Method and apparatus for charging batteries

A method and apparatus for efficiently charging lead-acid batteries applies small voltage steps to probe the charging efficiency of a battery being charged. The application of a voltage step causes the current to change from a base current to a surge current immediately after the voltage step, and to decay asymptotically to a plateau current after the surge current. A current ratio, defined as the difference between the plateau current and the base current divided by the difference between the surge current and the base current, is used as an indicator of the charging efficiency. The output voltage of the power supply charging the battery is then adjusted according to the measured current ratio. A current-voltage slope, defined as the difference between the plateau current and the base current divided by the magnitude of the voltage step, may also be used as an indicator of the charging efficiency for controlling the charging process. Alternatively, in a current-controlled charging process, small current steps are used to probe the charging efficiency. For a current step, the induced voltage changes are measured, and a transient-plateau voltage ratio is calculated. The charging current is then adjusted according to the calculated voltage ratio.

FIELD OF THE INVENTION 
This invention relates generally to battery chargers and more particularly 
to a method and apparatus for charging batteries that dynamically controls 
the charging voltage or current to achieve efficient charging. 
BACKGROUND OF THE INVENTION 
Batteries such as lead-acid batteries have been used for many diverse 
applications. For example, lead-acid batteries have been used as a 
starting, lighting and ignition power source for vehicles (SLI), as a 
power source for starting, lighting and other auxiliary power requirements 
in marine applications, and as a motive power source for use in golf carts 
and other electric vehicles. In addition, lead-acid batteries have been 
employed in a variety of stand-by power applications to provide a power 
source when the main power source becomes inoperable, as by, for example, 
interruption of electricity. Other representative applications for 
lead-acid batteries include uniform power distribution and power damping 
applications. 
While the extent of discharge and the particular cycling requirements of a 
lead-acid battery for a specific application vary widely, one criterion 
remains constant. Specifically, it is important to ensure that proper 
charging of such batteries is carried out. Undercharging lead-acid 
batteries can result in less than optimum output and service life. For 
example, undercharging can result in perhaps permanent sulfation of part 
of the active materials, as well as stratification of the electrolyte and 
uneven use of the active materials. 
On the other hand, undue overcharging of lead-acid batteries likewise can 
result in permanent damage to the batteries and can present potential 
safety hazards caused by, for example, dissociating the water in the 
electrolyte of the battery to gas. Further, overcharging lead-acid 
batteries can accelerate positive grid corrosion and even lead to bulging 
and/or buckling of the battery plates. Among other undesirable aspects of 
undue overcharging are an increase in the specific gravity of the 
electrolyte, possible oxidation of the separators and the undue heat 
generated that can accelerate various problems. 
The time and manner in which lead-acid batteries are charged is also 
important. For example, many applications require charging within a 
relatively short period of time. In such circumstance, it is important to 
optimize the current or voltage used while, at the same time, avoiding the 
use of currents higher than the battery can accept for charging 
conversion. 
U.S. Pat. No. 5,583,416 and U.S. Pat. No. 5,656,920, which are assigned to 
the same assignee as the present application and hereby incorporated by 
reference in their entirety, each disclose inventive methods and apparatus 
for charging batteries which avoid undercharging, overcharging and their 
associated adverse effects. For example, U.S. Pat. No. 5,583,416 discloses 
a method and apparatus for charging batteries which periodically applies 
voltage steps to the battery being charged to monitor the charging 
acceptance of the battery. At the beginning of the charging process, an 
initial target voltage is applied to the battery. The monitoring process 
includes increasing the applied voltage in two predetermined steps. The 
corresponding charging currents are measured at the initial applied 
voltage and at the two voltage steps. Based on these measurements, the 
current differentials (i.e., the current change for each voltage step 
range) are determined. The current differentials are compared to determine 
whether the increased voltage or the decreased voltage results in a more 
optimal charge acceptance, as indicated by a lower current differential. 
The target charging voltage is then adjusted in the direction of the 
smaller current differential, which indicates a more optimal charge 
acceptance. This monitoring process is repeated throughout the charging 
process to continuously adjust the charging voltage to approach a more 
optimized charge acceptance level. Alternatively, the charging current is 
controlled and stepped and the corresponding voltages are measured to 
determine the voltage differentials. 
U.S. Pat. No. 5,656,920 discloses a charging method and apparatus which 
periodically applies voltage sweeps to the battery being charged to 
determine the optimal charging acceptance of that battery. Specifically, 
the charging voltage is "swept" across a range of values and the resulting 
current changes are measured. The range of the sweep is preferably from 
about the open-circuit voltage of the battery to just above the voltage 
region that provides the desired optimal charging performance. The 
current-voltage curve developed by this sweep is then analyzed to 
determine the charging voltage that corresponds to the optimal charging 
performance. The analysis of the current-voltage sweep curve is carried 
out, for example, by comparing the slope values at different points on the 
sweep curve to determine minimum or specific values. The voltage sweeps 
are performed periodically and the charging voltage is adjusted 
accordingly to provide optimized charging performance. 
