JP2021150220A - Method of estimating battery state, device, program, and storage medium - Google Patents

Method of estimating battery state, device, program, and storage medium Download PDF

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JP2021150220A
JP2021150220A JP2020050590A JP2020050590A JP2021150220A JP 2021150220 A JP2021150220 A JP 2021150220A JP 2020050590 A JP2020050590 A JP 2020050590A JP 2020050590 A JP2020050590 A JP 2020050590A JP 2021150220 A JP2021150220 A JP 2021150220A
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open circuit
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voltage
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JP7449738B2 (en
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典靖 岩根
Noriyasu Iwane
典靖 岩根
真司 横山
Shinji Yokoyama
真司 横山
悦藏 佐藤
Etsuzo Sato
悦藏 佐藤
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Furukawa Electric Co Ltd
Furukawa Automotive Systems Inc
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Furukawa Automotive Systems Inc
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    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/10Energy storage using batteries
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00Road transport of goods or passengers
    • Y02T10/60Other road transportation technologies with climate change mitigation effect
    • Y02T10/70Energy storage systems for electromobility, e.g. batteries

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Abstract

To provide a method of accurately estimating a full-charging amount or a correlation of an open circuit voltage and a charging rate for batteries having different characteristics, a device, a program, and a storage medium.SOLUTION: A method of estimating a battery state, includes: steps 202, 206, and 212 of measuring a voltage and a charging/discharging current of a battery in time series; steps 203 and 213 of calculating an open circuit voltage of the battery at two different time points on the basis of the measured voltage; a step 214 of calculating an open circuit voltage change amount ΔOCV between the two different time points on the basis of the open circuit voltage; a step 207 of calculating an electric amount change amount ΔQ at the two different time points on the basis of the measured charging/discharging current; and a step 216 of calculating proportions ΔOCV/ΔQ and ΔQ/ΔOCV of the open circuit voltage change amount and the electric amount change amount. A full-charging capacity of the battery is estimated on the basis of the proportion of the open circuit voltage change amount and the electric amount change amount and the existed correlation with the full-charging capacity of a plurality of batteries having different full-charging capacity.SELECTED DRAWING: Figure 1

Description

本発明は、バッテリ状態を推定する方法、装置、プログラムおよび記録媒体に関し、特にバッテリの満充電容量、および、開回路電圧と充電率との相関を推定する方法等に関する。 The present invention relates to a method for estimating a battery state, an apparatus, a program, and a recording medium, and more particularly to a method for estimating a full charge capacity of a battery and a correlation between an open circuit voltage and a charge rate.

バッテリは、使用環境によりまた経時的に特性が大きく変化するため、常にバッテリ状態を把握することが求められている。特に、自動車用スタータバッテリなどの車両に搭載されるバッテリでは、バッテリの故障・異常が事故などの重大な事象につながる可能性があることから、バッテリの故障・異常を検知する車載センサには、バッテリ状態、特にバッテリの満充電容量SOHや、開回路電圧OCVと充電率SOCとの相関を推定する手段が搭載されていることが一般的である。 Since the characteristics of a battery change significantly with time depending on the usage environment, it is required to constantly grasp the battery state. In particular, in the case of batteries mounted on vehicles such as automobile starter batteries, battery failures / abnormalities may lead to serious events such as accidents. Therefore, in-vehicle sensors that detect battery failures / abnormalities are used. Generally, a means for estimating the battery state, particularly the full charge capacity SOH of the battery, and the correlation between the open circuit voltage OCV and the charge rate SOC is installed.

これらの推定方法として、充電状態の異なる2つのタイミングの電圧V1、V2および満充電時の電圧VM、充電率SOC=0%時の電圧V0、および2点間の電流積算量Qを用いて、満充電容量SOH=Q×(VM−V0)/|V1−V2|として求める方法(特許文献1)や、充電前後のSOC差と充電中の充電電流積算値とに基づいて、満充電容量を算出する方法(特許文献2)が提案されている。 As these estimation methods, the voltages V1 and V2 at two timings with different charging states, the voltage VM at the time of full charge, the voltage V0 at the time of charging rate SOC = 0%, and the current integration amount Q between the two points are used. Full charge capacity Based on the method of obtaining as SOH = Q × (VM-V0) / | V1-V2 | (Patent Document 1), the SOC difference before and after charging, and the integrated charging current value during charging, the full charge capacity is determined. A method for calculating (Patent Document 2) has been proposed.

特開平8−179018号公報Japanese Unexamined Patent Publication No. 8-179018 特開2014−185896号公報Japanese Unexamined Patent Publication No. 2014-185896

しかしながら、特許文献1に記載の方法では、満充電時の電圧VMおよび充電率SOC=0%時の電圧V0が既知である必要がある。また、特許文献2に記載の方法では、充電前後のSOC差を求める手段が必要であり、このためにはOCVとSOCとの相関が既知である必要がある。このように、従来の方法では、推定を行うバッテリの特性(VM、V0、OCVとSOCとの相関など)が既知である必要があり、特性が異なるバッテリへの交換や、経時的劣化により特性が変化した場合には、推定が困難あるいは大幅な精度低下をきたしてしまう。 However, in the method described in Patent Document 1, it is necessary to know the voltage VM at the time of full charge and the voltage V0 at the time of charge rate SOC = 0%. Further, in the method described in Patent Document 2, a means for obtaining the SOC difference before and after charging is required, and for this purpose, it is necessary that the correlation between OCV and SOC is known. As described above, in the conventional method, it is necessary to know the characteristics of the battery to be estimated (such as the correlation between VM, V0, OCV and SOC), and the characteristics are due to replacement with a battery having different characteristics or deterioration over time. If is changed, it will be difficult to estimate or the accuracy will be significantly reduced.

このため、特性が異なるバッテリに対しても、精度よく満充電容量SOHや、開回路電圧OCVと充電率SOCとの相関を推定できる方法、装置、プログラム、および該プログラムを記録した記録媒体が求められていた。 Therefore, even for batteries having different characteristics, a method, an apparatus, a program, and a recording medium on which the full charge capacity SOH and the correlation between the open circuit voltage OCV and the charge rate SOC can be estimated with high accuracy are required. Was being done.

