BATERY VOLAGE

BATERY VOLAGE
United States Patent [191
[l l]
4,388,582
Saar et al.
[45]
Jun. 14, 1983
[54] APPARATUS’AND METHOD FOR
FOREIGN PATENT DOCUMENTS
CHARGING BA'I'I‘ERIES
[75] Inventors: David A. Saar, Timonium; Richard T.
Walter, Baltimore; John L. Bowman,
Primary Examiner—,-William M. Shoop
Jr., Towson, all of Md.
Black & Decker Inc., Newark, Del.
Attorney, Agent, or Firm-Ronald B. Sherer; Harold
Weinstein
[73] Assignee:
[21] Appl. No.: 337,296
Jan. 5, 1982
[22] Filed:
[57]
Continuation of Ser. No. 911,268, May 31, 1978, aban
doned.
[51]
[52]
_
Int. Cl.3 ........................ .. H02J 7/04; H03K 5/00
U.S. Cl. ...................................... .. 320/20; 320/39;
328/ 132
[53]
Field of Search ............................ .. 320/20, 22-24,
320/39, 40, 46; 328/132
References Cited
U.S. PATENT DOCUMENTS‘
[56] '
3,590,229
3,660,748
3,890,556
3,936,718
6/1971
5/ 1972
6/1975
2/1976
4,114,083 9/1978
4,118,661 10/1978
ABSTRACT
A method and apparatus are presented for charging
batteries at a high rate without damaging or reducing
the life of the battery. The method comprises monitor
Related U.S. Application Data
[63]
1438002 10/ 1968 ‘ Fed. Rep. of Germany ...... .. 320/46
Humphreys .
Clayton .
Melling et a1. .
Melling et a1. .
Benham et a1. ..................... .. 320/39
Siekierski et al. ................... .. 320/40
ing the level of energy stored in the battery, preferably
by monitoring a particular battery characteristic. The
variation of the characteristic with time is analyzed,
preferably by measuring successive values of the char
acteristic, computing the slope and comparing succes
sive slope values so as to identify in?ection points and
other signi?cant events in the variation of the character
istic.
Apparatus for performing these methods and for con
trolling the supply of energy is disclosed which com
prises suitable power supply and a programed mi
crocomputer for measuring successive values of the
characteristic, performing the required computations,
and controlling the supply of energy applied to the
battery by the power supply.
24 Claims, 14 Drawing Figures
VBOALTEGRY
TIME
NICKEL'CADMIUM BATTERY CHARGING CYCLE
US. Patent
Jun. 14, 1983
Sheet 1 of6
4,388,582
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US, Patent
Jun. 14, 1983
Sheet 4 of6
30
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4,388,582
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US. Patent
4,388,582
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CONSTANT'VOLTAGE CHARGING CURVE
NI CKEL' CADMIUM BATTERY
1
4,388,582
2
either of which causes gradual deterioration of the bat
tery and premature failure.
In part, the failures of the prior art have been due to
APPARATUS AND METHOD FOR CHARGING
BATTERIES
the inability to accurately indicate full battery charge;
This is a continuation of application Ser. No. 911,268,
?led May 31, 1978, now abandoned.
this has been due either to the failure of the prior art to
select the proper mode of indication, or to the fact that,
even if a reasonably good indicator has been selected,
CROSS-REFERENCE TO RELATED
APPLICATION
The subject matter of the present application is re
lated to that disclosed in co-pending U.S. Pat. applica
tion Ser. No. 337,174, co-?led on Jan. 5, 1982, entitled
“Method of Charging Batteries and Apparatus There
for,” which application is a continuation of U.S. Pat.
application Ser. No. 911,554, ?led May 31, 1978, now
abandoned.
the charging requirements of a battery vary substan
tially with individual cell chemistry, with individual
cell history and with ambient temperature. Thus, even
an indication mode which is reasonably well selected .
for a particular battery type may actually provide an
accurate indication only for a few cells having ideal
characteristics and only if the cells are charged under
proper conditions of ambient temperature.
For example, a major category of previous fast charg
ing systems has relied upon temperature cutoff to termi
FIELD OF THE INVENTION
nate the fast charge mode. However, these systems are
subject to several difficulties: they may damage the
This invention pertains to battery chargers in general
batteries due to the constant repetition of high tempera
and speci?cally to a method and apparatus for charging
ture conditions, even in specially manufactured (and
batteries which permits any battery to be brought to its
expensive) cells which are theoretically designed to
full state of charge at a very rapid rate and also at maxi
accept high temperatures; such systems may not be safe
mum ef?ciency without danger of damage to the bat
for use with defective cells; they actually ‘do not charge
tery or to the charger. This invention will be described
with particular reference to nickel-cadmium batteries 25 a battery to its full capacity, in high ambient tempera
ture conditions; the charge efficiency is low and the
but it is also capable of charging many other types of
systems are therefore wasteful; and in low ambient tem
batteries in the optimum manner for each of those par
ticular batteries.
PRIOR ART
Battery usage in various products, particularly for the
retail consumer, has increased tremendously in recent
years. However, batteries are still looked upon with
substantial disfavor by many consumers because so
much of their experience has been with primary cells
which are wasteful, which must be frequently replaced
‘and which can cause serious damage if leakage occurs.
perature, the battery may be driven to self-destruct by
30
venting or possibly explosion.
Another major category of prior art fast charging
systems relies on voltage cutoff. However, in many
types of battery systems including nickel-cadmium, this
termination mode is unreliable due to the large voltage
variation which can occur with temperature, or due to
cell history or individual cell characteristics. Thus, a
voltage cutoff system can destroy a battery through
venting. Except in unusual ideal conditions, it will
never properly charge a battery to its full capacity.
Rechargeable batteries have recently become more
popular in various devices, but-problems are still en
countered by the consumer. Frequently, he discovers
that his batteries have self-discharged and need recharg-'
termination is based on simple passage of time. How
ever, the accuracy of this system depends on the bat
ing at exactly the moment when he would like to use the
device, and recharging in most instances takes an incon
state of charge. There is a very high likelihood that this
will not be the case and that the battery will be either
veniently long period of time.
One solution to this is to provide maintenance charg
ing systems in which the battery can be left on constant
A third major category of prior art battery charging
tery, at the beginning of charge, having an assumed
45 over or under charged.
Most other charging methods which have been used
to date are based on combinations of one or more of the
charge between uses. Even this system is of no value if
above techniques. While some problems can be avoided
the consumer fails to put the battery back on charge
by these combinations, at least some of them still exist.
after use; in addition, most maintenance charging sys 50 Even the best fast charge systems require expensive cell
tems actually cause slow deterioration of the battery
constructions; but the additional cost only serves to
with time.
delay the battery deterioration which is caused by the
The solution to all of the above problems would be
charging system.
the provision of an adequate fast charging system which
A more recent technique, illustrated by U.S. Pat. No.
would reliably bring the battery up to its full state of 55 4,052,656, seeks the point at which the slope of the
charge in the shortest possible time and without risk of
voltage-versus-time curve for a given battery is zero.
damage. While the prior art is replete with attempts to
provide good fast charging systems, no satisfactory
system has yet' been developed. Most fast charging
systems today require very special conditions, such as
However, even this technique is subject to difficulties; it
may detect another point at which the voltage slope is
zero but at which the battery is only partially charged;
in addition, even if it properly locates the zero slope
point which is close to full charge, this inherently over
charges the battery and will cause battery deterioration
unusually expensive batteries which can accept the
output of the fast charge system. Even under these
special conditions, there remains a risk of serious dam
age to either the battery or to the charger. In addition,
the present fast charge techniques do not properly‘
charge the batteries. Depending on the termination
techniques and are subject to one or more of the above
mode used, all fast charge techniques of which we are
aware either overcharge or under charge the battery,
currently known battery chargers are designed to be
due to heating.
1
All of the battery charging systems of which we are
presently aware embody one or another of the above
listed defects. This is true despite the fact that most
3
4,388,582
4
used with only one type of battery and, in general, with
be kept at its full state of charge without gradual battery
only one selected number of battery cells of that partic
deterioration.
ular type. The concept of a battery charger which can
It is an additional object of this invention to provide
accurately and rapidly deliver full charge to a variety of
a novel and unique method of evaluating the state of
different batteries including different number of cells or 5 battery charge and of controlling the applied charge
different types of battery couples is totally beyond the
current in response to such evaluation so as to permit
present state of the battery charging art.
the battery to be brought to its full charge state at the
maximum possible rate and at maximum ef?ciency
OBJECTIVES
without causing damage or deterioration of the battery,
The overall object of the present invention is to over 10 such method also including safeguards to protect
come the dif?culties inherent in prior techniques of
against damage due to the introduction of a defective
cell or to the introduction of a cell which is already at
battery charging and to provide a new and improved
method of and apparatus for battery charging which
full charge.
fully charges batteries at a very rapid rate and at maxi
mum efficiency and without causing either fast or slow
become apparent as the description and illustration
deterioration of the battery.
A more speci?c object of this invention is the provi
sion of a method and apparatus for charging batteries
which accurately identi?es the moment when the bat
tery has reached full charge and which terminates
charging without either under or overcharging the
battery.
A further object of this invention is the provision of a
method and apparatus for fully charging different bat
teries including different numbers of cells at the maxi
mum possible rate and ef?ciency, from unknown start
ing conditions.
Another object of this invention is the provision of a
method and apparatus for fully charging different bat
teries comprising different chemical couples at the max
imum permissible rate and ef?ciency, from unknown
starting conditions.
Further objects and advantages of this invention will
thereof proceed.
