、請求項２乃至請求項１７記載の本発明はバッテリにおける放電時電圧降下成分分離算出方法に関するものであり、請求項１８及び２０記載の本発明はバッテリにおける放電時電圧降下成分分離算出装置に関するものである。
【００１０】
請求項１記載の発明は、バッテリから負荷に電力を供給したときバッテリから放電される放電電流とこれに伴って変化する端子電圧との関係を示す放電電流−端子電圧特性において、放電電流の大きさに応じて降下する端子電圧中の電圧降下成分を算出するバッテリにおける放電時電圧降下成分算出方法において、前記負荷に、ピーク値まで単調増加した後、ピーク値から定常値まで単調減少する突入電流が流れている期間、前記バッテリの放電電流と該放電電流に対応する端子電圧とを周期的に測定し、該測定した放電電流と端子電圧との相関を示す前記増加する突入電流に対する放電電流−端子電圧特性の第１の近似式と前記減少する突入電流に対する放電電流−端子電圧特性の第２の近似式とを求め、前記第１の近似式の放電電流０である点における前記バッテリの端子電圧と前記第２の近似式の放電電流０である点における前記バッテリの端子電圧との差を求め、該差を前記突入電流が流れたことによって発生した総濃度分極による電圧降下と見なすことを特徴とするバッテリにおける放電時電圧降下成分算出方法に存する。
【００１１】
上述した請求項１記載の手順によれば、負荷にピーク値まで単調増加した後、ピーク値から定常値まで単調減少する突入電流が流れている期間、バッテリの放電電流と該放電電流に対応する端子電圧とを周期的に測定してこれら放電電流と端子電圧との相関を示す増加する突入電流に対する放電電流−端子電圧特性の第１の近似式と前記減少する突入電流に対する放電電流−端子電圧特性の第２の近似式とを求める。
【００１２】
次に、第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧には濃度分極による電圧降下以外の電圧が０であるとして、これらの差によって前記突入電流が流れたことによって発生した総濃度分極による電圧降下を算出しているので、この濃度分極による電圧降下を利用することによって、濃度分極による電圧降下以外による電圧降下も分離して算出することができる。
【００１３】
請求項２記載の発明は、バッテリから負荷に電力を供給したときバッテリから放電される放電電流とこれに伴って変化する端子電圧との関係を示す放電電流−端子電圧特性において、放電電流の大きさに応じて降下する端子電圧中の電圧降下成分を分離して算出するバッテリにおける放電時電圧降下成分分離算出方法において、前記負荷に、ピーク値まで単調増加した後、ピーク値から定常値まで単調減少する突入電流が流れている期間、前記バッテリの放電電流と該放電電流に対応する端子電圧とを周期的に測定し、該測定した放電電流と端子電圧との相関を示す前記増加する突入電流に対する放電電流−端子電圧特性の第１の近似式と前記減少する突入電流に対する放電電流−端子電圧特性の第２の近似式とを求め、前記第１及び第２の近似式の放電電流０である点における前記バッテリの端子電圧の差を求め、該差を前記突入電流が流れたことによって発生した総濃度分極による電圧降下と見なし、該差に基づいて任意の電流値における濃度分極による電圧降下を算出するとともに、該算出した濃度分極による電圧降下を任意の電流値における端子電圧に加算して前記濃度分極以外による電圧降下を算出し、電圧降下成分を濃度分極によるものとそれ以外によるものとに分離して算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００１４】
上述した請求項２記載の手順によれば、負荷にピーク値まで単調増加した後、ピーク値から定常値まで単調減少する突入電流が流れている期間、バッテリの放電電流と該放電電流に対応する端子電圧とを周期的に測定してこれら放電電流と端子電圧との相関を示す増加する突入電流に対する放電電流−端子電圧特性の第１の近似式と前記減少する突入電流に対する放電電流−端子電圧特性の第２の近似式とを求める。
【００１５】
次に、第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差に基づいて任意の電流値における濃度分極による電圧降下を算出するとともに、この算出した濃度分極による電圧降下を任意の電流値における端子電圧に加算して濃度分極以外による電圧降下を算出し、電圧降下成分を濃度分極によるものとそれ以外によるものとに分離して算出する。以上のように、第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差を、突入電流が流れたことによって発生した総濃度分極による電圧降下と見なしているので、この総濃度分極による電圧降下を電流値とその電流値に至る時間とによって按分することで、濃度分極による電圧降下とそれ以外による電圧降下に分離して算出することができる。
【００１６】
請求項３記載の発明は、請求項２記載のバッテリにおける放電時電圧降下成分分離算出方法において、任意の電流値における濃度分極による電圧降下を、前記突入電流が流れている期間に生じる総濃度分極に対する任意の電流値までの放電電流が流れた期間に生じる濃度分極の比率を前記差に乗じて算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００１７】
上述した請求項３記載の手順によれば、濃度分極の大きさが電流の大きさとその流れている時間とに比例していることに着目し、任意の電流値における濃度分極による電圧降下を、突入電流が流れている期間に生じる総濃度分極に対する任意の電流値までの放電電流が流れた期間に生じる濃度分極の比率を差に乗じて算出しているので、任意時点での濃度分極による電圧降下を他と分離して算出することができる。
【００１８】
請求項４記載の発明は、請求項２又は３記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記任意の電流値が、単調増加する突入電流のピーク値であり、前記突入電流がピーク値まで増加する期間に生じる濃度分極の前記総濃度分極に対する比率を前記差に乗じて前記ピーク値における濃度分極による電圧降下を算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００１９】
上述した請求項４記載の手順によれば、突入電流がピーク値まで増加する期間に生じる濃度分極の総濃度分極に対する比率を上記差に乗じてピーク値における濃度分極による電圧降下を算出しているので、突入電流のピーク値での、端子電圧の電圧降下成分を濃度分極によるものとそれ以外のものに分離して算出することができる。
【００２０】
請求項５記載の発明は、バッテリから負荷に電力を供給したときバッテリから放電される放電電流とこれに伴って変化する端子電圧との関係を示す放電電流−端子電圧特性において、放電電流の大きさに応じて降下する端子電圧中の電圧降下成分を分離して算出するバッテリにおける放電時電圧降下成分分離算出方法において、前記負荷に、ピーク値まで単調増加した後、ピーク値から定常値まで単調減少する突入電流が流れている期間、前記バッテリの放電電流と該放電電流に対応する端子電圧とを周期的に測定し、該測定した放電電流と端子電圧との相関を示す前記増加する突入電流に対する放電電流−端子電圧特性の第１の近似式と前記減少する突入電流に対する放電電流−端子電圧特性の第２の近似式とを求め、前記第１及び第２の近似式の放電電流０である点における前記バッテリの端子電圧の差を求め、該差を前記突入電流が流れたことによって発生した濃度分極による電圧降下と見なし、該差に、前記突入電流が流れている総時間に対するピーク値に増加するまでの時間の比率を乗じて突入電流がピーク値に増加する期間に生じた濃度分極による電圧降下を算出するとともに、該算出した濃度分極による電圧降下をピーク値における端子電圧に加算して前記濃度分極以外による電圧降下成分を算出し、電圧降下成分を濃度分極によるものとそれ以外によるものとに分離して算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００２１】
上述した請求項５記載の手順によれば、請求項１と同様にして求めた第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差に、突入電流が流れている総時間に対するピーク値に増加するまでの時間の比率を乗じて突入電流がピーク値に増加する期間に生じた濃度分極による電圧降下を算出するとともに、この算出した濃度分極による電圧降下をピーク値における端子電圧に加算して濃度分極以外による電圧降下成分を算出し、電圧降下成分を濃度分極によるものとそれ以外によるものとに分離して算出する。以上のように、第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差を、突入電流が流れたことによって発生した濃度分極による電圧降下と見なしているので、この電圧降下に突入電流の総時間に対する増加時間の比率を乗じてピーク値における濃度分極による電圧降下を求め、これを端子電圧に加算してピーク値における濃度分極による電圧降下とそれ以外による電圧降下に分離して算出することができる。
【００２２】
請求項６記載の発明は、請求項５記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記算出したピーク値における濃度分極による電圧降下に、前記突入電流がピーク値に増加する期間の任意の電流値までの時間の前記突入電流がピーク値に増加する時間に対する比率を乗じて、前記突入電流がピーク値に増加する任意の電流値における濃度分極による電圧降下を算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００２３】
上述した請求項６記載の手順によれば、ピーク値における濃度分極による電圧降下に、突入電流がピーク値に増加する期間の任意の電流値までの時間の突入電流がピーク値に増加する時間に対する比率を乗じて、突入電流がピーク値に増加する任意の電流値における濃度分極による電圧降下を算出するので、突入電流の増加期間の任意の電流値での濃度分極による電圧降下とそれ以外の電圧降下とを分離して算出することができる。
【００２４】
請求項７記載の発明は、請求項６記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記差から、前記算出した突入電流がピーク値に増加する期間に生じた濃度分極による電圧降下を減算して、突入電流がピーク値から０に減少する期間に生じた濃度分極による電圧降下を算出し、該算出した減少する期間に生じた濃度分極による電圧降下に、前記突入電流がピーク値から減少する期間の任意の電流値までの時間の前記突入電流がピーク値から０に減少する時間に対する比率を乗じて、前記突入電流がピーク値から減少する任意の電流値における濃度分極による電圧降下を算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００２５】
上述した請求項７記載の手順によれば、突入電流の流れた期間の電圧降下である放電電流０のときの電圧差から、前記増加期間に生じた濃度分極による電圧降下を減算して、減少期間の濃度分極による電圧降下を算出し、この算出した減少期間に生じた濃度分極による電圧降下に、減少期間の任意の電流値までの時間の突入電流がピーク値から０に減少する時間に対する比率を乗じて、減少期間の任意の電流値における濃度分極による電圧降下を算出するので、突入電流の減少期間の任意の電流値での濃度分極による電圧降下とそれ以外の電圧降下とを分離して算出することができる。
【００２６】
請求項８記載の発明は、請求項２〜７の何れかに記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記濃度分極以外による電圧降下成分が、純抵抗及び活性化分極による電圧降下成分であることを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００２７】
上述した請求項８記載の手順によれば、濃度分極以外による電圧降下成分が、純抵抗及び活性化分極による電圧降下成分であって、端子電圧の電圧降下を濃度分極による電圧降下と純抵抗及び活性化分極による電圧降下とに分離して算出することができる。
【００２８】
請求項９記載の発明は、請求項２〜８の何れかに記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記算出した濃度分極による電圧降下を利用し、前記第１及び第２の近似式から濃度分極による電圧降下を除いて濃度分極以外による電圧降下を表す前記第１及び第２の近似式の各々に対応する第１及び第２の修正近似式を求め、該求めた第１及び第２の修正近似式と前記第１及び第２の近似式との差をそれぞれとり、前記第１及び第２の近似式の各々に対応する濃度分極のみによる電圧降下の第１及び第２の濃度成分近似式を求め、該求めた濃度成分近似式に任意の電流値を代入して任意の電流値における濃度分極による電圧降下成分を分離して算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００２９】
上述した請求項９記載の手順によれば、任意の電流値における濃度分極による電圧降下を利用し、第１及び第２の近似式から濃度分極による電圧降下を除いて濃度分極以外による電圧降下を表す第１及び第２の近似式の各々に対応する第１及び第２の修正近似式を求め、この求めた第１及び第２の修正近似式と第１及び第２の近似式との差をそれぞれとり、第１及び第２の近似式の各々に対応する濃度分極のみによる電圧降下の第１及び第２の濃度成分近似式を求め、この求めた濃度成分近似式に任意の電流値を代入して任意の電流値における濃度分極による電圧降下成分を分離して算出するので、濃度分極のみによる電圧降下が第１及び第２の濃度成分近似式により一般化され、個々の電圧降下を分離して算出しなくてもよくなる。
【００３０】
請求項１０記載の発明は、請求項９記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記第１及び第２の修正近似式と予め求めた純抵抗による電圧降下を表す式との差をとり、前記第１及び第２の近似式の各々に対応する活性化分極のみによる電圧降下の第１及び第２の活性化分極近似式を求め、該求めた活性化分極近似式に任意の電流値を代入して任意の電流値における活性化分極による電圧降下成分を分離して算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００３１】
上述した請求項１０記載の手順によれば、濃度分極による電圧降下を除いた第１及び第２の修正近似式と予め求めた純抵抗による電圧降下を表す式との差をとり、第１及び第２の近似式の各々に対応する活性化分極のみによる電圧降下の第１及び第２の活性化分極近似式を求め、この求めた活性化分極の近似式に任意の電流値を代入して任意の電流値における活性化分極による電圧降下成分を分離して算出するので、端子電圧の電圧降下を、濃度分極による電圧降下、純抵抗による電圧降下、及び、活性化分極による電圧降下に分解して算出することができる。
【００３２】
請求項１１記載の発明は、請求項２〜７の何れかに記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記算出した濃度分極による電圧降下を利用し、前記第１及び第２の近似式から濃度分極による電圧降下を除いて濃度分極以外による電圧降下を表す前記第１及び第２の近似式の各々に対応する第１及び第２の修正近似式を求め、該求めた第１及び第２の修正近似式の前記ピーク値に対応する点における単位電流変化当たりの２つの端子電圧変化の値の中間の値をバッテリの純抵抗の値として算出し、該算出した純抵抗の値に電流値を乗じて純抵抗による電圧降下を算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００３３】
上述した請求項１１記載の手順によれば、算出した濃度分極による電圧降下を利用し、第１及び第２の近似式から濃度分極による電圧降下を除いて濃度分極以外による電圧降下を表す第１及び第２の近似式の各々に対応する第１及び第２の修正近似式を求め、この求めた第１及び第２の修正近似式のピーク値に対応する点における単位電流変化当たりの２つの端子電圧変化の値の中間の値をバッテリの純抵抗の値として算出し、この算出した純抵抗の値に電流値を乗じて純抵抗による電圧降下を算出するので、濃度分極による電圧降下以外の電圧降下から純抵抗による電圧降下を分離して算出することができる。
【００３４】
請求項１２記載の発明は、請求項１１記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記中間の値を、前記濃度分極による電圧降下を除いた前記第１及び第２の近似式の前記ピーク値に対応する点における単位電流変化当たりの２つの端子電圧変化の値を加算平均して求めることを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００３５】
上述した請求項１２記載の手順によれば、中間の値を、濃度分極による電圧降下を除いた第１及び第２の近似式のピーク値に対応する点における単位電流変化当たりの２つの端子電圧変化の値を加算平均して求めているので、ピーク値に対応する点での活性化分極の変化が等しくなる場合には、第１及び第２の近似式のピーク値に対応する点における微分値を加算して２で割ることで、バッテリの純抵抗を測定することができる。
【００３６】
請求項１３記載の発明は、請求項１１記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記中間の値を、前記濃度分極による電圧降下を除いた前記第１及び第２の近似式の前記ピーク値に対応する点における単位電流変化当たりの２つの端子電圧変化の値に、前記突入電流が流れている総時間に占める前記単調増加期間及び前記単調減少期間の時間の割合をそれぞれ乗じた上で加算して求めることを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００３７】
上述した請求項１３記載の手順によれば、中間の値を、濃度分極による電圧降下を除いた第１及び第２の近似式のピーク値に対応する点における単位電流変化当たりの２つの端子電圧変化の値に、突入電流が流れている総時間に占める単調増加期間及び単調減少期間の時間の割合をそれぞれ乗じた上で加算して求めているので、活性化分極と濃度分極とが相互に影響し合うことを考慮した中間の値を求め、バッテリの純抵抗の値として測定することができる。
【００３８】
請求項１４記載の発明は、請求項１１記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記第１及び第２の近似式が二次式である場合、前記濃度分極による電圧降下を前記ピーク値に対応する電圧値から除いた値を、定数及び一次係数を前記第１の二次近似式と等しくした式に代入して二次係数を決定した二次式を前記第１の修正近似式として求めることを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００３９】
上述した請求項１４記載の手順によれば、第１及び第２の近似式が二次式である場合、濃度分極による電圧降下をピーク値に対応する電圧値から除いた値を、定数及び一次係数を前記第１の二次近似式と等しくした式に代入して二次係数を決定した二次式を第１の修正近似式として求めているので、精度良く濃度分極を除いた修正近似式を得ることができる。
【００４０】
請求項１５記載の発明は、請求項１４記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記ピーク値における前記濃度分極による電圧降下を除いた電圧値以外に、ピーク値と０の間の濃度分極による電圧降下を除いた２つの電圧値を求め、該３つの電圧値を利用して係数を決定した二次式を前記第２の修正近似式として求めることを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００４１】
上述した請求項１５記載の手順によれば、ピーク値における濃度分極による電圧降下を除いた電圧値以外に、ピーク値と０の間の濃度分極による電圧降下を除いた２つの電圧値を求め、該３つの電圧値を利用して係数を決定した二次式を第２の修正近似式として求めているので、濃度分極による電圧降下を除いた第２の二次修正近似式を簡単に求めることができる。
【００４２】
請求項１６記載の発明は、請求項１５記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記中間の値を求めるために、前記第１及び第２の修正近似式のピーク値での微分値を使用することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００４３】
上述した請求項１６記載の手順によれば、第１及び第２の修正近似式が共に二次式であるとき、ピーク値での微分値の中間の値を求めるだけでよいので、純抵抗を単純な計算によって測定することができる。
【００４４】
請求項１７記載の発明は、請求項１０記載のバッテリにおける放電時電圧降下成分分離算出方法において、前記第１及び第２の修正近似式と前記算出した純抵抗による電圧降下を表す式との差をとり、前記第１及び第２の近似式の各々に対応する活性化分極のみによる電圧降下の第１及び第２の活性化分極近似式を求め、該求めた活性化分極近似式に任意の電流値を代入して任意の電流値における活性化分極による電圧降下成分を分離して算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出方法に存する。
【００４５】
上述した請求項１７記載の手順によれば、第１及び第２の修正近似式と算出した純抵抗による電圧降下を表す式との差をとり、第１及び第２の近似式の各々に対応する活性化分極のみによる電圧降下の第１及び第２の活性化分極近似式を求め、この求めた活性化分極近似式に任意の電流値を代入して任意の電流値における活性化分極による電圧降下成分を分離して算出しているので、活性化分極のみによる電圧降下が第１及び第２の活性化分極近似式により一般化され、個々の電圧降下を分離して算出しなくて、端子電圧の電圧降下を、濃度分極による電圧降下、純抵抗による電圧降下、及び、活性化分極による電圧降下に分解して算出することができる。
【００４６】
請求項１８記載の発明は、図１の基本構成図に示すように、バッテリから負荷に電力を供給したときバッテリから放電される放電電流とこれに伴って変化する端子電圧との関係を示す放電電流−端子電圧特性において、放電電流の大きさに応じて降下する端子電圧中の電圧降下成分を分離して算出するバッテリにおける放電時電圧降下成分分離算出装置において、前記負荷に、ピーク値まで単調増加した後、ピーク値から定常値まで単調減少する突入電流が流れている期間、前記バッテリの放電電流と該放電電流に対応する端子電圧とを周期的に測定する電流・電圧測定手段２３ａ−１と、該電流・電圧測定手段により測定した放電電流と端子電圧との相関を示す前記増加する突入電流に対する放電電流−端子電圧特性の第１の近似式と前記減少する突入電流に対する放電電流−端子電圧特性の第２の近似式とを求める近似式算出手段２３ａ−２と、該電流・電圧測定手段により求めた前記第１及び第２の近似式の放電電流０である点における前記バッテリの端子電圧の差を求め、該差を前記突入電流が流れたことによって発生した総濃度分極による電圧降下と見なし、該差に基づいて任意の電流値における濃度分極による電圧降下を算出するとともに、該算出した濃度分極による電圧降下を任意の電流値における端子電圧に加算して前記濃度分極以外による電圧降下を算出し、電圧降下成分を濃度分極によるものとそれ以外によるものとに分離して算出する演算手段２３ａ−３とを備えることを特徴とするバッテリにおける放電時電圧降下成分分離算出装置に存する。
【００４７】
上述した請求項１８記載の手順によれば、負荷に、ピーク値まで単調増加した後、ピーク値から定常値まで単調減少する突入電流が流れている期間、バッテリの放電電流とこの放電電流に対応する端子電圧とを電流・電圧測定手段２３ａ−１が周期的に測定し、この測定した放電電流と端子電圧との相関を示す増加する放電電流に対する電流−電圧特性の第１の近似式と減少する放電電流に対する電流−電圧特性の第２の近似式とを近似式算出手段２３ａ−２が求める。そして、演算手段２３ａ−３が、電流・電圧測定手段により求めた第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差に基づいて任意の電流値における濃度分極による電圧降下を算出するとともに、この算出した濃度分極による電圧降下を任意の電流値における端子電圧に加算して濃度分極以外による電圧降下を算出し、電圧降下成分を濃度分極によるものとそれ以外によるものとに分離して算出するようになっている。以上のように、第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差を、突入電流が流れたことによって発生した総濃度分極による電圧降下と見なしているので、この総濃度分極による電圧降下を電流値とその電流値に至る時間とによって按分することで、濃度分極による電圧降下とそれ以外による電圧降下に分離して算出することができる。
【００４８】
請求項１９記載の発明は、請求項１８記載のバッテリにおける放電時電圧降下成分分離算出装置において、前記演算手段は、任意の電流値における濃度分極を、前記突入電流が流れている期間に生じる総濃度分極に対する任意の電流値までの放電電流が流れた期間に生じる濃度分極の比率を前記差に乗じて算出することを特徴とするバッテリにおける放電時電圧降下成分分離算出装置に存する。
【００４９】
上述した請求項１９記載の手順によれば、濃度分極の大きさが電流の大きさとその流れている時間とに比例していることに着目し、演算手段２３ａ−３が、任意の電流値における濃度分極による電圧降下成分を、突入電流が流れている期間に生じる総濃度分極に対する任意の電流値までの放電電流が流れた期間に生じる濃度分極の比率を差に乗じて算出しているので、任意時点での濃度分極による電圧降下を他と分離して算出することができる。
【００５０】
請求項２０記載の発明は、バッテリから車両の負荷に電力を供給したときバッテリから放電される放電電流とこれに伴って変化する端子電圧との関係を示す放電電流−端子電圧特性において、放電電流の大きさに応じて降下する端子電圧中の電圧降下成分を分離して算出するバッテリにおける放電時電圧降下成分分離算出装置において、前記負荷に、ピーク値まで単調増加した後、ピーク値から定常値まで単調減少する突入電流が流れている期間、前記バッテリの放電電流と該放電電流に対応する端子電圧とを周期的に測定する電流・電圧測定手段２３ａ−１と、該電流・電圧測定手段によって測定した放電電流と端子電圧との相関を示す前記増加する突入電流に対する放電電流−端子電圧特性の第１の近似式と前記減少する突入電流に対する放電電流−端子電圧特性の第２の近似式とを求める近似式算出手段２３ａ−２と、該近似式算出手段により求めた前記第１及び第２の近似式の放電電流０である点における前記バッテリの端子電圧の差を求め、該差を前記突入電流が流れたことによって発生した濃度分極による電圧降下と見なし、該差に、前記突入電流が流れている総時間に対する０からピーク値に増加するまでの時間の比率を乗じて突入電流が０からピーク値に増加する期間に生じた濃度分極による電圧降下を算出するとともに、該算出した濃度分極による電圧降下をピーク値における端子電圧に加算して前記濃度分極以外による電圧降下成分を算出し、電圧降下成分を濃度分極によるものとそれ以外によるものとに分離して算出する演算手段２３ａ−３とを備えることを特徴とするバッテリにおける放電時電圧降下成分分離算出装置に存する。
【００５１】
上述した請求項２０記載の手順によれば、請求項１８と同様に、演算手段２３ａ−３が、近似式算出手段２３ａ−２によって求めた第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差に、突入電流が流れている総時間に対する０からピーク値に増加するまでの時間の比率を乗じて突入電流が０からピーク値に増加する期間に生じた濃度分極による電圧降下を算出するとともに、この算出した濃度分極による電圧降下をピーク値における端子電圧に加算して濃度分極以外による電圧降下成分を算出し、電圧降下成分を濃度分極によるものとそれ以外によるものとに分離して算出するようにしている。以上のように、第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差を、突入電流が流れたことによって発生した濃度分極による電圧降下と見なしているので、この電圧降下に突入電流の総時間に対する増加時間の比率を乗じてピーク値における濃度分極による電圧降下を求め、これを端子電圧に加算してピーク値における濃度分極による電圧降下とそれ以外による電圧降下に分離して算出することができる。
【００５２】
【発明の実施の形態】
以下、本発明によるバッテリにおける放電時電圧降下成分分離算出装置を図２を参照して説明する前に、図３〜図９を参照して本発明によるバッテリにおける放電時電圧降下成分分離算出方法を説明する。
【００５３】
ところで、バッテリが例えば車両に搭載された場合、バッテリから電力供給されて動作する車両負荷として、１２Ｖ車、４２Ｖ車、ＥＶ車、ＨＥＶ車には、スタータモータ、モータジェネレータ、走行用モータなどの大電流を必要とする各種の負荷が搭載されている。例えば、スタータモータ又はこれに類する大電流負荷をオンしたとき、負荷には、その駆動開始の初期の段階で突入電流が流れた後、負荷の大きさに応じた定常値の電流が流れるようになる。因みに、負荷がランプである場合には、突入電流に相当するものをラッシュ電流と呼ぶこともある。
【００５４】
スタータモータとして直流モータを使用している場合、界磁コイルに流れる突入電流は、図３に示すように、負荷駆動開始直後の例えば３ミリ秒という短時間内に、ほぼ０から定常電流に比べて何倍も大きなピーク値、例えば５００（Ａ）まで単調増加した後、このピーク値から例えば１５０ミリ秒という短時間内に負荷の大きさに応じた定常値まで単調減少するような流れ方をし、バッテリから放電電流として供給される。したがって、負荷に突入電流が流れる状況で、バッテリの放電電流とこれに対応する端子電圧を測定することによって、０からピーク値に至る広い範囲の電流変化に対する端子電圧の変化を示すバッテリの放電電流（Ｉ）−端子電圧（Ｖ）特性を測定することができる。
【００５５】
そこで、スタータモータをオンしたときに流れる突入電流に相当する模擬的な放電として、０からほぼ２００Ａまで０．２５秒かけて増加し、同じ時間をかけてピーク値から０まで減少する放電を電子負荷を使用してバッテリに行わせ、そのときのバッテリの放電電流と端子電圧とを対にして短い一定周期で測定し、これによって得た測定データ対を横軸に放電電流、縦軸に端子電圧をそれぞれ対応させてプロットして図４に示すグラフを得た。図４のグラフに示す放電電流の増加時と減少時の放電電流−端子電圧特性は、最小二乗法を用いて以下のような二次式に近似できる。
Ｖ＝a1Ｉ2 ＋b1Ｉ＋c1 ……（１）
Ｖ＝a2Ｉ2 ＋b2Ｉ＋c2 ……（２）
なお、図中には、二次の近似式の曲線も重ねて描かれている。
【００５６】
図４中において、電流増加方向の近似曲線の切片と電流減少方向の近似曲線の切片の電圧差は、電流が流れていない０（Ａ）の時の電圧差であるため、純抵抗と活性化分極による電圧降下を含まない、放電によって新たに発生した濃度分極のみによる電圧降下と考えられる。従って、この電圧差は、濃度分極のみによるものであり、この電流０（Ａ）点の濃度分極をＶpolc0 とする。この濃度分極Ｖpolc0 は、突入電流の大きさに電流の流れた時間を乗じて積算したもの、すなわちＡｈ（短時間なので、以下Ａsec で表す）として求められる。
【００５７】
次に、この電流０（Ａ）点の濃度分極Ｖpolc0 を利用して電流ピーク値の濃度分極を算出する方法を説明する。今、電流ピーク値の濃度分極をＶpolcp とすると、Ｖpolcp は次式のように表される。
Ｖpolcp ＝［（電流増加時のＡsec ）／（放電全体のＡsec ）］×Ｖpolc0……（３）
なお、放電全体のＡsec は次式で表される。
放電全体のＡsec ＝（電流増加時のＡsec ＋電流減少時のＡsec ）
【００５８】
一般的には、電流増加時と減少時の電流は直線的に変化すると見なし得るので、簡略的には、Ｖpolc0 を、増加時間と減少時間の総時間Ｔｓを増加と減少に要した時間Ｔｚ及びＴｇで按分することによって、増加時に発生した濃度分極による電圧降下と減少時に発生した濃度分極による電圧降下に分解することができ、以下のように表現できる。
Ｖpolcp ＝［Ｔｚ／Ｔｓ］×Ｖpolc0 ……（３′）
なお、Ｔｚ＝Ｔｓの場合には、Ｖpolcp ＝Ｖpolc0 ／２となる。
【００５９】
また、この求まったピーク値での濃度分極Ｖpolcp に時間ｔｚの間の任意の時点の時間比率を乗じることによって、増加時の任意の時点の任意の電流値での濃度分極による電圧降下も求めることができる。さらに、濃度分極Ｖpolc0 からピーク値での濃度分極Ｖpolcp を差し引いたものは、減少時に発生した濃度分極とみなせるので、これに、時間Ｔｇの間の任意の時点の時間比率を乗じることによって、減少時の任意の時点の任意の電流値での濃度分極による電圧降下も求めることができる。
【００６０】
上述のようにして求めたピーク値における濃度分極Ｖpolcp を式（１）のピーク値における電圧に加算して、図５に示すように、ピーク値における濃度分極を削除する。なお、ピーク値における濃度分極を削除した後の電圧をＶ１とすると、Ｖ１は次式で表される。
Ｖ１＝a1Ｉp2＋b1Ｉp ＋c1＋Ｖpolcp
Ｉp はピーク値における電流値である。
【００６１】
次に、上述のようにして求めたＶ１を利用して次式で表される、図５に示すような純抵抗と活性化分極だけの電圧降下曲線を求める。
Ｖ＝a3Ｉ2 ＋b3Ｉ＋c3 ……（４）
【００６２】
式（１）および（４）で表される特性の初期状態、すなわち、電流が０（Ａ）の点に注目すると、初期状態での分極は等しいので、c3＝c1である。また、電流増加の初期状態から電流は急激に増加するが、濃度分極の反応は遅く、反応がほとんど進行していないとすると、式（１）および（４）の電流が０（Ａ）の点の微分値は等しくなるので、b3＝b1である。従って,c3＝c1 、b3＝b1 を代入することで、式（４）は
Ｖ＝a3Ｉ2 ＋b1Ｉ＋c1 ……（５）
と書き直され、未知数はa3のみとなる。
【００６３】
そこで、式（５）に電流増加のピーク値の座標（Ｉp 、Ｖ１）を代入してa3について整理すると、次式が求められる。
a3＝（Ｖ１−b1Ｉp −c1）／Ｉp2
【００６４】
従って、純抵抗と活性化分極だけの電圧降下曲線の式（４）が式（５）によって決定される。以上によって、任意時点での濃度分極による電圧降下とそれ以外、すなわち、純抵抗と活性化分極による電圧降下とを分離して求めることができるようになる。
【００６５】
以上のように電流増加方向での純抵抗と活性化分極だけの電圧降下曲線の式（５）が求まったところで、式（５）と元の式（１）との差を求めることによって、電流増加方向での濃度分極の大きさを示す、以下のような近似式が得られることになる。
Ｖcz＝（a3−a1）Ｉ2 ……（６ａ）
そして、この式に電流増加時の任意の電流値Ｉn を代入することによって、任意の電流値Ｉn での濃度分極による電圧降下Ｖczn を次式のように算出することができる。
Ｖczn ＝（a3−a1）Ｉn2 ……（６ｂ）
ここで、電流増加方向での活性化分極抵抗Ｒczは、以下のように表され、電流の大きさとともに変化していることが分かる。
Ｒcz＝（a3−a1）Ｉn ……（６ｃ）
【００６６】
一般に、純抵抗は化学反応にて生じるものでないので、バッテリの充電状態（ＳＯＣ）、温度などが変わらなければ一定であるので、１回のスタータモータ作動の間は一定であるといえる。これに対し、活性化分極抵抗は、イオン、電子の受渡しの際の化学反応に伴って生じる抵抗であるので、濃度分極と相互に影響し合うこともあって、活性化分極の電流増加曲線と電流減少曲線は完全に一致しないことから、式（５）は濃度分極を除いた純抵抗と活性化分極の電流増加方向の曲線であるということができる。
【００６７】
続いて、電流減少曲線からの濃度分極の削除の仕方を、以下説明する。純抵抗と活性化分極の電流減少方向の関係式は、電流ピーク値における濃度分極の削除と同様の方法で可能である。
【００６８】
今、ピーク値以外の２点をＡ点およびＢ点とし、各点における濃度分極ＶpolcA 、ＶpolcB を次式のようにして求める。
ＶpolcA ＝［（電流増加時開始からＡ点までのＡsec ）／（放電全体のＡsec ）］×Ｖpolc0 ……（７）
、又は、簡略的には、
ＶpolcA ＝［ピーク点からＡ点までの時間Ｔａ／Ｔｇ］×（Ｖpolc0 −Ｖpolcp ） ……（７′）
ＶpolcB ＝［（電流増加時開始からＢ点までのＡsec ）／（放電全体のＡsec ）］×Ｖpolc0 ……（８）
又は、簡略的には、
ＶpolcB ＝［ピーク点からＢ点までの時間Ｔｂ／Ｔｇ］×（Ｖpolc0 −Ｖpolcp ） ……（８′）
【００６９】
上式（７）および（８）によって、ピーク値以外に濃度分極を削除した２点が求まったら、この２点とピーク値との３点の座標を利用して次式で表される、図６に示すような、純抵抗と活性化分極の電流減少方向曲線が求められる。
Ｖ＝a4Ｉ2 ＋b4Ｉ＋c4 ……（９）
なお、式（９）の係数a4、b4、c4は、２点Ａ及びＢとピーク点の電流値と電圧値とを、式（９）にそれぞれ代入して立てた３点の連立方程式を解くことによって決定できる。なお、c4はc1に等しい値になる。
【００７０】
以上のように電流減少方向での純抵抗と活性化分極だけの電圧降下曲線の式（９）が求まったところで、式（９）と元の式（１）との差を求めることによって、電流減少方向での濃度分極の大きさを示す、以下のような近似式が得られることになる。
Ｖcg＝（a3−a1）Ｉ2 ＋（b4−b1）Ｉ ……（10ａ）
そして、この式に電流減少時の任意の電流値Ｉn を代入することによって、任意の電流値Ｉn での濃度分極による電圧降下Ｖcgn を次式のように算出することができる。
Ｖcgn ＝（a3−a1）Ｉn2＋（b4−b1）Ｉn ……（10ｂ）
ここで、電流減少方向での活性化分極抵抗Ｒcgは、以下のように表され、電流の大きさによって変化していることが分かる。
Ｒcg＝（a3−a1）Ｉn ＋（b4−b1） ……（10ｃ）
【００７１】
以上によって、任意の電流値における濃度分極による電圧降下を一般化して表され、濃度分極以外による電圧降下と分離して算出することができるようになる。
【００７２】
次に、純抵抗の算出の仕方を説明する。上式（５）で表される濃度分極を削除した純抵抗と活性化分極の電流増加方向の曲線と、式（９）で表される同じく濃度分極を削除した純抵抗と活性化分極の電流減少方向の曲線との相違は、活性化分極の相違によるものであるので、活性化分極を除けば純抵抗が求められる。
【００７３】
ところで、活性化分極が互いに等しい値となる両曲線のピーク値に着目し、ピーク値での電流増加の微分値Ｒ１と電流減少の微分値Ｒ２とを次式によって求める。
Ｒ１＝２×a3×Ｉp ×b3 ……（11ａ）
Ｒ２＝２×a4×Ｉp ×b4 ……（11ｂ）
上式によって求められる微分値Ｒ１およびＲ２の差は、一方が活性化分極の増加方向でのピーク値であるのに対し、他方が減少方向でのピーク値であることに基因する。そして、突入電流に相当する模擬的な放電として、０から２００Ａまで０．２５秒かけて増加し、同じ時間をかけてピーク値から０まで減少する放電を電子負荷を使用してバッテリに行わせた場合には、ピーク値近傍での両者の変化率が等しく、両者の中間に純抵抗による電流−電圧特性が存在すると理解できるので、両微分値を加算して２で割ることによって、純抵抗Ｒを次式によって求めることができる。
Ｒ＝（Ｒ１＋Ｒ２）／２ ……（12）
【００７４】
以上は、突入電流に相当する模擬的な放電を電子負荷を使用してバッテリに行わせた場合について説明したが、実車両の場合には、上述したようにスタータモータとして直流モータを使用しているとき、界磁コイルに突入電流が流れている間に電流はピークに達し、クランキングはピークに達した後ピーク電流の半分以下に低下した電流で作動している。従って、電流増加方向は３ミリ秒（ｍｓｅｃ）という短時間で終了していまい、電流増加ピーク値ではほとんど濃度分極が発生しない早い電流の変化であるが、電流減少方向は電流増加方向に比べて１５０ｍｓｅｃという長い時間電流が流れるので、減少方向とはいえ、大きな濃度分極が発生する。ただし、クランキング期間については、突入電流の流れている期間とは異質の現象が生じているので、この期間のバッテリの放電電流と端子電圧については、電流減少方向の電流−電圧特性を決定するためのデータとしては使用しないようにする。
【００７５】
このような状況で、実車両では、図７に示すように、電流増加方向は電流増加開始点とピーク値の２点間を結ぶ直線にて近似することができ、しかもこのピーク値５００（Ａ）での濃度分極の発生は０（Ａ）と近似することも可能である。この場合には、電流増加方向については、ピーク値の微分値としては、電流増加方向の近似直線の傾きを使用することになる。
【００７６】
ただし、このような場合には、電流増加方向の近似直線の傾きと、電流減少方向の二次の近似式のピーク点における接線の傾きとを単純に加算平均することはできない。何故ならば、このような状況では、ピーク点までとそれ以降で、活性化分極の発生度合いが全く異なり、ピーク値近傍での両者の変化率が等しくなるという前提が成立しなくなるからである。
【００７７】
このような場合には、純抵抗を求めるに当たって、濃度分極による電圧降下を除いた第１及び第２の近似式のピーク値に対応する点における単位電流変化当たりの２つの端子電圧変化の値、すなわち、傾きに、突入電流が流れている総時間に占める単調増加期間及び単調減少期間の時間の割合をそれぞれ乗じた上で加算すればよい。すなわち、総時間を単調増加及び単調減少にそれぞれ要した時間で比例按分した按分率を各傾きに乗じた上で加算することになる。このようにすることによって、活性化分極と濃度分極とが相互に影響し合うことを考慮して純抵抗を求めることができる。すなわち、活性化分極は原則電流値に応じた大きさのものが生じるが、その時々の濃度分極量に左右され、原則通りには生じることにならず、濃度分極が小さければ活性化分極も小さくなり、大きければ大きくなる。何れにしても、濃度分極による電圧降下を除いた２つの近似式のピーク値に対応する点における単位電流変化当たりの２つの端子電圧変化の値の中間の値をバッテリの純抵抗の値として測定することができる。このように純抵抗を求めることによって、純抵抗による電圧降下をこれ以外による電圧降下と分離して算出することができる。
【００７８】
上述のように純抵抗Ｒが求まったときには、図６に示すように、ＩＲ電圧降下直線を描くことができ、純抵抗に電流値を乗じることによって、任意の電流値における純抵抗による電圧降下を算出することができる。なお、純抵抗については、上述した方法以外の任意の方法によって求めることもできる。要するに、純抵抗が予めわかっていることによって、活性化分極による電圧降下を求めることができる。
【００７９】
ＩＲ電圧降下が算出できるようになったときには、電流増加方向の濃度分極を除いた上式（５）の近似式とＩＲとの差を求めることによって、電流増加方向での活性化分極の大きさを示す、以下のような近似式が得られることになる。
Ｖkz＝a3Ｉ2 ＋（b1−Ｒ）Ｉ ……（13ａ）