上記課題は、バッテリ(1)の状態を推定する方法(20)であって、バッテリ(1)の電圧と充放電電流とをそれぞれ時系列的に測定するステップ(202、206、212)と、測定した電圧に基づいて、異なる2つの時点における、バッテリ(1)の開回路電圧(OCV1、OCV2)を求めるステップ(203、213)と、開回路電圧(OCV1、OCV2)に基づいて、異なる2つの時点間における開回路電圧変化量(ΔOCV)を求めるステップ(214)と、測定した充放電電流に基づいて、異なる2つの時点間における、バッテリ(1)の電気量変化量(ΔQ)を求めるステップ(207)と、開回路電圧変化量と電気量変化量との比率(ΔOCV/ΔQ、ΔQ/ΔOCV)を求めるステッ
プ(216)と、満充電容量(SOH)が異なる複数のバッテリの、開回路電圧変化量と電気量変化量との比率(ΔOCV/ΔQ、ΔQ/ΔOCV)と、満充電容量(SOH)との既知の相関(30)、および、求めた比率(ΔOCV/ΔQ、ΔQ/ΔOCV)に基づいて、バッテリ(1)の満充電容量(SOH)を推定するステップ(217)とを含む、方法により解決することができる。
The above object is a method (20) for estimating the state of the battery (1), in which the voltage of the battery (1) and the charge / discharge current are measured in time series (202, 206, 212), respectively. Steps (203, 213) for obtaining the open circuit voltage (OCV1, OCV2) of the battery (1) at two different time points based on the measured voltage, and different 2 based on the open circuit voltage (OCV1, OCV2). Based on the step (214) for obtaining the open circuit voltage change amount (ΔOCV) between two time points and the measured charge / discharge current, the electric amount change amount (ΔQ) of the battery (1) is obtained between two different time points. Step (207), step (216) for obtaining the ratio (ΔOCV / ΔQ, ΔQ / ΔOCV) between the open circuit voltage change amount and the electric amount change amount, and opening of a plurality of batteries having different full charge capacities (SOH). The known correlation (30) between the ratio of the circuit voltage change amount and the electricity amount change amount (ΔOCV / ΔQ, ΔQ / ΔOCV) and the full charge capacity (SOH), and the obtained ratio (ΔOCV / ΔQ, ΔQ /). It can be solved by a method that includes a step (217) of estimating the full charge capacity (SOH) of the battery (1) based on ΔOCV).

すなわち、バッテリ(1)の電圧・電流の測定値から、現在の開回路電圧変化量と電気量変化量との比率(ΔOCV/ΔQ、ΔQ/ΔOCV)を求め、求めた比率を、予め複数のバッテリを用いて求められた既知の相関(30)と対応させて、満充電容量(SOH)を求めることにより、推定を行うバッテリ(1)の特性(VM、V0、OCVとSOCとの相関など)が未知でも、精度よく満充電容量SOHの推定を行うことが可能となる。 That is, the ratio (ΔOCV / ΔQ, ΔQ / ΔOCV) between the current open circuit voltage change amount and the electricity amount change amount is obtained from the measured values of the voltage and current of the battery (1), and a plurality of the obtained ratios are obtained in advance. The characteristics (VM, V0, OCV and SOC) of the battery (1) to be estimated by obtaining the full charge capacity (SOH) in correspondence with the known correlation (30) obtained using the battery, etc. ) Is unknown, it is possible to accurately estimate the full charge capacity SOH.

なお、本発明において、「時系列的」とは、異なる複数の時点を意味し、周期的か否かを問わない。例えば、「時系列的に測定」とは、周期的に行われる測定のみならず、必要に応じて、または、外部からの要求に応じて、異なる複数の時点で行われる不定期的な測定も含む。 In the present invention, "time-series" means a plurality of different time points, regardless of whether they are periodic or not. For example, "measurement in time series" means not only measurement performed periodically but also irregular measurement performed at different time points as needed or in response to an external request. include.

上記方法において、バッテリ(1)が車両に搭載されたバッテリ(1)である場合には、異なる2つの時点は、車両の走行前後の時点であることが望ましい。車載バッテリでは、車両の走行時にバッテリの充放電量が大きくなるため、満充電容量SOHの推定に必要な、開回路電圧変化量(ΔOCV)、電気量変化量(ΔQ)の値を大きくとることができ、推定誤差を小さく抑えることが可能となる。 In the above method, when the battery (1) is the battery (1) mounted on the vehicle, it is desirable that the two different time points are the time points before and after the vehicle travels. With an in-vehicle battery, the amount of charge and discharge of the battery increases when the vehicle is running. Therefore, the values of the open circuit voltage change amount (ΔOCV) and the electric amount change amount (ΔQ) required for estimating the full charge capacity SOH should be large. It is possible to keep the estimation error small.

また、上記方法は、電気量変化量(ΔQ)および推定した満充電容量(SOH)に基づいて、充電率変化量(ΔSOC)を求めるステップ(218)と、バッテリ(1)がほぼ満充電のときの充電率(SOCo)および開回路電圧(OCVo)を求めるステップ(210、220)と、開回路電圧変化量(ΔOCV)、充電率変化量(ΔSOC)、並びに、バッテリ(1)がほぼ満充電のときの充電率(SOCo)および開回路電圧(OCVo)に基づいて、バッテリ(1)の開回路電圧と充電率との相関(40)を推定するステップ(221)とをさらに含むことが望ましい。 Further, in the above method, the step (218) of obtaining the charge rate change amount (ΔSOC) based on the electric energy change amount (ΔQ) and the estimated full charge capacity (SOH) and the battery (1) are almost fully charged. Steps (210, 220) for obtaining the charge rate (SOCo) and open circuit voltage (OCVo) at the time, the amount of change in open circuit voltage (ΔOCV), the amount of change in charge rate (ΔSOC), and the battery (1) are almost full. It may further include a step (221) of estimating the correlation (40) between the open circuit voltage of the battery (1) and the charge rate based on the charge rate (SOCo) and open circuit voltage (OCVo) at the time of charging. desirable.