BRIEF DESCRIPTION OF THE INVENTION
In general, the present invention comprises a method
of applying a charge current to a battery, monitoring
selected battery parameters during the charging, infer
ring from changes in these parameters an indication of
the true charge COIldltlOILOf the battery, and controlling
the applied charging energy so as to bring the battery to
its full charge condition as quickly as possible without
damaging the battery. In addition, the general method
of this invention provides for the identi?cation of un
usual conditions which may occur in some cases, and
which require charge termination to protect either the
battery or the charger; furthermore, this method pro
vides for the application of a topping charge in appro
priate cases and for the application of a maintenance
charge to keep the battery at full charge, all of these
Still another object of this invention is the provision
being accomplished without danger of damaging either
of a method and apparatus for rapidly bringing a battery 35 the battery or the charger. All of these objectives are
to its full state of charge and terminating the fast rate
accomplished regardless of the actual voltage of the
charge at that point, this being accomplished without
battery; despite wide variation in individual cell charac
regard to the actual voltage of the battery, individual
teristics; despite previous harmful charging history in
cell characteristics, individual charging history of the
the case of a particular battery; and despite wide varia
particular battery, or the actual ambient temperature.
tions in the ambient temperature to which the battery
In another aspect, it is an object of this invention to
and/or the charger may be exposed.
provide a universal method for rapidly charging various
In particular, the present invention is based on the
types of batteries and to further provide an apparatus
discovery that the electrochemical potential of a battery
which selects the proper sub-method required to rap
exhibits speci?c types of nonlinear changes of its value
idly charge a battery of a particular type.
45 with respect to time as the battery is charged. The in
In a further aspect, an object ‘of this invention is the
vention is further based on the discovery that the true
provision of an apparatus for applying charge current to
charge state of the battery during charging may be
a battery and determining accurately the moment when
analyzed by ‘noting inflection points which occur as the
a battery has reached its full state of charge.
electrochemical potential changes with respect to time.
Still another object of this invention is the provision 50 In the case of speci?c batteries, proper charging may
of an improved method and apparatus for fast charging
involve determining the occurrence of either one or
batteries which recognizes accurately when a battery
more of such in?ection points, or of determining a par
has reached a full state of charge, which thereupon
ticular sequence of ordered in?ection points. Control
terminates the fast charge mode, and which subse
ling the proper charge mode may then involve simple
quently supplies a topping charge current to the battery 55 conversion from a high rate fast charge mode to a suit
to compensate for batteries which, due to a particular
charging history, may produce a false indication of full
state of charge.
Still another object of this invention is the provision
of a method and apparatus for charging batteries which
identi?es intermediate states in the charging cycle of a
particular battery and adjusts v‘the rate of charging cur
rent applied so as to maintain ‘the applied current at the
optimum level for rapid, ef?cient and non-destructive
charging.
able maintenance mode which prevents or compensates
for self-discharge of the battery. In other cases, proper
control of the battery charging sequency may involve a
combination of in?ection point determination with
other analyses of the variation of voltage with respect
to time or of the actual voltage at a particular time. In
all of these cases, a signi?cant aspect of this invention is
the determination of in?ection points in the curve
which represents the electrochemical potential of the
65 battery as a function of time.
An additional object of this invention is the provision
By way of illustration of the above general method,
of a method and apparatus for providing a non-destruc
tive maintenance charge mode by which a battery can
the following speci?cation describes appropriate varia
tions on the speci?c type of analysis which may be
4,388,582
5
performed to determine the inflection points, and also
6
describes variations in the analysis which may be neces
BATTERY CHARGING PROCESS
sary to accommodate differing modes of battery charg
In the course of recharging a nickel-cadmium battery,
it has been found that a very typical curve is produced
if the increasing battery voltage is plotted as a function
of time. FIG. 1 is a representation of a typical curve of
this type, as taken during a constant current charging
ing such as constant voltage, constant current, etc. Spe
ci?c applications include techniques for charging such
batteries as nickel-cadmium, lead acid, and silver-cad
mium.
cycle. A similarly typical curve can be obtained by
plotting current against time during a constant voltage
In further accordance with the present invention,
apparatus is described for implementing these various
methods. In a preferred embodiment, the apparatus
charging cycle, and a reproducible pattern also occurs if
neither voltage nor current are held constant This curve _
includes a suitable source of electrical energy, an analyt
may be divided into signi?cant regions, as indicated by
the Roman numerals between the vertical lines superim
ical device for determining the necessary controlling
parameters, and means for controlling the application of
posed on the curve. While the curve is subject to varia
energy from the source to the battery.
tions in speci?c values of voltage or of time, the general
form is similar for all nickel-cadmium batteries, includ
In the particular example of a normal, discharged
nickel-cadmium battery, a useful charging pattern in
ing one or more cells, and the following discussion
accord with this invention is to apply a fast-rate con
stant charge current to the battery until two consecu
tive in?ection points are passed, speci?cally, a ?rst one
at which the sign of the slope of dV/dt (that is, the sign
of d2V/dt2) changes from negative to positive followed
by a second one at which the sign changes from positive
to negative.
These analyses will be further clari?ed with reference
to the voltage variation of a normal nickel-cadmium
applies equally to all such batteries.
Region I of FIG. 1 represents the initial stage of
voltage change which occurs when the charging cycle
is ?rst started. In this Region, the voltage is subject to
significant variations based on the initial charge level of
the battery, its history of charge or discharge, etc. Since
the shape of this Region can vary, it is indicated in FIG.
25 1 by a dotted line.
battery in the detailed description hereinafter; for the
Because the information in Region I varies, it is usu
ally preferable to ignore this segment of the curve. The
present, it is suf?cient to note that one basic concept
battery will generally traverse Region I completely
presented herein is that of in?ection point analysis.
within the ?rst 30 to ‘60 seconds of charging and enter
Speci?c techniques of analysis and speci?c sequences
Region II; in general, the voltage in the Region I period
increases relatively rapidly from the initial shelf voltage
adapted to accommodate different battery couples may
readily be developed within the context of this general
and the short peaks which may occur in this Region are
not harmful.
As the battery approaches a more stable charging
procedure.
DESCRIPTION OF THE FIGURES
35 regime, it enters the portion of the curve designated
FIG. 1 is a graph illustrating the variation of voltage
Region II. Region II may be of fairly long duration with .
as a function of time during the charge cycle of a nickel
cadmium battery;
little or no increase in voltage. During this time, most of
the internal chemical conversion of the charging pro
cess takes place. When signi?cant portions of the active
'
FIG. 2 is a block diagram illustrating the primary
elements in a battery charger in accordance with this
material have been converted, the battery begins to
approach full charge and the voltage begins to increase
invention;
more rapidly. This inflection point A in the curve from
FIGS. 3 and 4 together comprise a schematic dia
gram illustrating speci?c circuits which may be pro
vided in accordance with this invention to form the
block diagram of FIG. 2;
FIGS. 5 through 9 schematically illustrate the se
quence of operations performed by the microcomputer
shown in FIG. 4;
FIGS. 10-13 are graphs illustrating the variation of
voltage as a function of time during the charge cycle of
several different batteries; and
FIG. 14 is a graph illustrating the variation of current
as a function of time during the charge cycle of a nickel
cadmium battery.
In the following speci?cation, an explanation is given
a decreasing rate of increase to a increasing rate of
increase is identi?ed as the transition from Region II to
45
Region III.
Region III is characterized by a relatively rapid volt
age increase as more and more of the active material is
converted to the charged state. As the battery ap
proaches full charge more closely, that is, when perhaps
90 to 95% of its active material has been converted
chemically, oxygen begins to evolve. This produces an
increase in the internal pressure and also an increase in
the temperature of the cell. Due to these effects, the
rapid increase in battery voltage begins to slow and
55 another inflection point occurs in'the curve. This sec
ond inflection point is identi?ed as the transition point
between Regions III and IV, point B.
teries. The inventive method for either monitoring or
Within Region IV, the ?nal portions of the active
terminating the battery charging process is next de
material are being converted to the chemical composi
scribed, including several alternative terminating modes
tion of the fully charged battery. At the same time, due
used for either protection or supplemental termination.
to oxygen evolution from material already converted,
The apparatus of this invention is then presented, in
the internal pressure increase and the heating contribute
cluding a preferred, detailed schematic circuit and a
to a slowing in the rate of voltage increase until the
preferred embodiment of the operational sequence per
voltage stabilizes at some peak value for a short period
formed by the microcomputer. Finally, a general de 65 of time. This is designated as the transition between
scription of the application of ‘this invention to other
Regions IV and V.
types of batteries and to other charging modes is pro
Within Region V, if charging is continued, the volt
of the battery charging process of nickel-cadmium bat
vided.
age of the cell starts to decrease due to additional heat~
7
4,388,582
ing as virtually all of the applied energy is converted
into heat and the negative temperature coef?cient of the
battery voltage causes the voltage to decrease. Contin
8
exactly that order, and only then, the battery charging
current can be discontinued or reduced to a mainte
nance or topping mode if desired, with absolute assur
ance that the battery has been brought to a full state of
ued application of charging energy in this Region
would eventually cause damage to the battery, either
through venting or damage to the separator.
As previously noted, the relative time duration, slope
ual cell characteristics. Because of the accuracy of this
determination, this method can even be applied to bat
or value of any portion of this curve may be modi?ed
teries which are constructed for use only with trickle
by such factors as the initial temperature of the battery,
the charge or discharge history of the battery, the par
ticular manufacturing characteristics and the individual
characteristics of the battery cell. However, the major
aspects of this curve and of each of its Regions will be
charge regardless of its temperature, history, or individ
chargers.