The methods disclosed in these two related U.S. applications provide 
satisfactory charging performances. However, these methods have their own 
system requirements. The step-charging method, for instance, requires a 
charging system which is capable of relatively precise voltage control so 
that the current differentials can be accurately determined. The 
voltage-sweep method also requires precise voltage control and is best 
suited for applications wherein the electrical system powered by the 
battery is relatively insensitive to the relatively large voltage changes 
caused by the voltage sweeps. 
OBJECTS OF THE INVENTION 
It is, therefore, a primary object of the present invention to provide an 
improved method and apparatus for charging batteries. It is a more 
specific object to provide such a method and apparatus that dynamically 
adjusts the electrical charging output supplied to the battery to achieve 
efficient charging performance without unduly overcharging or 
undercharging the battery. It is a related object to provide a method and 
apparatus for charging batteries that is interactive with the battery 
being charged so that the charging process will inherently take into 
account the specific factors affecting the charging characteristics of the 
specific battery being charged so as to optimize the charging profile of 
that specific battery. It is another related object to provide a simple 
interactive method and apparatus for charging batteries that regularly 
probes the charging efficiency during the charging process and adjusts the 
charging output to achieve substantially optimal charging performance. It 
is still another related object to provide such an interactive method and 
apparatus that can be used in a relatively noisy electrical environment 
and that does not need precise voltage control in the probing process. 
It is yet another object of the invention to provide an interactive method 
and apparatus for charging a battery that minimizes interference with the 
operation of other electrical systems connected to the battery being 
charged. 
It is still another object of the invention to provide an interactive 
charging method and apparatus which is capable of effectively controlling 
the level of charge below full charge in a periodic charging system such 
as a hybrid electric vehicle or the like. 
SUMMARY OF THE INVENTION 
The present invention accomplishes these objectives, and overcomes the 
drawbacks of the prior art by providing a method and apparatus for 
charging batteries which periodically applies small voltage or current 
steps to the battery to probe the charging efficiency of the battery. The 
current changes induced by a voltage step or voltage changes induced by a 
current step are used to derive a ratio which is used as a control 
parameter. The ratio is compared to a reference level, which may be fixed 
or dynamically adjusted during the charging process according to the 
calculated ratios. The charging voltage or current is then varied 
according to the result of the comparison. 
In accordance with a feature of one embodiment which applies voltage steps 
to probe the battery charging efficiency, a voltage detector detects the 
base current immediately before a voltage step is applied, a surge current 
after the voltage step is applied, and a plateau current after the surge 
current. The ratio is calculated as the difference between the plateau 
current and the base current divided by the difference between the surge 
current and the base current. Alternatively, the ratio may be a 
current-voltage slope, defined as the difference between the plateau 
current and the base current divided by the magnitude of the voltage step. 
In another embodiment which controls the charging current, current steps 
are applied to the battery to probe the charging efficiency. For each 
current step, a base voltage, a transient voltage, and a plateau voltage 
are measured for deriving a transient-plateau voltage ratio. The charging 
current is varied according to the transient-plateau voltage ratio to 
achieve efficient charging of the battery. 
These and other objects and advantages of the invention will be more 
readily apparent upon reading the following description of the preferred 
embodiment and upon reference to the accompanying drawings wherein:

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
In accordance with the present invention, small voltage or current steps in 
either the positive or negative direction are periodically applied to a 
battery being charged to probe the charging efficiency of the battery. The 
current changes induced by a voltage step or the voltage changes induced 
by a current step are then used to derive a quantitative indicator (or 
control parameter) for controlling the charging process. 
FIG. 1 shows a charging system 10 for a voltage-controlled charging process 
in which voltage steps are applied as probes to a battery 30 being 
charged, and the charging voltage is dynamically varied according to the 
results of the probing. The charging system 10 has a DC power supply 32 
which is connected to the battery 30 to a provide a charging voltage and 
charging current. A voltage controller 34 controls the voltage output of 
the DC power supply 32. The voltage controller 34 includes a voltage step 
generator 36 which is capable of causing the output voltage of the DC 
power supply to selectively change by a small voltage step. Preferably, 
the small voltage step falls in the range of 0.01 to 0.3 volt inclusive 
for a 12-volt battery, although larger or smaller voltage steps can 
likewise be employed without departing from the invention. 
As will be discussed in greater detail below, application of a small 
voltage step to the battery 30 induces transient changes in the charging 
current which can be analyzed to provide information about the charging 
efficiency of the battery 30. These transient current changes are detected 
by a current detector 38, and, once detected, analyzed by an analyzer 40. 
The analyzed result is then sent to the voltage controller 34, which uses 
the analyzed result to adjust the charging voltage so that the charging 
voltage is substantially optimized to efficiently charge the battery and 
to avoid both undue undercharging and overcharging. 
As mentioned above, the transient changes in the charging current induced 
by the voltage step provide information regarding the battery charging 
efficiency. By way of explanation, the effect of applying an exemplary 
voltage step 41 to a nearly fully charged, representative battery is 
illustrated in FIG. 2A. The charging voltage as a function of time is 
indicated by the voltage curve 42, and the charging current as a function 
of time is indicated by the current curve 44. Immediately before the 
voltage step 41 is applied, the charging current is in a substantially 
steady state condition defined as a base current 45. When the charging 
voltage is incremented by the voltage step 41, the current first surges 
for a fraction of a second (e.g., about 0.1 second) to a peak, and then 
asymptotically decays to a steady state condition represented by plateau 
50. This decay typically occurs within several tenths of a second. The 
peak current experienced during the surge is defined as the surge current 
48. The current represented by the plateau 50 is defined as the plateau 
current 50. 
