U.S. patent application number 09/791108 was filed with the patent office on 2001-11-01 for method for determining the state of charge of lead-acid rechargeable batteries.
Invention is credited to Brunn, Detief, Laig-Horstebrock, Helmut, Leiblein, Karl-Heinz, Meissner, Eberhard, Ubermeier, Dieter.
Application Number | 20010035738 09/791108 |
Document ID | / |
Family ID | 7632043 |
Filed Date | 2001-11-01 |
United States Patent
Application |
20010035738 |
Kind Code |
A1 |
Laig-Horstebrock, Helmut ;
et al. |
November 1, 2001 |
Method for determining the state of charge of lead-acid
rechargeable batteries
Abstract
A method for determining the state of charge of lead-acid
rechargeable batteries comprising a) substantially simultaneously
measuring measured-value pairs (U.sub.i, I.sub.i) of the
rechargeable battery voltage and current flowing at time ti over
time interval dt, b) selecting a group of said measured-value pairs
(U.sub.i, I.sub.i) for which only a discharge current flowed in the
last time interval dt, c) varying parameters Uo, R and C such that
a residual sum of squares between values U.sub.i given by formula
(1) U.sub.i=Uo+R*I.sub.i+1/C.intg.Idt (1) and measured values
U(t.sub.i) is minimized, wherein Uo represents no-load voltage, R
represents resistance and C represents capacitance, and d)
calculating the state of charge of the rechargeable battery from
the no load voltage obtained from formula (1).
Inventors: |
Laig-Horstebrock, Helmut;
(Frankfurt, DE) ; Meissner, Eberhard; (Wunstorf,
DE) ; Brunn, Detief; (Garbsen, DE) ; Leiblein,
Karl-Heinz; (Wunstorf, DE) ; Ubermeier, Dieter;
(Hannover, DE) |
Correspondence
Address: |
IP Department
Schnader Harrison Segal & Lewis
36th Floor
1600 Market Street
Philadelphia
PA
19103
US
|
Family ID: |
7632043 |
Appl. No.: |
09/791108 |
Filed: |
February 22, 2001 |
Current U.S.
Class: |
320/132 |
Current CPC
Class: |
G01R 31/379 20190101;
G01R 31/3828 20190101 |
Class at
Publication: |
320/132 |
International
Class: |
H02J 007/00 |
Foreign Application Data
Date |
Code |
Application Number |
Feb 23, 2000 |
DE |
100 08 354.4 |
Claims
What is claimed is:
1. A method for determining the state of charge of lead-acid
rechargeable batteries comprising: substantially simultaneously
measuring a) measured-value pairs (U.sub.i, I.sub.i) of the
rechargeable battery voltage and b) current flowing at time t.sub.i
over time interval dt, selecting a group of said measured-value
pairs (Ui, I.sub.i) for which only a discharge current flowed in
the last time interval dt, varying parameters Uo, R and C such that
a residual sum of squares between values U.sub.i given by formula
(1)U.sub.i=Uo+R*I.sub.i+1/C.intg.Idt (1)and measured values
U(t.sub.i) is minimized, wherein Uo represents no-load voltage, R
represents resistance, I.sub.i represents current intensity and C
represents capacitance, and calculating the state of charge of the
rechargeable battery from the no load voltage obtained from formula
(1).
2. The method as claimed in claim 1, wherein parameters Uo, R, a,
i.sub.o and C are varied such that a residual sum of squares
between values U.sub.i according to formula
(2)U.sub.i=Uo+R*I.sub.i+[a*i.sub.o*arc sin
h(I.sub.i/i.sub.o)-a*I.sub.i]+1/C.intg.Idt (2)and measured values
U(t.sub.i) is minimized, wherein Uo, R, I.sub.i and C are the same,
i.sub.o is current intensity, and a represents resistance.
