〉〉 Automotive Products・Electronics

Lead-acid Battery State Sensor～Development of Battery Full Charge Detection TechniqueWith Internal Resistance～
Noriyasu Iwane*

After we succeeded in launching the lead-acid battery state sensor as the only
one supplier in Japan, we have been making our best effort in improving theaccuracy to gain more market share. From the viewpoint of controlling the automotive fuel efficiency and securing the reliability of the automotive power source, we think that it is definitely
most important to detect the battery charge rate (SOC = State of Charge). It is necessary to combine several different elemental techniques to improve the estimated accuracy of the SOC. Oneof the typical ones among these techniques is the full charge detection. Its purpose is to detectthat the battery reaches almost full charging state and set the SOC at the point as Full-Charge
100% to be the starting point from there on. Therefore, this accuracy will influence the wholeestimated accuracy from there on. We have developed our original full charge detection technique applied from our original detection index “resistance ratio” which is based on the combination of the internal resistance increasing at charging and our battery equivalent circuit model
learning technique from the pulse discharge. And we have succeeded in improving the SOC
detection accuracy. Here, we are going to report the outline of our success mentioned above.

ABSTRACTINTRODUCTION
1.1. INTRODUCTION
Recently in the automobiles, the power source has beenrequired to be more reliable, as more and more electricaland electronic components are adopted and the optimum
fuel efficiency control is getting common as well. It is also
getting common to equip with the lead-acid battery state
sensor which monitors the state of an automotive battery
to secure its reliability. We, as the only one supplier of thislead-acid battery state sensor in Japan, launched our first
Battery State Sensor (BSS) in 2012 and have alreadyshipped more than 10 million in the cumulative total until
now. In near future, a major change is expected in the
structure of the overall power source system because
higher quality of the power source is required for the
automatic driving. And the market scale of lead-acid battery state sensors is expected to continue growing. Alongwith the growing market, we are making our best effort in
improving the performance of BSS to be more competitive to gain more market share. Figure 1 shows an example of our products.
It is the most fundamental function required to the BSS
to estimate the charged rate (SOC=State of Charge) at
any point in time against the full charge capacity. The
improvement of the accuracy and reliability of this function against the current level is always demanded*

Automotive Products & Electronics Laboratories, R&D Divisionbecause it is not only the index of the power supply ability of the battery at this point but also the basic information applied to the optimal fuel efficiency control of avehicle represented by the start-stop control. It is necessary to combine several different elemental techniques torealize the improvement of accuracy. One of the very
important ones among these techniques is the full charge
detection which detects that the battery reaches almost
full charge state. It plays not only to improve the SOC
estimation accuracy but also to cancel the accumulated
estimation errors to secure the stable power supply ability
by detecting signs of the battery approaching its fullcharge state to switch the SOC to 100% or the value ofFull Charge 100% which seems more certain. The fullcharge detection is very important because it influences
the SOC estimation accuracy. And almost every company
makes efforts in constructing the optimal detection logic
of it as well.

Figure 1 Battery state sensor (made by FAS).