バッテリ(1)の電圧・電流の測定値から求めたSOH、ΔQ、SOCo、OCVoから、相関(40)を求めることにより、特性が未知のバッテリ(1)に対しても、精度よく開回路電圧と充電率との相関の推定を行うことが可能となる。 By obtaining the correlation (40) from the SOH, ΔQ, SOCo, and OCVo obtained from the measured values of the voltage and current of the battery (1), the open circuit voltage can be accurately obtained even for the battery (1) whose characteristics are unknown. It is possible to estimate the correlation between and the charge rate.

さらに、上記課題は、上述した方法を実施する装置、プログラム、および該プログラムを記録した記録媒体によっても解決することができる。 Further, the above-mentioned problems can be solved by an apparatus, a program, and a recording medium on which the program is recorded, which implements the above-mentioned method.

本発明に係るバッテリ状態推定方法およびプログラムのフローチャートである。It is a flowchart of the battery state estimation method and a program which concerns on this invention. 本発明に係るバッテリ状態推定装置の概略構成図である。It is a schematic block diagram of the battery state estimation device which concerns on this invention. 開回路電圧変化量と電気量変化量との比率と、満充電容量との既知の相関を示す図である。It is a figure which shows the known correlation with the ratio of the open circuit voltage change amount and the electric amount change amount, and a full charge capacity. 推定されるバッテリの開回路電圧と充電率との相関の一例である。This is an example of the correlation between the estimated open circuit voltage of the battery and the charge rate.

本発明の実施態様であるバッテリ状態推定装置10の概略構成図を図2に示す。バッテリ状態推定装置10は、バッテリ1と充電回路2とに接続されている。バッテリ1は、例えば、車両用の鉛蓄電池である。充電回路2は、バッテリ1に接続され、充電電流を供給
する電源回路である。また、バッテリ1は負荷3に、例えばモータ、制御回路、照明装置などの車載の電気機器に接続されている。バッテリ1、充電回路2、負荷3、およびバッテリ状態推定装置10は車両(図示しない)に搭載されている。
FIG. 2 shows a schematic configuration diagram of the battery state estimation device 10 according to the embodiment of the present invention. The battery state estimation device 10 is connected to the battery 1 and the charging circuit 2. The battery 1 is, for example, a lead storage battery for a vehicle. The charging circuit 2 is a power supply circuit that is connected to the battery 1 and supplies a charging current. Further, the battery 1 is connected to the load 3 to an in-vehicle electric device such as a motor, a control circuit, and a lighting device. The battery 1, the charging circuit 2, the load 3, and the battery state estimation device 10 are mounted on a vehicle (not shown).

バッテリ状態推定装置10は、電圧測定部11と、電流測定部12、記憶部13と、制御部14とを備える。電圧測定部11、電流測定部12、および記憶部13は、制御部14と電気的に接続され、データや信号により相互に通信することができる。電圧測定部11、電流測定部12、記憶部13および制御部14は、ASICのように1チップに統合されていてもよい。 The battery state estimation device 10 includes a voltage measuring unit 11, a current measuring unit 12, a storage unit 13, and a control unit 14. The voltage measuring unit 11, the current measuring unit 12, and the storage unit 13 are electrically connected to the control unit 14 and can communicate with each other by data or signals. The voltage measuring unit 11, the current measuring unit 12, the storage unit 13, and the control unit 14 may be integrated into one chip like an ASIC.

電圧測定部11は、バッテリ1の端子間に接続され、端子間電圧を周期的に、および/または制御部14からの要求に応じて測定し、測定した電圧を制御部14に送出する。電流測定部12は、バッテリ1と充電回路2との間であって、バッテリ1および電流測定部12と負荷3とが並列に接続されるように、接続され、バッテリ1に流れる充放電電流、すなわちバッテリ1に流入する充電電流やバッテリ1から負荷3に流れる放電電流を、周期的に、および/または制御部14からの要求に応じて測定し、測定された電圧を制御部14に送出する。 The voltage measuring unit 11 is connected between the terminals of the battery 1, measures the voltage between the terminals periodically and / or in response to a request from the control unit 14, and sends the measured voltage to the control unit 14. The current measuring unit 12 is connected between the battery 1 and the charging circuit 2 so that the battery 1, the current measuring unit 12 and the load 3 are connected in parallel, and the charge / discharge current flowing through the battery 1. That is, the charging current flowing into the battery 1 and the discharging current flowing from the battery 1 to the load 3 are measured periodically and / or in response to a request from the control unit 14, and the measured voltage is sent to the control unit 14. ..

制御部14は、プロセッサを備え、電圧測定部11や電流測定部12から測定信号や測定データを取得し、バッテリ1の満充電容量SOHや、開回路電圧OCVと充電率SOCとの相関40を推定するための処理を実行・制御する。さらに、制御部14は、電圧測定部11や電流測定部12が測定を行うタイミングを制御するように構成してもよい。 The control unit 14 includes a processor, acquires measurement signals and measurement data from the voltage measurement unit 11 and the current measurement unit 12, and obtains the full charge capacity SOH of the battery 1 and the correlation 40 between the open circuit voltage OCV and the charge rate SOC. Execute and control the processing for estimation. Further, the control unit 14 may be configured to control the timing at which the voltage measurement unit 11 and the current measurement unit 12 perform measurement.

記憶部13は、RAM、SSD、フラッシュメモリなどの半導体メモリやHDDなどの磁気的メモリなどで構成されるコンピュータ読み取り可能な記録媒体である。記憶部13は、制御部14のプロセッサにより実行されるプログラムや、プログラムによる情報処理で用いられる各種パラメータ、推定した満充電容量SOHや開回路電圧OCVと充電率SOCとの相関40、制御部14が電圧測定部11及び電流測定部12から取得した測定値などを格納する。さらに、記憶部13には、満充電容量が異なる複数のバッテリの、開回路電圧変化量と電気量変化量との比率と、満充電容量との既知の相関30が格納されている。図3に相関30の一例を示す。 The storage unit 13 is a computer-readable recording medium composed of a semiconductor memory such as a RAM, an SSD, and a flash memory, a magnetic memory such as an HDD, and the like. The storage unit 13 includes a program executed by the processor of the control unit 14, various parameters used in information processing by the program, an estimated full charge capacity SOH, a correlation 40 between the open circuit voltage OCV and the charge rate SOC, and the control unit 14. Stores the measured values and the like acquired from the voltage measuring unit 11 and the current measuring unit 12. Further, the storage unit 13 stores a known correlation 30 between the ratio of the open circuit voltage change amount and the electric energy change amount of a plurality of batteries having different full charge capacities and the full charge capacity. FIG. 3 shows an example of the correlation 30.