3. The method as claimed in claim 1, wherein selected Uo are
compared with previous values in time, and wherein only values Uo
which satisfy formula
(3)dUo/dq=(Uo(t.sub.n)-Uo(t.sub.n-1))/(q(t.sub.n)-q(t.sub.n-1))<Dgr
(3)are used, wherein the limit Dgr per cell is selected from the
range 6V/Qo to -6V/Qo, and Qo is capacity of the battery.
4. The method as claimed in claim 1, wherein the only measured
value pairs (U.sub.i, I.sub.i) which are used are those in which
I.sub.i<0 and for which the following condition has been
satisfied since a last measured value with a positive current and a
time interval dt with a positive contribution Q.sup.+ to the state
of charge: the magnitude of Q.sup.- is either greater than the
magnitude of Q.sup.+, or the magnitude of Q.sup.- is greater than
about 2% of the battery capacity, where Q.sup.- represents an
(discharged) amount of charge which has been drawn since a last
measurement point with a positive battery current in an
uninterrupted discharge phase, and Q.sup.+ is an (charged) amount
of charge which has been introduced in a latest uninterrupted
(charging) phase with a positive battery current.
5. The method as claimed in claim 1, wherein measurement of data
and switching on and off of loads are synchronized such that
measured value pairs (U.sub.i, I.sub.i) with different current
intensities I.sub.i are obtained.
6. The method as claimed in claim 1, wherein switching on and off
of loads is timed such that measured value pairs (U.sub.i, I.sub.i)
with different current intensities I.sub.i are obtained.
Description
FIELD OF THE INVENTION
[0001] This invention relates to a method for determining the state
of charge of lead-acid rechargeable batteries by estimating their
no-load voltage during active operation in a vehicle.
BACKGROUND
[0002] It is desirable to determine the present state of charge of
a rechargeable battery for numerous applications. If the present
state of charge at a specific time is known, then the change in the
state of charge can be deduced by continuous measurement of the
current flowing, and by integrating it. However, the validity of
the present measured value deteriorates to an ever greater extent
due to the measurement uncertainty linked to this method, so that
the state of charge reading must be reset from time to time using a
different method.
[0003] In the case of a lead-acid rechargeable battery, assessment
of the present no-load voltage of the rechargeable battery is
highly suitable for this purpose since it is directly linked to the
state of charge (as discharging continues, sulfuric acid is
consumed from the electrolyte, and the no-load voltage of the
lead-acid rechargeable battery is directly dependent on the acid
density). However, to do this, the rechargeable battery is operated
without interruption for a certain time, during which time the
current flowing must be less than a very low threshold value. This
is because the lead-acid rechargeable battery produces its no-load
voltage only in the (virtually) unloaded state, while its voltage
in some cases differs greatly from this when charging or
discharging currents are flowing.
[0004] Depending on previous history, even in the unloaded state,
it often still takes a long time for the internal state of the
rechargeable battery to reach its equilibrium value, and for the
voltage to reach its no-load value. Even with modern rechargeable
batteries, the period of phases without any current flowing
required after previous charging phases and at low temperatures is
very long, in some cases from several hours up to a number of
days.
[0005] Thus, in operating modes without such long phases with no
current flowing, the method of measuring the no-load voltage for
determining the state of charge is in general suitable only to a
limited extent. One example of this is the starter rechargeable
battery in a motor vehicle where, often, only stationary times of a
few hours or, for example, when used in taxis, virtually no
stationary times at all occur. At room temperature and above, the
present no-load voltage which would be obtained if the current were
switched off briefly is itself a good measure of the real no-load
voltage of the rechargeable battery.
[0006] DE-19643012 A1 specifies a method in which no-load voltage
values Uo from the zero crossings of the current flowing through
the rechargeable battery are used to drive the voltage regulation
of the generator. This method places relatively stringent demands
on the measurement electronics. The flowing current generally
passes through the zero point very quickly, making interpolation
necessary, which can be achieved only with difficulty due to the
non-linearities of the current/voltage curve at low currents.