The transient current changes induced by applying the voltage step depend 
on the charging status of the battery. When a step 41 is applied to a 
battery which is charged to a different level than the exemplary battery 
30 depicted in FIG. 2A, the transients induced in the charging current 
will have a different profile, e.g., it might have a higher or lower surge 
current or a higher or lower plateau current. By way of another example, 
the effect of applying a voltage step to a substantially discharged 
battery is shown in FIG. 2B. When a voltage step 54 is applied to the 
substantially discharged battery, substantially no surge current can be 
identified and the charging current increases to the plateau current 56 
without experiencing a peak. Another way to look at this curve is that a 
surge current 58 is present, but it is substantially masked by the plateau 
current 56. 
In accordance with a feature of an embodiment of the invention, the base 
current 45, the surge current 48, and the plateau current 50 are measured 
and analyzed to provide information for controlling the charging process. 
Pursuant to this aspect of the invention, a ratio is derived from the 
measured currents and used as a control parameter for the charging process 
to control the charging voltage applied to the battery. 
In a preferred embodiment, the control parameter is a surge-plateau current 
ratio defined as the difference between the plateau current 50 and the 
base current 45 (i.e., the plateau current increase 52) divided by the 
difference between the surge current 48 and the base current (i.e., the 
surge current increase 49). The surge-plateau current ratio provides an 
effective indicator of the charging efficiency of the battery 30. By 
repeatedly applying voltage steps to the battery being charged and 
calculating a current ratio for each voltage step, the charging process 
can be controlled to ensure that the battery is being charged at an 
efficient rate for an appropriate length of time. By interactively 
adjusting the charging voltage applied to the battery 30, a substantially 
optimized charging performance, (e.g., high charging efficiency without 
undue overcharging or gassing), is achieved. 
In an alternative embodiment, the control parameter is a "current-voltage 
slope" defined as the difference between the plateau current 50 and the 
base current 45 divided by the magnitude of the voltage step (i.e., the 
difference between the plateau voltage and the base voltage). 
It will be appreciated that the surge-plateau current ratio and the 
current-voltage slope as defined above are both related to the 
current-voltage sweep curves developed by the method and apparatus 
disclosed in U.S. Pat. No. 5,656,920. More specifically, as discussed in 
detail in U.S. Pat. No. 5,656,920, for a battery at a given temperature, 
sweeping the charging voltage produces a current-voltage curve that is 
characteristic of the state-of-charge of the battery. In other words, at a 
given temperature, a battery being charged will exhibit a family of 
voltage sweep curves corresponding to different states-of-charge as the 
charging continues. FIG. 3 shows, as an example, voltage sweep curves for 
a commercially available Group 65 lead-acid battery which was fully 
charged and then discharged to various states at a rate of 4 Amperes. The 
five curves A-E correspond to the states-of-charge of 95%, 25%, 85%, 90%, 
and 100%, respectively. These sweep curves are generated using a voltage 
sweep from 12.5 volts to 16.5 volts at a sweep rate of 0.5 Volt/second. 
The temperature of the battery is about 73.5 F. 
As shown in FIG. 3, when the battery is not substantially charged, the 
current rises sharply with the charging voltage and often reaches the 
current limit of the power supply, as exemplified by curves B and C, which 
correspond to the states-of-charge of 25% and 85%, respectively. Thus, the 
voltage-current sweep curve of the battery in a relatively low 
state-of-charge tends to have fairly high slopes. For relatively high 
states-of-charge, however, the sweep curves have a common general shape 
which includes two relatively high-slope sections on the two sides of a 
relatively flat portion. For example, curve A, which corresponds to a 
state-of-charge of 95%, has a first upward portion A2, a relatively flat 
portion A1, and a second upward portion A3. The relatively flat portion A1 
has an inflection point IP where the sweep curve A has a minimum slope. 
The sweep curves provide useful information for determining an optimal 
range of the charging voltage which varies as the battery is being 
recharged. Turning again to curve A, to achieve optimal charging 
performance at this state-of-charge, the charging voltage should be in the 
relatively flat portion A1 of curve A. Setting the voltage in the portion 
A2 would involve utilizing less than optimal charging current. On the 
other hand, setting the charging voltage in the portion A3 well above the 
portion A1 could result in excessive gassing and, accordingly, less than 
optimal charging performance. Since the portion A1 which provides optimal 
charging performance also corresponds to the portion of the sweep curve 
with the lowest slopes, the slope of the curve at a given charging voltage 
can be used as an indicator as to whether the charging voltage is 
optimally set. 
It will be appreciated that the sweep curves of a given battery vary 
depending on many factors such as the temperature, the history of use of 
the battery, and the discharge rate prior to recharging, etc. 
Nevertheless, the sweep curves retain the general characteristics 
described above in conjunction with FIG. 3. Thus, the slope, i.e., the 
variation of the current as a function of the voltage, provides a good 
indicator for use in adjusting the charging voltage for optimizing 
charging performance. 