Furukawa Electric Review, No. 51 2020

44〉〉 Automotive Products・Electronics

Lead-acid Battery State Sensor ~Development of Battery Full Charge Detection Technique With nternal Resistance ~SOC
ESTIMATIONANDFULLCHARGECHARGE
2.2.SOCESTIMATIONAND
FULL
DETECTION
DETECTION
Unfortunately, it is impossible to measure the SOC (=theamount rate of electricity charged in a battery) directly inan actual vehicle. Therefore, it is necessary to estimate itby calculation with the BSS based on the information ofcurrent, voltage and temperature which can be directly
measured under the automotive environment. This is themost important function required to the BSS. There are
two important pillars for the estimating calculations: oneis the calculation of the change of SOC based on theamount of electricity in and out of a battery and the otheris the calculation of SOC based on the stable OpenCircuit Voltage (OCV) which has a linear relation with the
SOC of a lead-acid battery 2). However, we have to solve
some problems to secure the accuracy in a lead-acid battery equipped in an actual vehicle. First, as for the current
integration, the error of full charged capacity is cumulated
when converting the amount of electricity in and out tothe percentage of SOC. The full charged capacity isdecreasing little by little with the deterioration of the battery and it becomes an obstacle to secure the SOC accuracy. Equation (1) shows the relation between the SOC
and the full charged capacity.
SOC = (the amount of electricity charged / full charged
capacity) × 100(1)Next, as for the linear relation between a lead-acid battery and the stable OCV, we can say, first of all, that it isdifficult to measure the stable OCV accurately under theactual automotive environment. It is caused by the condition of a battery that either charge or discharge current isalways flowing to and from it during the actual operationof a vehicle and the over voltage is added to it. It isalmost impossible to measure the stable OCV directly
except for such a case of a weekend driver because along inactive time without any current flowing is necessary until the over voltage has dissipated. We havealready developed our original technique 3), 4) to estimate
the stable OCV based on the dissipation process of theover voltage and succeeded in reducing the SOC estimation error. But we have not solved the error perfectly, yet.
As the value of SOC against the voltage varies in eachindividual battery, it is practically impossible to equip abattery sensor with the relation logic adapted to eachindividual battery mounted in a vehicle. This individual difference generates the SOC estimation error. Further,along with using a battery, the relation may change fromthe initial condition caused by the influence of changes in
the concentration and the deterioration of its electrolyte.
It is a general method to secure the stable performanceof the power source under restrictions on the accuracy
that the SOC is switched to the value of 100% or FullCharge 100% at the point when detecting the full charge
condition of SOC around 100% and setting this as thestarting point and that the calculation & control is carriedout to control the SOC within a certain range based on
the starting point. And in addition to the method mentioned above, in order to maintain the accuracy of SOC
estimation, the OCV-SOC relation is matched to fit amounted battery with making use of the function of thefull charge detection to control the individual difference
between the stable OCV and the linear relation and thoseerrors generated by changes caused by the deterioration.

CONTENTSDEVELOPED TECHNIQUETECHNIQUE
3.3.CONTENTS
OFOFDEVELOPED
3.1

Full Charge Detection With Applying the“Resistance Ratio”
As mentioned above, the full charge detection of a battery has been applied ever since, and the behavior of current during charging has been mainly applied to it as a
specific technique. Figure 2 shows an example of therelation between the SOC and the charging current offour batteries different in sizes and made by different
makers when charging under the same condition with noinfluence from any disturbance.
60

Company A M-42
Company B M-42
Company C 55B24
Company D 85D23

50
Current（A）

We found out that a battery had such characteristic as
the internal resistance at charging increased whenapproaching the full charge state and focused on it.
Further, we combined it with our original battery equivalent circuit model 1) learning technique by pulse discharging to design our original detection index “resistanceratio”. We have developed such technique as to maintainthe accuracy by applying it even for any battery of different sizes or made by different manufacturers. In addition,
we have developed the correction technique against mainouter error factors in the detection together with it andhave succeeded in developing the logic as well to maintain the accuracy in the practical range of automotive
environment.

40
30
20
10
0

70

75

80

85

90

95

100

SOC
（%）
Figure 2 Relation between the charging current and the SOC.