[0007] Thus, it would be advantageous to provide a method which
allows a conclusion to be drawn about the present no-load voltage
of the rechargeable battery, as well as an estimate to be made of
the no-load voltage while the rechargeable battery is on load,
without artificially interrupting operation.
SUMMARY OF THE INVENTION
[0008] The invention relates to a method for determining the state
of charge of lead-acid rechargeable batteries including a)
substantially simultaneously measuring measured-value pairs
(U.sub.i, I.sub.i) of the rechargeable battery voltage and current
flowing at time t.sub.i over time interval dt, b) selecting a group
of the measured-value pairs (U.sub.i, I.sub.i) for which only a
discharge current flowed in the last time interval dt, c) varying
parameters Uo, R and C such that a residual sum of squares between
values U.sub.i given by formula (1):
U.sub.i=Uo+R*I.sub.i+1/C.intg.Idt (1)
[0009] and measured values U(t.sub.i) is minimized, wherein Uo
represents no-load voltage, R represents resistance and C
represents capacitance, and d) calculating the state of charge of
the rechargeable battery from the no-load voltage obtained from
formula (1).
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 is a graph of applied current and voltage response of
a battery over time.
[0011] FIG. 2 is a graph of voltage versus battery capacity.
[0012] FIG. 3 is a graph of applied current and voltage response of
a battery over time.
[0013] FIG. 4 is a graph of applied current and voltage response of
a battery over time.
DETAILED DESCRIPTION
[0014] The method according to the invention essentially comprises
two steps, namely, determination of the voltage Uo which the
battery would have if the load were briefly disconnected and,
following this, a calculation of the state of charge from the
no-load voltage obtained in this way.
[0015] In the method according to the invention, a large number of
measurement points are assessed, thereby allowing scattered data to
be dealt with better and accuracy to be considerably improved.
[0016] The instantaneous no-load voltage is obtained by regularly
measuring measured-value pairs (U.sub.i, I.sub.i) of the present
voltage and current at substantially the same time, and by using an
equalization calculation to match these to a resistance
relationship having a number of free parameters. One of the
parameters is an approximation to the present no-load battery
voltage Uo. The conventional mathematical sign rule for battery
currents is used in the following text:
[0017] Charging currents for the rechargeable battery are regarded
as positive currents, and discharge currents are regarded as
negative currents.
[0018] In the method according to the invention, a selection is
made from measured-value pairs (U.sub.i, I.sub.i). The goal in this
case is to ensure that non-equilibrium states of the electrodes
which result from previous charging phases have already been
dissipated since the use of measured-value pairs (U.sub.i, I.sub.i)
from such states would lead to corrupt results. In particular, the
measured-value pairs (U.sub.i, I.sub.i) which are used are those
which lie in a discharge phase, that is to say, for which the
present current and the current from the previous measurement are
less than zero. Furthermore, care is taken to ensure that a
previous charging phase (with current values greater than zero) is
sufficiently far in the past.
[0019] A resistance rule in the following form has been proven for
the determination, according to the invention, of the instantaneous
voltage for zero current from a number of measured-value pairs
(U.sub.i, I.sub.i):
U.sub.i=U.sub.o+R*I.sub.i+[a*I.sub.o*arc sin
h(I.sub.i/I.sub.o)-a*I.sub.i]- +1/C.intg.Idt. (2)
[0020] Uo, R, a, I.sub.o and C are in this case the parameters to
be varied. R and a are resistance, I.sub.o and I.sub.i are current
intensity, C is capacitance, and U.sub.o represents the no-load
voltage determined using this algorithm.