The plateau-surge current ratio is also a good indicator of the charge 
acceptance that can be effectively used in controlling the charging 
process. The relationship between the plateau-surge current ratio 
developed by applying a small voltage step to the battery as described 
above and the sweep curves can best be seen by referring to FIG. 4. FIG. 4 
shows the changes in battery current as a function of time as consecutive 
voltage steps separated by a fixed time interval are applied to a 
partially discharged battery. As discussed above, for each voltage step 60 
in the voltage curve 62 there is a surge current peak 64 in the current 
curve 66 which decays asymptotically to a plateau current 68. As can be 
seen in FIG. 4, when viewed together, the plateau currents 68 trace a 
curve which resembles the voltage-current sweep curve A of FIG. 3. 
The surge current 48 can generally be considered the result of the 
capacitance of the battery 30 being charged. A small change in voltage 
will require a current surge to charge or discharge the electrolyte double 
layers of the electrodes. When the battery 30 is substantially discharged 
or if the charging voltage is well below the optimal charging level, this 
capacitance effect is essentially masked by the large charge acceptance of 
the battery. In such a case, the current ratio will be high, (e.g., close 
to one), which is the case shown in FIG. 2B. 
When the battery is partially discharged, a point which corresponds to the 
minimum current ratio occurs at or near the inflection point on the sweep 
curve A in FIG. 3 where the slope has a minimum value. This minimum ratio 
is different for different types of batteries, depending on factors such 
as the construction and materials of the specific battery. For flooded, 
maintenance-free automobile batteries with thin electrodes, the ratio may 
be close to zero. Other battery types, especially those with thicker 
plates and higher-gassing antimonial alloys, generally have a higher 
minimum ratio which typically is still a low fraction (e.g., less than 
0.5). 
It will be appreciated that a single surge-plateau current ratio or a 
current-voltage slope measured at a given charging voltage does not by 
itself indicate whether the charging voltage is in the optimal range such 
as the portion A1 of curve A in FIG. 3 or in ranges A2 or A3 of that 
curve. Nevertheless, a variety of techniques of this invention may be used 
to interactively adjust the charging voltage according to the measured 
surge-plateau current ratio or the current-voltage slope to achieve 
substantially optimal charging performance. 
Two different exemplary interactive voltage adjustment techniques employing 
voltage steps to probe the charging state of the battery are described 
below. It will be appreciated, however, that these two techniques are 
described here only as examples, and other charging techniques which 
adjust the charging voltage according to the measured plateau-surge 
current ratio or current-voltage slope may be used without deviating from 
the scope or spirit of the present invention. 
TECHNIQUE ONE 
In this technique, which is particularly useful for automotive 
applications, a voltage step such as that shown in FIG. 2A is periodically 
applied to the battery being charged. The measured ratio induced by each 
voltage step is compared to a predetermined fixed reference level. The 
charging voltage is then adjusted according to the result of the 
comparison. The term "ratio" as used herein in the context of applying 
small voltage steps to probe the battery charge conditions, unless 
otherwise specified, is intended to cover both the surge-plateau current 
ratio and the current-voltage slope as defined above. 
As illustrated in FIG. 5, at the beginning of the charging process, the 
initial parameters, including the initial charging voltage and the fixed 
reference level, are set (step 70). The initial charging voltage is set by 
the voltage controller 34 at a relatively low initial value. As 
illustrated in FIG. 3, for a substantially discharged battery, the 
charging current increases rapidly with the charging voltage and often 
reaches the current limit of the power supply 32. 
As the charging continues, the charging voltage and current as well the 
charging time are detected and may optionally be displayed on a monitoring 
device (step 71). It is then determined whether the charging voltage 
exceeds a preset upper voltage limit (MAX V) (step 72). If so, the voltage 
is decreased (step 81). If not, the current is also checked to see whether 
it exceeds a preset upper current limit (MAX I) (step 73). If so, the 
voltage is decreased (step 81). If it is determined that the current is 
negative (step 74), then the voltage is increased to provide positive 
current to the battery. If the voltage and current do not exceed the 
preset limits, and the charging current is not negative, it is then 
determined whether the battery has been fully charged (step 75). If so, 
the charging is either stopped or switched into a conditioning mode (step 
83). 
When it is determined that the time to measure the ratio has arrived (step 
76), the voltage controller 34 causes the power supply 32 to change the 
charging voltage by a small step of a predetermined magnitude (step 77), 
which can be either positive or negative. The current detector 38 senses 
the current changes caused by this voltage step (step 78). The measured 
current values are then used by the analyzer 40 to calculate a ratio (step 
79). The voltage controller 24 then compares the measured ratio to the 
fixed reference level (step 80). 
In the preferred embodiment, if the ratio is higher than the reference 
value, the charging voltage is increased (step 81). As illustrated in FIG. 
3, the slope of the sweep curve A in the portion A2 decreases as the 
voltage moves up. Thus, if the voltage is in the portion A2, increasing 
the charging voltage tends to reduce the ratio, thereby bringing the ratio 
closer to the reference level. On the other hand, if the measured ratio is 
below the reference level, then the charging voltage is decreased (step 
82). The above described process from applying a voltage step through 
resetting the charging voltage is then periodically repeated as the 
charging continues. 