O
identi?able in any non-defective nickel-cadmium bat
tery which is brought from a substantially discharged
state to a fully charged state at a constant, relatively
high current.
In speci?c accordance with the present invention, the
above described curve and the information contained
therein are utilized in a novel manner to provide an
improved battery charging method. This method is
much more accurate than those previously used and is,
in fact, so improved that it permits rapid charging of
any nickel-cadmium battery cell in a minimum time
considering reasonable system cost.
It should be noted that the exact sequence of occur
rence of these inflection points is critical to this inven
tion. While the preferred method of this invention in
5
volves ignoring the voltage changes which occur
within the ?rst 30-60 seconds of the charging cycle, the
changes which occur in Region I may overlap slightly
into the time period within which the data sampling
apparatus of this invention is operative. In that event, an
inappropriate in?ection point may occur near the begin
ning of Region II. The apparatus of this invention is
designed so that it will ignore such in?ection points
until those identi?ed above occur in the proper se
quence.
An alternative statement of this technique can be
made based on the identi?cation of changes of sign of
25 the second derivative of the voltage with respect to
Up to the present time, rapid charging techniques for
time. Speci?cally, Region II is characterized by the
batteries have carried the risk of serious damage to the
gradual decrease of the slope or rate of change of volt
age versus time. For a fully discharged battery, Region
battery. To help in avoiding this problem, ordinary
battery cells are usually manufactured for use in con
II constitutes the largest portion of the charging period
junction only with so-called “trickle chargers” which
30 with voltage over most of this period increasing at a
require some 16-24 hours to bring a battery from a
substantially discharged state to approximately its fully
charged state. Even when this time penalty is accepted,
relatively low rate. As the battery approaches full
charge, the voltage again starts to increase somewhat
more rapidly. Thus, the slope which has been becoming
such chargers can be harmful to the battery cells over a
progressively smaller and smaller starts to become
long period of use.
35 larger again. This can be described as an in?ection point
Rapid chargers are available for nickel-cadmium cells
or a change in sign of the second derivative of voltage
which will bring a battery to approximately full charge
with respect to time. Thus, we have a ?rst such change
within aproximately one hour. However, these chargers
in sign giving indication that the battery is nearing the
require the use of high priced cells manufactured by
full charge state.
special techniques so that the cells are capable of with
During Region III the slope of the voltage-time
standing the possible harmful effects of rapid charging.
curve increases further and further as the battery comes
This is due to the fact that the chargers cut off by one or
another of the methods described above with their at
closer to full charge. At or near the full charge point,
there is the transition between Regions III and IV at
tendant inaccuracies.
INFLECTION POINT ANALYSIS
which the slope of voltage stops increasing and starts
45 decreasing to smaller and smaller values as Region IV
progresses. Here again, a change in the sign of the sec
In accordance with this invention, a new method of
ond derivative of the voltage-time curve occurs. This
controlling the battery charge process is provided
decreasing slope in Region IV indicates that virtually
which identi?es exactly the conditions in the particular
battery undergoing charge and correspondingly con
trols the application of charge current. Because of this
for example, as little as 15 minutes for a fully discharged
all of the active material in the cell has been changed to
the charged state and that the energy going into the cell
is beginning to convert into heat rather than continuing
the charging process. Thus it is desirable to terminate
charge during the early or middle part of Region IV of
the voltage time curve.
These two above described changes in sign of the
battery. As the battery approaches full charge, its con
dition is identi?ed accurately and the charging current
second derivative of the voltage-time curve are charac
teristic of nickel-cadmium and other electrochemical
new technique, a high rate charge current can be ap
plied to the battery so that the battery is brought
through its initial stages in the minimum possible time,
is reduced or cut off at exactly the proper moment in the
cells during the charging process. They provide a
unique and reliable indication of the state of charge of
Application of this new technique requires very so 60 the battery. A particularly important aspect of the
phisticated processing of the available information. In
method of this invention'is, accordingly, the use of one
concise form, as applied speci?cally to nickel-cadmium
or more of these observable changes of sign of the sec
batteries, the method of this invention involves the
ond derivative of the voltage-time curve to determine
identi?cation of the in?ection point between Regions II
when to terminate battery charging.
and III and by the identi?cation of the subsequent or 65
The method of this invention of observing these in
following in?ection point between Regions III and IV.
flection points, or of changes in the sign of the second
Once these two in?ections points have been identi?ed
derivative of the voltage-time curve of the battery
charge cycle.
and it has been con?rmed that their occurrence is in
charging process, can be implemented in several ways
4,388,582
10
including the apparatus hereinafter described. For other
types of electrochemical cells or different types of
and entering Region V. Within a fairly short time after
it has been placed on charge (e.g., 1-3 minutes) the
charging systems, other sequences of in?ection points , battery will enter Region V and its voltage will begin to
may be required, but the detection of all of these types
decrease. As soon as the negative voltage change is
of second derivative sign changes and speci?c sequen
large enough to indicate to the apparatus that the funcces of them are intended to be included within the scope
tion of voltage with respect to time is no longer mono
of this general method.
tonic, the apparatus will discontinue the fast charge
One principal advantage of in?ection point analysis is
rate. Preferably, the charging mode then shifts into a
that it does not depend on the actual value of the volt
maintenance mode as will be hereinafter described.
age of the cell nor does it depend upon the value of the
Since the high rate is only maintained for a short period
rate of change, or slope, of voltage. It is an analysis of
of time, the battery will not be damaged by this se- .
those points where the rate of change of voltage (that is,
the slope of voltage) changes from decreasing to in
creasing or from increasing to decreasing. In turn, these
quence. It is also noted that even defective batteries will
not be driven into a hazardous condition by the continu
ation of a maintenance charge mode after shut down of
points are directly related to the actual chemical occur- _
the high rate due to a negative voltage change.
rences within the battery being charged.
Thus, determination of state of charge and hence the ‘
most appropriate time to terminate charge is dependent
VOLTAGE SLOPE ANALYSIS
While the charge pro?le of nickel-cadmium batteries
only upon very universal characteristics of such batter
does not lend itself to advantageous use of this tech
ies and not on the particular cell characteristics or char 20 nique, other battery couples exhibit pro?les wherein
acteristics which might be due to the history of use such
termination should be predicated upon the occurrence
as storage or very heavy use. It is thus more reliable and
of a particular voltage slope. Thus, in a couple wherein
a more valid indication of the most appropriate time at
Region V involves a slow downward drift of voltage
which to terminate charge than previous methods.
rather than a sharp decrease as in the nickel-cadmium
In some cases, the in?ection point technique which is
appropriate for normal conditions may not be adequate,
25
for example, if a battery is damaged or defective or if a
user inadvertently places a fully charged battery on
charge. In these cases, the normal indicative points may
not occur at all or they may possibly occur within the
?rst period of time in which the apparatus is not sam
pro?le, the occurrence of a negative slope is useful in
the same manner as the absolute voltage change analysis
just described.
VOLTAGE LEVEL ANALYSIS
In some cases of dried or otherwise damaged nickel
cadmium cells, application of a charging current can
cause the voltage to increase to. a level signi?cantly
pling data. In order to protect against these possibilities,
the present invention further includes the provision of
beyond the normal voltage of an operative, cell. Ac
speci?c controlling techniques or modes which may be
cordingly, the apparatus of this invention includes the
used in combination with the basic method described 35 provision of a voltage level sensing means which termi
above.
ABSOLUTE VOLTAGE CHANGE ANALYSIS
A ?rst of these techniques which can be incorporated
nates charge if a predetermined level of voltage is en
countered. In other battery couples, this may serve as a
primary charge termination mode rather than as a sec
ondary safeguard.
is that of terminating the application of charging cur
rent to the battery immediately upon the occurrence of
TIME ANALYSIS
a negative change of voltage. By reviewing the curve of
In other defective cells, the application of a high
charge current may simply be allowed to continue for
an undue length of time because the energy is being
FIG. 1 it will be noted that there is no point in the
normal charge cycle when a negative voltage change
occurs. Thus, if a negative voltage change is encoun 45 converted to heat or to oxygen evolution, etc. In these
tered, it must mean that the battery is either defective of
instances, the defect in the cell may prevent the in?ec
that it is already fully charged and that it has entered
tion points from occurring and a maximum time cutoff
Region V of the curve. Accordingly, provision is pref
erably included to terminate the high rate charge imme
diately upon the occurrence of a negative voltage
change. Preferably, the value of this change should be
large enough so that termination is not inadvertently
caused by inaccuracies in the monitoring equipment.
It is also noted that the absolute voltage change anal
ysis is utilized to prevent fast charging of a fully
charged battery which is inadvertently placed on fast
charge by the operator. Speci?cally, a fully charged
is provided.
In each of the above cases, the exact quantity chosen
for the negative voltage change, for the negative
change in voltage slope, for the absolute level of volt
age reached, or for the maximum time reached is, of
course a predetermined number based on the type of
cell for which the particular charger is intended.
MAINTENANCE CHARGE MODE
After the main charge regime is terminated by one or _
battery to which a high current is applied will traverse
more of the above ?ve methods of analysis, it is pre
most, if not all of Regions I, II and III very quickly. In
ferred to proceed into two other charge regimes. The
many cases, this will occur in the time period which a 60 ?rst of these is a programed overcharge or surcharge to
normally discharged battery would require to traverse
Region I. Since the system is instructed not to look for
in?ection points during the ?rst 30 to 60 second portion
of the cycle, at least one and perhaps both of the signi?
cant in?ection points, point A and B will pass before the 65
system begins to monitor for them.