[0021] The term with the parameters a and I.sub.o takes account of
non-linearities and is required, in particular, in the event of
major current changes. Otherwise, for simplicity, it can generally
be omitted. The last part of the equation takes account of
capacitive effects in the battery due to integration of the current
which has flowed. This results in a simplified equation:
U.sub.i=U.sub.o+R*I.sub.i+1/C.intg.Idt, (1)
[0022] wherein U.sub.o R, I.sub.i and C are the same as in equation
(2). If there is any scattering in the measured values or noise is
superimposed, the systematic signals are, of course, appropriately
large to achieve sufficient accuracy. Determination of the
correlation coefficients between current and voltage can provide
information relating to this.
[0023] Thus, in the method according to the invention for
estimating the present no-load voltage of a lead-acid rechargeable
battery:
[0024] measured-value pairs (U.sub.i, I.sub.i) of the rechargeable
battery voltage and the current flowing at time t.sub.i are
recorded at the same time at time interval dt, with the only value
pairs which are considered being those for which only a discharge
current flowed in the last time interval,
[0025] then, using a group of measured-value pairs (U.sub.i,
I.sub.i) selected in such a way, parameters Uo, R and C are varied
such that the residual sum of squares between the values U.sub.i
given by the formula
U.sub.i=Uo+R*i.sub.i+1/C.intg.Idt (1)
[0026] and the measured values U(t.sub.i) is minimized,
[0027] finally, the state of charge of the rechargeable battery is
deduced from the voltage obtained in this way. (In this case, R is
resistance, C is capacitance and U.sub.o represents the no-load
voltage determined using this algorithm.)
[0028] The following formula is used to work with greater
accuracy:
U.sub.i=Uo+R*I.sub.i+[a*i.sub.o*arc sin
h(I.sub.i/i.sub.o)-a*I.sub.i]+1/C.- intg.Idt. (2)
[0029] (In this case, R and a are resistance, I.sub.i and i.sub.o
are current intensity, C has the dimension capacitance and U.sub.o
represents the no-load voltage determined using this algorithm.) In
a further refinement of the method, U.sub.o determined from
equations (1) or (2) is compared with previous values in time, and
the only value pairs (U, I) which are considered are those to which
the following relationship applies:
dUo/dq=(Uo(t.sub.n)-Uo(t.sub.n-1))/(q(t.sub.n)-q(t.sub.n-1))<Dgr.
(3)
[0030] The limit Dgr per cell is selected from the range 6V/Qo to
-6V/Qo, preferably subject to the condition Abs(Dgr).ltoreq.1V/Qo.
Qo is in this case the capacity of the battery.
[0031] It has been proven that the calculated Uo with one or two
adjacent values should be averaged once again, with equation (3)
being used only then as a criterion to decide whether these values
Uo are suitable for use as a point of origin for determining the
no-load voltage.
[0032] Alternatively, there should be a sufficiently long previous
discharge phase (with a current of less than zero) before measured
values are taken, to be precise such that the amount of charge
Q.sup.- discharged during this period is at least equal to the
amount of charge Q.sup.+ introduced during a previous charging
phase (with a current greater than zero). If required, an amount of
charge Q may even be deliberately discharged to achieve this
aim.
[0033] The amount of charge Q.sup.- required for this purpose is,
from experience, not more than about 2-3% of the battery capacity.
It is thus sufficient to discharge an amount of charge
corresponding to Q.sup.-<2-3% of the battery capacity to reach
the pure discharge region.
[0034] An estimate of the maximum amount of charge Q.sup.- required
for this purpose from a starter rechargeable battery with a rated
voltage of 12V and a battery capacity Qo is:
Q.sup.-=Qo*(U-12V)/60V, (4)
[0035] where U is the battery voltage measured during a short
current pause.
[0036] A particularly advantageous special case according to the
invention occurs when the (negative) overvoltage occurring while
discharging the amount of charge Q.sup.- is on average greater than
the (positive) overvoltage which occurs during the previous
charging. The time interval from which the measured-value pairs
(U.sub.i, I.sub.i) are taken is selected, for example, such that
the state of charge in this period is reduced by less than 5%, and
preferably by less than 2%, of the battery capacity.