The fixed reference level is preferably of a low value (e.g., 0.1 to 0.3 
when the control parameter is the surge-plateau current ratio). As 
described above, the surge-plateau current ratio of a substantially 
discharged battery tends to be high (e.g., close to 1) at relatively low 
voltages at the beginning, but falls gradually as the state-of-charge and 
the charging voltage rise. Similarly, the current-voltage slope also tends 
to be higher at the beginning of the charging process and falls as the 
battery is charged. If the reference value is set too high, the ratio 
(which may be either the surge-plateau current ratio or the 
current-voltage slope) might drop below the reference value well before 
the battery becomes fully charged, and the charging voltage would 
accordingly be reduced to a level that is too low to fully charge the 
battery in a reasonable period of time. 
On the other hand, setting the reference level too low may in certain cases 
lead to overcharging of the battery. Depending on the construction and 
material of the battery, the minimum ratio of a battery being charged may 
remain higher than the fixed reference level even when the battery is 
substantially fully charged. In such a case, the interactive adjustment 
process described above would continue to increase the charging voltage to 
the upper voltage limit of the power supply and keep it there, which could 
cause undue overcharging and gassing of the battery. 
In order to avoid such overcharging, it is preferred to set an upper limit 
of the charging voltage that is sufficiently low to ensure that the 
battery will not enter the very high gassing region of the sweep curve 
(e.g., portion A3 of curve A). This is necessary because it is not 
possible to determine from a single probe whether the battery has entered 
the undesirable gassing region (A3 in Curve A of FIG. 3) or is still in 
the lower region A2 in FIG. 3. For automobile batteries the upper charging 
voltage may be set at 15-15.5 volts. This works well with an automotive 
electrical system because the system voltage is already limited to about 
15 volts to protect other system components. 
It should be noted that it is generally preferable to charge the battery at 
the lowest voltage that will achieve a high charge. Such a voltage is 
generally at or below the above mentioned inflection point. 
A problem with a fixed reference value is that high currents demand high 
voltages to overcome battery polarization such as resistance. When the 
battery approaches full charge, the voltage must be reduced fairly quickly 
to avoid pushing the charge into the upper part of the charging curve. For 
a fixed reference value, this can be conveniently done by restricting the 
upper voltage and by making the reference value moderate when compared to 
the ideal value measured on a fully charged battery. 
TECHNIQUE TWO 
Instead of using a fixed reference level through out the charging process 
as in Technique One described above, it is also possible to use a 
reference level which is dynamically adjusted over the charging process to 
allow more optimal tuning of the charging voltage. 
For example, in the following technique, the reference level is set to a 
relatively high fixed value at the beginning of the charging process. A 
voltage step is periodically applied to the battery 30 being charged, a 
ratio (either the current ratio or the slope) is computed and compared to 
the reference level, and the charging voltage is adjusted accordingly. 
When the measured ratio falls below the initial reference level, a second 
reference level which is dynamically adjusted by weighted averaging is 
used in the subsequent charging process. 
In more detail, referring to FIGS. 6A and 6B, at the beginning of the 
charging process, initial charging parameters are set (step 84). This 
involves setting a first reference level that is fixed, and the initial 
value of a second reference level that can be varied later. The charging 
voltage is initially set at a relatively low voltage. The first reference 
level is set at a relatively high value (e.g., 0.5 to 0.9 when the 
surge-plateau ratio is used as the control parameter). 
During the charging process, the voltage and current are checked. If the 
voltage exceeds the upper voltage limit (MAX.sub.-- V) (step 86) or if the 
current exceeds the upper current limit (MAX.sub.-- I) (step 87), the 
charging voltage is reduced (step 97). Alternatively, if it is determined 
that the battery has been fully charged (step 88), the charging process is 
stopped or switched into a conditioning mode (step 98). 
When it is determined that the time to probe has arrived (step 89), the 
voltage controller applies a voltage step to the battery (step 90), and 
the resultant current changes are detected (step 91). A ratio (which may 
be either the surge-plateau current ratio or the current-voltage slope) is 
derived from the current changes (step 92). The ratio is then compared to 
the fixed first reference level (step 93). If the ratio is greater than 
the first reference level, then the ratio is saved in the variable 
R.sub.-- SAVE (step 100) and the voltage is increased (step 101). 
If, on the other hand, it is determined that the ratio has fallen below the 
first fixed reference level (step 93), then the second (adjustable) 
reference level is used in the subsequent control. Specifically, the 
calculated ratio is compared to the second reference level. If the ratio 
is smaller than the second reference level, the second reference is 
adjusted by weighted averaging as: 
EQU Ref.sub.-- Level2=(Ref.sub.-- Level2*z+ratio)/(z+1), 
where Ref.sub.-- Level2 is the value of the second reference level, and z 
is a weighting constant. The ratio is saved in a variable called R.sub.-- 
SAVE (step 96). The charging voltage is then decremented (step 97), 
preferably according to the difference between the ratio and the second 
reference level. 