.
Therefore, as monitoring of the fully charged battery
begins, the battery will be passing through Region IV
insure that all possible active material in the cell is fully
converted to the charged state and that all possible
capacity in the cell will be available to the user. The
preferred method of overcharge or surcharge is to
charge at a relatively low charge rate for a ?xed amount
of time depending on the type and size of the cell. This
guarantees that .the cell is given a full amount of addi
tional charge but at a low enough rate to avoid damage.
11
4,388,582
-
The ?xed time also means that the cell is not subject to
long periods of time of overcharge which would subject
the cell to increased internal pressures and heat which
would eventually damage internal structures such as
separators.
At the end of the surcharge or overcharge period it is
very desirable to provide only a maintenance charge
which is used to compensate for the internal self-dis
charge characteristics of all electrochemical cells in
cluding nickel-cadmium cells. Nickel-cadmium cells
can self-discharge as much as 10% to 30% per month
depending on the storage temperature and the particu
lar characteristics of the cell. One method of mainte
nance charging is to apply a low to medium charge
current for a short period of time one or more times per
day. The preferred rate is a charging rate of “C” (a
charge rate representing the same number of amperes of
charge as the ampere-hour rated capacity of the cell) for
15 to 30 seconds every 6 hours. This provides approxi
mately twice the typical loss rate in ampere hours of the
cell without causing any signi?cant heating or pressure
buildup in the cell. The particular charge rate and par
ticular choice of charged time to resting time can be
'
12
the full charge current to be applied to the battery
through the ampli?er 12 for a predetermined period of
time, usually between 30 and 60 seconds, which allows
the battery to be brought through the segment of FIG.
1 identi?ed as Region I. For nickel-cadmium batteries
of the sub-C size, the preferred time is 40 seconds. This
application of power can be at full rated current since
even a defective battery or a fully charged battery will
not be seriously damaged by the application of this
power for this short an interval. The application of
power is controlled by the micro computer 18 by its
selection of the appropriate current control resistor 20
through which to apply the input signal to the current
ampli?er 12. After an appropriate period of time has
passed as described above, the microcomputer 18 makes
use of the analog-to-digital converter (A/D) to deter
mine the battery voltage. The converter 22 is preferably
of the successive approximation type in which succes
sive approximate digital values of battery voltage gen
erated by the microcomputer 18 are compared to the
actual battery voltage until a close approximation is
achieved. This information is then fed back into the
microcomputer 18 which then proceeds to execute its
varied over a very wide range. The method is merely to
program so as to charge the battery in accordance with
replace the calculated or measured energy lost to self 25 the method described above.
discharge of the cell.
In addition to the basic elements of the block diagram
already mentioned, the circuit should provide certain
CHARGING APPARATUS
additional features. If the battery charger is of a type
FIG. 2 is a block diagram showing the major ele
adapted to handle a variety of battery sizes and types, a
ments of electronic circuitry which are used in accor 30 battery type selection circuit 24 is included which se
dance with this invention to implement the above de
lects the speci?c program for the given battery type
scribed charging method. The ?ow of charging current
from several stored in the computer. This may be done
in FIG. 2 runs from an AC power input plug 8, connect
either by the operator or automatically by some identi?
able to an ordinary source of line current, to a power
cation means such as particular terminal types provided
supply 10 which converts the AC input to low voltage
on the battery itself.
DC. Next, the current passes through a resistor-con
The system also preferably includes a temperature
trolled current ampli?er 12, and then through a char
cutoff circuit 26. The purpose of this circuit is to pre
ge/test switch 14 and ?nally to the output terminals 15
vent charging if the ambient temperature is either so
at which a single or multi-cell vbattery to be charged is
low or so high as to cause damage to the battery or to
connected. The power supply may, of course, be an 40 the charging circuit itself.
alternative source of DC power such as a larger battery
Reset circuit 28 is provided to reset the entire mi
or a converter operated from a DC source. The ampli
?er is preferably a standard series-pass current regulator
although other types of controllable current ampli?ers
could be used. The charge/test switch 14 normally
connects the current ampli?er 12 to the battery for the
application of charging current; this switch also in
crocomputer program to time zero as soon as power is
supplied to the system, or in the event of a power inter
ruption. This is done to prevent upredictable charging
effects which might occur if the computer were to be
initiated at an incorrect point in its program.
Finally, the operator display circuit 30 provides for
cludes a test position for use in a test mode which is
communicating such information as may be appropriate
described below.
The remainder of the block diagram illustrates a pre
ferred embodiment of the apparatus for performing the
method of this invention. In the illustrated embodiment,
to the operator. In the case of a simple charger for use
by a consumer, the display 30 may consist only of an
illuminatable lamp to indicate that charging is in pro
cess. In the case of a complex battery charger used by a
a start switch 16 is provided; this comprises a momen
quali?ed technician, the display circuit may provide for
tary contact switch for initiating the sequence of opera
the display of a variety of different information which
tions. It is connected to one input port of a microcom 55 may be of use to the technician in evaluating the condi
puter 18. In the preferred embodiment of this invention,
tion of the battery.
this is an Intel type 8048 microcomputer. This is a self
contained computer including a program memory for
storing instructions, a register memory and a central
FIGS. 3 and 4 together comprise a schematic dia
gram of one suitable embodiment of FIG. 2. The respec
tive segments of the circuit as identi?ed in FIG. 2 are
processing unit (CPU) for controlling the execution of 60 enclosed in dotted line boxes identi?ed by correspond
the stored instructions. The 8048 microcomputer is
ing numbers.
more completely described in the publication entitled
In the speci?c embodiment of these ?gures, 8 a con
“Microcomputer User’s Manual” No. 98-A270A, pub
ventional line plug is provided for connection to a
lished by the Intel Corporation of Santa Clara, Calif.
source of power. The power supply 10 includes a trans~
95051, which is included herewith as Appendix A.
65 former T1 and a full wave bridge recti?er made up of
When the start switch 16 is actuated, which could be
diodes D1—D4. The output from the bridge, which may
accomplished automatically on connection of a battery
be approximately 20 volts DC, is applied through
to the output lines, the microcomputer 18 ?rst allows ampli?er 12 and switch 14 to the battery (shown in
4,388,582
13
dotted line illustration). A portion of the bridge output
14
ladder R43-R50 as selected by the computer. Resistors
R44'—R50 each have values which are twice the value of
is also applied to a ?lter made up of resistor R1, diode
D5 and capacitor C1 and to voltage regulator IC1. Regu
the preceding sequential resistor. The computer, under
lated voltages of 25 volts and 5 volts for use in the other
portions of the circuit are taken at the indicated output
terminals.
The resistor-controlled current ampli?er 12 operates
the instruction of its program as will be described here
inafter, selects an initial minimum value, for example, byv
turning on only R43. This develops a voltage across
ICzc which is compared in IC3C to the signal received
according to outputs taken from the microcomputer 18
from the battery. If this minimum voltage supplied from
through current control resistors 20 shown in FIG. 4. In
accordance with its internal program, the computer 18
selects a current level by completing a circuit through
one of the current control resistors R29, R30, or R31.
the computer is not equal to or greater than the battery
voltage, then successively increased values are tried by
the computer until a match is reached. This information .
is communicated back to the computer from the output
of IC3c and the computer uses the last input to the com
This controls the input to operational ampli?er 1C2],
which is taken at the midpoint of a voltage divider made
up of the parallel combination of resistors R13 and R17,
and the selected current control resistor. The output
from the ampli?er ICzb is compared to the voltage de
parison circuit as the battery voltage.
In reset circuit 28, the comparator IC3d ampli?es a
signal derived from the 25 volt supply and compares it
to a 5 volt reference. If the 25 volt signal goes below
approximately 10 volts, as would occur upon the re
moval of power from‘ the system either due to a power
veloped across a current shunt resistor R5. Any error
signal due to a difference is ampli?ed by operational
ampli?er ICza and applied to driver transistor Q3. The
output of transistor Q3 is applied to current control
failure or due to the operator unplugging the charger,
the output signal from the comparator instructs the
computer to return all of its programming functions to
the initial conditionsj that is, those which must be used
transistors Q1 and Q; to produce a very stable constant
current which is applied to the battery through S10.
If the output current to the battery cannot reach the
when a new charge cycle is initiated. This can occur
selected current level, for example because there is no 25 either during power-down as the power is falling from _
battery connected, transistor Q3 is turned fully on
normal input to zero due to a power failure or during
power-up as the power is building from zero to its nor
which, through the comparison ampli?er IC3a’ supplies
a signal to the computer which turns the system off.
As shown in FIG. 3, a momentary contact push but
ton switch 16, which may be operator-controlled or
may be built into the battery socket, supplies a signal to
mal level when the system is ?rst connected to a power
source. In either case, this system is useful to ensure that
the computer does not begin a cycle at some indetermi
nate midpoint in its cycle with inappropriate informa
the battery to indicate that the charging cycle should be
initiated. This could also be accomplished by monitor
ing for the presence of battery voltage or current flow.
tion stored in its memory.
The display system 30 is utilized by the computer to
communicate appropriate information to an operator.
Selection circuit 24 (FIG. 3) comprises a plurality of 35 As illustrated, the display preferably comprises two
selector switches S3, S4 which allow the operator to
seven segment display elements and transistors Q4 and
Q5 which form a conventional strobing control which
enables eight output lines to control both displays. Al
select a particular computer program appropriate to a
particular battery. Diodes D7-D10 are provided to pro
tect the computer 18. Alternatively, this selection could
be provided automatically by using different sets of
unique terminals to which different battery types are
connected. Also, the entire selection circuit 24 might be
omitted if the charger is intended for use with only a
40
ternatively, the display might comprise simply a single
indicator lamp.