図3は、横軸に単位電気量変化量当たりの開回路電圧変化量ΔOCV/ΔQ、縦軸に満充電容量SOHをとったグラフであり、満充電容量が既知の、満充電容量の異なる多数のバッテリから求めたデータ31、32、33・・・が点で示されている。図から明らかなとおり両者には相関があり、線形近似した相関30が破線で示されている。記憶部13には、相関30がテーブルや近似式など形式で格納されており、制御部14は格納された相関30を読み出して、推定するバッテリのΔOCV/ΔQに対応する満充電容量SOHを求めることができる。なお、開回路電圧変化量と電気量変化量との比率は、単位電気量変化量当たりの電圧変化量ΔOCV/ΔQの逆数、すなわち単位電圧変化量に対する電気量変化量ΔQ/ΔOCVであってもよい。 FIG. 3 is a graph in which the horizontal axis is the open circuit voltage change amount ΔOCV / ΔQ per unit electric energy change amount and the vertical axis is the full charge capacity SOH. Data 31, 32, 33 ... Obtained from the battery of the above are indicated by dots. As is clear from the figure, there is a correlation between the two, and the linearly approximated correlation 30 is shown by the broken line. The correlation 30 is stored in the storage unit 13 in a format such as a table or an approximate expression, and the control unit 14 reads the stored correlation 30 to obtain the full charge capacity SOH corresponding to the estimated ΔOCV / ΔQ of the battery. be able to. The ratio of the open circuit voltage change amount to the electric amount change amount is the reciprocal of the voltage change amount ΔOCV / ΔQ per unit electric amount change amount, that is, even if the electric amount change amount ΔQ / ΔOCV with respect to the unit voltage change amount. good.

次に、本発明の実施態様であるバッテリの状態推定方法20を、図1のフローチャート20を参照しながら説明を行う。バッテリ状態推定装置10の記憶部13には、フローチャート20に示された機能を、制御部14のプロセッサで実行するためのプログラムが記録されている。 Next, the battery state estimation method 20 according to the embodiment of the present invention will be described with reference to the flowchart 20 of FIG. In the storage unit 13 of the battery state estimation device 10, a program for executing the function shown in the flowchart 20 by the processor of the control unit 14 is recorded.

状態推定は、車両の走行(ステップ205〜210)前の停止状態(ステップ202、203)から、走行後の停止状態(212〜)にわたって実行される。バッテリ1の充放電は主として車両の走行時に行われるため、走行前後の測定値を用いることで推定の過程
で必要となるパラメータΔOCV、ΔQの大きさを大きくとることができる。また、必要となる他のパラメータである開回路電圧OCVは、バッテリ1の充放電量が小さな車両停止時のほうが、安定かつ高い精度で測定または推定が可能となる。このため、走行前後の停止時の測定結果に基づいて、満充電容量SOHや、開回路電圧OCVと充電率SOCとの相関40の推定を行うことにより、誤差が小さく高精度な推定を行うことが可能となる。以下、推定方法20を処理順序にしたがって説明する。
The state estimation is executed from the stopped state (steps 202, 203) before the vehicle travels (steps 205 to 210) to the stopped state (212 to) after the vehicle travels. Since charging / discharging of the battery 1 is mainly performed when the vehicle is running, the magnitudes of the parameters ΔOCV and ΔQ required in the estimation process can be increased by using the measured values before and after the running. Further, the open circuit voltage OCV, which is another required parameter, can be measured or estimated with stability and high accuracy when the vehicle is stopped when the charge / discharge amount of the battery 1 is small. Therefore, by estimating the full charge capacity SOH and the correlation 40 between the open circuit voltage OCV and the charge rate SOC based on the measurement results at the time of stopping before and after running, it is possible to perform highly accurate estimation with small error. Is possible. Hereinafter, the estimation method 20 will be described according to the processing order.

はじめに、制御部14は、車両が走行状態にあるか否かを判定し、走行状態にある場合には停止状態になるまで待つ(ステップ201)。車両の停止が判定されると、制御部14は、電圧測定部11にバッテリ1の端子間電圧を測定するよう要求して、電圧測定部11が測定した電圧を取得し、または、電圧測定部11が周期的に測定している最新の電圧を記憶部13から取得する(ステップ202)。 First, the control unit 14 determines whether or not the vehicle is in the traveling state, and if it is in the traveling state, waits until the vehicle is in the stopped state (step 201). When it is determined that the vehicle is stopped, the control unit 14 requests the voltage measuring unit 11 to measure the voltage between the terminals of the battery 1, and acquires the voltage measured by the voltage measuring unit 11 or the voltage measuring unit. The latest voltage measured periodically by 11 is acquired from the storage unit 13 (step 202).

次に、制御部14は、取得した電圧から、開回路電圧OCV1を求める(ステップ203)。バッテリ1の充放電量が小さい状態が続いて、充放電による分極が十分解消して電圧が安定している場合には、取得した測定電圧を開回路電圧OCV1とみなすことができる。これに対して、電圧が安定していない場合には、時系列的に複数の電圧をサンプリングし、近似式を用いて電圧の収束値を推定することにより、開回路電圧OCV1を求めることができる。 Next, the control unit 14 obtains the open circuit voltage OCV1 from the acquired voltage (step 203). When the charge / discharge amount of the battery 1 continues to be small and the polarization due to charge / discharge is sufficiently eliminated and the voltage is stable, the acquired measured voltage can be regarded as the open circuit voltage OCV1. On the other hand, when the voltage is not stable, the open circuit voltage OCV1 can be obtained by sampling a plurality of voltages in time series and estimating the convergence value of the voltage using an approximate expression. ..

以上の動作を車両が走行を開始する時点まで繰り返して(ステップ204)、開回路電圧OCV1を更新する。最終的に、OCV1は、車両が走行を開始する時点における開回路電圧となる。 The above operation is repeated until the time when the vehicle starts traveling (step 204), and the open circuit voltage OCV1 is updated. Finally, OCV1 becomes the open circuit voltage at the time when the vehicle starts traveling.