As shown in Figure 2, the charging current of a battery
is decreasing along with the progress of the charge andthe increase of SOC. The detection techniques to use thedecrease of current as an index are most generally andFurukawa Electric Review, No. 51 202045〉〉 Automotive Products・Electronics

Lead-acid Battery State Sensor ~Development of Battery Full Charge Detection Technique With nternal Resistance ~R_charge = ΔV / I(2)ΔV : Difference between the charging voltage and theopen circuit voltage
I : Charging current
There is a merit to adopt the resistance as an index as
the detection sensitivity is improved and as easy settingof the threshold is realized because the resistance value
is highly increased in the shape of a hyperbolic curvealong with the decrease of current as the current is adenominator of the equation.
And as a corrective action against the error in the current behavior at charging caused by individual differenceof each battery, we tried to combine the charging resistance with the internal resistance gained from the equivalent circuit model learning technique by the pulse discharge which is a feature of our BSS. An example of theequivalent circuit model of a lead-acid battery is shown in
Figure 3.
Rct1

Rct2

（reaction resistance 2）（reaction resistance 1）

Rohm（conductive resistance,
solution resistance）

C1（double layer
capacitance 1）

C2（double layer
capacitance 2）

Figure 3 An example of the equivalent circuit model.

One of the great pillars for our lead-acid battery state
detection technique is to learn the equivalent circuit models including every resistant element in a battery by carrying out the pulse discharge during an idle period of avehicle and the state of battery is estimated based on thislearnt information 5). As the pulse discharge internal resistance during an idle period of a vehicle is reflecting thesize of battery, the difference of the designed internal
resistance value, and the changes caused by the deterioration, we thought that the influence caused by the individual difference of batteries could be improved if correcting the resistance value at charging with the information of internal resistance measured by the pulse discharge. As a result of examination, we designed our original index, that is the resistance ratio = R_ratio and adopted it. Our way of thinking of the resistance ratio (R_ratio)
is shown in Equation (3).
R_ratio = f (R_charge, Rohm, Rct1)(3)“f” is a function to calculate “R_ratio”, and “Rohm” and“Rct1” learnt by the pulse discharge and the charge current resistance “R_charge” are given to the “ f ” as its
input. As shown in Figure 3, Rohm reflects the conductive
resistance of a mounted battery and Rct1 reflects thereaction resistance at the pulse discharge. The relation
between the resistance ratio R_ratio and the SOC calculated by the optimized equation and coefficients is shownin Figure 4.
150

Resistance ratio

frequently applied. On the other hand, as shown in Figure
2, it is difficult to set a clear threshold, because the curveof decreasing current following the increasing SOC
slopes very gently down to zero. And when setting thesame current threshold, such a case was known that
there was a large difference in the relation of the charging
current and the SOC even if the sizes of batteries were
the same. An example shown in Figure 2 shows actual
gaps between each SOC as large as 93% to 98% whensetting the threshold current at 5 A. Naturally enough, theerror becomes much larger when considering the influence of disturbance. Therefore, it is estimated that highly
accurate detection of the full charge cannot be realizedwith only setting a simple threshold on the current value.
At first, we tried to use the resistance at charging as anindex to improve the accuracy of detection mentioned
above. Equation (2) shows our way of thinking of theresistance at charge R_charge.

Company A M-42
Company B M-42
Company C 55B24
Company D 85D23

100

50

0
70

75

80

85

90

95

100

SOC
（%）
Figure 4 Relation between R_ratio and SOC.

When setting 120 as a threshold of the resistance ratio
at which the average period required until detecting thefull charge from start of charging is as same level as thatin case of the detection at current 5 A shown in Figure 2,
the range of actual SOC was as small as 97% to 98%,
that is, the estimation error has become only one fifth ofthat in the case of applying a simple current value as anindex. In this way we have realized the detection at a highsensitivity but with little influence from the individual difference of batteries.
3.2 Influencing Factors to the Full Charge Detection
The relation curves shown in Figure 4 above are theresults after charging under the same condition. However,
the relation between the resistance ratio and the SOC
may change depending on the difference in the actual
operating environment. The difference will be major factors to cause disturbance errors. There are three major
factors as mentioned bellow.
Furukawa Electric Review, No. 51 202046〉〉 Automotive Products・Electronics

Lead-acid Battery State Sensor ~Development of Battery Full Charge Detection Technique With nternal Resistance ~Resistance ratio