Finally, element 14 (FIG. 3) comprises a charge/test
switch. In the normal, charge position S11, and S16 con
nect the current controlled ampli?er 12 and resistor
single battery type.
Temperature cut-off circuit 26 comprises a safety 45 network (items 12 and 20 of FIG. 2) so that current
from power supply 10 is supplied through S11, to transis
circuit to prevent operation at temperatures outside a
tors Q1 and Q; to switch S16 to the battery with a return
predetermined permissible range. In the particular ar
rangement shown, the voltage at the midpoint of the
voltage divider comprising resistor R36 and thermistor
TH1 controls the input to both sides of the comparator
ampli?er IC31,. In the case of a high temperature (e.g.,
125° F.), the resistance of TH] is low which reduces the
voltage input to the positive side of IC3b; in the case of
a low temperature (e.g., 25° F.), the resistance of TH] is
high which increases the voltage at the negative side of
IC31,. Either extreme produces a low output signal from
1C3], which instructs the computer to discontinue charg
mg.
'
In subcircuit 22, the battery develops an input signal
across the voltage divider R4/R67 which is ampli?ed in
operational ampli?er IC2d. The resistances R64, R65 and
R66 and capacitors C9 and C10 comprise a ?lter on the
output of IC;,] and this signal is used as one input to
comparator ampli?er IC3C.
At the same time, another input to comparator 1C3C is
developed through operational ampli?er ICZC from a
voltage divider comprising the parallel resistors R52 and
R53 and a binary coded combination of the resistor
path through resistor R5. In the test position, the battery
is connected through S11, to transistors Q1 and Q2
through switch S16 to resistor R2 and returning through
resistor R5 to the battery. For example, this could allow
the system to be used to discharge the battery at a pre
determined rate and, by means of appropriate program
ming, to determine and display the ampere-hour capac—
ity of the battery. In addition, switch S1,, provides an
alternate signal to the microcomputer 18 to instruct it to
enter the charge program or a separate discharge pro
gram wherein it tests the condition of the battery.
In one embodiment of FIGS. 3 and 4, the following
circuit elements were used:
R1
10 ohm l watt
R15
R2
.3 ohm 1 watt
R17
8.2K ohm i watt
10k ohm l watt
R3
R4
lk ohm 1 watt
100k ohm
R13
R19
Trimpot 100k ohm
lOOk ohm i watt
R5
R6
R7
R3
.l ohm 1 watt
10 ohm } watt
12 ohm } watt
560 ohm 5 watt
R20
R21
R22
R23
22k ohm } watt
10k ohm i watt
220k ohm 1 watt
10k ohm i watt
4,388,582
15
R9
R10
R11
R12
R13
560 ohm 1 watt
10k ohm 1 watt
Trimpot 100k ohm
1k ohm 1 watt
10k ohm 1 watt
R24
R25
R26
R27
R23
10k ohm 1 watt
10k ohm 1 watt
10k ohm 1 watt
Trimpot 3k ohm
8.2k ohm 1 watt
R14
2.2k ohm 1 watt '
R29
100k ohm 1 watt
R15
R31
R32
R33
R34
R35
R36
R37
1 Megohm 1 watt
4.7k ohm 1 watt
10k ohm 1 watt
1 Megohm 1 watt
33k ohm 1 watt
22k ohm 1 watt
4.7k ohm 1 watt
22k ohm 1 watt
R30
R61
R52
R53
R64
R55
R55
R57
R33
R39
R40
R41
R42
R43
R44
R45
R45
R47
R43
R49
R50
R52
R53
R54
33k ohm 1 watt
680 ohm 1 watt
1k ohm 1 watt
lk ohm 1 watt
1.8k ohm 1 watt
5k ohm 1 watt
10k ohm 1 watt
20k ohm 1 watt
40k ohm 1 watt
80k ohm 1 watt
160k ohm 1 watt
320k ohm 1 watt
640k ohm 1 watt
270 ohm 1 watt
Trimpot 3k ohm
10k ohm 1 watt
C1
C2
C3
C4
C5
C5
C7
C3
C9
C10
D1
D2
D3
D4
D5
D6
R55
100k ohm 1 watt
D7
12k ohm 1 watt
10k ohm 1 watt
1 Megohm 1 watt
10k ohm 1 watt
47k ohm 1 watt
33k ohm 1 watt
22k ohm 1 watt
100k ohm 1 watt
1000 microfarads 35 volts
.1 microfarads 35 volts
10 microfarads 35 volts
1 microfarads 35 volts
.1 microfarads 35 volts
20 picafarads 35 volts
10 microfarads 35 volts
.1 microfarads 35 volts
10 microfarads 35 volts
10 microfarads 35 volts
3 amp 50 volts
3 amp 50 volts
3 amp 50 volts
3 amp 50 volts
1 amp 50 volts
Zener diode
5.6 volts 1 watt
Type IN4148
R56
2.2k ohm 1 watt
D3
Type IN4l48
R57
10k ohm 1 watt
D9
Type IN4l48
.1 amp 50 volts
.1 amp 50 volts
“reset” mode. In the flow chart, the “start” block 110
signi?es the application of the start signal to the com
puter due to the closing of the start switch 16 of FIG. 2.
Immediately, the internal total time register is set at 0.
This is indicated by block 112. The further steps of the
process shown in FIGS. 5-8 are then performed by the
microcomputer.
'10
10k ohm 1 watt
D10
tery and the time that has elapsed. If the comparison
shows that the maximum allowable total time has been
15 reached, the sequence moves to block 118 which indi
cates the execution of the sequence of instructions to
stop the charging cycle, including either turning off the
charging current or turning it to a lower value. This
20
R59
220k ohm 1 watt
D11
Type IN4148
R60
10k ohm 1 watt
D11
Type IN4148
Q1
Q2
Q3
Q4
Q5
1C1
PNP transistor 3 amp 40 volt type TIP-30
NPN transistor 15 amp 40 volt type TIP-35
NPN transistor .5 amp 40 volt type MPS A05
NPN transistor .5 amp 40 volt type MPS A05
NPN transistor .5 amp 40 volt type MPS A05
Voltage regulator 5 volt .5 amp type 78M05
1C2
1C3
1C4
T1
Quad operational ampli?er type LM 324
Quad comparator type MC 3302
Microcomputer type 8048
Transformer 120/240 volt AC input
LED1
LED;
F1
F2
TH]
S1
S2
S3
S4
S5
7 segment light-emitting diode display common cathode
7 segment light~emitting diode display common cathode
Slow blow fuse, 1 amp
Fuse, 5 amps
Thermistor RL28F1
Switch 3 pole double throw (3 amp contacts)
Switch SPST N.O. momentary
Switch SPST
Switch SPST
Switch SPST
.1 amp 50 volts
.1 amp 50 volts
10-20 volt AC output 1-5 amps
FLOW CHART—MICROCOMPUTER
OPERATION
FIGS. 5-8 comprise a flow chart of the basic opera
may also involve changing to a timed overcharge mode
or to a surcharge mode to to a maintenance mode if
desired.
If the total time has not been reached, which it will
not this ?rst time through, the microcomputer goes on
to block 120. Here, the time register is again used to
25
determine whether this is the ?rst time through this
sequence of steps. If it is, then the program moves to the
series of steps 122-128 which direct the computer to set
up certain registers within the computer so that they are
30 ready for use later in the program. First, as indicated at
block 122, a ?ag identi?ed as F0 is cleared. This ?ag
will later be set upon the occurrence of a ?rst in?ection
Type IN4148
.1 amp 50 volts
The next step in the process, identi?ed as block 114,
is to increment the total time register. Then the program
moves to block 116 which does a comparison between
a maximum allowable time as set for the particular bat
.1 amp 50 volts
R53
16
sets all operations of the computer 18 to an initial or
-continued
point or change in sign of the second derivative. The
program then continues through block 124, 126 and 128.
35 As indicated in the drawing, each of these steps controls
the placement of an initial value in particular registers,
namely, “Minimum Slope”, “Maximum Slope”, and
_ “Maximum Voltage Sum” respectively. The “Minimum
Slope” register is set to a large number, while the “Max
40
imum Slope” and ”Maximum Voltage Sum” registers
are each set to a large negative number such as
—- 10,000. The use of these registers will be described
below. Thereafter, the program moves to block 130
designated “loop 2”. This is a common return location
45 to which the program is redirected after each of several
alternative sequences have been completed. In this in
stance, after the three registers have been initialized as
described above, the program moves through block 130
to block 132.
50
In block 132, the stated interrogation is “has two
seconds gone by?”. Block 132 together with the closed
loop 133 for a negative response to this interrogation
simply amount to a delay circuit to prevent the program
from proceeding until a period of time, arbitrarily se
55 lected to be two seconds, has passed since the last time
that thetime register was incremented in accordance
with block 114. After each such increment, a two sec
ond timer is restarted and it runs while the computer
program proceeds through its next sequence of steps. At
tions which are performed within the microcomputer.
The ?ow chart illustrated in FIGS. 5—8 summarizes the 60 the end of the sequence, the program returns to block
130 and the computer is held in the delay loop until two
program steps and has been prepared at a level of detail
seconds have passed. The time register is then incre
which would permit an experienced programmer to
complete the detailed implementation of this invention
mentally increased and the computer proceeds to its
next sequence of steps.
in a type 8048 microcomputer but which, at the same
The program then continues through the previously
time, is not so detailed as to require repetitious descrip 65
tion of iterative steps.