If the measured ratio is greater than the reference level, then it is 
further determined whether the difference between the ratio and the second 
reference level exceeds a preset value x (step 99). If the difference is 
smaller than x, the ratio is saved in the variable R.sub.-- SAVE (step 
100), and the charging voltage is increased, preferably by an amount 
according to the difference between the ratio and the second reference 
level. 
If, however, the difference between the ratio and the second reference 
level exceeds x, then the charge acceptance of the battery has changed 
markedly, and the simple control scheme of increasing (or decreasing) the 
charging voltage when the ratio is greater (or smaller) than the presently 
used reference level can no longer be reliably used for controlling the 
charging process. 
In the preferred embodiment, the detection of a ratio-reference difference 
greater than x starts a sequence of dynamically switching the voltage 
adjustment direction to allow the measured ratio to move toward a more 
stable lower value. This sequence is generally illustrated in FIG. 6B. The 
second reference is first reset (step 102) by weighted averaging as: 
EQU Ref.sub.-- Level2=(Ref.sub.-- Level2*z+ratio)/(z+1). 
It is then determined whether the measured ratio is smaller than R.sub.-- 
SAVE (step 103). If the ratio is smaller than R.sub.-- SAVE, then the 
value of R.sub.-- SAVE is replaced by that of the ratio (step 104). 
Because the application of the last voltage change appears to have 
generated a lower ratio, which indicates a more optimal charging 
condition, the next voltage change is applied in the same voltage 
adjustment direction as that of the previous change so that the ratio may 
be further reduced. The direction (i.e., positive or negative) of the 
voltage adjustment will be maintained as long as each probe voltage step 
results in a further reduction of the ratio as compared to the previous 
ratio saved in R.sub.-- SAVE. 
If, however, it is determined that the probe voltage step results in a 
ratio that is greater than the previous ratio saved in R.sub.-- SAVE (step 
103), then the direction of the voltage adjustment is reversed (step 106). 
In other words, the next voltage adjustment will be applied in a direction 
opposite to that of the last one so that the voltage change is likely to 
result in a reduction of the ratio. R.sub.-- SAVE is then reset to contain 
the value of the ratio (step 104). 
In this way, the charging voltage is periodically adjusted, and the second 
reference level is dynamically reset by weighted averaging, to achieve 
optimal charging performance. The minimum stable ratio search technique 
illustrated in FIG. 6B provides a transition from high current at low 
states-of-charge to a balance point between high-efficiency low-rate 
charging (e.g., the portion A2 of curve A of FIG. 3) and undue gassing 
(e.g., portion A3 of curve A of FIG. 3). 
The two exemplary techniques described above illustrate that simple yet 
effective charging techniques can be developed based on the use of voltage 
steps to repeatedly probe the charging state of the battery 30 and to 
dynamically and interactively adjust the charging output of the DC power 
supply 32 to achieve substantially optimized charging performance. 
In a preferred embodiment, the surge-plateau current ratio is used as the 
control parameter for the charging process. Using the current ratio 
associated with the voltage steps as the control parameter of the charging 
process has many advantages. For example, because the plateau current 50 
resulting from the application of a voltage step is generally smaller than 
the surge current 48, the current ratio is generally within the range of 
zero to one. In other words, the current ratio is generally "normalized." 
Due to its generally finite range and predictable behavior, the current 
ratio can be handled easily by the voltage controller 34 in the 
interactive charging process. 
It is possible, however, for the current ratio to go outside the range of 0 
to 1. For instance, the ratio can be higher than one at the beginning of 
the charge process when the battery is highly discharged. In such a case, 
the surge current region does not rise fast enough to surpass the 
asymptotic current and the measured "surge current" would be somewhat 
dependent on timing. For convenience, any reading of the current ratio 
above 1 may be treated as 1 and any reading below 0 may be treated as 0. 
This will avoid wild or spurious readings and keep the control parameter 
for all batteries in a normalized range. Using the fixed range of 0 to 1 
allows batteries of similar construction but different capacities to be 
controlled easily using either Technique one or Technique two described 
above. 
Furthermore, because both the surge current 48 and the plateau current 50 
induced by the application of a voltage step vary substantially linearly 
with the magnitude of the voltage step, the current ratio is substantially 
independent of the magnitude of the voltage step as long as the voltage 
step is sufficiently small. Thus, it is not crucial to have precise 
control of the magnitude of the voltage steps. This is especially 
advantageous in commercial automotive charging systems where precise 
voltage control is difficult or expensive to achieve. 
Moreover, the time required for measuring a current ratio is relatively 
short, because the plateau current 50 is reached quickly after the 
application of a voltage step, typically within 0.3-1.0 second depending 
on the battery type. Such fast response time is important for avoiding 
disturbances to the measurement in an automotive electrical system having 
a variety of devices which are frequently turned on or off. 
An important advantage of using small voltage steps as probes is that each 
voltage step is significantly smaller than the nominal operation voltage 
of the battery 30 being charged. Thus, no high voltage pulses or current 
surges will be generated which could cause interference with other devices 
connected to the battery 30, such as changing the headlight intensity or 
affecting the alternator loading which could be noticeable and annoying to 
the vehicle operator. In addition, unlike some prior art charging systems, 
the inventive system will not generate large pulses that create 
electromagnetic fields, thereby avoiding interference and other adverse 
effects. 