そして、この式に電流増加時の任意の電流値Ｉn を代入することによって、電流増加方向での任意の電流値Ｉn での活性化分極による電圧降下Ｖknを次式のように算出することができる。
Ｖkzn ＝a3Ｉn2＋（b1−Ｒ）Ｉn ……（13ｂ）
ここで、電流増加方向での活性化分極抵抗Ｒkzは、以下のように表され、電流の大きさによって変化していることが分かる。
Ｒkz＝a3Ｉn ＋（b1−Ｒ） ……（13ｃ）
【００８０】
なお、電流減少方向の濃度分極を除いた純抵抗と活性化分極だけの電圧降下曲線の式（９）とＩＲとの差を求めることによって、電流減少方向での活性化分極の大きさを示す式
Ｖkg＝a4Ｉ2 ＋（b4−Ｒ）Ｉ ……（14ａ）
が得られる。そして、この式に電流減少時の任意の電流値Ｉn を代入することによって、電流減少方向の任意の電流値Ｉn での活性化分極による電圧降下Ｖkgを次式のように算出することができる。
Ｖkgn ＝a4Ｉn2＋（b4−Ｒ）Ｉn ……（14ｂ）
ここで、電流減少方向での活性化分極抵抗Ｒkgは、以下のように表される。
Ｒkg＝a4Ｉn ＋（b4−Ｒ） ……（14ｃ）
【００８１】
以上によって、任意の電流値における活性化分極による電圧降下を一般化して表され、活性化分極以外による電圧降下と分離して算出することができるようになる。
【００８２】
また、最近の車両では、モータとしては、マグネットモータなどのＤＣブラッシレスなどの三相入力を必要とする交流モータが使用されることが増えてきている。このようなモータの場合、突入電流はそれ程早く短時間にピーク値に達することがなく、１００ｍｓｅｃほどの時間を要し、電流増加方向においても濃度分極の発生が起こるので、上述した模擬的な放電の場合と同様に、電流増加方向の電流変化曲線は二次近似することが必要になる。
【００８３】
また、活性化分極の電流減少方向の近似をする場合、ピーク値とこれ以外の２点を定める際、図８に示すように、Ｂ点として電流０（Ａ）の点を使用すると、近似式を求める際の計算を簡略化することができる。
【００８４】
さらに、例えば、ピーク電流の１／２程度の電流値に対応する点に濃度分極の削除した点を定めた場合、図９に示すように、この点とピーク値の２点を結ぶ直線に一次近似してもよい。この場合、電流減少方向については、ピーク値の微分値としては、電流減少方向の近似直線の傾きを使用することになるが、二次曲線を使用したものと変わらない、精度のよい純抵抗が求められる。
【００８５】
以上要するに、濃度分極による電圧降下を除いた２つの近似式と元の近似式との差を求めることによって、濃度分極による電圧降下の近似式を求めることができる。また、濃度分極による電圧降下を除いた２つの近似式のピーク値に対応する点における単位電流変化当たりの２つの端子電圧変化の値の中間の値をバッテリの純抵抗の値として測定することができる。さらに、求めた純抵抗によるＩＲ直線式と濃度分極による電圧降下を除いた２つの近似式との差を求めることによって活性化分極による電圧降下の近似式を求めることができる。
【００８６】
そこで、車載バッテリ純抵抗測定方法を、負荷として、増加する放電電流及び減少する放電電流のいずれにおいても濃度分極の発生を伴う突入電流が流れる例えばスタータモータが使用されている場合について具体的に説明する。
【００８７】
負荷が動作されると、バッテリからは定常値を越えて単調増加しピーク値から定常値に単調減少する放電電流が流れる。このときのバッテリの放電電流と端子電圧とを、例えば１００マイクロ秒（μｓｅｃ）の周期にてサンプリングすることで周期的に測定し、バッテリの放電電流と端子電圧との組が多数得られる。
【００８８】
このようにして得られたバッテリの放電電流と端子電圧との組の最新のものを、所定時間分、例えばＲＡＭなどの書換可能な記憶手段としてのメモリに格納、記憶して収集する。メモリに格納、記憶して収集した放電電流と端子電圧との組を用いて、最小二乗法により、端子電圧と放電電流との相関を示す増加する放電電流及び減少する放電電流に対する電流−電圧特性について式（１）及び（２）に示すような２つの二次近似式を求める。次に、この２つの近似式から濃度分極による電圧降下を削除し、濃度分極を含まない修正した二次近似式を求める。
【００８９】
このために、まず、式（１）及び（２）の近似式の電流が流れていない０（Ａ）の時の電圧差を、純抵抗と活性化分極による電圧降下はなく、濃度分極によるものであるとして求める。また、この電圧差を利用して、増加する放電電流についての電流−電圧特性の近似式（１）上の電流ピーク値での濃度分極による電圧降下を求める。このために、濃度分極は、電流の大きさに電流の流れた時間を乗じた電流時間積によって変化していることを利用する。
【００９０】
増加する放電電流についての電流−電圧特性の近似式上の電流ピーク値での濃度分極による電圧降下が求まったら次に、濃度分極の含まない近似式と含む近似式のいずれも定数及び一次係数が等しいとして、含まない近似式の二次係数を定め、増加する放電電流についての電流−電圧特性の近似式について修正した二次近似式（５）を求める。
【００９１】
次に、減少する放電電流に対する電流−電圧特性について近似式（２）から濃度分極の含まない近似式を求める。このために、ピーク値以外に濃度分極を削除した２点を求める。この際に、濃度分極は、電流の大きさに電流の流れた時間を乗じた電流時間積によって変化していることを利用する。そして、ピーク値以外に濃度分極を削除した２点が求まったら、この２点とピーク値との３点の座標を利用して、減少する放電電流についての電流−電圧特性の近似式（２）について修正した二次近似式（９）を求める。
【００９２】
上述のようにして求められた二次近似式（５）及び（９）と元の近似式（１）及び（２）との差をとって、濃度分極近似式（６ａ）及び（14ａ）が求められる。また、純抵抗Ｒを求めることにより、ＩＲ直線式と二次近似式（５）及び（９）との差を取ることによって活性化分極近似式（13ａ）及び（14ａ）が求められる。
【００９３】
なお、純抵抗を求めるためには、上式（５）で表される濃度分極を削除した純抵抗と活性化分極の電流増加方向の修正二次近似式と、式（９）で表される濃度分極を削除した純抵抗と活性化分極の電流減少方向の修正二次近似式は、活性化分極の相違によるものであるので、活性化分極を除けば純抵抗が求められる。このために、両近似式のピーク値に着目し、ピーク値での電流増加の微分値と電流減少の微分値との差は、一方が活性化分極の増加方向であるのに対し、他方が減少方向であることに基因するものであるが、ピーク値近傍での両者の変化率の中間に純抵抗による電流−電圧特性が存在するとし、両微分値に突入電流が流れている総時間に占める単調増加期間及び前記単調減少期間の時間の割合をそれぞれ乗じた上で加算することによって、純抵抗を求める。
【００９４】
例えば、電流増加時間が３ｍｓｅｃ、電流減少時間が１００ｍｓｅｃとし、ピーク値での電流増加の微分値をＲpolk1 、と電流減少の微分値をＲpolk2 とすると、以下のようなようにして純抵抗Ｒを算出することができる。
Ｒ＝Ｒpolk1 ×１００／１０３＋Ｒpolk2 ×３／１０３
【００９５】
上述したようなことを可能にして本発明の車載バッテリ純抵抗測定方法を実施する装置の具体的な実施の形態を、図２に戻って以下説明する。
【００９６】
図２は本発明の車載バッテリにおける放電時電圧降下成分分離算出方法を適用した本発明の一実施形態に係る車載バッテリにおける放電時電圧降下成分分離算出装置の概略構成を一部ブロックにて示す説明図であり、本実施形態の車載バッテリの純抵抗測定装置は、エンジン３に加えてモータジェネレータ５を有するハイブリッド車両に搭載されている。
【００９７】
そして、このハイブリッド車両は、通常時はエンジン３の出力のみをドライブシャフト７からディファレンシャルケース９を介して車輪１１に伝達して走行させ、高負荷時には、バッテリ１３からの電力によりモータジェネレータ５をモータとして機能させて、エンジン３の出力に加えてモータジェネレータ５の出力をドライブシャフト７から車輪１１に伝達し、アシスト走行を行わせるように構成されている。
【００９８】
また、このハイブリッド車両は、減速時や制動時にモータジェネレータ５をジェネレータ（発電機）として機能させ、運動エネルギを電気エネルギに変換してバッテリ１３を充電させるように構成されている。
【００９９】
なお、モータジェネレータ５はさらに、図示しないスタータスイッチのオンに伴うエンジン３の始動時に、エンジン３のフライホイールを強制的に回転させるスタータモータとして用いられるが、その場合にモータジェネレータ５には、短時間に大きな突入電流が流される。スタータスイッチのオンによりモータジェネレータ５によってエンジン３が始動されると、イグニッションキー（図示せず。）の操作解除に伴って、スタータスイッチがオフになってイグニッションスイッチやアクセサリスイッチのオン状態に移行し、これに伴ってバッテリ１３から流れる放電電流は、定常電流に移行する。
【０１００】
話を構成の説明に戻すと、本実施形態の車載バッテリの純抵抗測定装置は、アシスト走行用のモータやスタータモータとして機能するモータジェネレータ５等、電装品に対するバッテリ１３の放電電流Ｉや、ジェネレータとして機能するモータジェネレータ５からのバッテリ１３に対する充電電流を検出する電流センサ１５と、バッテリ１３に並列接続した１Ｍオーム程度の抵抗値を有し、バッテリ１３の端子電圧Ｖを検出する電圧センサ１７とを備えている。
【０１０１】
また、本実施形態の車載バッテリの純抵抗測定装置は、上述した電流センサ１５及び電圧センサ１７の出力がインタフェース回路（以下、「Ｉ／Ｆ」と略記する。）２１におけるＡ／Ｄ変換後に取り込まれるマイクロコンピュータ（以下、「マイコン」と略記する。）２３をさらに備えている。
【０１０２】
そして、前記マイコン２３は、ＣＰＵ２３ａ、ＲＡＭ２３ｂ、及び、ＲＯＭ２３ｃを有しており、このうち、ＣＰＵ２３ａには、ＲＡＭ２３ｂ及びＲＯＭ２３ｃの他、前記Ｉ／Ｆ２１が接続されており、また、上述した図示しないスタータスイッチ、イグニッションスイッチやアクセサリスイッチ、モータジェネレータ５以外の電装品（負荷）のスイッチ等が、さらに接続されている。
【０１０３】
前記ＲＡＭ２３ｂは、各種データ記憶用のデータエリア及び各種処理作業に用いるワークエリアを有しており、前記ＲＯＭ２３ｃには、ＣＰＵ２３ａに各種処理動作を行わせるための制御プログラムが格納されている。
【０１０４】
なお、上述した電流センサ１５及び電圧センサ１７の出力である電流値及び電圧値は、短い周期で高速にサンプリングされてＩ／Ｆ２１を介して、マイコン２３のＣＰＵ２３ａに取り込まれ、取り込まれた電流値及び電圧値は前記ＲＡＭ２３ｂのデータエリア（記憶手段に相当する）に収集され、各種の処理のために使用される。
【０１０５】
次に、前記ＲＯＭ２３ｃに格納された制御プログラムに従いＣＰＵ２３ａが行う処理を、図１０のフローチャートを参照して説明する。
【０１０６】
バッテリ１３からの給電を受けてマイコン２３が起動しプログラムがスタートすると、ＣＰＵ２３ａは、まず初期設定を実行する（ステップＳ１）。
【０１０７】
ステップＳ１の初期設定が済んだならば、次に、ＣＰＵ２３ａは、イグニッション（ＩＧ）スイッチがオンされたか否かを判定し（ステップＳ２）、判定がＹＥＳにならないときには他の処理（ステップＳ３）を行う。なお、このステップＳ３の処理では、５００μｓｅｃのサンプリング周期で放電電流及び端子電圧を測定して収集することも行っており、この処理をステップＳ２の判定がＹＥＳになるまで繰り返す。そして、ＩＧスイッチのオンが検出されたときには（ステップＳ２のＹＥＳ）、急激に変化するスタータモータの駆動時の急激に変化する突入電流を測定することができるように、サンプリング周期を５００μｓｅｃから１００μｓｅｃに短くする（ステップＳ４）。
【０１０８】
その後、電流センサ１５の検出したバッテリ１３の放電電流Ｉと電圧センサ１７の検出したバッテリ１３の端子電圧ＶとのＡ／Ｄ変換値を対にしてＩ／Ｆ２１を介して読み込み、読み込んだ実データをＲＡＭ２３ｂのデータエリアに格納、記憶して収集する実データ収集処理を実行する（ステップＳ５）。
【０１０９】
このステップＳ５において実データ収集処理を行っている過程で、収集した前後の実データの大小関係を比較することによって突入電流のピーク値を検出する（ステップＳ６）。ピーク値が検出されたとき（ステップＳ６のＹＥＳ）には、ピーク値検出からの時間を計時し、所定時間が経過するまで実データの収集を継続し、所定時間経過した時点（ステップＳ７のＹＥＳ）で、ピーク値の前後の所定時間分の実データを保持する（ステップＳ８）とともに、ピーク値を検出してから所定時間後にサンプリング周期を元の５００μｓｅｃに戻す（ステップＳ９）。
【０１１０】
そして、収集保持した所定時間分の実データが分析され、最小二乗法を適用して、電流−電圧特性の二次近似式を求めるのに適当なものであるかどうかが判定される。すなわち、バッテリから、０からピーク値まで単調増加する放電電流とピーク値から定常値まで単調減少する放電電流が流れているかどうかを分析する分析処理を行う（ステップＳ１０）。
【０１１１】
ステップＳ１０における分析の結果、電流−電圧特性の二次近似式を求めるのに適当なものが収集されているとき（ステップＳ１１のＹＥＳ）、増加する放電電流及び減少する放電電流に対する式（１）及び（２）で表される電流−電圧特性の二次近似式を求める近似式算出処理を実行する（ステップＳ１２）。
【０１１２】
ステップＳ１２の二次近似式算出処理によって求まった二次近似式から、上述した方法によって濃度分極近似式、バッテリの純抵抗、及び活性化分極近似式を求めるための演算処理を実行する。そして、求まった濃度分極近似式及び活性化分極近似式に任意の電流値を代入することによって、任意の電流値における濃度分極及び活性化分極による電圧降下を他の電圧降下成分と分離してそれぞれ算出することができる（ステップＳ１３）。なお、この演算処理においては、二次式に濃度分極による電圧降下が含まれている場合、この電圧降下を除いた修正二次近似式を求める修正二次近似式算出処理を行い、この修正二次近似式を用いてバッテリの純抵抗を求めるための演算処理を実行することになり、この場合には、増加する突入電流及び減少する突入電流に対する放電電流−端子電圧特性の２つの修正二次近似式のピーク値での微分値を算出した上で、２つの微分値の中間の値をバッテリの純抵抗として求める演算を行う。そして、この求めたバッテリの純抵抗は種々の目的で使用するため、ＲＡＭ２３ｂのデータエリアに格納されて記憶される（ステップＳ１４）。ステップＳ１４の処理が終了したら、次にステップＳ２の判定がＹＥＳとなるのを待つ。
【０１１３】
この微分値の中間の値を求める方法としては、突入電流の流れ形によって２つの方法がある。
突入電流の増加方向の時間と減少方向の時間とがほぼ等しいときには、２つの微分値の加算平均値を純抵抗として求める演算を行う。
これに対して、突入電流の増加方向の時間と減少方向の時間とが大きく異なるときには、増加する放電電流に対する電流−電圧特性の修正二次近似式のピーク値での微分値に、放電電流の総時間に占める増加する放電電流の流れた時間の比率を乗じたものと、減少する放電電流に対する電流−電圧特性の２つの修正二次近似式のピーク値での微分値に、放電電流の総時間に占める減少する放電電流の流れた時間の比率を乗じたものとを加算した加算値を純抵抗として求める演算を行う。
いずれの方法で純抵抗を求めた場合にも、バッテリの純抵抗は２つの微分値の中間の値として求められる。
【０１１４】
また、図１０のフローチャートに示した例では、第１及び第２の近似式が共に二次近似式としているが、第１の近似式が一次近似式であるときには、修正近似式を求める処理は当然に不要になる。そして、この場合には、一次式の傾きを微分値に代えて利用することになる。
【０１１５】
また、本実施形態の車載バッテリの純抵抗測定装置ではフローチャートにおけるステップＳ５が請求項中の電流・電圧測定手段に対する処理となっており、ステップＳ１２が請求項中の近似式算出手段に対応する処理となっており、ステップＳ１３が請求項中の演算手段に対応する処理となっている。
【０１１６】
次に、上述のように構成された本実施形態の車載バッテリの純抵抗測定装置の動作（作用）について説明する。
【０１１７】
まず、スタータモータの駆動開始に伴いバッテリ１３が放電を行っている状態で、スタータモータに定常値を越えて単調増加しピーク値から定常値に単調減少する突入電流が流れたときのバッテリの端子電圧と放電電流とが周期的に測定される。
【０１１８】
また、本実施形態の車載バッテリの純抵抗測定装置では、周期的に測定されたピーク値の前後の所定時間分の実データを、ＲＡＭ２３ｂのデータエリアに格納、記憶して収集され、収集された放電電流Ｉと端子電圧Ｖとの所定時間分の実データは分析され、最小二乗法を適用して、電流−電圧特性の二次の近似式を求めるのに適当なものであるかどうかが判定される。すなわち、バッテリから定常値を越えて単調増加しピーク値から定常値以下に単調減少する放電電流が流れているかどうかが分析される。
【０１１９】
このため、電流−電圧特性の二次の近似式を求めるのに適当なものが収集されるまで、近似式算出処理が行われることがなく、近似式算出処理も、既に収集した所定時間分の実データを用いて行われればよいので、端子電圧と放電電流との周期的な測定に同期して処理を行わなくてもよく、早い処理速度を必要としない。
【０１２０】
なお、上述した実施の形態では、スタータモータが駆動開始されるときの放電電流に含まれる突入電流についてのみ注目して本発明を実施しているが、大きさこそ異なるもののスタータモータと同様に駆動開始時に突入電流の流れるスタータモータ以外の負荷にも等しく適用することができる。ただし、この場合には、ＩＧスイッチの代わりに、負荷駆動開始時点を負荷スイッチのオン操作を捕らえて、ステップＳ４の処理を行うことになり、それ以外の処理は図１０のフローチャートと実質的に同じ処理を行うことでよい。
【０１２１】
なお、上述のように端子電圧の電圧降下成分を分離して算出し、知ることができることによって、各成分の変化によって車載バッテリの各種の状態を推定するために利用することができるようになるが、車載以外のバッテリにも適用できることは、具体的な適用例を挙げて説明するまでもなく明らかである。
【０１２２】
【発明の効果】
以上説明したように、請求項１記載の発明によれば、負荷に突入電流が流れている期間、バッテリの放電電流とこの放電電流に対応する端子電圧とを周期的に測定し、この測定の結果得られる放電電流と端子電圧との相関を示す増加する放電電流に対する放電電流−端子電圧特性の第１の近似式と、減少する放電電流に対する電流−電圧特性の第２の近似式とを求め、第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差を、突入電流が流れたことによって発生した総濃度分極による電圧降下と見なしているので、バッテリを通常状態で使用している際でも、バッテリから負荷に電力を供給したときバッテリから放電される放電電流とこれに伴って変化する端子電圧との関係を示すＩ−Ｖ特性において、濃度分極による電圧降下以外による電圧降下も分離して算出するために利用することができるバッテリにおける放電時電圧降下成分算出方法を提供することができる。
【０１２３】
請求項２又は１８記載の発明によれば、負荷に突入電流が流れている期間、バッテリの放電電流とこの放電電流に対応する端子電圧とを周期的に測定し、この測定の結果得られる放電電流と端子電圧との相関を示す増加する放電電流に対する放電電流−端子電圧特性の第１の近似式と、減少する放電電流に対する電流−電圧特性の第２の近似式とを求め、第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差を、突入電流が流れたことによって発生した総濃度分極による電圧降下と見なしているので、この差に基づいて任意の電流値における濃度分極による電圧降下を算出して濃度分極による電圧降下とそれ以外による電圧降下に分離して算出できるバッテリにおける放電時電圧降下成分分離算出方法又は装置を提供することができる。
【０１２４】
上述した請求項３又は１９記載の発明によれば、濃度分極の大きさが電流の大きさとその流れている時間とに比例していることに着目し、任意の電流値における濃度分極による電圧降下を、突入電流が流れている期間に生じる総濃度分極に対する任意の電流値までの放電電流が流れた期間に生じる濃度分極の比率を差に乗じて算出しているので、任意時点での濃度分極による電圧降下を他と分離して算出しているので、任意時点での濃度分極による電圧降下を他と分離して算出することができるバッテリにおける放電時電圧降下成分分離算出方法又は装置を提供することができる。
【０１２５】
上述した請求項４記載の発明によれば、突入電流がピーク値まで増加する期間に生じる濃度分極の総濃度分極に対する比率を上記差に乗じてピーク値における濃度分極による電圧降下を算出して、突入電流のピーク値での、端子電圧の電圧降下成分を濃度分極によるものとそれ以外のものに分離して算出できるので、突入電流のピーク値での端子電圧から濃度分極による電圧降下を削除するために利用することができるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１２６】
上述した請求項５又は２０記載の発明によれば、第１及び第２の近似式の放電電流０である点におけるバッテリの端子電圧の差を、突入電流が流れたことによって発生した濃度分極による電圧降下と見なしているので、この電圧降下に突入電流の総時間に対する増加時間の比率を乗じてピーク値における濃度分極による電圧降下を求め、これを端子電圧に加算してピーク値における濃度分極による電圧降下とそれ以外による電圧降下に分離して算出できるので、バッテリを通常状態で使用している際、すなわち、車両使用中でも、車載バッテリから車両の負荷に電力を供給したときバッテリから放電される放電電流とこれに伴って変化する端子電圧との関係を示すＩ−Ｖ特性において、放電電流の大きさに応じて降下する端子電圧中の電圧降下成分を分離して算出するバッテリにおける放電時電圧降下成分分離算出方法又は装置を提供することができる。
【０１２７】
上述した請求項６記載の発明によれば、突入電流の任意の電流値での端子電圧から濃度分極による電圧降下を削除するために利用することができるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１２８】
上述した請求項７記載の発明によれば、突入電流の減少期間の任意の電流値での端子電圧から濃度分極による電圧降下を削除するために利用することができるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１２９】
上述した請求項８記載の発明によれば、濃度分極以外による電圧降下成分が、純抵抗及び活性化分極による電圧降下成分であって、端子電圧の電圧降下を濃度分極による電圧降下と純抵抗及び活性化分極による電圧降下とに分離して算出できるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１３０】
上述した請求項９記載の発明によれば、濃度分極のみによる電圧降下が第１及び第２の濃度成分近似式により一般化され、個々の電圧降下を分離して算出しなくてもよいバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１３１】
上述した請求項１０記載の発明によれば、端子電圧の電圧降下を、濃度分極による電圧降下、純抵抗による電圧降下、及び、活性化分極による電圧降下に分解して算出することができるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１３２】
上述した請求項１１記載の発明によれば、濃度分極による電圧降下以外の電圧降下から純抵抗による電圧降下を分離して算出することができるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１３３】
上述した請求項１２記載の発明によれば、ピーク値に対応する点での活性化分極の変化が等しくなる場合には、第１及び第２の近似式のピーク値に対応する点における微分値を加算して２で割ることで、バッテリの純抵抗を測定し、簡単に純抵抗による電圧降下成分を分離して算出できるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１３４】
上述した請求項１３記載の発明によれば、活性化分極と濃度分極とが相互に影響し合うことを考慮した中間の値を求め、バッテリの純抵抗の値として測定し、精度良く純抵抗による電圧降下成分を分離して算出できるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１３５】
上述した請求項１４記載の発明によれば、精度良く濃度分極を除いた修正近似式を得ることができ、精度良く電流増加時の電圧降下成分を分離して算出できるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１３６】
上述した請求項１５記載の発明によれば、濃度分極による電圧降下を除いた第２の二次修正近似式を簡単に求めることができ、精度良く電流減少時の電圧降下成分を分離して算出できるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１３７】
上述した請求項１６記載の発明によれば、第１及び第２の修正近似式が共に二次式であるとき、ピーク値での微分値の中間の値を求めるだけの単純な計算によって純抵抗を測定し、簡単に純抵抗による電圧降下成分を分離して算出できるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【０１３８】
上述した請求項１７記載の発明によれば、活性化分極のみによる電圧降下が第１及び第２の活性化成分近似式により一般化され、個々の電圧降下を分離して算出しなくて、端子電圧の電圧降下を、濃度分極による電圧降下、純抵抗による電圧降下、及び、活性化分極による電圧降下に分解して算出できるバッテリにおける放電時電圧降下成分分離算出方法を提供することができる。
【図面の簡単な説明】
【図１】本発明のバッテリにおける放電時電圧降下成分分離算出装置の基本構成を示すブロック図である。
【図２】本発明のバッテリにおける放電時電圧降下成分算出方法を適用した本発明の一実施形態に係る車載バッテリにおける放電時電圧降下成分分離算出装置の概略構成を一部ブロックにて示す説明図である。
【図３】スタータモータ駆動開始時の突入電流を伴う放電電流の一例を示すグラフである。
【図４】二次近似式で表したＩ−Ｖ特性の一例を示すグラフである。
【図５】増加方向の近似式からの濃度分極の除き方の一例を説明するためのグラフである。
【図６】減少方向の近似式からの濃度分極の除き方の一例を説明するためのグラフである。
【図７】増加方向を一次近似式で表したＩ−Ｖ特性の一例を示すグラフである。
【図８】減少方向の近似式からの濃度分極の除き方の他の例を説明するためのグラフである。
【図９】減少方向の近似式からの濃度分極の除き方の別の例を説明するためのグラフである。
【図１０】図２中のマイコンが放電時電圧降下成分分離算出のため予め定めたプログラムに従って行う処理を示すフローチャートである。
【図１１】放電に伴う端子電圧の電圧降下の内訳を一般的に示すＩ−Ｖ特性を示すグラフである。
【符号の説明】
２３ａ−１電流・電圧測定手段（ＣＰＵ）
２３ａ−２近似式算出手段（ＣＰＵ）
２３ａ−３演算手段（ＣＰＵ）[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for calculating a voltage drop component in a discharge current-terminal voltage (IV) characteristic in a battery, and a voltage drop component separation calculation method during discharge in which a voltage drop component is calculated by calculating the calculated voltage drop component. More specifically, the discharge current-terminal voltage (IV) indicating the relationship between the discharge current discharged from the battery when the power is supplied from the battery to the load and the terminal voltage that changes accordingly. In the characteristics, the voltage drop component calculation method for the battery that calculates the voltage drop component in the terminal voltage that drops according to the magnitude of the discharge current, and the voltage drop during discharge in the battery that calculates the voltage drop component separately The present invention relates to a component separation calculation method and apparatus.
[0002]
[Prior art]
In general, a battery can be used repeatedly within the range of its charge capacity by performing charging that covers the discharge current, but of course, when an unexpected situation such as overdischarge or insufficient electrolyte occurs. Even if these situations do not occur, the dischargeable capacity, which is the amount of power that can be supplied to the load by discharge, rapidly decreases when used over a long period of time and changes over time. For this reason, in a state where the dischargeable capacity is reduced due to aging, even if a discharge exceeding the charging occurs for a short period of time, for example, in the case of a battery mounted on a vehicle, the starter motor is started after the engine is stopped. This can lead to a situation where the engine cannot be restarted.
[0003]
Incidentally, it is known that when a new product is compared with a battery that has changed over time, the net resistance of the battery that has changed over time compared to a new product is increased. Therefore, it is considered to measure the pure resistance of the battery as a guide for battery replacement at the time of periodic inspection. This is because by knowing the pure resistance, the degree of deterioration can be determined in consideration of the ratio between the pure resistance and the polarization resistance component. Also, if the pure resistance is known, it can be used to estimate the open circuit voltage of the battery.
[0004]
Generally, when current is discharged from a battery, a drop occurs in the terminal voltage of the battery. This voltage drop is due to the internal impedance (synthetic resistance) of the battery, but IR loss (pure resistance, ie, voltage drop due to ohmic resistance) due to the structure of the battery and polarization due to chemical reaction. It can be divided into voltage drops due to resistance components (activation polarization, concentration polarization). When the battery discharge current-terminal voltage (IV) characteristics are obtained, as shown in FIG. 11, the voltage drop due to IR loss is constant because the pure resistance maintains a constant value if the battery condition is the same. It is known to show a change that increases linearly with the magnitude of the current.
[0005]
[Problems to be solved by the invention]
However, the voltage drop due to the polarization resistance component does not maintain a constant value of polarization, and varies depending on the magnitude of the discharge current and the discharge time. For this reason, it is known that various states of the battery cannot be directly estimated from the IV characteristics including the polarization resistance component. Therefore, conventionally, the voltage drop component in the terminal voltage that drops according to the magnitude of the discharge current in the IV characteristics, such as measuring only the pure resistance for which the polarization resistance component was calculated, is calculated separately. Technology to do is needed.
[0006]
In addition, there is a need for a battery that can be used effectively when it is in use.
[0007]
Therefore, in view of the above-described situation, the present invention provides an IV characteristic indicating a relationship between a discharge current discharged from a battery and a terminal voltage that varies with the discharge current when power is supplied from the battery in use to the load. It is an object of the present invention to provide a discharging voltage drop component calculation method in a battery that calculates a voltage drop component in a terminal voltage that drops according to the magnitude of the discharge current.
[0008]
The invention also provides a method and apparatus for calculating a voltage drop component separation during discharge in a battery that separates and calculates a voltage drop component due to concentration polarization in a terminal voltage that drops according to the magnitude of the discharge current in the IV characteristic. The issue is to provide.
[0009]
[Means for Solving the Problems]
In order to solve the above-mentioned problems, the present invention relates to a discharge voltage drop component calculation method for a battery, and the discharge voltage drop component separation calculation method for a battery according to claims 2 to 17. The present invention according to claims 18 and 20 relates to a voltage drop component separation / calculation device for discharging in a battery.
[0010]
According to the first aspect of the present invention, in the discharge current-terminal voltage characteristic indicating the relationship between the discharge current discharged from the battery when power is supplied from the battery to the load and the terminal voltage that changes with the discharge current, the magnitude of the discharge current is large. In the method for calculating a voltage drop component during discharge in a battery that calculates a voltage drop component in a terminal voltage that drops according to the inrush current, an inrush current that monotonously increases from the peak value to a steady value after being monotonously increased from the peak value to the peak value. During the period when the battery is flowing, the discharge current of the battery and the terminal voltage corresponding to the discharge current are periodically measured, and the discharge current with respect to the increased inrush current indicating the correlation between the measured discharge current and the terminal voltage − A first approximate expression of the terminal voltage characteristic and a second approximate expression of the discharge current-terminal voltage characteristic with respect to the decreasing inrush current are obtained, and the discharge current 0 of the first approximate expression is obtained. A difference between the terminal voltage of the battery at a point and the terminal voltage of the battery at a point where the discharge current of the second approximate expression is 0, and the difference is the total concentration polarization generated by the flow of the inrush current. The present invention resides in a method for calculating a voltage drop component during discharge in a battery, characterized in that it is regarded as a voltage drop due to.