150

100

Next, Figure 7 shows an example of the relation
between the resistance ratio and the SOC based on thevarious charging voltage levels when other conditions
than charging voltage (temperature=0°C, SOC at initialcharging=70%) are fixed.
150

Resistance ratio1) Temperature
2) SOC at initial charging
3) Charging voltage
The result of each influence is explained as follows.
Figure 5 shows an example of the relation between theresistance ratio and the SOC based on the various temperature levels when other conditions than temperature(SOC at initial charging = 70%, charging current = 14.4 V)
are fixed.
-10℃
0℃
10℃
25℃
45℃
65℃

100

50

0
70

50

Charging voltage: 13.5V
Charging voltage: 14.4V
Charging voltage: 15.3V

75

80

85

90

95

100

SOC（%）
0
70

75

80

85

90

95

100

SOC
（%）
Figure 5 Difference of the relation between the resistance ratio
and the SOC caused by the different temperature.

Figure 5 explains that the lower the temperature
becomes, at the lower SOC the resistance ratio tends toincrease. When assuming the threshold is 120, there is a
gap of 87% to 99% in SOC at –10°C to +65°C even if thesensitivity and the accuracy are improved by using theresistance ratio. Therefore, no full charge detection can becorrect unless the proper SOC value shall be set in accordance with the temperature when the temperature varies.
As shown in Figure 6, lower the SOC at initial charging
becomes, at the lower SOC the resistance ratio increases. When setting the threshold at 120 and assuming the
SOC at initial charging = 30% which will occur extremely
seldom in an actual vehicle, there will be the gap of 73%
to 99% in the SOC at detection. Therefore, no full charge
detection can be correct unless the proper SOC value
shall be set in accordance with the SOC at initial charging
when it varies as well as the temperature.

Resistance ratio

150

100

SOC at initial charging: 30%
SOC at initial charging: 50%
SOC at initial charging: 70%
SOC at initial charging: 90%

40

50

60

70

As shown in Figure 7, the lower the charging becomes,
at the lower SOC the resistance ratio increases. Whensetting the threshold at 120 and assuming the charging
voltage as 13.5 V to 15.3 V, the range of SOC at detectionis 82% to 95%. Therefore, it explains that no full charge
detection can be correct unless the proper SOC value
shall be set in accordance with the charging voltage when
it varies as well as either the temperature or the SOC atinitial charging.
As mentioned above, our originally designed resistanceratio is successful in realizing the high accuracy against
batteries various in their sizes and manufactures whencharged under the same condition. However, it is necessary to add proper correction by considering the error
factors caused by disturbance, those are 1) temperature,2) SOC at initial charging and 3) charging voltage in orderto maintain the accuracy even if the condition varies
under the actual automotive environment.
3.3 Counter Measures Against the Influencing Factors
We have adopted such logic against those three error
factors mentioned in the former chapter, that carries out
the calculation fundamentally based on our way shown inEquation (4) below.
Full charged SOC = g (R_ratio, temperature, SOC atinitial charging, charging voltage)(4)

50

0
30

Figure 7 Difference of the relation between the resistanceratio and the SOC caused by difference of charging
voltage.

80

90

100

SOC
（%）
Figure 6 Difference of the relation between the resistance ratio
and the SOC caused by difference of SOC at initialcharging.

“g” is a function to calculate the SOC when detecting
the full charge, and each of the error factors, temperature,
the SOC at initial charging and the charge voltage are
input to the “g” as well as the resistance ratio R_ratio as
its input. Those three error factors were explained one by
one in Figure 5 to Figure 7 shown above. However, influence caused by each error factor is actually not indepenFurukawa Electric Review, No. 51 2020

47

Lead-acid Battery State Sensor ~Development of Battery Full Charge Detection Technique With nternal Resistance ~

15
10
5
0
-5

-10

13

13.5

14

14.5

15

15.5

Charging voltage（V）
Figure 8 Error of the full charge detection when ignoring thecharging voltage.