As has previously been noted, when power is ?rst
applied to the system, the reset circuit 26 automatically
described loop. The interrogation of block 116 is asked
and answered in the same manner as previously de
scribed and, since the maximum allowable time has not
17
4,388,582
18
yet been reached, the program moves directly to block
120. When the interrogation of block 120 is asked, the
answer will be in the negative since this is the second
>
It should be noted that the value K2 is a small number.
Its purpose is to prevent spurious or transient errors
caused by drift in the electronic circuit values, or small
time through this sequence. At this point, the program
negative changes in the battery voltage, etc., from shut
directs the computer through location 1 in FIG. 5 to
location 1 in FIG. 6 and thus into block 134.
This instruction, namely, to read the voltage and put
ting down the charging sequence. It is also noted that
this test is preferably performed even during the initial
period identi?ed as Region I of FIG. 1 wherein the
in “Tempsum”, operates the analog-to-digital converter
battery voltage is varying in a somewhat undetermined
as previously described in connection with FIG. 2 and
manner. This is because a negative change in battery
voltage which exceeds K2 even in this Region is also
indicative of a defective battery. K; may equal 25 mil1i-,
volts per cell for nickel-cadmium batteries.
The program sequence next proceeds to block 136
The next stage in the process, identi?ed as block 146,
where the descriptive step is stated as “Calculate Dif
interrogates the timing system to determine whether a
ference=Tempsum-K1”.
15 slope calculation should be done. This actually repre
This is followed immediately by block 138 which
sents the beginning of the inflection point analysis previ
requires whether the difference is negative. If the differ
ously described; as will be clear from the following
stores the resultant digital statement of the battery volt
agevin a storage register in the microprocessor. This
register is referred to as “Tempsum”.
ence is either 0 or greater than 0, the answer is no and
description of FIGS. 5 and 6, the phrase “Slope Calcu
the computer is directed by step 139 to stop charging.
lation” used in this program identi?es the series of steps
This represents a sequence of steps which would be the 20 which locate the in?ection points in the curve of FIG.
same as that stated above with regard to block 118. If
1.
the difference is negative, then the answer is yes and the
As indicated in step 146, the slope calculation is per
program proceeds to block 140.
formed every minute beginning at an arbitary time iden
In fact, the combination of steps 134, 136, and 138 is
ti?ed as K3 seconds. K3 is the time interval chosen to
a test for an excessively high level of battery voltage. 25 allow the battery to pass through the initial stage identi
Thus, K1 is preset at a value which, for the particular
?ed previously as Region I and is usually between 30
and 60 seconds. K3 is preferably 40 seconds in the case
level of voltage, which could only be reached by a
of nickel-cadmium batteries.
defective battery. Accordingly, if the value of voltage
The ?rst several times through the program, the in»
in the register “Tempsum” equals or exceeds K1, the 30 terrogation of step 146 will be answered in the negative
battery must necessarily be defective, or some portion
and, as indicated, the program returns to step 130. Thus,
of the charger is defective, and the charging sequence
until the total time registers equal the value K3, the
must be stopped immediately. For example, K] may
program simply directs the computer to monitor the
equal 2 volts per cell for a nickel-cadmium battery. In
time and voltage to make sure that neither assigned
normal charging, the battery voltage will never equal
maximum has been exceeded, these checks being per
K1, and the answer to the interrogation of step 138 will
formed at steps 116 and 134-138 respectively, and also
be af?rmative so that the program proceeds normally to
monitors the voltage for a negative drop in steps
step 140.
140-144. Once the total time register reaches K3, the
In step 128, the register “Max. Voltage Sum” was set
interrogation of step 146 is answered in the af?rmative
to an initial large negative number. In step 140, the
and the program passes through connection point 2 and
value in “Tempsum” and the value in “Max. Voltage
enters the series of steps shown in FIG. 7.
Sum” are compared. If the value in “Tempsum” is
In FIG. 7, the program continues with step 148
greater than that in “Max. Voltage Sum”, then the value
which refers two additional register locations in the
in “Tempsum” is placed in the “Max. Voltage Sum”
microcomputer. One is called “Sum” and the other is
register by instruction 142 and the program proceeds to 45 “Oldsum”. In step 148, the contents of the register
step 144. If not, then the “Max. Voltage Sum” register
“Sum” are moved into the register location “Oldsum”
value'is left unchanged and the program proceeds di
and the previous contents of the register “Oldsum” are
rectly to step 144.
cancelled. In Block 150, the contents of the latest read
In step 144, the difference between the values used in
ings in “Tempsum” are transferrerd into the register
“Tempsum” and in “Max. Voltage Sum” are compared
location “Sum”. The sequence then moves to block 152
to another constant K2, which is preset according to the
where a test is made to see if the time is equal to K3
battery being charged. In fact, the test being performed
seconds. If it is, the program returns through Loop 2,
by the series of program steps 140, 142 and 144 is that of
step 130. Thus, the ?rst entry into the steps of FIG. 7 at
checking to see if the voltage has moved downwardly
T=K3 simply sets a voltage reading in the “Sum” regis
by more than a given minimum amount from a previ 55 ter which will later be transferred into “Oldsum”. Cal
ously achieved maximum value. As described above in
culation of a slope requires at least two points on the
the section entitled Absolute Voltage Change Analysis,
line and therefore the ?rst calculation can only be done
if this has occurred, this must indicate that the battery
when the time equals 1 minute plus K3 when the previ
has already passed its maximum charge level and is in
ous voltage value is present for comparison to the new
the region indicated as Region V in FIG. 1, or that the 60 value. Of course, this is really an approximation of the
battery is defective. Accordingly, the program is in
slope rather than an accurate determination.
battery being charged, represents an excessively high
structed to move to block 145 which stops the charging
Accordingly, if the time elapsed equals K3 seconds.
process in the same manner as steps 118 and 139.
the sequence goes back to loop 2, block 130 and contin
ues for another minute. Subsequently, when the time
If this is not the case; that is, if the latest value of
battery voltage present in “Tempsum” is either equal to
or greater than the largest value previously recorded,
then it is known that the battery is somewhere in Re
gions I—IV and charging can safely continue.
65
equals K3 plus any integral number of minutes, the se
quence goes on to block 154 where the difference in
value between the “Sum” register and the “Oldsum”
register is calculated and put into a register location
19
4,388,582
called “Slope”. The sequence then continues to block
156.
In step 156, the register “Min. Slope” which was set
to an initial large value in step 124 is used. Speci?cally,
the value in “Slope” is subtracted from the value in
“Min. Slope” and the result tested to see if it is greater
than or equal to 0. If the “Slope” register is less than the
20
it is less than the value in register “Max. Slope” by an
increment K5 which may be approximately the same in
value as K4. This is the test for the Region III-to-Region
IV transition shown in FIG. 1. If the slope is less than
“Max. Slope” by K5, then the charge cycle has reached
this second in?ection point and the charge cycle is
complete. The sequence then goes to block 172 and, the
previous “Minimum Slope” register, which had been
charging process is terminated in the same manner as
initialized to a very large number, the “Slope” value is
put into the “Minimum Slope” register. Thus, once per
minute, each time through this program sequence, a
described in regard to step 118. If, however, the latest
slope is not less than the “Max. Slope” by a suf?cient
increment, then the sequence returns to block 130 and
continues until one of the four charge method analyses
described above causes the charging sequence to stop.
In this way, this flow of operations takes the appara
tus through the methods of analysis described above,
testing at appropriate time intervals for time analysis of
slope is calculated and a check is done to see if the new
value of slope is less than the previous lowest slope
reading. If it is, this new slope is put into the “Minimum
Slope” register in block 158 and the sequence continues
to block 160. If the newest slope is not less than the
minimum slope, the sequence also goes to block 160.
excessive total time elapsed, for excessively high volt
Here, the slope reading just taken is subtracted from
age on the cell or battery, indicating possible damage,
for a drop in voltage from one period to another of
the “Max. Slope” register which was initialized at block
126 to a very small number. If this difference is less than 20 suf?cient magnitude indicating that the cell or battery is
in Region V or for the sequence of second derivative
0, meaning that the new value in the “Slope” register is
greater than the previous value in the “Max. Slope”
register, then this slope value'is put into the “Max.
Slope” register and replaces the old contents. This is
tests indicating that the cell or battery has gone through
the transition from Regions III to IV, as described in
FIG. 1 in the change of sign of second derivative test.
done in block 162.
25
VOLTAGE PROFILE ANALYSIS
Next, the sequence ?ows to block 164 where a test is
done to see if the ?ag F?, which was cleared in step 122,
The present invention, as thus far described, has been
is set. Up to this time, it has not, so the sequence will
directed to the pro?le of voltage change with time
proceed through connection point 3 to block 166. At
which occurs in a battery when the charging system
block 166, a test is done to see if the latest slope value is 30 used is of the type generally known as a “constant cur
greater than the minimum slope by a preselected incre
rent” charger. This type of voltage change is actually
ment, K4. The value of K4 is selected to de?ne some
obtainable in several different ways. First, it may be
minimum value of positive change which must occur, to
avoid transient effects, before the system is allowed to
current to the battery and measuring the change of
recognize that the slope has stopped decreasing and is
now increasing. In the case of nickel-cadmium batteries,
K4 may be 15 millivolts per minute per cell. Once this
occurs, an in?ection point will have been. identi?ed by
obtained by applying a steady unchanging charging
35
voltage with time. In this method, the charger power
supply and current ampli?er may be chosen to provide
a predetermined current level at any battery voltage
between zero and a value slightly in excess of the volt
approximation.