[0011]
According to the above-described procedure according to the first aspect, the battery discharge current and the discharge current correspond to a period during which an inrush current monotonously increasing from the peak value to the steady value flows after the load monotonously increases to the peak value. A first approximate expression of the discharge current-terminal voltage characteristic with respect to an increasing inrush current showing the correlation between the discharge current and the terminal voltage by periodically measuring the terminal voltage and the discharge current-terminal voltage with respect to the decreasing inrush current. A second approximate expression of characteristics is obtained.
[0012]
Next, assuming that the voltage other than the voltage drop due to concentration polarization is 0 at the terminal voltage of the battery at the point where the discharge current is 0 in the first and second approximate expressions, the inrush current flows due to the difference between them. Since the voltage drop due to the total concentration polarization generated by the above is calculated, the voltage drop due to the concentration polarization can be separately calculated by using the voltage drop due to the concentration polarization.
[0013]
According to the second aspect of the present invention, in the discharge current-terminal voltage characteristic indicating the relationship between the discharge current discharged from the battery when the power is supplied from the battery to the load and the terminal voltage that changes with the discharge current, the magnitude of the discharge current is large. In the battery voltage drop component separation calculation method for a battery that separates and calculates a voltage drop component in a terminal voltage that drops according to the voltage, the load monotonically increases from a peak value to a steady value after monotonously increasing to a peak value. Periodically measuring the discharge current of the battery and the terminal voltage corresponding to the discharge current during a period of decreasing inrush current, and the increasing inrush current indicating the correlation between the measured discharge current and the terminal voltage A first approximate expression of the discharge current-terminal voltage characteristic with respect to and a second approximate expression of the discharge current-terminal voltage characteristic with respect to the decreasing rush current are obtained, and the first and second A difference in terminal voltage of the battery at a point where the discharge current is 0 in a similar equation is obtained, and the difference is regarded as a voltage drop due to total concentration polarization caused by the flow of the inrush current, and an arbitrary current is determined based on the difference. The voltage drop due to the concentration polarization in the value is calculated, and the voltage drop due to the concentration polarization is calculated by adding the voltage drop due to the concentration polarization to the terminal voltage at an arbitrary current value. The present invention resides in a method for separately calculating a voltage drop component at the time of discharging in a battery, wherein the calculation is performed separately for the battery and the other battery.
[0014]
According to the above-described procedure according to the second aspect, the discharge current of the battery and the discharge current correspond to the period during which an inrush current that monotonously increases from the peak value to the steady value flows after the load monotonously increases to the peak value. A first approximate expression of the discharge current-terminal voltage characteristic with respect to an increasing inrush current showing the correlation between the discharge current and the terminal voltage by periodically measuring the terminal voltage and the discharge current-terminal voltage with respect to the decreasing inrush current. A second approximate expression of characteristics is obtained.
[0015]
Next, the voltage drop due to the concentration polarization at an arbitrary current value is calculated based on the difference between the terminal voltages of the battery at the point where the discharge current is 0 in the first and second approximate expressions, and the voltage due to the calculated concentration polarization is calculated. The voltage drop due to other than concentration polarization is calculated by adding the drop to the terminal voltage at an arbitrary current value, and the voltage drop component is calculated separately from that due to concentration polarization and other than that due to concentration polarization. As described above, the difference between the terminal voltages of the battery at the point where the discharge current is 0 in the first and second approximate expressions is regarded as a voltage drop due to the total concentration polarization caused by the inrush current flowing. By dividing the voltage drop due to the total concentration polarization according to the current value and the time to reach the current value, the voltage drop can be separated into the voltage drop due to the concentration polarization and the voltage drop due to the other.
[0016]
According to a third aspect of the present invention, in the method for calculating the voltage drop component separation during discharge in the battery according to the second aspect, the voltage drop due to the concentration polarization at an arbitrary current value is the total concentration polarization generated during the period during which the inrush current flows. In the battery voltage drop component separation calculation method for a battery, the ratio is calculated by multiplying the difference by the ratio of concentration polarization generated during a period in which a discharge current up to an arbitrary current value flows.
[0017]
According to the above-described procedure of claim 3, paying attention to the fact that the magnitude of concentration polarization is proportional to the magnitude of current and the time during which it flows, the voltage drop due to concentration polarization at an arbitrary current value is Since the ratio is calculated by multiplying the ratio of the concentration polarization that occurs during the period when the discharge current flows up to an arbitrary current value with respect to the total concentration polarization that occurs during the inrush current flow, the voltage due to the concentration polarization at any time The descent can be calculated separately from the others.
[0018]
According to a fourth aspect of the present invention, in the battery voltage drop component separation calculation method for the battery according to the second or third aspect, the arbitrary current value is a peak value of a rush current that monotonously increases, and the rush current is a peak value. A method for calculating a voltage drop component separation during discharge in a battery, wherein a voltage drop due to the concentration polarization at the peak value is calculated by multiplying the ratio by the ratio of the concentration polarization generated during a period of increasing to a value with respect to the total concentration polarization, to the peak value Exist.
[0019]
According to the above-described procedure according to claim 4, the voltage drop due to the concentration polarization at the peak value is calculated by multiplying the above ratio by the ratio of the concentration polarization generated during the period in which the inrush current increases to the peak value to the total concentration polarization. Therefore, the voltage drop component of the terminal voltage at the peak value of the inrush current can be calculated separately for those due to concentration polarization and those other than that.
[0020]
The invention according to claim 5 is a discharge current-terminal voltage characteristic showing a relationship between a discharge current discharged from the battery when power is supplied from the battery to the load and a terminal voltage which changes in accordance with the discharge current. In the battery voltage drop component separation calculation method for a battery that separates and calculates a voltage drop component in a terminal voltage that drops according to the voltage, the load monotonically increases from a peak value to a steady value after monotonously increasing to a peak value. Periodically measuring the discharge current of the battery and the terminal voltage corresponding to the discharge current during a period of decreasing inrush current, and the increasing inrush current indicating the correlation between the measured discharge current and the terminal voltage A first approximate expression of the discharge current-terminal voltage characteristic with respect to and a second approximate expression of the discharge current-terminal voltage characteristic with respect to the decreasing rush current are obtained, and the first and second A difference in terminal voltage of the battery at a point where the discharge current is 0 in a similar formula is obtained, and the difference is regarded as a voltage drop due to concentration polarization generated by the flow of the inrush current, and the inrush current flows in the difference. The voltage drop due to the concentration polarization that occurred during the period when the inrush current increases to the peak value is calculated by multiplying the ratio of the peak value to the peak value with respect to the total time, and the voltage drop due to the calculated concentration polarization is peaked. The voltage drop component due to other than the concentration polarization is calculated by adding to the terminal voltage in the value, and the voltage drop component is calculated separately by the concentration polarization and other than that due to the concentration polarization. It exists in the descent component separation calculation method.
[0021]
According to the procedure described in claim 5, the inrush current flows in the difference between the terminal voltages of the battery at the point where the discharge current is zero in the first and second approximate expressions obtained in the same manner as in claim 1. Calculate the voltage drop due to the concentration polarization that occurred during the period when the inrush current increases to the peak value by multiplying the ratio of the peak value with respect to the total time to increase to the peak value, and calculate the voltage drop due to the calculated concentration polarization to the peak value. The voltage drop component due to other than concentration polarization is calculated by adding to the terminal voltage at, and the voltage drop component is calculated separately for those due to concentration polarization and those due to other than that. As described above, since the difference in the terminal voltage of the battery at the point where the discharge current is 0 in the first and second approximate expressions is regarded as a voltage drop due to concentration polarization caused by the inrush current flowing, Multiply the voltage drop by the ratio of the increase time to the total time of the inrush current to obtain the voltage drop due to the concentration polarization at the peak value, and add this to the terminal voltage to add the voltage drop due to the concentration polarization at the peak value and the voltage drop due to other than that. It can be calculated separately.
[0022]
According to a sixth aspect of the present invention, in the discharge voltage drop component separation calculation method for the battery according to the fifth aspect, an arbitrary period of time during which the inrush current increases to a peak value due to a voltage drop due to concentration polarization at the calculated peak value. The voltage drop due to concentration polarization at any current value at which the inrush current increases to the peak value is calculated by multiplying the ratio of the time until the current value to the time at which the inrush current increases to the peak value. The present invention resides in a method for calculating a voltage drop component separation during discharge in a battery.
[0023]
According to the above-described procedure according to claim 6, due to the voltage drop due to the concentration polarization at the peak value, the time until the inrush current increases to the peak value up to an arbitrary current value in the period in which the inrush current increases to the peak value. Multiply the ratio to calculate the voltage drop due to concentration polarization at any current value at which the inrush current increases to the peak value, so the voltage drop due to concentration polarization at any current value during the inrush current increase period and other voltages It can be calculated separately from the descent.
[0024]
According to a seventh aspect of the present invention, in the battery voltage drop component separation calculation method for the battery according to the sixth aspect, a voltage drop due to concentration polarization that occurs during a period in which the calculated inrush current increases to a peak value is calculated from the difference. By subtracting, a voltage drop due to concentration polarization that occurs during a period in which the inrush current decreases from the peak value to 0 is calculated, and the inrush current decreases from the peak value to a voltage drop due to the concentration polarization that occurs during the calculated decrease period. By multiplying the ratio of the time until the arbitrary current value during the decreasing period to the time when the inrush current decreases from the peak value to 0, the voltage drop due to the concentration polarization at the arbitrary current value at which the inrush current decreases from the peak value is obtained. The present invention resides in a method for calculating a voltage drop component separation at the time of discharging in a battery.
[0025]
According to the above-described procedure according to claim 7, the voltage drop due to the concentration polarization generated during the increase period is subtracted from the voltage difference at the discharge current 0 that is the voltage drop during the period when the inrush current flows. The voltage drop due to the concentration polarization in the period is calculated, and the ratio of the time until the inrush current from the peak value to zero is reduced to the voltage drop due to the concentration polarization generated during the calculated decrease period. Is used to calculate the voltage drop due to concentration polarization at any current value during the decrease period, so that the voltage drop due to concentration polarization at any current value during the inrush current decrease period is separated from other voltage drops. Can be calculated.
[0026]
According to an eighth aspect of the present invention, in the battery voltage drop component separation calculation method for a battery according to any one of the second to seventh aspects, a voltage drop component other than the concentration polarization is a voltage drop due to pure resistance and activation polarization. The present invention resides in a voltage drop component separation calculation method during discharge in a battery, which is a component.
[0027]
According to the above-described procedure of claim 8, the voltage drop component due to other than concentration polarization is a voltage drop component due to pure resistance and activation polarization, and the voltage drop of the terminal voltage is divided into the voltage drop due to concentration polarization, the pure resistance, and It can be calculated separately from the voltage drop due to activation polarization.
[0028]
According to a ninth aspect of the present invention, in the battery voltage drop component separation calculation method for a battery according to any one of the second to eighth aspects, the voltage drop caused by the calculated concentration polarization is used, and the first and second voltage drop components are used. First and second modified approximate expressions corresponding to each of the first and second approximate expressions representing the voltage drop due to other than concentration polarization are obtained by excluding the voltage drop due to concentration polarization from the approximate expression, and the obtained first The first and second voltage drop due to only the concentration polarization corresponding to each of the first and second approximate expressions is obtained by taking the difference between the first and second approximate expressions and the second modified approximate expression, respectively. And calculating a voltage drop component due to concentration polarization at an arbitrary current value by substituting an arbitrary current value into the calculated concentration component approximate expression. Voltage drop component separation calculation method It resides in.
[0029]
According to the procedure described in claim 9, the voltage drop due to the concentration polarization at an arbitrary current value is used, and the voltage drop due to other than the concentration polarization is excluded from the first and second approximate expressions by excluding the voltage drop due to the concentration polarization. First and second modified approximate expressions corresponding to the first and second approximate expressions to be expressed are obtained, and a difference between the obtained first and second modified approximate expressions and the first and second approximate expressions is obtained. And the first and second concentration component approximate expressions of the voltage drop due to only the concentration polarization corresponding to each of the first and second approximate expressions are obtained, and an arbitrary current value is obtained from the obtained concentration component approximate expression. By substituting and calculating the voltage drop component due to the concentration polarization at an arbitrary current value, the voltage drop due to the concentration polarization alone is generalized by the first and second concentration component approximation formulas, and the individual voltage drops are separated. Therefore, it is not necessary to calculate.
[0030]