[0037] The parameters obtained in carrying out the equalization
calculation (including the instantaneous no-load voltage) may in
general be dependent on the state of charge and the battery
temperature. These parameters should, therefore, change as little
as possible during the phase from which the measured-value pairs
(U.sub.i, I.sub.i) are selected. If necessary, the duration of the
phase may need to be limited appropriately. The estimation of the
duration is based, for example, on the change in the state of
charge which occurs and is detected by integration of the current
which has flowed.
[0038] Furthermore, it is desirable for the accuracy of the method
for the discharge current for the selected measured-value pairs
(U.sub.i, I.sub.i) not to be constant, but to change as much as
possible. In this case as well, an appropriate selection of the
measured-value pairs (U.sub.i, I.sub.i) used can be made or,
alternatively, changing current loads may be deliberately applied.
In addition, according to the invention, the measured data
detection can be synchronized to switching on and off electrical
loads, in particular, pulsed loads to achieve the desired effect.
The method according to the invention also applies to the starting
process powered from a battery.
[0039] The selection of the measured-value pairs (U.sub.i, I.sub.i)
used for matching to the function (1) or (2) is thus made such that
the flowing (discharge) currents I.sub.i are not constant but, for
example, have changes at least on the order of magnitude of about
0.01 A per Ah of battery capacity.
[0040] The measured data detection and the switching on and off of
loads, in particular, with pulse-controlled loads, are synchronized
in such a way that measured-value pairs (U.sub.i, I.sub.i) with
different current intensities I.sub.i are obtained. Switching on
and off loads may also be provoked, to be precise in such a way
that measured-value pairs (U.sub.i, I.sub.i) with different current
intensities I.sub.i are obtained.
[0041] The method can be supplemented by assessment of the voltage
response after a previous charge, by observing the change over a
period of time and then, if this is below a lower threshold value,
using the present voltage measured value as an approximate value
for the no-load voltage. If this condition is not yet satisfied,
then the deliberate controlled discharge mentioned above is carried
out. The mean current flowing during the discharge phase should not
be too high, to avoid creating renewed inhomogeneities in the
electrodes and in the electrolyte.
[0042] Another procedure, which is highly advantageous in practice,
is for the preselection of the measurement points initially to be
based on the limitation of a negative (that is to say discharge)
current, and then to carry out the parameter adaptation, and then
to select the values to be used, from the value Uo obtained in this
way, in accordance with a criterion.
[0043] That is to say, those measurement points which will finally
be used to determine the state of charge are selected after their
suitability has been checked.
[0044] It is thus advantageous to proceed in such a way that the
no-load voltage Uo at the time t.sub.n, calculated using the
formula (1) is compared with that obtained for a previous time
t.sub.n-1. In this case, the only values of Uo used for calculation
of the state of charge are those for which only a slight dependency
has been found between the voltage Uo and the amount of charge
flowing between the times t.sub.n and t.sub.n-i. These are values
for which:
dUo/dq=(Uo(t.sub.n)-Uo(t.sub.n-1))/(q(t.sub.n)-q(t.sub.n-1))<Dgr.
(3)
[0045] The limit value Dgr is selected from the range 6V/Qo to
-6V/Qo per series-connected cell of the rechargeable battery,
preferably subject to the condition Abs (Dgr).ltoreq.1V/Qo per
series-connected cell. Qo is in this case the capacity of the
battery.
[0046] It is also possible to select from the values Uo determined
according to the invention, only those values for which the linear
regression to the values Uo plotted against the converted charge
has a trend which is less than Dgr, where Dgr per battery cell is
selected from the range from 6V/Qo to -6V/Qo, preferably subject to
the condition Abs (Dgr)<1V/Qo.