車両の走行が判定されると、制御部14は、走行前後の電気量変化量ΔQを求める。具体的には、まず電気量変化量ΔQを0にリセットする(ステップ205)。次に、制御部14は、電流測定部12にバッテリ1の充放電電流を測定するよう要求して、電流測定部12が測定した電流の大きさを取得し、または、電流測定部12が周期的に測定している最新の電流の大きさを記憶部13から取得する(ステップ206)。 When the traveling of the vehicle is determined, the control unit 14 obtains the amount of change in the amount of electricity ΔQ before and after the traveling. Specifically, first, the amount of change in the amount of electricity ΔQ is reset to 0 (step 205). Next, the control unit 14 requests the current measurement unit 12 to measure the charge / discharge current of the battery 1, acquires the magnitude of the current measured by the current measurement unit 12, or causes the current measurement unit 12 to cycle. The latest magnitude of the current being measured is acquired from the storage unit 13 (step 206).

次に、制御部14は、ΔQを更新する(ステップ207)。より具体的には、取得した電流に、直前の測定電流の取得からの時間間隔(例えば、測定周期)を乗じて、測定間に変化したバッテリ1の電気量を求めて、ΔQに加算する。このように、測定した電流から求めた電気量を積算することにより、車両走行開始時点から現時点までの電気量変化量ΔQを求めることができる。 Next, the control unit 14 updates ΔQ (step 207). More specifically, the acquired current is multiplied by the time interval (for example, the measurement cycle) from the acquisition of the immediately preceding measured current to obtain the amount of electricity of the battery 1 that has changed during the measurement, and added to ΔQ. By integrating the amount of electricity obtained from the measured current in this way, it is possible to obtain the amount of change in the amount of electricity ΔQ from the time when the vehicle starts running to the present time.

次に、制御部14は、バッテリ1が満充電あるいは満充電に近い状態(以下、単に「満充電状態」という。)にあるかを判定する(ステップ208)。例えば、充放電電流が所定の閾値より小さくなったときに、満充電状態であると判定することできる。また、電圧測定部11で測定した充電電圧と開回路電圧との差を、電流測定部12で測定した充電電流で除した充電抵抗によって、満充電状態を判定してもよい。満充電状態であると判定された場合には、制御部14は、バッテリ1の充電抵抗に基づいて充電率SOCoを求める(ステップ210)。この際、充電抵抗に加えてエンジン始動時の放電抵抗やパルス放電による抵抗を加えて、充電率SOCoを求めても良い。さらに、温度や充電電圧などの影響を考慮して、求めた充電率SOCoの値を微調整してもよい。充電率SOCoの推定に代えて、簡便的に充電率SOCo=100%としてもよい。 Next, the control unit 14 determines whether the battery 1 is in a fully charged state or a state close to a fully charged state (hereinafter, simply referred to as a “fully charged state”) (step 208). For example, when the charge / discharge current becomes smaller than a predetermined threshold value, it can be determined that the battery is in a fully charged state. Further, the fully charged state may be determined by the charging resistance obtained by dividing the difference between the charging voltage measured by the voltage measuring unit 11 and the open circuit voltage by the charging current measured by the current measuring unit 12. When it is determined that the battery is fully charged, the control unit 14 obtains the charge rate SOCo based on the charge resistance of the battery 1 (step 210). At this time, the charge rate SOCo may be obtained by adding the discharge resistance at the time of starting the engine and the resistance due to pulse discharge in addition to the charge resistance. Further, the obtained charge rate SOCo value may be finely adjusted in consideration of the influence of temperature, charging voltage and the like. Instead of estimating the charge rate SOCo, the charge rate SOCo may be simply set to 100%.

他方、満充電判定(ステップ208)の結果、満充電状態でないと判定された場合には、SOCoの推定(ステップ210)をスキップする。 On the other hand, if it is determined that the battery is not in the fully charged state as a result of the fully charged determination (step 208), the SOCo estimation (step 210) is skipped.

その後、制御部14は、車両が停止状態となるまで、ステップ206〜210を繰り返す(ステップ211)。最終的に、電気量変化量ΔQは、車両の走行開始時点から走行終了時点までに、バッテリ1の充放電により生じた電気量の変化量となる。また、車両走行中にステップ208で満充電と判定された場合には、最終的な充電率SOCoは、車両走行終了時の充電率となる。 After that, the control unit 14 repeats steps 206 to 210 until the vehicle is stopped (step 211). Finally, the amount of change in the amount of electricity ΔQ is the amount of change in the amount of electricity generated by charging / discharging the battery 1 from the start of traveling of the vehicle to the end of traveling. If it is determined in step 208 that the vehicle is fully charged while the vehicle is running, the final charge rate SOCo is the charge rate at the end of the vehicle running.

車両の停止が判定されると、制御部14は、電圧測定部11にバッテリ1の端子間電圧を測定するよう要求して、電圧測定部11が測定した電圧を取得し、または、電圧測定部11が周期的に測定している最新の電圧を記憶部13から取得する(ステップ212)。そして、制御部14は、取得した電圧から、走行終了時点の開回路電圧OCV2を求める(ステップ213)。バッテリ1の充放電量が小さい状態が続き、充放電による分極が十分解消して電圧が安定している場合には、取得した測定電圧を開回路電圧OCV2とみなすことができる。これに対して、電圧が安定していない場合には、時系列的に電圧をサンプリングし、近似式を用いて電圧の収束値を推定することにより、開回路電圧OCV2を求めることができる。 When it is determined that the vehicle is stopped, the control unit 14 requests the voltage measuring unit 11 to measure the voltage between the terminals of the battery 1, and acquires the voltage measured by the voltage measuring unit 11 or the voltage measuring unit. The latest voltage measured periodically by 11 is acquired from the storage unit 13 (step 212). Then, the control unit 14 obtains the open circuit voltage OCV2 at the end of traveling from the acquired voltage (step 213). When the charge / discharge amount of the battery 1 continues to be small and the polarization due to charge / discharge is sufficiently eliminated and the voltage is stable, the acquired measured voltage can be regarded as the open circuit voltage OCV2. On the other hand, when the voltage is not stable, the open circuit voltage OCV2 can be obtained by sampling the voltage in time series and estimating the convergence value of the voltage using an approximate expression.