According to a tenth aspect of the present invention, in the discharge voltage drop component separation calculation method for the battery according to the ninth aspect, a difference between the first and second modified approximate expressions and an expression representing a voltage drop due to a pure resistance obtained in advance. To obtain first and second activation polarization approximations of the voltage drop due to only the activation polarization corresponding to each of the first and second approximations, and the obtained activation polarization The present invention resides in a voltage drop component separation calculation method at the time of discharging in a battery, wherein an arbitrary current value is substituted into an approximate expression and a voltage drop component due to activation polarization at an arbitrary current value is separated and calculated.
[0031]
According to the procedure described in claim 10, the difference between the first and second modified approximate expressions excluding the voltage drop due to the concentration polarization and the expression representing the voltage drop due to the pure resistance obtained in advance is obtained. First and second activation polarization approximation expressions for voltage drop due to only the activation polarization corresponding to each of the second approximation expressions are obtained, and an arbitrary current value is substituted into the obtained activation polarization approximation expression. Since the voltage drop component due to activation polarization at any current value is calculated separately, the voltage drop of the terminal voltage is broken down into voltage drop due to concentration polarization, voltage drop due to pure resistance, and voltage drop due to activation polarization. Can be calculated.
[0032]
The invention according to claim 11 is the method for calculating the voltage drop component separation during discharge in the battery according to any one of claims 2 to 7, wherein the first and second voltage drop due to the calculated concentration polarization is used. First and second modified approximate expressions corresponding to each of the first and second approximate expressions representing the voltage drop due to other than concentration polarization are obtained by excluding the voltage drop due to concentration polarization from the approximate expression, and the obtained first And an intermediate value of two terminal voltage changes per unit current change at a point corresponding to the peak value of the second modified approximate expression is calculated as a value of the pure resistance of the battery, and the calculated value of the pure resistance A method for calculating a voltage drop component separation during discharge in a battery is characterized in that a voltage drop due to a pure resistance is calculated by multiplying the current value by a current value.
[0033]
According to the above-described procedure according to claim 11, the voltage drop due to the concentration polarization is used, and the first and second approximate expressions are used to remove the voltage drop due to the concentration polarization and express the voltage drop due to other than the concentration polarization. The first and second modified approximate expressions corresponding to the first and second approximate expressions are obtained, and two per unit current change at the points corresponding to the peak values of the obtained first and second modified approximate expressions are obtained. The intermediate value of the terminal voltage change value is calculated as the value of the pure resistance of the battery, and the voltage drop due to the pure resistance is calculated by multiplying the calculated pure resistance value by the current value. It can be calculated by separating the voltage drop due to the pure resistance from the voltage drop.
[0034]
According to a twelfth aspect of the present invention, in the discharge voltage drop component separation calculation method for the battery according to the eleventh aspect, the intermediate value is calculated using the first and second approximate expressions excluding the voltage drop due to the concentration polarization. The present invention resides in a method for calculating a voltage drop component separation during discharge in a battery, wherein the value of two terminal voltage changes per unit current change at a point corresponding to the peak value is obtained by averaging.
[0035]
According to the above-described procedure of claim 12, the two terminal voltages per unit current change at the point corresponding to the peak value of the first and second approximate expressions excluding the voltage drop due to the concentration polarization. Since the value of the change is obtained by averaging, if the change in activation polarization at the point corresponding to the peak value becomes equal, the differentiation at the point corresponding to the peak value of the first and second approximate expressions By adding the values and dividing by 2, the pure resistance of the battery can be measured.
[0036]
According to a thirteenth aspect of the present invention, in the battery voltage drop component separation calculation method for the battery according to the eleventh aspect, the intermediate value is calculated using the first and second approximate expressions excluding the voltage drop due to the concentration polarization. The value of two terminal voltage changes per unit current change at the point corresponding to the peak value was multiplied by the ratio of the time of the monotonically increasing period and the monotonically decreasing period to the total time during which the inrush current flows. The present invention resides in a method for calculating a voltage drop component separation during discharge in a battery, which is obtained by adding the above.
[0037]
According to the above-described procedure according to claim 13, two terminal voltages per unit current change at a point corresponding to the peak value of the first and second approximate expressions excluding the voltage drop due to concentration polarization. Since the change value is obtained by multiplying the ratio of the time of the monotonically increasing period and the monotonically decreasing period to the total time during which the inrush current flows, the activation polarization and the concentration polarization are mutually determined. It is possible to obtain an intermediate value in consideration of influencing each other and measure the value as a pure resistance value of the battery.
[0038]
According to a fourteenth aspect of the present invention, in the discharge voltage drop component separation calculation method for the battery according to the eleventh aspect, when the first and second approximate expressions are quadratic expressions, the voltage drop due to the concentration polarization is A secondary expression in which a secondary coefficient is determined by substituting a value obtained by removing a voltage value corresponding to a peak value into an expression in which a constant and a primary coefficient are equal to the first secondary approximation is used as the first modified approximation. The present invention resides in a method for calculating a voltage drop component separation at the time of discharging in a battery, which is obtained as an equation.
[0039]
According to the above-described procedure according to claim 14, when the first and second approximate expressions are quadratic expressions, the value obtained by removing the voltage drop due to the concentration polarization from the voltage value corresponding to the peak value is obtained as a constant and a first order. Since the quadratic formula obtained by substituting the coefficient into the formula equal to the first quadratic approximate expression to determine the quadratic coefficient is obtained as the first corrected approximate formula, the corrected approximate formula excluding the concentration polarization with high accuracy is obtained. Can be obtained.
[0040]
According to a fifteenth aspect of the present invention, in the battery voltage drop component separation calculation method for the battery according to the fourteenth aspect, in addition to the voltage value excluding the voltage drop due to the concentration polarization at the peak value, the peak value is between zero and zero. During discharge in a battery, two voltage values excluding a voltage drop due to concentration polarization are obtained, and a quadratic expression in which a coefficient is determined using the three voltage values is obtained as the second modified approximate expression. It exists in the voltage drop component separation calculation method.
[0041]
According to the procedure of claim 15 described above, in addition to the voltage value excluding the voltage drop due to the concentration polarization at the peak value, two voltage values excluding the voltage drop due to the concentration polarization between the peak value and 0 are obtained, Since the quadratic expression in which the coefficient is determined using the three voltage values is obtained as the second correction approximate expression, the second quadratic correction approximate expression excluding the voltage drop due to concentration polarization can be easily obtained. Can do.
[0042]
According to a sixteenth aspect of the present invention, in the battery voltage drop component separation calculation method for the battery according to the fifteenth aspect, in order to obtain the intermediate value, a differential at a peak value of the first and second modified approximate expressions. The present invention resides in a method for calculating a voltage drop component separation at the time of discharging in a battery characterized by using a value.
[0043]
According to the procedure described in claim 16, when the first and second modified approximate expressions are both quadratic expressions, it is only necessary to obtain an intermediate value of the differential value at the peak value. It can be measured by simple calculations.
[0044]
The invention according to claim 17 is the invention according to claim 1. 0 In the method for calculating the voltage drop component separation during discharge in the mounted battery, the difference between the first and second modified approximate expressions and the expression representing the calculated voltage drop due to the pure resistance is calculated, and the first and second approximations are performed. First and second activation polarization approximations of voltage drop due only to activation polarization corresponding to each of the equations are obtained, and the obtained activations polarization The present invention resides in a voltage drop component separation calculation method at the time of discharging in a battery, wherein an arbitrary current value is substituted into an approximate expression and a voltage drop component due to activation polarization at an arbitrary current value is separated and calculated.
[0045]
According to the above-described procedure according to claim 17, a difference between the first and second modified approximate expressions and the expression representing the calculated voltage drop due to the pure resistance is taken and corresponds to each of the first and second approximate expressions. The first and second activation polarization approximation equations for the voltage drop due to the activation polarization alone are obtained, and the obtained activation is obtained. polarization By substituting an arbitrary current value into the approximate expression and calculating a voltage drop component due to activation polarization at an arbitrary current value, the voltage drop due to only activation polarization is the first and second activations. polarization It is generalized by an approximate expression, and the voltage drop of the terminal voltage is decomposed into a voltage drop due to concentration polarization, a voltage drop due to pure resistance, and a voltage drop due to activation polarization without calculating individual voltage drops separately. Can be calculated.
[0046]
According to the eighteenth aspect of the present invention, as shown in the basic configuration diagram of FIG. 1, when electric power is supplied from the battery to the load, the discharge indicates the relationship between the discharge current discharged from the battery and the terminal voltage that changes accordingly. In a current-terminal voltage characteristic, in a battery voltage drop component separation calculation device for discharging in a battery that separates and calculates a voltage drop component in a terminal voltage that drops according to the magnitude of a discharge current, the load is monotonously up to a peak value. After the increase, the current / voltage measuring means 23a-1 for periodically measuring the discharge current of the battery and the terminal voltage corresponding to the discharge current during a period when the inrush current monotonously decreasing from the peak value to the steady value flows. And a first approximate expression of the discharge current-terminal voltage characteristic with respect to the increasing inrush current indicating the correlation between the discharge current measured by the current / voltage measuring means and the terminal voltage, and the Approximation expression calculating means 23a-2 for obtaining a second approximate expression of the discharge current-terminal voltage characteristics with respect to a small inrush current, and the discharge currents of the first and second approximate expressions obtained by the current / voltage measuring means. A difference between the terminal voltages of the battery at a point of 0 is obtained, the difference is regarded as a voltage drop due to the total concentration polarization generated by the flow of the inrush current, and the concentration polarization at an arbitrary current value is determined based on the difference. The voltage drop is calculated, and the voltage drop due to the concentration polarization is added to the terminal voltage at an arbitrary current value to calculate the voltage drop due to other than the concentration polarization, and the voltage drop component depends on the concentration polarization and otherwise A battery voltage drop component separation and calculation device for discharging in a battery, characterized in that it comprises a calculation means 23a-3 for calculation separately.
[0047]
According to the above-described procedure according to claim 18, the load current corresponds to the discharge current of the battery and the discharge current during a period in which the inrush current monotonously increases from the peak value to the steady value flows after the load monotonously increases to the peak value. The current / voltage measuring means 23a-1 periodically measures the terminal voltage to be measured, and the first approximate expression and decrease of the current-voltage characteristic with respect to the increasing discharge current indicating the correlation between the measured discharge current and the terminal voltage. The approximate expression calculation unit 23a-2 obtains a second approximate expression of current-voltage characteristics with respect to the discharge current to be generated. Then, the calculation means 23a-3 is based on the concentration polarization at an arbitrary current value based on the difference in the terminal voltage of the battery at the point where the discharge current is 0 in the first and second approximate expressions obtained by the current / voltage measurement means. The voltage drop is calculated, and the voltage drop due to the concentration polarization is added to the terminal voltage at an arbitrary current value to calculate the voltage drop due to other than the concentration polarization, and the voltage drop component is caused by the concentration polarization and others They are calculated separately. As described above, the difference between the terminal voltages of the battery at the point where the discharge current is 0 in the first and second approximate expressions is regarded as a voltage drop due to the total concentration polarization caused by the inrush current flowing. By dividing the voltage drop due to the total concentration polarization according to the current value and the time to reach the current value, the voltage drop can be separated into the voltage drop due to the concentration polarization and the voltage drop due to the other.
[0048]
According to a nineteenth aspect of the present invention, in the battery according to the eighteenth aspect, the voltage drop component separation calculation at the time of discharging is performed. apparatus In the above, the calculation means calculates the concentration polarization at an arbitrary current value, and the ratio of the concentration polarization generated during a period when the discharge current flows up to an arbitrary current value to the total concentration polarization generated during the period when the inrush current flows. The present invention resides in a voltage drop component separation calculation device for discharging in a battery, wherein the calculation is performed by multiplying the difference.
[0049]
According to the above-described procedure of claim 19, paying attention to the fact that the magnitude of the concentration polarization is proportional to the magnitude of the current and the time during which the current flows, The voltage drop component due to concentration polarization is calculated by multiplying the difference by the ratio of concentration polarization that occurs during the period when the discharge current flows up to an arbitrary current value with respect to the total concentration polarization that occurs during the period when the inrush current flows. The voltage drop due to concentration polarization at an arbitrary time can be calculated separately from others.
[0050]
The invention according to claim 20 is a discharge current-terminal voltage characteristic showing a relationship between a discharge current discharged from the battery when power is supplied from the battery to a load of the vehicle and a terminal voltage which changes in accordance with the discharge current. In the battery voltage drop component separation calculation device for discharging in a battery that separates and calculates the voltage drop component in the terminal voltage that drops according to the magnitude of the load, the load monotonically increases to the peak value, and then the steady value from the peak value Current / voltage measuring means 23a-1 for periodically measuring the discharge current of the battery and the terminal voltage corresponding to the discharge current during the period when the rush current that monotonously decreases until the current / voltage measurement means The first approximate expression of the discharge current-terminal voltage characteristic for the increasing inrush current showing the correlation between the measured discharge current and the terminal voltage and the decreasing inrush current. The approximate expression calculating means 23a-2 for obtaining the second approximate expression of the discharge current-terminal voltage characteristics, and the discharge current 0 in the first and second approximate expressions obtained by the approximate expression calculating means. The difference between the terminal voltages of the battery is obtained, the difference is regarded as a voltage drop due to concentration polarization caused by the flow of the inrush current, and the difference increases from 0 to the peak value with respect to the total time during which the inrush current flows. The voltage drop due to the concentration polarization that occurred during the period when the inrush current increases from 0 to the peak value by multiplying by the ratio of the time until the calculation is performed, and the calculated voltage drop due to the concentration polarization is added to the terminal voltage at the peak value. And calculating means 23a-3 for calculating a voltage drop component other than the concentration polarization and calculating the voltage drop component separately for the concentration polarization and for the other. It consists in the discharge time of a voltage drop component separation calculating device in a battery according to claim.