1.02

1.05
1
0.95
0.9

60

0.85
13.5
13.6
13.7
13.8
13.9
14
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
15
15.1
15.2
15.3

Normalized value（= Correction coeﬃcient）

The degree of errors varies because the degree of influence caused by the charging voltage varies depending on
the other conditions mentioned above. Typical trend of
the influence to the SOC at the full charge detection isshown in Figure 9.

1
0.98
0.96

Temperature（℃）

Estimation error（％）

20

normalized in order to set the charging voltage 14.4 V as
the standard value 1. The curve plotted over the actually
measured dots is the output of the function to which the
charging voltage is entered as its input. If applying thisfunction, the predicted relative value at any charging voltage can be calculated based on the value at 14.4 V
charging. Using it as the correction coefficient, the estimated SOC adopted on the assumption that the charging
voltage is 14.4 V can be corrected to be the estimated
SOC corresponding to the actual charging voltage.
Our basic thought on the correction against the influence of charging voltage is mentioned above. However,
the absolute value will change with keeping the trend
shown in Figure 9 when the condition varies, although thetemperature and the SOC at initial charging are fixed at a
certain condition. In order to make it able to consider thedifference in the degree of influence on the charging voltage caused by temperature and the SOC at initial charging, it is necessary to calculate the correction coefficientby the 4-dimensional function to which the charging voltage, temperature and the SOC at initial charging areentered as its input after carrying out the same analysis
as shown in Figure 9 under many conditions and investigating the relation of the coefficient against temperatureand the SOC at initial charging to replace the coefficientof the function which calculates the correction coefficientfor the influence of charging voltage to the function oftemperature and the SOC at initial charging. As it is difficult to visualize a complete 4-dimensional function, an
example of SOC at initial charging=70%, a 3-dimensional
curved surface of correction coefficient against charging
voltage and temperature is shown below in Figure 10.

Correction coeﬃcient

dent but affected each other. The degree of influence may
change linked with the change of other conditions, while
there are no changes in the trend of individual influence.
Therefore, the actual equation becomes very complex.
Our fundamental way of thinking is explained based on
an example of our corrective action against the influenceof charging voltage adopted at the last.
In Figure 8 shown below, the estimation error whenestimated in the range of temperature from –10 to +65°C
and the SOC at initial charging=70 to 90% based on theequation which has already included the countermeasureagainst the influence caused by the SOC at initial charging and is based on the assumption that the charging
voltage is fixed at 14.4 V. As it can be estimated from thetrend shown in Figure 7, the actual SOC tends to belower than the estimated value when charging at low temperature and it looks like as if a positive error is added on
the estimated value.

〉〉 Automotive Products・Electronics

20-20

Charging voltage（V）

0.94

Figure 10 A 3-dimensional curved surface of correction
coefficient vs. charging voltage and temperature.

0.92
0.9
0.88
0.86
13

13.5

14

14.5

15

15.5

Charging voltage（V）
Figure 9 Normalized SOC at full charge detection against
various charging voltage.

Those dots shown in Figure 9 are the relative values of
averaged SOC actually measured when detecting the fullcharge of a battery under a single resistance ratio andOur way to correct the influence of charging voltage
has been already mentioned above. That of the temperature is about the same and that of the SOC at initialcharging is as well. Integrating all of those mentioned
above, the equation (4) is finally completed. Using theequation (4) which even includes correcting the influenceof charging voltage, we have improved the errors shownin Figure 8 to be those shown in Figure 11 below.

Furukawa Electric Review, No. 51 2020

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Lead-acid Battery State Sensor ~Development of Battery Full Charge Detection Technique With nternal Resistance ~Estimation error
（％）

20
15
10
5
0
-5

-10

13

13.5

14

14.5

15

15.5

Charging voltage（V）
Figure 11 Error of the estimated full charge when considering
the charging voltage.