'
age of the battery at full charge. The current level is
If the slope value has not increased over the “Mini 40 chosen on the basis of factors such as the charge ef?
mum Slope” value by this necessary increment, the
ciency, the cost of the power supply and ampli?er, and
the desired time to fully charge a totally discharged
battery. In general, in nickel-cadmium batteries of the C
size or sub-C size, the current applied is about three
suf?ciently. If the latest slope is greater than “Min. 45 times the C-rate of the battery. The C-rate of a battery
sequence returns to block 130 which is the loop 2 re
turn. This means that the slope is either continuing to
become less or if it is increasing, it has not increased
Slope” by K4, meaning that in?ection point has been
passed (or that the sign of the second derivative has
changed), the sequence ?ows to block 168 where ?ag
is a current in amperes which is numerically equal to its
ampere-hour capacity. A “BC” current would bring a
battery to full charge in about 20 minutes.
F¢ is complemented or set. This means, referring to
In other cases, charging rates such as C or 5C may be
FIG. 1, that the transition into Region III has been 50 selected; these would fully charge a discharged battery
made and that the charge cycle is well along toward
in about one hour or in about 12 minutes, respectively.
completion. From block 168 the sequence also contin
A second method of obtaining the voltage pro?le of
ues back to block 130 to continue the process as previ
FIG. 1 is by applying the charging current in pulses and
ously described.
measuring the rest voltage of the battery when the cur
At this point, although it is not shown in the ?ow 55 rent is zero. This is known as trough voltage sensing. In
chart, it is usually preferable to replace the value in the
a sense, the voltage measurements are taken at a “con
“Max. Slope” register with the value in the “Slope”
stant” current level of zero amps. The pro?le of voltage
register. This insures that additional slope values after
with time will correspond in form, although not in
the ?rst in?ection point will be compared to the actual
scale, to that shown in FIG. 1 and exactly the same
slope at the ?rst in?ection point and not to an earlier 60 method of analysis as described above may be applied.
value which may have been carried because it was
A third method of obtaining this same pro?le is to
slightly larger that the in?ection point value.
apply a current which may vary cyclically but which
Eventually, the process will continue through suf?
has a constant average value. If the measured voltage is
cient cycles so that it will arrive again at step 164. Now,
averaged over a similar time period, thus compensating
the response to this interrogation will be “yes” and the 65 for the cyclic variations in current, the voltage pro?le
program will proceed through the connection point
obtained is exactly the same in form as that shown in
“FURTHR” into FIG. 9. There, the sequence contin
FIG. 1, and again, the same method of analysis may be
ues to block 170 where the slope value is tested to see if
applied.
21
4,388,582
22
A fourth method of obtaining the same pro?le is to
period of time is calculated by determining how long it
allow the current to vary but to measure the voltage
takes to add 25% of the full battery capacity to the
battery at the surcharge rate. At the end of that time,
only at the time when the current equals some prese
lected constant level; again, this produces the same
results as the other methods just described.
In all of these instances, the voltage pro?le for a
given battery will assume the same general form. Since
the battery charger automatically terminates the full
charge mode and begins a maintenance mode cycle
which simply compensates for self-discharge.
FIG. 12 illustrates the charging curve for a lithium
the novel method of analysis described in this speci?ca
battery having an iron sul?de electrode. In this case, the
in?ection points occur much earlier in the charge cycle
tion is a function only of the form of the pro?le and not
of its actual value, this method may be applied to any of 10 and there are almost no distinguishing features of the
these charging techniques. For convenience, all of these
voltage pro?le after the second in?ection point. Be- _
methods are commonly referred to by the term “voltage
cause of this voltage pro?le, it would be extremely
pro?le”.
difficult to provide a reliable fast charger for such a
battery using only prior art techniques. In accordance
APPLICATION OF VOLTAGE PROFILE
with the present invention, the in?ection points can be
determined very precisely. This indicates that the bat
tery is approximately at 45% of capacity. Accordingly,
a charging program for a lithium battery of this type
ANALYSIS TO OTHER BATTERY COUPLES
FIGS. 10-13 illustrate a variety of voltage pro?les for
particular examples of several different types of batter
ies, all of which have been developed using the “con
may use the same system for determining in?ection
stant current” method referred to above. Speci?cally, 20 points as have been described above, coupled with a
FIG. 10 is a representative pro?le obtained in the case
timing sequence. When a battery is attached to the char
of a nickel-iron battery. It will be noted that the general
ger, a timer is started and it is set to discontinue the full
appearance of this curve is similar to that of FIG. 1 and
charge rate when enough time has passed to add ap
in particular, similar inflection points occur at A’ and B’
proximately 55% of the total battery capacity to the
as the battery approaches full charge. Thus, exactly the 25 battery. If no in?ection points are encountered during
same technique can be applied to the nickel-iron battery
this period, the timer alone shuts off the system at the
as has been described for the nickel-cadmium. The only
end of the period. This accommodates a battery which
differences are that the constants must be selected in
may be placed on charge although it already has a rea
accordance with the needs of the particular battery,
sonably full charge.
considering its internal construction and the level of 30 However, if the in?ection points are encountered
current which it can accept, the number of cells and the
before the time has expired, then the timer is simply
corresponding maximum voltage; and the maximum
restarted. This ensures that a battery which was dis—
time or maximum voltage which can be accepted with
charged, or only partially charged, initially will receive,
-its full charge.
out damage. Also, the small scale of the changes in the
voltage pro?le require the system of voltage measure
35
ment to have a higher resolution than is true in the case
of a nickel-cadmium battery. In principle, however, the
method of charging is substantially identical.
FIG. 13 illustrates still another variation of voltage
pro?le, namely, that for a silver cadmium battery. In
this instance, simple determination of two consecutive
in?ection points is not suf?cient; addition of energy to a ,
FIG. 11 illustrates the charging curve of a representa
battery which is fully discharged should produce four
tive lead acid battery. Once again, it can be seen that the 40 consecutive in?ection points before full charge is
?ve Regions as described in connection with FIG. 1 are
reached.
repeated in the case of the typical lead acid pro?le and
In order to fully charge this battery, another combi
similar inflection points A” and B" occur. The only
nation of the in?ection point analysis method with the
differences are that the overall change of voltage is
alternative charge termination modes previously de
larger and the rate of change in Region III is greater. 45 scribed will fully charge this battery. Speci?cally, the
However, since the Regions are the same and the se
charger is arranged to seek the four consecutive in?ec
quence of in?ection points is the same, essentially the
tion points which indicate that the battery being
same method as described in connection with nickel~
charged has gone through its entire cycle from fully
discharged to fully charged; if this occurs, the charger
cadmium batteries and nickel iron batteries can again be
used for lead acid batteries.
terminates the application of the fast rate charge cur
rent. However, this termination mode alone is not suf?
cient. In addition, the system is instructed to compare
the total voltage to some preselected value after each
However, it has been found that full (100%) charging
of a lead acid battery can be better obtained by the
additional application of a surcharge after the second
inflection point has been reached. This is due to the
in?ection point is measured. If the voltage is above the
internal chemistry of the lead acid battery which causes 55 preselected level when an in?ection point is reached, it
the ?nal addition of energy to occur at a slower rate
will then be known that the battery was not fully dis
than in the case of a nickel-cadmium battery. Therefore,
charged when the charge program was started and that
the optimum charge method for lead acid batteries is to
the battery is now fully charged. Accordingly, the ap
plication of the full rate current is discontinued. Thus,
apply the in?ection point method of analysis as previ
ously described, and, when the second in?ection point
between Regions III and IV is identi?ed, the microcom
60 the system accommodates both batteries which are
puter is instructed to shift the charging rate to an inter
mediate level. This intermediate rate is then applied for
a ?xed period of time.
In general, lead acid batteries have a structure which 65
permit the constant current to be about C or 2C in the
fast charge mode. The surcharge rate selected is gener
ally about one-half of the full charge rate. The ?xed
placed on charge While already either fully or partially
charged and also batteries which are fully discharged;
in both cases, the charger brings the battery precisely to
its full charge capacity without the harmful effects of
prior art charging techniques.
Of course, in devising the method and system for
each of the batteries mentioned in connection with
FIGS. 10-13, the additional safeguards to prevent seri
4,388,582
23
ous overcharge and to shut the system off in the event
that either the battery or the charger is defective are
also included; thus, a maximum total time limit, a maxi
241
1-9 can be converted to a method of inflection point
analysis for the constant voltage case by changing the
word “voltage” to “current” and by reversing all words
such as “increasing”, “decreasing”, “positive”, “nega
mum voltage limit, a negative change in voltage, and a
negative slope limit may all be included as appropriate.
tive”, etc.