The frequency at which the voltage steps should be applied to the battery 
to probe the charging status depends on many factors, such as the 
precision of voltage control desired, the tolerance of disturbances caused 
by applying the voltage steps, and the size of the voltage steps. 
Generally, if the magnitude of the voltage steps is relatively small 
(e.g., 0.01 volt to 0.02 volt), the voltage steps can be applied fairly 
often (e.g., 1 voltage step every second), and small charging voltage 
adjustments can be made accordingly. On the other hand, if the voltage 
step is relatively large (e.g., about 0.2 volt or higher), the voltage 
steps may be applied less frequently, such as once every 10 to 20 seconds, 
and correspondingly large voltage adjustments can be made. 
It should be noted that the voltage steps can be either positive or 
negative, i.e., a voltage step can be up or down from the base voltage 
level. The same relationship between the surge current 48 and the plateau 
current 50 exists for both step directions if the power supply 32 has a 
sufficiently fast response and is not near its current limit. Whether the 
positive or negative steps are preferred depends on the charging 
situations. With a downward voltage step, the surge current pulse 48 may 
be truncated if the base current 45 is close to zero. On the other hand, 
if the power supply is already operating near the upper current limit, 
which is frequently the case at the beginning of the charging process of a 
substantially discharged battery, applying a positive voltage step may not 
have a discernible effect on the charging current. In such a case, 
however, a negative step can be used for measuring the current ratio. 
Accordingly, downward voltage steps may be used at the upper current limit 
of the power supply, and upward steps can be made when the charging 
current is low. A transition from downward steps to upward steps could 
occur when the first instance of negative current is encountered. 
By virtue of the use of a ratio (either the surge-plateau current ratio or 
the current-voltage slope) associated with each voltage step as a 
meaningful indicator of the battery charging efficiency, and the 
interactive nature of the voltage adjustment, the method of the present 
invention automatically takes into account the charging characteristics of 
the battery 30 being charged. For instance, the method of the present 
invention automatically compensates for the internal resistance of the 
battery 30 being charged which varies with the size and construction 
components of the battery 30. As a result, at the same charging current 
limits, higher charging voltages are generally applied to small batteries 
to compensate for their higher internal resistance, and lower charging 
voltages are applied to larger batteries of the same general construction 
which have lower internal resistance. 
Another advantage of the invention is that the inventive method compensates 
for the temperature effects, including polarization effects, on the 
charging characteristics of the battery. Colder batteries generally 
receive a higher voltage even though their currents will generally be 
lower due the lower charge acceptance caused by the lower solubility of 
discharge products at lower temperatures. By virtue of its interactive 
nature, the inventive method is capable of compensating for the 
temperature effects to efficiently charge the batteries. 
The method also adjusts the charging voltage in response to the charge 
acceptance of the battery 30 at different charging stages; a factor which 
is affected by the history of use of the battery. For example, the rate at 
which the battery 30 was previously discharged affects the current 
acceptance of the battery. Thus, batteries that have been rapidly 
discharged generally recharge more swiftly by charging at a high rate 
until the battery is nearly fully charged. The charging voltage then 
begins to drop rapidly, resulting in a low end current. In contrast, in 
batteries that have been slowly discharged, especially those that have 
discharged during extended shelf storage, the charging voltage and current 
begin to taper off well before the full charge point. As another example, 
a battery that was 100% discharged and then 90% recharged will charge 
quite differently from a battery that was 10% discharged at the same rate. 
The following Examples are provided to illustrate the general operational 
principles and the effectiveness of the present method for charging 
lead-acid batteries. The plateau-surge current ratio is used in these 
examples as the control parameter. 
EXAMPLE 1 
FIGS. 7A and 7B illustrate the charging process of a commercially available 
Group 65 automotive battery 30 using Technique One described above. The 
reference level for the current ratio is fixed at 0.2, and the upper limit 
for the charging voltage is set at 15.5 volts. The voltage steps applied 
to the battery 30 are negative steps with a 0.1 volt magnitude. FIG. 7A 
shows the output voltage curve 140 and current curve 142 of the DC power 
supply 32, and the cumulated charging capacity curve 144 in Ampere-hour 
(AH). FIG. 7B shows the state-of-charge curve 146 of the battery as a 
function of time. 
As can be seen in FIG. 7A, the charging voltage starts at a relatively low 
value (curve 140), while the current (curve 142) at the beginning of the 
charging process is substantially limited by the power-corrected current 
output capability of the power supply 32. The high current in the initial 
charging stage efficiently charges the battery 30 when the charge 
acceptance is high. As the charging progresses, the charging voltage is 
gradually increased until it reaches a plateau 148 corresponding to the 
preset voltage limit. After the measured current ratio becomes smaller 
than the reference level at point 150, the charging voltage is gradually 
reduced as the state-of-charge of the battery approaches 100%, and the 
current falls nearly to zero. 
The existence of a plateau portion 148 in the voltage curve 140 indicates 
that imposing an upper limit on the charging voltage (in this case at 15.5 
volts) may reduce the maximum current output and therefore compromise the 
charging efficiency when the upper voltage limit is reached. Such an upper 
voltage limit is, however, necessary in certain cases to avoid undue 
overcharging and possible damage to other components attached to the 
battery system, such as light bulbs. 