[0051]
According to the above-described procedure of the twentieth aspect, similarly to the twentieth aspect, the calculating means 23a-3 is the discharge current 0 of the first and second approximate expressions obtained by the approximate expression calculating means 23a-2. Concentration polarization generated during the period when the inrush current increases from 0 to the peak value by multiplying the difference in the terminal voltage of the battery at the point by the ratio of the time until the peak value increases from 0 to the total time during which the inrush current flows The voltage drop due to concentration polarization is calculated, and the voltage drop due to concentration polarization is added to the terminal voltage at the peak value to calculate the voltage drop component due to other than concentration polarization. They are calculated separately. As described above, since the difference in the terminal voltage of the battery at the point where the discharge current is 0 in the first and second approximate expressions is regarded as a voltage drop due to concentration polarization caused by the inrush current flowing, Multiply the voltage drop by the ratio of the increase time to the total time of the inrush current to obtain the voltage drop due to the concentration polarization at the peak value, and add this to the terminal voltage to add the voltage drop due to the concentration polarization at the peak value and the voltage drop due to other than that. It can be calculated separately.
[0052]
DETAILED DESCRIPTION OF THE INVENTION
Before describing a voltage drop component separation calculation apparatus for a battery according to the present invention with reference to FIG. 2, a voltage drop component separation calculation method for a battery according to the present invention will be described with reference to FIGS. explain.
[0053]
By the way, when a battery is mounted on a vehicle, for example, a 12V vehicle, a 42V vehicle, an EV vehicle, or an HEV vehicle has a large load such as a starter motor, a motor generator, or a traveling motor. Various loads that require current are installed. For example, when a starter motor or a similar large current load is turned on, an inrush current flows through the load at an early stage of driving, and then a steady-state current corresponding to the size of the load flows. Become. Incidentally, when the load is a lamp, the one corresponding to the inrush current may be called a rush current.
[0054]
When a DC motor is used as the starter motor, the inrush current flowing in the field coil is, as shown in FIG. 3, compared with a steady current from approximately 0 within a short time of, for example, 3 milliseconds immediately after the start of load driving. After a monotonically increasing peak value, for example, 500 (A), the flow is such that the peak value monotonously decreases from this peak value to a steady value according to the load within a short time of, for example, 150 milliseconds. And supplied as a discharge current from the battery. Therefore, by measuring the battery discharge current and the corresponding terminal voltage in a situation where an inrush current flows through the load, the battery discharge current showing the change in the terminal voltage with respect to a wide range of current changes from 0 to the peak value. (I)-terminal voltage (V) characteristics can be measured.
[0055]
Therefore, as a simulation discharge corresponding to the inrush current that flows when the starter motor is turned on, an electric discharge that increases from 0 to approximately 200 A over 0.25 seconds and decreases from the peak value to 0 over the same time is an electron. The load is used for the battery, and the discharge current of the battery and the terminal voltage at that time are measured in a short constant cycle, and the measurement data pair obtained by this is the discharge current on the horizontal axis and the terminal on the vertical axis. The voltages are plotted in correspondence with each other to obtain a graph shown in FIG. The discharge current-terminal voltage characteristics when the discharge current increases and decreases as shown in the graph of FIG. 4 can be approximated by the following quadratic expression using the least square method.
V = a1I2 + b1I + c1 (1)
V = a2I2 + b2I + c2 (2)
In the drawing, a curve of a quadratic approximate expression is also drawn.
[0056]
In FIG. 4, the voltage difference between the intercept of the approximate curve in the current increasing direction and the intercept of the approximate curve in the current decreasing direction is the voltage difference at 0 (A) when no current flows. This is considered to be a voltage drop only due to concentration polarization newly generated by discharge, which does not include a voltage drop due to polarization. Therefore, this voltage difference is only due to the concentration polarization, and the concentration polarization at the current 0 (A) point is assumed to be Vpolc0. The concentration polarization Vpolc0 is obtained by multiplying the magnitude of the inrush current by the time during which the current flows, ie, Ah (because it is a short time, it will be expressed as Asec hereinafter).
[0057]
Next, a method for calculating the concentration polarization of the current peak value using the concentration polarization Vpolc0 at the current 0 (A) point will be described. Now, assuming that the concentration polarization of the current peak value is Vpolcp, Vpolcp is expressed by the following equation.
Vpolcp = [(Asec when current increases) / (Asec of the entire discharge)] × Vpolc0 (3)
Note that Asec of the entire discharge is expressed by the following equation.
Asec of overall discharge = (Asec when current increases + Asec when current decreases)
[0058]
In general, since the current at the time of increase and decrease can be considered to change linearly, for simplicity, Vpolc0 is set to the time Tz required to increase and decrease the total time Ts of the increase time and the decrease time. By dividing by Tg, it can be divided into a voltage drop due to concentration polarization occurring at the time of increase and a voltage drop due to concentration polarization occurring at the time of decrease, which can be expressed as follows.
Vpolcp = [Tz / Ts] × Vpolc0 (3 ′)
When Tz = Ts, Vpolcp = Vpolc0 / 2.
[0059]
Further, by multiplying the concentration polarization Vpolcp at the obtained peak value by the time ratio at an arbitrary time point during the time tz, a voltage drop due to the concentration polarization at an arbitrary current value at an arbitrary time point when increasing is obtained. Can do. Further, the value obtained by subtracting the concentration polarization Vpolcp at the peak value from the concentration polarization Vpolc0 can be regarded as the concentration polarization generated at the time of decrease. Therefore, by multiplying this by the time ratio at an arbitrary point in time Tg, A voltage drop due to concentration polarization at an arbitrary current value at an arbitrary point in time can also be obtained.
[0060]
The concentration polarization Vpolcp at the peak value obtained as described above is added to the voltage at the peak value of Equation (1), and the concentration polarization at the peak value is deleted as shown in FIG. Note that V1 is expressed by the following equation, where V1 is the voltage after removing the concentration polarization at the peak value.
V1 = a1Ip2 + b1Ip + c1 + Vpolcp
Ip is the current value at the peak value.
[0061]
Next, using V1 obtained as described above, a voltage drop curve of only pure resistance and activation polarization as shown in FIG.
V = a3I2 + b3I + c3 (4)
[0062]
When attention is paid to the initial state of the characteristics represented by the equations (1) and (4), that is, the point where the current is 0 (A), the polarization in the initial state is equal, so c3 = c1. In addition, although the current increases rapidly from the initial state of the current increase, if the reaction of concentration polarization is slow and the reaction hardly progresses, the currents of the formulas (1) and (4) are points of 0 (A). Since the differential values of are equal, b3 = b1. Therefore, by substituting c3 = c1 and b3 = b1, equation (4) becomes
V = a3I2 + b1I + c1 (5)
And the unknown is only a3.
[0063]
Therefore, when the coordinates (Ip, V1) of the peak value of current increase are substituted into equation (5) and arranged for a3, the following equation is obtained.
a3 = (V1-b1Ip-c1) / Ip2
[0064]
Therefore, equation (4) of the voltage drop curve with only pure resistance and activation polarization is determined by equation (5). As described above, the voltage drop due to the concentration polarization at an arbitrary time point and other than that, that is, the pure resistance and the voltage drop due to the activation polarization can be obtained separately.
[0065]
As described above, when the formula (5) of the voltage drop curve of only the pure resistance and the activation polarization in the current increasing direction is obtained, the difference between the formula (5) and the original formula (1) is obtained to obtain the current The following approximate expression indicating the magnitude of concentration polarization in the increasing direction is obtained.
Vcz = (a3−a1) I2 (6a)
Then, by substituting an arbitrary current value In at the time of current increase into this equation, a voltage drop Vczn due to concentration polarization at an arbitrary current value In can be calculated as follows.
Vczn = (a3-a1) In2 (6b)
Here, the activation polarization resistance Rcz in the direction of current increase is expressed as follows, and it can be seen that it varies with the magnitude of the current.
Rcz = (a3−a1) In (6c)
[0066]
In general, since pure resistance is not caused by a chemical reaction, it is constant unless the state of charge (SOC), temperature, etc. of the battery changes, so it can be said that it is constant during one starter motor operation. On the other hand, the activation polarization resistance is a resistance caused by a chemical reaction at the time of delivery of ions and electrons. Therefore, the activation polarization resistance may interact with the concentration polarization, and the current increase curve of the activation polarization Since the current decrease curves do not coincide completely, it can be said that the equation (5) is a curve in the current increasing direction of the pure resistance and activation polarization excluding concentration polarization.
[0067]
Next, how to remove concentration polarization from the current decrease curve will be described below. The relational expression between the pure resistance and the activation polarization current decreasing direction can be obtained by the same method as the deletion of the concentration polarization at the current peak value.
[0068]
Now, two points other than the peak value are set as point A and point B, and concentration polarizations VpolcA and VpolcB at each point are obtained as follows.
VpolcA = [(Asec from start of current increase to point A) / (Asec of the entire discharge)] × Vpolc0 (7)
Or, for simplicity,
VpolcA = [time Ta / Tg from peak point to point A] × (Vpolc0−Vpolcp) (7 ′)
VpolcB = [(Asec from start to B point when current increases) / (Asec of the entire discharge)] × Vpolc0 (8)
Or simply:
VpolcB = [time Tb / Tg from peak point to B point] × (Vpolc0−Vpolcp) (8 ′)
[0069]
When two points from which concentration polarization is deleted in addition to the peak value are obtained by the above formulas (7) and (8), the three points of the two points and the peak value are used to express the following formula: As shown in FIG. 6, a current decreasing direction curve of pure resistance and activation polarization is obtained.
V = a4I2 + b4I + c4 (9)
The coefficients a4, b4, and c4 in Equation (9) solve a three-point simultaneous equation obtained by substituting the current values and voltage values of the two points A and B and the peak point into Equation (9), respectively. Can be determined. Note that c4 is equal to c1.
[0070]
As described above, when the equation (9) of the voltage drop curve with only the pure resistance and the activation polarization in the current decreasing direction is obtained, the difference between the equation (9) and the original equation (1) is obtained to obtain the current. The following approximate expression showing the magnitude of concentration polarization in the decreasing direction is obtained.
Vcg = (a3-a1) I2 + (b4-b1) I (10a)
Then, by substituting an arbitrary current value In when the current is reduced into this equation, the voltage drop Vcgn due to the concentration polarization at the arbitrary current value In can be calculated as the following equation.
Vcgn = (a3-a1) In2 + (b4-b1) In (10b)
Here, the activation polarization resistance Rcg in the current decreasing direction is expressed as follows, and it can be seen that it varies depending on the magnitude of the current.
Rcg = (a3-a1) In + (b4-b1) (10c)
[0071]
As described above, the voltage drop due to concentration polarization at an arbitrary current value is generalized and can be calculated separately from the voltage drop due to other than concentration polarization.
[0072]
Next, how to calculate the pure resistance will be described. The pure resistance from which the concentration polarization represented by the above formula (5) is deleted and the curve of the current increase direction of the activation polarization, and the pure resistance from which the concentration polarization is deleted and the current of the activation polarization represented by the formula (9). Since the difference from the curve in the decreasing direction is due to the difference in activation polarization, pure resistance is required except for activation polarization.
[0073]
By the way, paying attention to the peak values of both curves where the activation polarizations are equal to each other, the differential value R1 of the current increase and the differential value R2 of the current decrease at the peak value are obtained by the following equations.
R1 = 2 × a3 × Ip × b3 (11a)
R2 = 2 × a4 × Ip × b4 (11b)
The difference between the differential values R1 and R2 obtained by the above equation is based on the fact that one is the peak value in the increasing direction of the activation polarization while the other is the peak value in the decreasing direction. As a simulated discharge corresponding to the inrush current, the battery is discharged using an electronic load, increasing from 0 to 200 A over 0.25 seconds and decreasing from the peak value to 0 over the same time. In this case, it can be understood that the rate of change of both of them in the vicinity of the peak value is equal, and that there is a current-voltage characteristic due to the pure resistance in the middle of the two. R can be obtained by the following equation.
R = (R1 + R2) / 2 (12)
[0074]
The above describes the case where the battery is subjected to a simulated discharge corresponding to the inrush current using an electronic load. However, in the case of an actual vehicle, a DC motor is used as the starter motor as described above. When the inrush current flows through the field coil, the current reaches a peak, and the cranking operates at a current that has dropped to less than half of the peak current after reaching the peak. Therefore, the current increase direction does not end in a short time of 3 milliseconds (msec), and the current increase peak value is a rapid current change that hardly causes concentration polarization, but the current decrease direction is compared with the current increase direction. Since a current flows for a long time of 150 msec, a large concentration polarization occurs although it is in a decreasing direction. However, since a phenomenon different from the period during which the inrush current flows occurs in the cranking period, the current-voltage characteristics in the current decreasing direction are determined for the battery discharge current and the terminal voltage during this period. Do not use it as data.
[0075]
In such a situation, in the actual vehicle, as shown in FIG. 7, the current increasing direction can be approximated by a straight line connecting the current increasing start point and the peak value, and the peak value 500 (A The occurrence of concentration polarization at) can be approximated to 0 (A). In this case, for the current increasing direction, the slope of the approximate straight line in the current increasing direction is used as the differential value of the peak value.
[0076]
However, in such a case, the slope of the approximate straight line in the current increasing direction and the slope of the tangent at the peak point of the quadratic approximate expression in the current decreasing direction cannot be simply averaged. This is because in such a situation, the degree of occurrence of activation polarization is completely different up to and after the peak point, and the assumption that the rate of change of both in the vicinity of the peak value is not satisfied.
[0077]
In such a case, in determining the pure resistance, two terminal voltage change values per unit current change at a point corresponding to the peak values of the first and second approximate expressions excluding the voltage drop due to concentration polarization, That is, the slope may be added after multiplying the ratio of the time of the monotonically increasing period and the monotonically decreasing period in the total time during which the inrush current flows. In other words, the total time is proportionally divided by the time required for monotonous increase and monotonous decrease, and the slope is multiplied by each slope and added. By doing so, the pure resistance can be obtained in consideration of the fact that the activation polarization and the concentration polarization influence each other. In other words, the activation polarization has a magnitude corresponding to the current value in principle, but it depends on the amount of concentration polarization at that time and does not occur in principle. If the concentration polarization is small, the activation polarization is small. The bigger it is, the bigger it becomes. In any case, the intermediate value of the two terminal voltage changes per unit current change at the point corresponding to the peak values of the two approximate expressions excluding the voltage drop due to concentration polarization is measured as the value of the battery pure resistance. can do. Thus, by calculating | requiring a pure resistance, the voltage drop by a pure resistance can be calculated separately from the voltage drop by others.