Similarly, with regard to FIGS. 10-13, the particular
CURRENT PROFILE ANALYSIS
The description of this invention as set forth above
batteries identi?ed there can be charged by the constant
has been given in terms of the battery analysis method
which applies when the state of charge of the battery is
voltage technique. In each case, the general method of
in?ection point analysis as set forth in the speci?cation
exactly corresponds to that which has already been
measured under “constant current” conditions. In addi
described.
tion, it is possible to charge the battery in a “constant
voltage” mode, to measure the change in current with
the passage of time, and to apply similar methods of
in?ection point analysis to the resultant pro?le of
changing current with time. This technique involves the
RATE OF CHARGING
A primary bene?t of the present invention is that any
normal battery, that is, any battery which is not defec
tive, canbe charged at a relatively high rate. In using
selection of a constant voltage to be applied to the bat
previously known battery charging methods, it has been
tery by the charger; the voltage chosen is selected so
that the current which it applies to the battery during
necessary to limit the application of high rate charging
currents to batteries which are especially adapted to
the bulk of the charge time is reasonable on the basis of 20 accommodate the inadequate shut-off modes in use.
the same parameters as described in the case of the
This is due to the fact that previous methods cannot
constant current charger, namely, the charger effi
stop the fast charge current at the proper moment and
ciency, the cost, and the time required to fully charge a
discharged battery. Once again, this application of con
stant voltage produces a known and predictable form
for the curve traced by the change in current with time.
Actually, the term “constant voltage” is applied
equally to systems in which the actual applied voltage is
constant throughout the charge period, to systems in
which the current is always measured when the voltage
is at a preselected value, or to systems in which a pulsat
ing applied voltage has a constant average and in which
the measured current is correspondingly averaged. All
of these systems produce a curve of current against time
which has the same general form and which may be
treated by means of the same inflection point analysis;
accordingly, this pro?le is referred to herein as the
25
the various harmful effects previously noted can occur.
Only batteries designed to withstand these effects can
be used and even such batteries experience shortened
lives, etc.
In contrast, the method of the present invention pro
vides such precise control over the application of en
ergy to the battery that it can be used to fast charge
even those batteries which were previously intended for
charging only by slow rate methods.
The term “trickle charge” usually refers to a charge
rate such that the battery receives its full charge only
over a period of 12 to 24 hours. Thus, typical trickle
chargers apply a current of between 0.05C and 0.1C. In
curve is exactly the same in form as that shown in FIG.
accordance with previous methods, the terms “fast
charge” or “quick charge” are generally applied to
rates in excess of 0.2C; that is, charge rates which would
charge a battery in less than 5 hours.
All batteries accept currents of the “fast charge”
1 except that the entire curve is inverted. Thus, the
method of in?ection point analysis as applied to this
particular battery is governed by the current-accept
“current pro?le”.
.
In the particular case of a nickel-cadmium battery,
the current pro?le is illustrated in FIG. 14. In fact, this
level for limited periods of time. The upper limit for a
ance capability of the battery; that is, of its internal and
pro?le is exactly the same as has been described in con
nection with FIG. 1 except that all of the pertinent 45 external connections, and of its internal plates, and also
by its internal ion transit time. This level is generally
analyses regarding signs, direction of change, etc. are
reversed. Initially, the current decreases in a manner
given by the manufacturer. For example, sub-C size
corresponding to that in Region I in which the voltage
nickel-cadmium batteries available from General Elec
tric can accept fast charge current at the 4C rate; lead
acid batteries of the sealed type available from Gates
v.Energy Products, Inc. can accept fast charge current at
the 0.3C rate.
of FIG. 1 increased. This is followed by an intervalin
which the current decreases slowly; this is normally the
longest time interval and the one in which the major
increase occurs in the energy stored in the battery. This
corresponds to the increasing voltage of Region II of
FIG. 1.
The inflection point which must be identi?ed be
tween this interval and the next Region of sharply de
creasing current occurs at the same point in time as
point A in FIG. 1. However, it identi?es a change in the
sign of the second derivative of current from positive to
negative whereas Point A in FIG. 1 identi?ed a change
in the sign of the second derivative of voltage from
negative to positive. Similarly, the in?ection point be
tween Regions III and IV is now identi?ed as that at
Even though batteries could accept such fast charge
currents, presently known chargers are not capable of
shutting off the fast charge current at the proper mo
ment and even batteries which structurally could accept
fast rate currents can only be charged at the trickle
charge rate. In general, any charge rate above the 5
hour rate (0.2C) has previously required a special bat
tery design.
Because of the accuracy with which the present in
vention determines the full charge level, the present
charging method permits the use of fast charge currents
with many batteries which could previously be charged
only by slow, trickle charge rates. This is particularly
which the second derivative changes from negative to
positive whereas in FIG. 1, the change was from posi 65
true in the categories of nickel-cadmium batteries and
tive to negative.
lead acid batteries which predominate among the re
Thus, the entire description of the method of in?ec
chargeable battery couples presently available.
tion point analysis as applied in connection with FIGS.
25
4,388,582
Thus, the present method permits essentially all of
26
particularly electrical characteristics might also be ana
lyzed. It is noted that this pro?le may also vary with
nickel-cadmium batteries presently in use by consumers
to be recharged in a time on the order of 1 hour. Lead
acid batteries of the gel type can be charged in a time on
the order of 2 hours; those of the liquid type can be even
other battery conditions; in fact, as previously de
scribed, the analysis of this invention partially depends
more quickly charged.
In general terms, the present invention permits the
on the fact that other battery conditions affect the pro
?le.
In addition to the extremely precise method of in?ec
application of a high rate; that is, a rte in excess of 0.2C
and up to the rated current acceptance level of the
tion point analysis as hereinbefore described, the pres
ent invention also encompasses the analysis for other
critical points in the pro?le of variation with time of a
battery; normal batteries so charged by the system of
the present invention will receive a full charge and will
not be damaged.
characteristic of the battery which changes with the.
energy level stored in the battery. In addition, there
fore, to in?ection point analysis, the present invention is
also in part directed to improvements in method and‘
apparatus for charging batteries which relate to detailed
FINISH MODE
In the case of nickel-cadmium batteries, the in?ection
point analysis described above brings a battery to essen
analyses of the pro?le of battery characteristics, the
tially 100% charge. Thus, when the second in?ection
analyses involving combinations of such factors as limit
point has been reached, the charger can shift into a
ing value, slope, and passage of time. By analysing the
maintenance mode in which short pulses of high rate
pro?le of the particular characteristic for the battery
charging current are applied periodically to compensate 20 under charge, particular combinations of these events
for self-discharge. For example, a 1C current may be
may be identi?ed and used by those familar with batter
applied for 15 seconds every 6 hours. Other mainte
ies and the art of battery charging to provide improved
nance cycles might be used if desired.
techniques of fast battery charging without departing
In actual practice, repetitive charging of the battery
from the spirit of the present invention. 4
to exactly the second in?ection point may cause minute 25
In addition, the present invention presents numerous
reversible degradation because this point occurs a small
subcombinations of this method which have not previ
fraction of a percentage point below 100% charge. This
ously been known; the many variations of these combi
degradation may be reversed when the battery is left on
maintenance or when the operator, occasionally, places
nations which will readily occur to those familiar with
the battery and battery charging art are also intended to
the battery on charge even though it is not discharged. 30 be included.
This drives the voltage slightly into Region V of FIG.
Particular emphasis has also been placed on the
1 so that cut-off occurs in accordance with block 145 of
charging of nickel-cadmium batteries and lead acid
FIG. 6 which reverses the degradation.
batteries in view of the importance of these couples.
To completely prevent even the possibility of such
The speci?c methods perfected for charging such bat
degradation, a surcharge current of 0.1C can be applied
teries are also fully within the contemplation of the
for a few hours after the second in?ection point has
present invention.
been reached. The above-described maintenance cycle
Finally, a speci?c apparatus has been disclosed for
may then begin.
performing the method of this invention. A great many
In the case of lead acid batteries, as has previously
obvious variations of this apparatus will be readily ap
been discussed, an interval of low rate charging may be 40 parent which correspond generally to the alternative
useful to completely charge the battery; thereafter, an
methods described. It is fully intended that the appara
appropriate maintenance mode is used to compensate
tus claims in this application be extended to cover all
for self-discharge. In other battery couples, other ?nish
such alternative embodiments of this basic apparatus.
ing techniques may be utilized as appropriate.
We claim:
1. A method of rapidly and ef?ciently charging a
SUMMARY
battery of the type in which the voltage characteristic
thereof varies with the state of charge of the battery and
in which the voltage characteristic varies with time
during charging to exhibit an in?ection point prior to
the battery attaining substantial full charge, the in?ec
tion point characterized by a change in the slope of the
voltage characteristic from successive increases in slope
The foregoing speci?cation describes a battery
charging method which basically utilizes the in?ection
point analysis method to identify very precisely signi?
cant points in the variation of the electrochemical en
ergy in a battery during its charge cycle. Accordingly,
the appended claims are broadly directed to this method
and are intended to include all variations of this method
as may be obvious to those skilled in the art.
Among the many possible variations, it should be
noted that the above apparatus particularly described
to a decrease, the method comprising the steps of:
supplying electrical energy to the battery for charg
55
ing thereof;
monitoring said voltage characteristic of the battery
periodically during charging;
has made use of an approximation technique for deter
mining the occurrence of an in?ection point. It is, of
course, fully within the contemplation of this invention
to use this or other approximation techniques for locat 60
ing critical points in a pro?le, or to provide a circuit
computing the slope of the variation of said moni‘
tored voltage characteristic with time;
storing the maximum value of the so-computed slope
which is capable of directly monitoring the second
comparing each successively computed slope value
derivative for a change in sign. Similar variations may
also be used with regard to other parametric pro?les.
Another set of variations comprises the particular
battery characteristic selected for analysis. While the
present description has been directed particularly to the
voltage or current, pro?les of other characteristics,
with said stored maximum value;
identifying the inflection point exhibited in the varia
65
values;
. tion of said voltage characteristic prior to the bat
tery attaining substantial full charge by identifying
.a change in the so-compared slope values from
successive increases in slope to a decrease; and
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