The full charge detection with the maximum error range
from +3.35% to – 6.03% has been realized by our theoretical calculation based on our evaluation data tested ona total of 18 batteries of various models in the range ofthe battery temperature=–10°C to +65°C, the SOC at initial charging = 70% or more, and the charging voltage=13.5 V to 15.3 V.

CONCLUSION
4.4.CONCLUSION
As mentioned above, as a result of that we have madeuse of the merit of our equivalent circuit model learningtechnique based on our original pulse charging method to
introduce our original index “resistance ratio” and that wehave combined the correction techniques against thethree disturbance factors at the full charge detection suchas 1) temperature, 2) SOC at initial charging and 3) charging voltage, we have succeeded in the development of
the highly accurate full charge detection technique whichis stable in the practical range of the temperature, the
SOC at initial charging and the charging voltage.
However, on the other hand, in the actual automotive
environment, we have no such stable charging as that in
our assumed environment where our logic was adopted
and there are not only the charging voltage switched stepby step but also busy switching between charging anddischarging. As a matter of fact, in our logic loaded on an
actual vehicle, the weighted averaging process wasadded to secure the equivalent accuracy based on thecurrent data and the voltage data typical in an actual
vehicle. Even though, a guard function is equipped to
bypass the processing when it is judged as difficult tomaintain the accuracy. Further, it is required to continue
improving the logic to be freer from any restriction andeasier to use.
And in our full charge detection, it is required to add noless than a certain quantity of charging to reach thethreshold. In general, the nearer the threshold is set to
SOC = 100% strictly, the higher the accuracy of SOC at
the detection can be. But on the other hand, the longer
period is required to continue charging. We have already
improved this problem with introducing our original index〉〉 Automotive Products・Electronics

resistance ratio. However, as there is an infinite variety of
how to use a vehicle. It is applicable to have a very accurate estimation with setting the strict threshold in such avehicle like a taxi as is expected to have a long operatingtime almost every day. But on the other hand, in such avehicle as is used only for dairy shopping, the function
falls into such condition that it seldom works. As a matterof course, it is preferable to set the threshold reached in ashort time from the viewpoint of frequency of functional
operation, but such detection is meaningless since it cannot maintain the required accuracy. To make appropriate
responses to the problem mentioned above, it is necessary to be able to judge objectively the accuracy against
the range and the probability of securing the functional
operation based on not only our logic but also statistical
data about the operation time of vehicles driving all over
the world as the background.
Furthermore, the full charge detection technique is oneof the elemental techniques to realize the SOC estimation. The final target is to secure the accuracy of the SOC
estimation. It is necessary to make well-balanced
improvement of the accuracy of other related techniques
further and to develop such techniques as to make car
manufacturers of our customers happy as well.

REFERENCES
1) Masayuki Itagaki: Electrochemistr y Impedance, Mar uzen
Publishing (2011) (in Japanese).
2) Katsunori Oshiage, Atsushi Baba, Ichiro Maruta and Teruyoshi
Mihara: Batter y Management Engineering, Tokyo Denki
University Publishing (in Japanese).
3) Noriyasu Iwane: “Lead-Acid Batter y State Sensor”, Furukawa
Journal No. 120, (2007) (in Japanese).
4) Noriyasu Iwane: “Battery State Sensor ~Curve Fitting of Leadacid Battery’s Voltage Relaxation with Expanded Kalman-filter”,
Furukawa Review No.44, (2013).
5) Noriyasu Iwane, Naoya Takahashi and Taiji Mitsuyama: “LeadAcid Battery Equivalent Circuit Model Learning from Dynamic
Current & Voltage and Response Voltage Estimation with
Applying It”, Autumn Meeting 2013 of the Electrochemical
Society of Japan (in Japanese).

Furukawa Electric Review, No. 51 202049