[0078]
When the pure resistance R is obtained as described above, an IR voltage drop straight line can be drawn as shown in FIG. 6, and by multiplying the pure resistance by the current value, the voltage drop due to the pure resistance at an arbitrary current value can be obtained. Can be calculated. In addition, about pure resistance, it can also obtain | require by arbitrary methods other than the method mentioned above. In short, since the pure resistance is known in advance, a voltage drop due to activation polarization can be obtained.
[0079]
When the IR voltage drop can be calculated, the magnitude of the activation polarization in the current increasing direction is obtained by obtaining the difference between the approximate expression of the above equation (5) excluding the concentration polarization in the current increasing direction and the IR. An approximate expression such as that shown below is obtained.
Vkz = a3I2 + (b1-R) I (13a)
Then, by substituting an arbitrary current value In at the time of increasing current into this equation, a voltage drop Vkn due to activation polarization at an arbitrary current value In in the direction of increasing current can be calculated as follows. .
Vkzn = a3In2 + (b1-R) In (13b)
Here, the activation polarization resistance Rkz in the direction of increasing current is expressed as follows, and it can be seen that it varies depending on the magnitude of the current.
Rkz = a3In + (b1-R) (13c)
[0080]
The magnitude of the activation polarization in the current decreasing direction is shown by obtaining the difference between the IR and the voltage drop curve equation (9) with only the pure resistance and the activation polarization excluding the concentration polarization in the current decreasing direction. formula
Vkg = a4I2 + (b4-R) I (14a)
Is obtained. Then, by substituting an arbitrary current value In at the time of current reduction into this equation, a voltage drop Vkg due to activation polarization at an arbitrary current value In in the current decreasing direction can be calculated as follows.
Vkgn = a4In2 + (b4-R) In (14b)
Here, the activation polarization resistance Rkg in the current decreasing direction is expressed as follows.
Rkg = a4In + (b4-R) (14c)
[0081]
As described above, the voltage drop due to the activation polarization at an arbitrary current value is generalized and can be calculated separately from the voltage drop due to other than the activation polarization.
[0082]
In recent vehicles, an AC motor requiring a three-phase input such as a DC brushless motor such as a magnet motor is increasingly used as a motor. In the case of such a motor, the inrush current does not reach the peak value in such a short time, it takes about 100 msec, and concentration polarization occurs in the direction of increasing current. As in the case of, the current change curve in the direction of current increase needs to be quadratic approximated.
[0083]
In addition, when approximating the current decreasing direction of activation polarization, when the peak value and the other two points are determined, as shown in FIG. Can be simplified.
[0084]
Further, for example, when a point where concentration polarization is deleted is determined at a point corresponding to a current value of about ½ of the peak current, as shown in FIG. 9, a primary line is formed on a straight line connecting this point and the two points of the peak value. You may approximate. In this case, for the current decrease direction, the slope of the approximate straight line in the current decrease direction is used as the differential value of the peak value. However, the accurate pure resistance is the same as that using the quadratic curve. Desired.
[0085]
In short, by calculating the difference between the two approximate expressions excluding the voltage drop due to concentration polarization and the original approximate expression, the approximate expression of voltage drop due to concentration polarization can be determined. In addition, an intermediate value between two terminal voltage changes per unit current change at a point corresponding to the peak values of the two approximate expressions excluding the voltage drop due to concentration polarization can be measured as the value of the pure resistance of the battery. it can. Furthermore, an approximate expression of the voltage drop due to activation polarization can be obtained by obtaining the difference between the obtained IR linear expression based on the pure resistance and two approximate expressions excluding the voltage drop due to concentration polarization.
[0086]
Therefore, the in-vehicle battery pure resistance measurement method will be specifically described in the case where, for example, a starter motor is used, in which an inrush current accompanied by generation of concentration polarization occurs in any of an increasing discharge current and a decreasing discharge current as a load. To do.
[0087]
When the load is operated, a discharge current flows from the battery that monotonously increases beyond the steady value and monotonously decreases from the peak value to the steady value. The battery discharge current and terminal voltage at this time are periodically measured, for example, by sampling at a period of 100 microseconds (μsec), and a large number of sets of battery discharge current and terminal voltage are obtained.
[0088]
The latest set of the battery discharge current and terminal voltage obtained in this way is stored, stored and collected in a memory as a rewritable storage means such as a RAM for a predetermined time. Current-voltage characteristics for increasing and decreasing discharge currents showing correlation between terminal voltage and discharge current by least square method using a set of discharge current and terminal voltage stored in memory, stored and collected Two quadratic approximation equations as shown in equations (1) and (2) are obtained. Next, a voltage drop due to concentration polarization is deleted from these two approximate equations, and a modified quadratic approximate equation not including concentration polarization is obtained.
[0089]
For this purpose, first, the voltage difference at 0 (A) when the current of the approximate expression of equations (1) and (2) does not flow is caused by concentration polarization without a voltage drop due to pure resistance and activation polarization. Asking. Further, using this voltage difference, a voltage drop due to concentration polarization at the current peak value in the approximate expression (1) of the current-voltage characteristic for the increasing discharge current is obtained. For this purpose, the concentration polarization uses the fact that it changes by the current-time product obtained by multiplying the magnitude of the current by the time when the current flows.
[0090]
Once the voltage drop due to the concentration polarization at the current peak value on the approximate expression of the current-voltage characteristic for the increasing discharge current is obtained, the constant and the first order coefficient of both the approximate expression not including the concentration polarization and the approximate expression including the concentration polarization are next. A quadratic coefficient of an approximate expression not included is determined as being equal, and a quadratic approximate expression (5) obtained by correcting the approximate expression of the current-voltage characteristic for the increasing discharge current is obtained.
[0091]
Next, an approximate expression that does not include concentration polarization is obtained from the approximate expression (2) for the current-voltage characteristics with respect to the decreasing discharge current. For this purpose, two points other than the peak value are obtained by deleting the concentration polarization. At this time, the concentration polarization uses the fact that it changes by the current-time product obtained by multiplying the current magnitude by the time when the current flows. Then, when two points from which the concentration polarization is deleted are obtained in addition to the peak value, the approximate expression (2) of the current-voltage characteristic for the decreasing discharge current is obtained using the coordinates of the three points of the two points and the peak value. A quadratic approximate expression (9) corrected for is obtained.
[0092]
Taking the difference between the quadratic approximate expressions (5) and (9) obtained as described above and the original approximate expressions (1) and (2), the concentration polarization approximate expressions (6a) and (14a) are obtained. Desired. Further, by obtaining the pure resistance R, the activation polarization approximations (13a) and (14a) are obtained by taking the difference between the IR linear equation and the quadratic approximation equations (5) and (9).
[0093]
In order to obtain the pure resistance, a modified quadratic approximate expression in the current increasing direction of the pure resistance and activation polarization obtained by deleting the concentration polarization represented by the above formula (5) and the formula (9) are used. Since the modified quadratic approximate expression in the current decreasing direction of the pure resistance from which the concentration polarization is deleted and the activation polarization is due to the difference in the activation polarization, the pure resistance is obtained except for the activation polarization. For this reason, paying attention to the peak values of both approximate equations, the difference between the differential value of the current increase and the differential value of the current decrease at the peak value is that one is the increasing direction of activation polarization, while the other is Although it is based on the decreasing direction, the current-voltage characteristic due to the pure resistance exists in the middle of the rate of change of both in the vicinity of the peak value, and the total time during which the inrush current flows in both differential values. The net resistance is obtained by multiplying the monotonically increasing period and the ratio of the monotonically decreasing period, and adding them together.
[0094]
For example, assuming that the current increase time is 3 msec and the current decrease time is 100 msec, the differential value of the current increase at the peak value is Rpolk1, and the differential value of the current decrease is Rpolk2, the pure resistance R is calculated as follows. can do.
R = Rpolk1 × 100/103 + Rpolk2 × 3/103
[0095]
A specific embodiment of the apparatus that enables the above-described method and implements the vehicle battery pure resistance measuring method of the present invention will be described below with reference to FIG.
[0096]
FIG. 2 is a partial block diagram illustrating a schematic configuration of a discharge voltage drop component separation calculation apparatus for an in-vehicle battery according to an embodiment of the present invention to which the discharge voltage drop component separation calculation method for the vehicle battery of the present invention is applied. As shown in the figure, the on-vehicle battery pure resistance measuring device of this embodiment is mounted on a hybrid vehicle having a motor generator 5 in addition to the engine 3.
[0097]
In this hybrid vehicle, normally, only the output of the engine 3 is transmitted from the drive shaft 7 to the wheels 11 through the differential case 9 and travels. When the load is high, the motor generator 5 is driven by the electric power from the battery 13. In addition to the output of the engine 3, the output of the motor generator 5 is transmitted from the drive shaft 7 to the wheels 11 to perform assist traveling.
[0098]
In addition, this hybrid vehicle is configured to cause the motor generator 5 to function as a generator (generator) during deceleration or braking and to convert the kinetic energy into electric energy to charge the battery 13.
[0099]
The motor generator 5 is further used as a starter motor that forcibly rotates the flywheel of the engine 3 when the engine 3 is started when a starter switch (not shown) is turned on. A large inrush current flows in time. When the engine 3 is started by the motor generator 5 by turning on the starter switch, the starter switch is turned off and the ignition switch and the accessory switch are turned on with the release of the operation of an ignition key (not shown). Accordingly, the discharge current flowing from the battery 13 shifts to a steady current.
[0100]
Returning to the description of the configuration, the on-vehicle battery pure resistance measuring device of the present embodiment is configured such that the discharge current I of the battery 13 with respect to the electrical components, such as the motor generator 5 functioning as an assist running motor and a starter motor, and the generator A current sensor 15 that detects a charging current for the battery 13 from the motor generator 5 that functions as a voltage sensor 17 that has a resistance value of about 1 M ohm connected in parallel to the battery 13 and detects the terminal voltage V of the battery 13; It has.
[0101]
In addition, in the vehicle battery pure resistance measuring apparatus according to the present embodiment, the outputs of the current sensor 15 and the voltage sensor 17 described above are captured after A / D conversion in the interface circuit (hereinafter abbreviated as “I / F”) 21. A microcomputer (hereinafter abbreviated as “microcomputer”) 23.
[0102]
The microcomputer 23 includes a CPU 23a, a RAM 23b, and a ROM 23c. Among these, the CPU 23a is connected to the I / F 21 in addition to the RAM 23b and the ROM 23c. A switch, an ignition switch, an accessory switch, a switch of an electrical component (load) other than the motor generator 5 are further connected.
[0103]
The RAM 23b has a data area for storing various data and a work area used for various processing operations, and the ROM 23c stores a control program for causing the CPU 23a to perform various processing operations.
[0104]
Note that the current values and voltage values that are the outputs of the current sensor 15 and the voltage sensor 17 described above are sampled at high speed in a short cycle, and are taken into the CPU 23a of the microcomputer 23 via the I / F 21. The voltage value is collected in the data area (corresponding to the storage means) of the RAM 23b and used for various processes.
[0105]
Next, processing performed by the CPU 23a according to the control program stored in the ROM 23c will be described with reference to the flowchart of FIG.
[0106]
When the microcomputer 23 is activated to receive power from the battery 13 and the program is started, the CPU 23a first performs initial setting (step S1).
[0107]
When the initial setting in step S1 is completed, the CPU 23a next determines whether or not the ignition (IG) switch is turned on (step S2). If the determination is not YES, the CPU 23a performs other processing (step S3). Do. In the process of step S3, the discharge current and the terminal voltage are also measured and collected at a sampling period of 500 μsec, and this process is repeated until the determination in step S2 becomes YES. When the ON state of the IG switch is detected (YES in step S2), the sampling period is changed from 500 μsec to 100 μsec so that the rapidly changing inrush current at the time of driving the rapidly changing starter motor can be measured. Shorten it (step S4).
[0108]
Thereafter, the A / D conversion value of the discharge current I of the battery 13 detected by the current sensor 15 and the terminal voltage V of the battery 13 detected by the voltage sensor 17 are read through the I / F 21 as a pair, and the read actual data Is collected in the data area of the RAM 23b, and actual data collection processing is executed (step S5).
[0109]
In the process of performing the actual data collection process in step S5, the peak value of the inrush current is detected by comparing the magnitude relationship of the collected actual data before and after (step S6). When the peak value is detected (YES in step S6), the time from the detection of the peak value is counted, and the collection of actual data is continued until the predetermined time elapses. When the predetermined time has elapsed (YES in step S7) ) Holds actual data for a predetermined time before and after the peak value (step S8), and returns the sampling period to the original 500 μsec after a predetermined time after detecting the peak value (step S9).
[0110]
Then, the actual data collected and held for a predetermined time is analyzed, and it is determined whether or not it is appropriate for obtaining a quadratic approximate expression of current-voltage characteristics by applying the least square method. That is, an analysis process is performed to analyze whether a discharge current that monotonously increases from 0 to the peak value and a discharge current that monotonously decreases from the peak value to the steady value flows from the battery (step S10).
[0111]
As a result of the analysis in step S10, when appropriate ones for obtaining the quadratic approximate expression of the current-voltage characteristic are collected (YES in step S11), the expression (1) for the increasing discharge current and the decreasing discharge current And the approximate expression calculation process which calculates | requires the secondary approximate expression of the electric current-voltage characteristic represented by (2) is performed (step S12).
[0112]