次に、制御部14は、走行開始時点の開回路電圧OCV1と、走行終了時点の開回路電圧OCV2との差をとることにより、走行開始時点と走行終了時点との間における開回路電圧変化量ΔOCVを求める(ステップ214)。 Next, the control unit 14 takes the difference between the open circuit voltage OCV1 at the start of running and the open circuit voltage OCV2 at the end of running, so that the amount of change in the open circuit voltage between the start of running and the end of running Obtain ΔOCV (step 214).

また、制御部14は、車両走行中の電気量変化量ΔQの絶対値が所定の閾値より大きい否かを判定する(ステップ215)。電気量変化量ΔQの絶対値が所定の閾値以下の場合には、誤差の影響が大きくなり、推定結果の精度が劣化する懸念があることから、走行開始前の開回路電圧OCV1を求める工程(ステップ202、203)に戻って、次に車両の走行前後の時点における、開回路電圧変化量ΔOCVと電気量変化量ΔQを求める。 Further, the control unit 14 determines whether or not the absolute value of the amount of change in the amount of electricity ΔQ while the vehicle is running is larger than a predetermined threshold value (step 215). When the absolute value of the amount of change in electric energy ΔQ is equal to or less than a predetermined threshold value, the influence of the error becomes large and there is a concern that the accuracy of the estimation result deteriorates. Returning to steps 202 and 203), the open circuit voltage change amount ΔOCV and the electric amount change amount ΔQ at the time before and after the vehicle travels are obtained.

車両走行中の電気量変化量ΔQの絶対値が所定の閾値より大きい場合には、対応する開回路電圧変化量ΔOCVも大きいと考えられることから、高い推定精度が期待できる。この場合、制御部14は、求めた開回路電圧変化量ΔOCVと電気量変化量ΔQとから、両者の比率を求める(ステップ216)。本実施態様では、記憶部13に格納されている既知の相関30が、単位電気量変化量当たりの電圧変化量と満充電容量との相関であることから、比率としてΔOCV/ΔQを求める。 When the absolute value of the amount of change in the amount of electricity ΔQ while the vehicle is running is larger than a predetermined threshold value, the corresponding amount of change in the open circuit voltage ΔOCV is also considered to be large, so that high estimation accuracy can be expected. In this case, the control unit 14 obtains the ratio of both from the obtained open circuit voltage change amount ΔOCV and the electric amount change amount ΔQ (step 216). In the present embodiment, since the known correlation 30 stored in the storage unit 13 is the correlation between the voltage change amount per unit electric amount change amount and the fully charged capacity, ΔOCV / ΔQ is obtained as a ratio.

次に、制御部14は、記憶部13に格納されている既知の相関30を参照して、求めたΔOCV/ΔQに対応する満充電容量SOHを求めることにより、満充電容量SOHを推定する(ステップ217)。なお、記憶部13に格納されている既知の相関30が、単位電圧変化量に対する電気量変化量と満充電容量との相関であるときには、比率としてΔQ/ΔOCVを求めて、対応する満充電容量SOHを推定することができる。推定した満充電容量SOHは記憶部13に格納され、必要に応じて車両やバッテリ1の制御に利用することができる。 Next, the control unit 14 estimates the full charge capacity SOH by obtaining the full charge capacity SOH corresponding to the obtained ΔOCV / ΔQ with reference to the known correlation 30 stored in the storage unit 13 (). Step 217). When the known correlation 30 stored in the storage unit 13 is the correlation between the amount of change in the amount of electricity and the full charge capacity with respect to the amount of change in the unit voltage, ΔQ / ΔOCV is obtained as a ratio and the corresponding full charge capacity is obtained. SOH can be estimated. The estimated full charge capacity SOH is stored in the storage unit 13 and can be used for controlling the vehicle and the battery 1 as needed.

以上により、推定を行うバッテリ1の特性(VM、V0、OCVとSOCとの相関など)が未知の場合でも、バッテリ1の電圧・電流の測定値から、精度よく満充電容量SOHを推定することが可能となる。 From the above, even if the characteristics of the battery 1 to be estimated (VM, V0, correlation between OCV and SOC, etc.) are unknown, the full charge capacity SOH can be accurately estimated from the measured values of the voltage and current of the battery 1. Is possible.

バッテリ状態推定装置10は、さらに、図4に示すようなバッテリ1の開回路電圧OCVと充電率SOCとの相関40を推定することができる。具体的には、まずステップ205〜207により求めた車両の走行前後の時点における電気量変化量ΔQを、ステップ217で推定した満充電容量SOHで除して、充電率変化量ΔSOCを求める(ステップ218)。求めた充電率変化量ΔSOCは、車両の走行前後の時点における開回路電圧変化
量ΔOCVに対応する充電率変化量ΔSOCである。よって、開回路電圧変化量ΔOCVと充電率変化量ΔSOCとから、開回路電圧OCVと充電率SOCとの相関40の傾き42を求めることができる。
The battery state estimation device 10 can further estimate the correlation 40 between the open circuit voltage OCV of the battery 1 and the charge rate SOC as shown in FIG. Specifically, first, the amount of change in electricity amount ΔQ obtained in steps 205 to 207 before and after the vehicle travels is divided by the full charge capacity SOH estimated in step 217 to obtain the amount of change in charge rate ΔSOC (step). 218). The obtained charge rate change amount ΔSOC is a charge rate change amount ΔSOC corresponding to the open circuit voltage change amount ΔOCV before and after the vehicle travels. Therefore, the slope 42 of the correlation 40 between the open circuit voltage OCV and the charge rate SOC can be obtained from the open circuit voltage change amount ΔOCV and the charge rate change amount ΔSOC.