[0047] A further improvement in the accuracy of the calculation is
obtained in that the state of charge value SOC (t.sub.o) obtained
in this way at a specific time t.sub.o for determining the state of
charge is linked to the general time t by means of other methods
for determining the state of charge or else by means of methods for
determining the change in the state of charge .DELTA.SOC (t.sub.o,
t) in the time from t.sub.o to t, in which case .DELTA.SOC
(t.sub.o, t) is advantageously calculated from the converted amount
of charge determined by integration of the current flowing through
the rechargeable battery.
[0048] In a further embodiment of the invention, the erroneous
state of charge values SOC (t.sub.i) obtained at different times
t.sub.i are linked by means of other methods for determining the
erroneous state of charge values or by means of methods for
determining the erroneous change in the state of charge .DELTA.SOC
(t.sub.o, t.sub.i+1) in the time from t.sub.i to t.sub.i+1, and a
present state of charge value SOC is thus determined, with this
value being obtained by using a minimization method, preferably the
least square errors method.
[0049] The voltage values Uo obtained may also be compared with a
limit value Uo-min, with undershooting being indicated and/or an
action being taken. The limit Uo-min is selected such that it
corresponds approximately to the equilibrium voltage of the
rechargeable battery after its rated capacity has been drawn.
[0050] In summary, the procedure according to the invention is as
follows:
[0051] 1. Measure the voltage U(t) and the current I(t)
[0052] 2. If I(t)>0, then the measurement is rejected, return to
1; otherwise
[0053] 3. If the previous measurements I (t-1) , I (t-2), . . .
>0, return to 1; otherwise
[0054] 4. Apply equation (1) or (2) to a set of value pairs U, I,
and thus obtain Uo
[0055] 5. (OPTIONALLY: form the average over a number of Uo
obtained in this way, provided there is no measured value where
I>0 inbetween)
[0056] 6. Apply equation (3) and confirm whether the discharge is
in the region where there is little relationship between the
voltage and the amount of charge drawn; if no, this is rejected,
return to 1; otherwise
[0057] 7. Use Uo to calculate the state of charge via the
relationship for voltage, electrolyte concentration and state of
charge.
[0058] The method will be explained in more detail in the following
text with reference to Examples 1 to 5 and FIGS. 1 to 4.
EXAMPLE 1
[0059] FIG. 1 shows the typical profile of the current and voltage
for a vehicle battery when driving in a town. This is a six-cell
lead-acid battery with a capacity of 48 Ah. The battery state of
charge is approximately 70%.
[0060] The parameters in equation (1) were applied to this driving
cycle and adapted with the simplification a=0 and io=0. The values
obtained for all the Uo are entered as circles in FIG. 1.
[0061] FIG. 2 shows the selection of the points Uo which may be
suitable for determining the state of charge. The usable values are
located where the curve has a flat profile. It is preferred that
the values be averaged and the criterion of equation (3) then be
applied. The values Uo which remain after applying the criterion of
equation (3) with Dgr=0.1 are shown in FIG. 3.
[0062] The result shows that, in this example, the no load voltage
Uo can be determined after drawing approximately 1 Ah. A no-load
voltage level of approximately 12.4 V is obtained. For this
specific battery, this results in a state of charge of
approximately 67% from the relationship between the no-load voltage
and the state of charge, which is a good match to the initial value
of approximately 70% minus the approximately 1.5 Ah drawn in the
meantime.
EXAMPLE 2
[0063] In operating phases where there is little dynamic variation
in current, states with a changing current intensity may be
provoked to make it possible to use the method according to the
invention. For example, as a changing load from a battery with a
rated capacity of, for example, 80 Ah, a current with an amplitude
of 20 A is switched on and off, for example, every 3 seconds for a
time period with a duration of, for example, 30 s and the voltage
and currents are recorded using a measurement clock cycle of, for
example, 0.5 s. After this period, a further current flow (for
example a constant current of, for example, 5 A resulting from
normal operation) can be drawn until the total amount of charge
drawn is approximately 0.25 Ah. The above changing load is then
repeated for a further 30 s.