An arithmetic process for obtaining a concentration polarization approximate expression, a battery pure resistance, and an activation polarization approximate expression from the secondary approximate expression obtained by the secondary approximate expression calculation process in step S12 is executed by the method described above. Then, by substituting an arbitrary current value into the obtained concentration polarization approximate expression and activation polarization approximate expression, the voltage drop due to the concentration polarization and activation polarization at the arbitrary current value is separated from other voltage drop components, respectively. It can be calculated (step S13). In this calculation process, when the voltage drop due to concentration polarization is included in the quadratic expression, a corrected quadratic approximate expression calculation process for obtaining a corrected quadratic approximate expression excluding the voltage drop is performed, and this correction An arithmetic process for obtaining the pure resistance of the battery is executed using the following approximate expression. In this case, two correction secondary of the discharge current-terminal voltage characteristics for the increasing inrush current and the decreasing inrush current are performed. After calculating the differential value at the peak value of the approximate expression, an operation is performed to obtain an intermediate value between the two differential values as the pure resistance of the battery. The obtained pure resistance of the battery is stored and stored in the data area of the RAM 23b for use for various purposes (step S14). When the process in step S14 is completed, the process waits for the determination in step S2 to be YES.
[0113]
There are two methods for obtaining an intermediate value of the differential value depending on the flow shape of the inrush current.
When the time in the increase direction of the inrush current is substantially equal to the time in the decrease direction, a calculation is performed to obtain the addition average value of the two differential values as a pure resistance.
On the other hand, when the time in the increase direction and the time in the decrease direction of the inrush current are greatly different, the discharge current of the discharge current is changed to the differential value at the peak value of the modified quadratic approximate expression of the current-voltage characteristic for the increasing discharge current. Multiplying the ratio of the increasing discharge current flow time to the total time and the differential value at the peak value of the two modified quadratic approximations of the current-voltage characteristics for the decreasing discharge current, the total discharge current An operation is performed to obtain an added value obtained by adding the product of the ratio of the time during which the decreasing discharge current flows in the time as the pure resistance.
When the pure resistance is obtained by any method, the pure resistance of the battery is obtained as an intermediate value between the two differential values.
[0114]
In the example shown in the flowchart of FIG. 10, the first and second approximate expressions are both quadratic approximate expressions. However, when the first approximate expression is the primary approximate expression, the process for obtaining the corrected approximate expression is as follows. Naturally it becomes unnecessary. In this case, the slope of the linear expression is used instead of the differential value.
[0115]
Further, in the on-vehicle battery pure resistance measuring device of this embodiment, step S5 in the flowchart is processing for the current / voltage measuring means in the claims, and step S12 is processing corresponding to the approximate expression calculating means in the claims. Step S13 is processing corresponding to the calculation means in the claims.
[0116]
Next, the operation (action) of the on-vehicle battery pure resistance measuring apparatus of the present embodiment configured as described above will be described.
[0117]
First, in the state where the battery 13 is discharged as the starter motor starts driving, the terminal of the battery when an inrush current that monotonously increases beyond the steady value and monotonously decreases from the peak value to the steady value flows to the starter motor. Voltage and discharge current are measured periodically.
[0118]
Further, in the vehicle battery pure resistance measuring device of the present embodiment, the actual data for a predetermined time before and after the periodically measured peak value is stored and stored in the data area of the RAM 23b and collected. Actual data for a predetermined time of the discharge current I and the terminal voltage V is analyzed, and it is determined whether or not it is appropriate for obtaining a quadratic approximate expression of the current-voltage characteristic by applying the least square method. Is done. That is, it is analyzed whether or not a discharge current that monotonously increases beyond the steady value and monotonously decreases from the peak value to the steady value or less flows from the battery.
[0119]
For this reason, the approximate expression calculation process is not performed until an appropriate expression for obtaining the secondary approximate expression of the current-voltage characteristic is collected. Since it is only necessary to use actual data, the processing does not have to be performed in synchronization with the periodic measurement of the terminal voltage and the discharge current, and a high processing speed is not required.
[0120]
In the above-described embodiment, the present invention is implemented by paying attention only to the inrush current included in the discharge current when the starter motor starts to be driven. However, the drive is performed in the same manner as the starter motor having a different size. The present invention can be equally applied to loads other than the starter motor through which an inrush current flows at the start. However, in this case, instead of the IG switch, the load driving start time is captured when the load switch is turned on, and the process of step S4 is performed, and other processes are substantially the same as the flowchart of FIG. The same processing may be performed.
[0121]
In addition, as described above, the voltage drop component of the terminal voltage can be separately calculated and learned, so that it can be used to estimate various states of the in-vehicle battery by the change of each component. It is obvious that the present invention can be applied to a battery other than an on-vehicle battery, without mentioning a specific application example.
[0122]
【The invention's effect】
As described above, according to the first aspect of the present invention, during the period when the inrush current flows through the load, the discharge current of the battery and the terminal voltage corresponding to the discharge current are periodically measured. A first approximate expression of the discharge current-terminal voltage characteristic with respect to an increasing discharge current and a second approximate expression of a current-voltage characteristic with respect to a decreasing discharge current showing the correlation between the resulting discharge current and the terminal voltage are obtained. Since the difference between the terminal voltages of the battery at the point where the discharge current is zero in the first and second approximate expressions is regarded as a voltage drop due to the total concentration polarization generated by the flow of the inrush current, the battery is in a normal state. In the IV characteristics indicating the relationship between the discharge current discharged from the battery when the power is supplied from the battery to the load and the terminal voltage that changes in accordance with the discharge current. It is possible to provide a discharge at a voltage drop component calculation method in a battery which can be a voltage drop due to the addition voltage drop utilized to calculate separately.
[0123]
Claim 2 Or According to the invention described in item 18, the discharge current of the battery and the terminal voltage corresponding to the discharge current are periodically measured during the period when the inrush current flows through the load, and the discharge current and the terminal voltage obtained as a result of the measurement are measured. The first approximate expression of the discharge current-terminal voltage characteristic with respect to the increasing discharge current and the second approximate expression of the current-voltage characteristic with respect to the decreasing discharge current are obtained, and the first and second approximations are obtained. Since the difference in the terminal voltage of the battery at the point where the discharge current is 0 in the equation is regarded as a voltage drop due to the total concentration polarization generated by the inrush current flowing, the concentration polarization at an arbitrary current value based on this difference Battery voltage drop component separation calculation method in battery that can be calculated separately by calculating voltage drop due to concentration and dividing into voltage drop due to concentration polarization and other voltage drop Or An apparatus can be provided.
[0124]
According to the above-described invention according to claim 3 or 19, paying attention to the fact that the magnitude of concentration polarization is proportional to the magnitude of current and the time during which it flows, voltage drop due to concentration polarization at an arbitrary current value Is calculated by multiplying the difference by the ratio of the concentration polarization that occurs during the period when the discharge current flows up to an arbitrary current value with respect to the total concentration polarization that occurs during the period when the inrush current flows. Since the voltage drop due to the battery is calculated separately from the others, the voltage drop due to concentration polarization at any time can be calculated separately from the others and the voltage drop component separation calculation method at the time of discharge in the battery can be calculated Or equipment Can be provided.
[0125]
According to the invention described in claim 4 described above, the voltage drop due to the concentration polarization at the peak value is calculated by multiplying the above ratio by the ratio of the concentration polarization generated during the period in which the inrush current increases to the peak value to the total concentration polarization, Since the voltage drop component of the terminal voltage at the peak value of the inrush current can be calculated separately from the one due to concentration polarization and the others, the voltage drop due to the concentration polarization is deleted from the terminal voltage at the peak value of the inrush current. Therefore, it is possible to provide a method for calculating a voltage drop component separation during discharge in a battery that can be used for the purpose.
[0126]
According to the invention described in claim 5 or 20, the difference between the terminal voltages of the battery at the point where the discharge current is 0 in the first and second approximate expressions is due to the concentration polarization generated by the flow of the inrush current. Since the voltage drop is considered, the voltage drop is multiplied by the ratio of the increase time to the total time of the inrush current to obtain the voltage drop due to the concentration polarization at the peak value, and this is added to the terminal voltage, resulting from the concentration polarization at the peak value. Since it can be calculated separately for voltage drop and voltage drop due to other than that, it is discharged from the battery when power is supplied from the in-vehicle battery to the vehicle load when the battery is used in normal condition, that is, even when the vehicle is in use In the IV characteristics indicating the relationship between the discharge current and the terminal voltage that changes accordingly, the voltage drop in the terminal voltage that drops according to the magnitude of the discharge current. Discharge when the voltage drop component separation calculation method in a battery is calculated by separating the components Or An apparatus can be provided.
[0127]
According to the above-described invention of claim 6, there is provided a method for calculating a voltage drop component separation during discharge in a battery that can be used to remove a voltage drop due to concentration polarization from a terminal voltage at an arbitrary current value of an inrush current. Can be provided.
[0128]
According to the seventh aspect of the invention described above, the voltage drop component separation at the time of discharge in the battery that can be used to eliminate the voltage drop due to the concentration polarization from the terminal voltage at an arbitrary current value during the rush current reduction period. A calculation method can be provided.
[0129]
According to the invention described in claim 8 above, the voltage drop component due to other than concentration polarization is a voltage drop component due to pure resistance and activation polarization, and the voltage drop of the terminal voltage is divided into the voltage drop due to concentration polarization, the pure resistance, and It is possible to provide a discharge voltage drop component separation calculation method in a battery that can be calculated separately from a voltage drop due to activation polarization.
[0130]
According to the ninth aspect of the invention described above, in the battery in which the voltage drop due only to the concentration polarization is generalized by the first and second concentration component approximation formulas, the individual voltage drops need not be calculated separately. It is possible to provide a voltage drop component separation calculation method during discharge.
[0131]
According to the invention described in claim 10, the battery voltage can be calculated by decomposing the voltage drop of the terminal voltage into a voltage drop due to concentration polarization, a voltage drop due to pure resistance, and a voltage drop due to activation polarization. It is possible to provide a voltage drop component separation calculation method during discharge.
[0132]
According to the eleventh aspect of the present invention, there is provided a method for calculating a voltage drop component separation at the time of discharge in a battery capable of calculating a voltage drop caused by a pure resistance from a voltage drop other than a voltage drop caused by concentration polarization. Can do.
[0133]
According to the twelfth aspect of the invention described above, when the change in activation polarization at the point corresponding to the peak value becomes equal, the differential value at the point corresponding to the peak value of the first and second approximate expressions. By adding and dividing by 2, it is possible to provide a battery voltage drop component separation calculation method for discharging in a battery that can measure the pure resistance of the battery and easily separate and calculate the voltage drop component due to the pure resistance.
[0134]
According to the invention described in claim 13 described above, an intermediate value in consideration that the activation polarization and the concentration polarization mutually influence each other is obtained, measured as the value of the pure resistance of the battery, and accurately determined by the pure resistance. It is possible to provide a discharge voltage drop component separation calculation method for a battery that can calculate the voltage drop component separately.
[0135]
According to the above-described invention according to the fourteenth aspect, it is possible to obtain a corrected approximate expression excluding the concentration polarization with high accuracy, and to accurately separate and calculate the voltage drop component at the time of current increase. A separation calculation method can be provided.
[0136]
According to the invention described in claim 15, the second quadratic modified approximate expression excluding the voltage drop due to the concentration polarization can be easily obtained, and the voltage drop component at the time of the current decrease is accurately separated and calculated. It is possible to provide a method for calculating a voltage drop component separation at the time of discharge in a battery that can be discharged.
[0137]
According to the invention described in claim 16 described above, when both the first and second modified approximate expressions are quadratic expressions, the pure resistance can be obtained by a simple calculation that only obtains an intermediate value of the differential value at the peak value. It is possible to provide a battery voltage drop component separation calculation method for discharging in a battery that can easily measure and calculate a voltage drop component due to a pure resistance.
[0138]
According to the invention described in claim 17, the voltage drop due only to the activation polarization is generalized by the first and second activation component approximation formulas, and the individual voltage drops are not calculated separately. It is possible to provide a discharge voltage drop component separation calculation method in a battery that can calculate the voltage drop by dividing the voltage drop into a voltage drop due to concentration polarization, a voltage drop due to pure resistance, and a voltage drop due to activation polarization.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a basic configuration of a discharging voltage drop component separation calculation apparatus for a battery according to the present invention.
FIG. 2 is an explanatory diagram partially showing a schematic configuration of a discharge voltage drop component separation calculation apparatus for an in-vehicle battery according to an embodiment of the present invention to which a discharge voltage drop component calculation method for a battery of the present invention is applied. It is.
FIG. 3 is a graph showing an example of a discharge current accompanied with an inrush current at the start of driving a starter motor.
FIG. 4 is a graph showing an example of an IV characteristic represented by a quadratic approximate expression.
FIG. 5 is a graph for explaining an example of how to remove concentration polarization from an approximate expression in an increasing direction.
FIG. 6 is a graph for explaining an example of how to remove concentration polarization from an approximate expression in a decreasing direction.
FIG. 7 is a graph showing an example of an IV characteristic in which an increasing direction is expressed by a first-order approximation formula.
FIG. 8 is a graph for explaining another example of how to remove concentration polarization from an approximate expression in a decreasing direction.
FIG. 9 is a graph for explaining another example of how to remove concentration polarization from an approximate expression in a decreasing direction.
FIG. 10 is a flowchart showing processing performed by the microcomputer in FIG. 2 according to a predetermined program for calculating a voltage drop component separation during discharge.
FIG. 11 is a graph showing IV characteristics generally showing a breakdown of a voltage drop of a terminal voltage due to discharge.
[Explanation of symbols]
23a-1 Current / voltage measuring means (CPU)
23a-2 Approximate expression calculation means (CPU)
23a-3 Calculation means (CPU)