次に、制御部14は、満充電状態における充電率SOCoを求めることができたか否かを判定する(ステップ219)。充電率SOCoを求めることができた場合には、車両走行停止直後に推定された開回路電圧OCV2を、満充電状態のときの閉開回路電圧OCVoとする(ステップ220)。充電率SOCoを求めることができた場合とは、すなわち走行中に満充電判定がなされた場合であるから、充電率SOCoには、車両走行終了時の満充電状態の充電率が記録されている。そして、車両走行停止直後に推定された開回路電圧OCV2は、充電率SOCoに対応する開回路電圧である。 Next, the control unit 14 determines whether or not the charge rate SOCo in the fully charged state could be obtained (step 219). When the charge rate SOCo can be obtained, the open circuit voltage OCV2 estimated immediately after the vehicle stops running is set to the closed circuit voltage OCVo in the fully charged state (step 220). Since the charge rate SOCo can be obtained, that is, the case where a full charge determination is made during driving, the charge rate SOCo records the charge rate in the fully charged state at the end of vehicle driving. .. The open circuit voltage OCV2 estimated immediately after the vehicle stops running is the open circuit voltage corresponding to the charge rate SOCo.

したがって、求めたOCVoおよびSOCoから相関40上の点41を特定することができる。特定された点41と傾き42とから直線を求めることにより、バッテリ1の開回路電圧OCVと充電率SOCとの相関40を推定することができる(ステップ221)。推定した相関40は、テーブルや近似式など所望の形式で記憶部13に格納され、必要に応じて車両やバッテリ1の制御に利用することができる。他方、ステップ219において、満充電状態における充電率SOCoを求められていない場合には、開回路電圧OCVと充電率SOCとの相関40を推定せずに終了する。 Therefore, the point 41 on the correlation 40 can be identified from the obtained OCVo and SOCo. By obtaining a straight line from the specified point 41 and the slope 42, the correlation 40 between the open circuit voltage OCV of the battery 1 and the charge rate SOC can be estimated (step 221). The estimated correlation 40 is stored in the storage unit 13 in a desired format such as a table or an approximate expression, and can be used for controlling the vehicle or the battery 1 as needed. On the other hand, in step 219, when the charge rate SOC in the fully charged state is not obtained, the process ends without estimating the correlation 40 between the open circuit voltage OCV and the charge rate SOC.

以上の方法により、推定を行うバッテリ1の特性(VM、V0、OCVとSOCとの相関など)が未知の場合でも、バッテリ1の電圧・電流の測定結果から、精度よく開回路電圧OCVと充電率SOCとの相関40を推定することが可能となる。 By the above method, even if the characteristics of the battery 1 to be estimated (VM, V0, correlation between OCV and SOC, etc.) are unknown, the open circuit voltage OCV and charging can be performed accurately from the measurement results of the voltage and current of the battery 1. It is possible to estimate the correlation 40 with the rate SOC.

以上、本発明にかかるバッテリの状態を推定する方法、装置、プログラム、および該プログラムを記録した記録媒体ついて説明を行ったが、本発明は上記の実施の形態に限定されるものではなく、本発明の概念及び特許請求の範囲に含まれるあらゆる態様を含む。例えば、上述した実施態様では、車載用の鉛バッテリの状態推定方法等を一例として説明したが、太陽光発電などで発電された電気を蓄積しておくバッテリなどの車載以外の、また鉛蓄電池以外のバッテリの状態推定にも適用することが可能である。また、記憶部に格納されている既知の相関30は線形近似ではなく、多変数関数近似による相関であってもよい。 Although the method, apparatus, program for estimating the state of the battery according to the present invention, and the recording medium on which the program is recorded have been described above, the present invention is not limited to the above embodiment, and the present invention is not limited to the above embodiment. Includes all aspects of the concept of the invention and claims. For example, in the above-described embodiment, a method of estimating the state of a lead battery for an in-vehicle use has been described as an example, but a battery for storing electricity generated by solar power generation or the like other than the in-vehicle use, or a lead-acid battery other than the lead-acid battery. It can also be applied to battery state estimation. Further, the known correlation 30 stored in the storage unit may be a correlation by a multivariable function approximation instead of a linear approximation.

1 バッテリ
2 充電回路
3 負荷
10 バッテリ状態推定装置
11 電圧測定部
12 電流測定部
13 記憶部
14 制御部
1 Battery 2 Charging circuit 3 Load 10 Battery state estimation device 11 Voltage measuring unit 12 Current measuring unit 13 Storage unit 14 Control unit

Claims (7)