[0064] After evaluation of the voltage/current pairs for each
changing load, a total of 6 matching parameters remain (the 5
parameters Uo, R, a, I,, C from equation (2) as well as q), which
must be stored in the long term. It is advantageous for this
procedure to be repeated more frequently.
[0065] From two such phases with a changing load, the first stage
is to deduce whether the measurement points were usable and, if
yes, then to use them to estimate the no-load voltage. If the
signals have higher-frequency superimposed elements, a measurement
clock cycle of 0.5 s is not sufficient. In this case, it is
advantageous to use a measurement clock cycle of 0.1 s, for
example, for recording and to average the results, for example,
every 1 s ("low-pass filter").
EXAMPLE 3
[0066] The method according to the invention is suitable in certain
operating conditions to deduce the present no-load voltage
Uo(t.sub.o) of the rechargeable battery at time to and, from this,
to deduce its state of charge SOC (t.sub.o) even when current is
flowing to or from the rechargeable battery. However, its use may
not be possible in other operating conditions since the
preconditions are not satisfied.
[0067] In order to make it possible to deduce the present state of
charge in these general cases at time t as well, it is within the
scope of the invention for a link to be made to other methods for
determining the state of charge. For example, in this case,
advantageous methods include methods for determining the change in
the state of charge .DELTA.SOC, for example, by integration of the
current I flowing in the time from t.sub.o to t.
[0068] In this case, by way of example:
SOC(t)=SOC(t.sub.o)+.DELTA.SOC (t.sub.o, t) where .DELTA.SOC
(t.sub.o, t)=1/Qo.intg.Idt.
EXAMPLE 4
[0069] The method according to the invention is suitable in certain
operating conditions to deduce the present no-load voltage
Uo(t.sub.o) of the rechargeable battery at the time to and, from
this, to deduce its state of charge SOC (t.sub.o) even when current
is flowing to or from the rechargeable battery. Furthermore, as in
Example 3, a link can be made to methods for determining the change
in the state of charge .DELTA.SOC. Both the determination of the
state of charge SOC(t.sub.o) and the determination of the change in
the state of charge .DELTA.SOC are, however, subject to a
measurement error, which is composed of the uncertainty in the
measurements of the voltage and time and any other error
sources.
[0070] If the present state of charge SOC (t.sub.i) is determined
repeatedly, for example n times, at different times t. (i=1, 2, . .
. , n) during continuous operation and the change in the state of
charge .DELTA.SOC (t.sub.o, t.sub.i+1) between these times is also
determined, then this results in an overdefined problem.
[0071] It is within the scope of the invention to use a
minimization method to calculate a state of charge and, thus, to
reduce the errors mentioned above. The precision of the method is
in consequence increased the greater the number of independent
determinations of the state of charge that are possible. It is
likewise within the scope of the invention for a link to be made to
other methods for determining the state of charge, to increase the
number of independent determinations of the state of charge.
EXAMPLE 5
[0072] At relatively low temperatures (<0.degree. C.), there is
a noticeable discrepancy between the calculated Uo and the no-load
voltage of the rechargeable battery which would be produced after a
long waiting time. However, Uo is a valuable parameter even in
these cases. It has been found that Uo can be used as an early
warning for a battery voltage which will soon collapse with a
constant medium load.
[0073] FIG. 4 shows a representative example, in which the voltage
response U of a battery is plotted against the applied current I.
This profile contains slow current changes as well as current
changes which correspond approximately to a frequency of 1 to 0.3
Hz. One example of this is denoted I_. The relatively rapid current
changes are used for evaluation. In FIG. 4, the Uo values
determined in accordance with the method according to the invention
are shown as large circles. If, for example, Uo falls below the
value Uo-Uo min=11.5V/6 cells, the voltage will collapse very soon.
It has been found that, in general, approximately 10 to 20% of the
battery capacity is then still available.
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