Claims

A terminal voltage that drops according to the magnitude of the discharge current in the discharge current-terminal voltage characteristics that show the relationship between the discharge current discharged from the battery when power is supplied from the battery to the load and the terminal voltage that changes accordingly. In the method of calculating the voltage drop component during discharge in the battery to calculate the voltage drop component in
Periodically measure the discharge current of the battery and the terminal voltage corresponding to the discharge current during a period when an inrush current that monotonously increases from the peak value to the steady value flows through the load. ,
A first approximate expression of the discharge current-terminal voltage characteristic for the increasing inrush current and a second approximate expression of the discharge current-terminal voltage characteristic for the decreasing inrush current showing the correlation between the measured discharge current and the terminal voltage. And
A difference between the terminal voltage of the battery at a point where the discharge current is 0 in the first approximate expression and the terminal voltage of the battery at a point where the discharge current is 0 in the second approximate expression;
A method for calculating a voltage drop component during discharge in a battery, wherein the difference is regarded as a voltage drop due to total concentration polarization caused by the flow of the inrush current.

A terminal voltage that drops according to the magnitude of the discharge current in the discharge current-terminal voltage characteristics that show the relationship between the discharge current discharged from the battery when power is supplied from the battery to the load and the terminal voltage that changes accordingly. In the discharge voltage drop component separation calculation method in the battery to separate and calculate the voltage drop component in the battery,
Periodically measure the discharge current of the battery and the terminal voltage corresponding to the discharge current during a period when an inrush current that monotonously increases from the peak value to the steady value flows through the load. ,
A first approximate expression of the discharge current-terminal voltage characteristic for the increasing inrush current and a second approximate expression of the discharge current-terminal voltage characteristic for the decreasing inrush current showing the correlation between the measured discharge current and the terminal voltage. And
Obtaining a difference in terminal voltage of the battery at a point where the discharge current of the first and second approximate expressions is 0, and regarding the difference as a voltage drop due to total concentration polarization caused by the flow of the inrush current; Based on the difference, calculate a voltage drop due to concentration polarization at an arbitrary current value, add the voltage drop due to the calculated concentration polarization to a terminal voltage at an arbitrary current value to calculate a voltage drop due to other than the concentration polarization, A method for separately calculating a voltage drop component during discharge in a battery, wherein the voltage drop component is separately calculated for concentration polarization and for other than that.

In the battery voltage drop component separation calculation method for discharging according to claim 2,
The voltage drop due to the concentration polarization at an arbitrary current value is multiplied by the ratio of the concentration polarization generated during the period when the discharge current flows up to the arbitrary current value with respect to the total concentration polarization generated during the period when the inrush current flows. A method for calculating a voltage drop component separation during discharge in a battery, characterized in that:

In the battery voltage drop component separation calculation method for discharging in the battery according to claim 2 or 3,
The arbitrary current value is a peak value of a rush current that monotonously increases,
A voltage drop during discharge in a battery, wherein a voltage drop due to the concentration polarization at the peak value is calculated by multiplying the difference by a ratio of the concentration polarization generated during a period in which the inrush current increases to a peak value with respect to the total concentration polarization. Component separation calculation method.

A terminal voltage that drops according to the magnitude of the discharge current in the discharge current-terminal voltage characteristics that show the relationship between the discharge current discharged from the battery when power is supplied from the battery to the load and the terminal voltage that changes accordingly. In the discharge voltage drop component separation calculation method in the battery to separate and calculate the voltage drop component in the battery,
Periodically measure the discharge current of the battery and the terminal voltage corresponding to the discharge current during a period when an inrush current that monotonously increases from the peak value to the steady value flows through the load. ,
A first approximate expression of the discharge current-terminal voltage characteristic for the increasing inrush current and a second approximate expression of the discharge current-terminal voltage characteristic for the decreasing inrush current showing the correlation between the measured discharge current and the terminal voltage. And
A difference in terminal voltage of the battery at a point where the discharge current of the first and second approximate expressions is 0 is obtained, and the difference is regarded as a voltage drop due to concentration polarization generated by the flow of the inrush current. And the voltage drop due to the concentration polarization occurring during the period in which the inrush current increases to the peak value by multiplying the ratio of the time until the peak value increases to the peak value with respect to the total time during which the inrush current flows. The voltage drop due to concentration polarization is added to the terminal voltage at the peak value to calculate a voltage drop component due to other than the concentration polarization, and the voltage drop component is calculated separately from that due to concentration polarization and other than that due to concentration polarization. The voltage drop component separation calculation method at the time of discharge in a battery.

In the battery voltage drop component separation calculation method of claim 5,
Multiplying the voltage drop due to concentration polarization at the calculated peak value by the ratio of the time until the arbitrary current value during the period when the inrush current increases to the peak value to the time when the inrush current increases to the peak value, the inrush A method of calculating a voltage drop component separation during discharge in a battery, comprising calculating a voltage drop due to concentration polarization at an arbitrary current value at which the current increases to a peak value.

In the battery discharge voltage drop component separation calculation method according to claim 6,
From the difference, the voltage drop due to the concentration polarization generated during the period when the calculated inrush current increases to the peak value is subtracted to calculate the voltage drop due to the concentration polarization generated during the period when the inrush current decreases from the peak value to zero. And
The ratio of the time from the peak value to the arbitrary current value during the period in which the inrush current decreases to the time in which the inrush current decreases from the peak value to 0 is calculated as the voltage drop due to the concentration polarization occurring in the calculated decreasing period. A voltage drop component separation calculation method for discharging in a battery, characterized by multiplying and calculating a voltage drop due to concentration polarization at an arbitrary current value at which the inrush current decreases from a peak value.

In the battery voltage drop component separation calculation method in the battery according to any one of claims 2 to 7,
A voltage drop component separation calculation method for discharging in a battery, wherein the voltage drop component other than the concentration polarization is a voltage drop component due to pure resistance and activation polarization.

In the battery voltage drop component separation calculation method for discharging according to any one of claims 2 to 8,
Using the calculated voltage drop due to concentration polarization, the voltage drop due to concentration polarization is excluded from the first and second approximate expressions, and each of the first and second approximate expressions expressing the voltage drop due to other than concentration polarization is used. Find the corresponding first and second modified approximate equations,
The difference between the obtained first and second modified approximate expressions and the first and second approximate expressions is taken, respectively, and the voltage drop due to only the concentration polarization corresponding to each of the first and second approximate expressions is taken. Obtain first and second density component approximation formulas,
A method for calculating a voltage drop component separation during discharge in a battery, wherein an arbitrary current value is substituted into the obtained concentration component approximate expression, and a voltage drop component due to concentration polarization at an arbitrary current value is separated and calculated.

In the battery voltage drop component separation calculation method for discharging according to claim 9,
The difference between the first and second modified approximate expressions and the expression representing the voltage drop due to the pure resistance obtained in advance is taken, and the voltage drop due to only the activation polarization corresponding to each of the first and second approximate expressions is taken. Find first and second activation polarization approximations,
A method for calculating and separating a voltage drop component during discharge in a battery, wherein an arbitrary current value is substituted into the obtained activation polarization approximation formula to separate and calculate a voltage drop component due to activation polarization at an arbitrary current value .

In the battery voltage drop component separation calculation method in the battery according to any one of claims 2 to 7,
Using the calculated voltage drop due to concentration polarization, the voltage drop due to concentration polarization is excluded from the first and second approximate expressions, and each of the first and second approximate expressions expressing the voltage drop due to other than concentration polarization is used. Find the corresponding first and second modified approximate equations,
An intermediate value between two terminal voltage changes per unit current change at a point corresponding to the peak value of the obtained first and second modified approximate equations is calculated as a value of the pure resistance of the battery, and the calculation A method for calculating a voltage drop component separation during discharge in a battery, wherein a voltage drop due to the pure resistance is calculated by multiplying the value of the pure resistance by the current value.

In the battery discharge voltage drop component separation calculation method according to claim 11,
The intermediate value is obtained by averaging the two terminal voltage change values per unit current change at a point corresponding to the peak value of the first and second approximate expressions excluding the voltage drop due to the concentration polarization. A method for calculating a voltage drop component separation at the time of discharging in a battery.

In the battery discharge voltage drop component separation calculation method according to claim 11,
The intermediate value is changed to the value of two terminal voltage changes per unit current change at a point corresponding to the peak value of the first and second approximate expressions excluding the voltage drop due to the concentration polarization. A method of calculating a voltage drop component separation during discharge in a battery, wherein the calculation is performed by multiplying the respective ratios of the time of the monotonically increasing period and the monotonically decreasing period occupying the total time during which the battery flows.

In the battery discharge voltage drop component separation calculation method according to claim 11,
When the first and second approximate expressions are quadratic expressions, a value obtained by removing the voltage drop due to the concentration polarization from the voltage value corresponding to the peak value is used as a constant and a first-order coefficient as the first quadratic approximation. A method for calculating a voltage drop component separation during discharge in a battery, wherein a secondary expression obtained by substituting into an expression equal to the expression to determine a secondary coefficient is obtained as the first modified approximate expression.

In the battery discharge voltage drop component separation calculation method according to claim 14,
In addition to the voltage value excluding the voltage drop due to the concentration polarization at the peak value, two voltage values excluding the voltage drop due to the concentration polarization between the peak value and 0 are obtained, and the coefficient is calculated using the three voltage values. A method of calculating a voltage drop component separation during discharge in a battery, wherein the quadratic expression that determines the above is obtained as the second modified approximate expression.

In the battery voltage drop component separation calculation method for discharging according to claim 15,
In order to obtain the intermediate value, the differential value at the peak value of the first and second modified approximate equations is used, and the voltage drop component separation calculation method at the time of discharging in the battery is characterized.

In the discharge time of a voltage drop component separation calculation method in a battery according to claim 1 0 Symbol mounting,
The difference between the first and second modified approximate expressions and the expression representing the voltage drop due to the calculated pure resistance is taken, and the voltage drop due to only the activation polarization corresponding to each of the first and second approximate expressions is taken. Obtain first and second activation polarization approximations,
A method for calculating and separating a voltage drop component during discharge in a battery, wherein an arbitrary current value is substituted into the obtained activation polarization approximation formula to separate and calculate a voltage drop component due to activation polarization at an arbitrary current value .

The terminal voltage that drops according to the magnitude of the discharge current in the discharge current-terminal voltage characteristics that show the relationship between the discharge current discharged from the battery when power is supplied from the battery to the load and the terminal voltage that changes accordingly. In the battery voltage drop component separation calculation device at the time of discharging in the battery to separate and calculate the voltage drop component in,
Periodically measuring the discharge current of the battery and the terminal voltage corresponding to the discharge current during a period when an inrush current that monotonously increases from the peak value to the steady value flows through the load. Current / voltage measuring means;
A first approximate expression of the discharge current-terminal voltage characteristic for the increasing inrush current and the discharge current-terminal voltage characteristic for the decreasing inrush current showing the correlation between the discharge current measured by the current / voltage measuring means and the terminal voltage. An approximate expression calculating means for obtaining a second approximate expression of:
The difference between the terminal voltages of the battery at the point where the discharge current is zero in the first and second approximate expressions obtained by the approximate expression calculating means is obtained, and the difference is the total concentration generated by the flow of the inrush current. Considering a voltage drop due to polarization, a voltage drop due to concentration polarization at an arbitrary current value is calculated based on the difference, and the concentration polarization is calculated by adding the calculated voltage drop due to concentration polarization to a terminal voltage at an arbitrary current value. An apparatus for calculating a voltage drop component separation during discharge in a battery, comprising: a calculation means for calculating a voltage drop due to other than the above, and calculating a voltage drop component separately according to concentration polarization and other than that due to concentration polarization.

The apparatus for calculating a voltage drop component separation during discharge in the battery according to claim 18,
The calculation means calculates a ratio of a voltage drop component due to concentration polarization at an arbitrary current value to a concentration polarization generated during a period when a discharge current flows up to an arbitrary current value with respect to a total concentration polarization generated during the period when the inrush current flows. Multiplying the difference to calculate the voltage drop component separation calculation device at the time of discharging in the battery.

The terminal voltage that drops according to the magnitude of the discharge current in the discharge current-terminal voltage characteristics that show the relationship between the discharge current discharged from the battery when power is supplied from the battery to the load and the terminal voltage that changes accordingly. In the battery voltage drop component separation calculation device at the time of discharging in the battery to separate and calculate the voltage drop component in,
Periodically measuring the discharge current of the battery and the terminal voltage corresponding to the discharge current during a period when an inrush current that monotonously increases from the peak value to the steady value flows through the load. Current / voltage measuring means;
A first approximate expression of the discharge current-terminal voltage characteristic for the increasing inrush current and the discharge current-terminal voltage characteristic for the decreasing inrush current showing the correlation between the discharge current measured by the current / voltage measuring means and the terminal voltage. An approximate expression calculating means for obtaining a second approximate expression of:
A difference in terminal voltage of the battery at a point where the discharge current is 0 in the first and second approximate expressions obtained by the approximate expression calculating means is obtained, and the concentration polarization generated by the flow of the inrush current is obtained. The voltage drop due to concentration polarization that occurs during the period when the inrush current increases to the peak value by multiplying the difference by the ratio of the time until the peak value increases with respect to the total time during which the inrush current flows. In addition, the voltage drop due to the concentration polarization is added to the terminal voltage at the peak value to calculate a voltage drop component other than the concentration polarization, and the voltage drop component is caused by the concentration polarization and the others An apparatus for calculating a voltage drop component separation during discharge in a battery, comprising: a calculation means for calculating by separation.