バッテリの状態を推定する方法であって、
前記バッテリの電圧と充放電電流とをそれぞれ時系列的に測定するステップと、
測定した前記電圧に基づいて、異なる2つの時点における、前記バッテリの開回路電圧を求めるステップと、
前記開回路電圧に基づいて、前記異なる2つの時点間における開回路電圧変化量を求めるステップと、
測定した前記充放電電流に基づいて、前記異なる2つの時点間における、前記バッテリの電気量変化量を求めるステップと、
前記開回路電圧変化量と前記電気量変化量との比率を求めるステップと、
満充電容量が異なる複数のバッテリの、開回路電圧変化量と電気量変化量との比率と、満充電容量との既知の相関、および、求めた前記比率に基づいて、前記バッテリの満充電容量を推定するステップと、
を含む、方法。
A method of estimating the state of the battery
The step of measuring the voltage of the battery and the charge / discharge current in chronological order, respectively.
The step of obtaining the open circuit voltage of the battery at two different time points based on the measured voltage, and
A step of obtaining the amount of change in the open circuit voltage between the two different time points based on the open circuit voltage, and
A step of obtaining the amount of change in the amount of electricity of the battery between the two different time points based on the measured charge / discharge current, and a step of obtaining the amount of change in the amount of electricity of the battery.
The step of obtaining the ratio between the amount of change in the open circuit voltage and the amount of change in the amount of electricity,
Based on the known correlation between the ratio of the open circuit voltage change amount and the electricity amount change amount of a plurality of batteries having different full charge capacities and the full charge capacity, and the obtained ratio, the full charge capacity of the battery is obtained. And the steps to estimate
Including methods.
前記バッテリは、車両に搭載されたバッテリであり、
前記異なる2つの時点は、前記車両の走行前後の時点である、
請求項1に記載の方法。
The battery is a battery mounted on a vehicle.
The two different time points are the time points before and after the vehicle travels.
The method according to claim 1.
前記電気量変化量および推定した前記満充電容量に基づいて、充電率変化量を求めるステップと、
前記バッテリがほぼ満充電のときの充電率および開回路電圧を求めるステップと、
前記開回路電圧変化量、前記充電率変化量、並びに、前記バッテリがほぼ満充電のときの充電率および開回路電圧に基づいて、前記バッテリの開回路電圧と充電率との相関を推定するステップと、
をさらに含む、請求項1または2に記載の方法。
A step of obtaining a charge rate change amount based on the electricity amount change amount and the estimated full charge capacity, and a step of obtaining the charge rate change amount.
Steps to obtain the charge rate and open circuit voltage when the battery is almost fully charged, and
A step of estimating the correlation between the open circuit voltage and the charge rate of the battery based on the open circuit voltage change amount, the charge rate change amount, and the charge rate and the open circuit voltage when the battery is almost fully charged. When,
The method according to claim 1 or 2, further comprising.
バッテリの状態を推定する装置であって、
前記バッテリの電圧を測定する電圧測定部と、
前記バッテリの充放電電流を測定する電流測定部と、
満充電容量が異なる複数のバッテリの、開回路電圧変化量と電気量変化量との比率と、満充電容量との既知の相関を格納する記憶部と、
前記電圧測定部、前記電流測定部、および前記記憶部と通信可能な制御部と、
を備え、
前記制御部は、
前記電圧測定部により測定された前記バッテリの電圧と、前記電流測定部により測定された前記バッテリの充放電電流とを、それぞれ時系列的に取得し、
取得した前記電圧に基づいて、異なる2つの時点における、前記バッテリの開回路電圧を求め、
前記開回路電圧に基づいて、前記異なる2つの時点間における開回路電圧変化量を求め、
取得した前記充放電電流に基づいて、前記異なる2つの時点における、前記バッテリの電気量変化量を求め、
前記開回路電圧変化量と前記電気量変化量との比率を求め、
前記相関および求めた前記比率に基づいて、前記バッテリの満充電容量を推定する
ように構成されている、
装置。
A device that estimates the state of the battery
A voltage measuring unit that measures the voltage of the battery,
A current measuring unit that measures the charge / discharge current of the battery,
A storage unit that stores a known correlation between the ratio of the open circuit voltage change amount and the electricity amount change amount and the full charge capacity of a plurality of batteries having different full charge capacities.
A voltage measuring unit, a current measuring unit, and a control unit capable of communicating with the storage unit,
With
The control unit
The voltage of the battery measured by the voltage measuring unit and the charge / discharge current of the battery measured by the current measuring unit are acquired in time series, respectively.
Based on the acquired voltage, the open circuit voltage of the battery at two different time points is obtained.
Based on the open circuit voltage, the amount of change in the open circuit voltage between the two different time points is obtained.
Based on the acquired charge / discharge current, the amount of change in the amount of electricity of the battery at the two different time points was obtained.
Obtain the ratio of the open circuit voltage change amount and the electric amount change amount,
It is configured to estimate the full charge capacity of the battery based on the correlation and the calculated ratio.
Device.
前記制御部は、さらに、
前記電気量変化量および推定した前記満充電容量に基づいて、充電率変化量を求め、
取得した前記電圧に基づいて、前記バッテリがほぼ満充電のときの充電率および開回路電圧を求め、
前記開回路電圧変化量、前記充電率変化量、並びに、前記バッテリがほぼ満充電のときの充電率および開回路電圧に基づいて、前記バッテリの開回路電圧と充電率との相関を推定する
ように構成されている、請求項4に記載の装置。
The control unit further
Based on the amount of change in the amount of electricity and the estimated full charge capacity, the amount of change in the charge rate was obtained.
Based on the acquired voltage, the charge rate and open circuit voltage when the battery is almost fully charged are obtained.
To estimate the correlation between the open circuit voltage and the charge rate of the battery based on the open circuit voltage change amount, the charge rate change amount, and the charge rate and the open circuit voltage when the battery is almost fully charged. The device according to claim 4, which is configured in the above.
バッテリの電圧を測定する電圧測定部と、
前記バッテリの充放電電流を測定する電流測定部と、
満充電容量が異なる複数のバッテリの、開回路電圧変化量と電気量変化量との比率と、満充電容量との既知の相関を格納する記憶部と、
プロセッサを備え、前記電圧測定部、前記電流測定部、および前記記憶部と通信可能な制御部と、
を備える、バッテリの状態を推定する装置の制御プログラムであって、
前記プロセッサに、
前記電圧測定部により測定された前記バッテリの電圧と、前記電流測定部により測定された前記バッテリの充放電電流とを、それぞれ時系列的に取得し、
取得した前記電圧に基づいて、異なる2つの時点における、前記バッテリの開回路電圧を求め、
前記開回路電圧に基づいて、前記異なる2つの時点間における開回路電圧変化量を求め、
取得した前記充放電電流に基づいて、前記異なる2つの時点における、前記バッテリの電気量変化量を求め、
前記開回路電圧変化量と前記電気量変化量との比率を求め、
前記相関および求めた前記比率に基づいて、前記バッテリの満充電容量を推定する
機能を実行させる、
プログラム。
A voltage measuring unit that measures the voltage of the battery and
A current measuring unit that measures the charge / discharge current of the battery,
A storage unit that stores a known correlation between the ratio of the open circuit voltage change amount and the electricity amount change amount and the full charge capacity of a plurality of batteries having different full charge capacities.
A control unit including a processor and capable of communicating with the voltage measuring unit, the current measuring unit, and the storage unit.
A control program for a device that estimates the state of a battery.
To the processor
The voltage of the battery measured by the voltage measuring unit and the charge / discharge current of the battery measured by the current measuring unit are acquired in time series, respectively.
Based on the acquired voltage, the open circuit voltage of the battery at two different time points is obtained.
Based on the open circuit voltage, the amount of change in the open circuit voltage between the two different time points is obtained.
Based on the acquired charge / discharge current, the amount of change in the amount of electricity of the battery at the two different time points was obtained.
Obtain the ratio of the open circuit voltage change amount and the electric amount change amount,
The function of estimating the full charge capacity of the battery is executed based on the correlation and the obtained ratio.
program.
請求項6に記載されたプログラムが記録された、コンピュータ読み取り可能な記録媒体。 A computer-readable recording medium on which the program according to claim 6 is recorded.
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