EXAMPLE 2 
FIGS. 8A and 8B illustrate the charging process of a battery mounted in a 
commercially available vehicle with an internal combustion engine. The 
vehicle has an alternator coupled to the engine for generating electrical 
energy when the engine is operating. The battery is charged by the 
electrical energy generated by the alternator, and the charging process is 
controlled according to Technique One described above. 
The battery is first discharged by turning on the high-beam headlights of 
the vehicle with the engine off. This is indicated in the current curve 
150 as a -20 Ampere current drain. After the battery has been discharged 
about 20 Ah, the engine is turned on at idle speed, and the alternator 
starts to charge the battery. As shown in the state-of-charge curve 156 in 
FIG. 8B, the battery is rapidly recharged to a fully charged state. As can 
be seen in the voltage curve 152 in FIG. 8A, the charging voltage rises at 
the beginning to the set limit and then smoothly drops to a relatively low 
voltage at the end. The upper limit of the charging voltage in this 
example is set at 15 volt. As previously noted, it is generally desired by 
automobile manufacturers to keep the charging voltages as low as possible 
to extend the life of other electrical components, such as light bulbs, of 
the automobile. 
EXAMPLE 3 
FIGS. 9A and 9B illustrate an exemplary charging process for a typical 
Commercially available Group 65 battery using Technique Two described 
above. In this example, the initial reference level is set at 0.9. FIG. 9A 
shows the voltage curve 160, the current curve 162, and the cumulative 
capacity curve 164. FIG. 9B shows the state-of-charge curve 166. 
At the beginning of the charging process, the current (curve 162) stays at 
the preset upper current limit (80 Amp) of the power supply 32, while the 
charging voltage (curve 160) is gradually increased. At point 168, the 
measured current ratio falls below the initial reference level. The "lower 
ratio" search sequence as described in conjunction with FIG. 6B is then 
performed in which the periodic voltage steps scan the charging voltage up 
or down. The reference level is also adjusted in this sequence according 
to the measured current ratio. Thus, voltage steps are periodically 
applied to the battery 30, and the charging voltage (curve 160) is 
periodically adjusted according to the measured current ratios in 
comparison with the new reference level. As shown in FIG. 9A, the charging 
voltage (curve 160) and current (curve 162) fall gradually as the battery 
30 approaches its fully charged state. 
EXAMPLE 4 
FIG. 10 shows another exemplary charging process which uses Technique Two 
described above to charge a battery to a substantially full level and then 
switches to a conditioning mode. Instead of letting the current drop to 
zero and the voltage drop to a relatively low value near the end of the 
charging process, this process maintains a small but steady charge current 
as shown by the current curve 170, and the voltage (voltage curve 172) is 
allowed to vary. This has the effect of equalizing the cells and 
destratifying the electrolyte of the battery. 
It should be noted that the measurement of the plateau current should be 
taken after the it has sufficiently stabilized to ensure an accurate 
determination of the ratio. The time between measuring the surge current 
and measuring the plateau current should be sufficiently large such that 
further increase of time yields only a sufficiently small variation of the 
ratio (e.g., by less than 0.005). 
TECHNIQUE THREE 
The two techniques and four examples described above apply voltage steps to 
the battery being charged to probe the charging efficiency, and the 
charging voltage is adjusted to optimize the charging performance. It will 
be appreciated, however, that in accordance with the invention a 
controlled charging process can also be implemented by controlling the 
charging current and applying small current steps to probe the battery 
being charged. 
FIG. 11 shows a charging system 200 constructed according to the invention 
for current-controlled charging. The system 200 includes a controller 202 
which controls the current output of a DC power supply 204 for charging 
the battery 206. The controller 202 has a step generator 208 for 
controlling the DC power supply 204 to generate current steps in the 
charging current. The voltage changes in response to the current step are 
detected by a voltage detector 210. An analyzer 212 determines a control 
parameter from the detected voltage changes in response to the current 
step. The charging current is then varied by the current controller 202 
according to the control parameter. 
FIG. 12 shows a general example of how the charging voltage changes in 
response to a current step. The charging current as a function of time is 
indicated by the current curve 216, and the charging voltage as a function 
of time is indicated by the voltage curve 218. Immediately before the 
current step 220 is applied, the charging voltage is in a substantially 
steady state condition defined as a base voltage 222. When the charging 
current is increased by the current step 220, the charging voltage 
initially rises rapidly and then levels off to a new steady state 
condition represented by the plateau voltage 224. The plateau voltage is 
typically reached within several tenths of a second after the current 
step, depending on the specific type and construction of the battery being 
charged. 
In contrast to the response of the charging current to a voltage step as 
illustrated in FIG. 2A, the application of a current step typically does 
not generate a surge peak in the charging voltage. Rather, the charging 
voltage continuously rises from the base voltage 222 to the plateau 
voltage 224. For illustration purposes, the current step 220 in FIG. 12 is 
in the positive direction. It will be appreciated, however, that negative 
current steps may be applied for probing the battery, and the voltage 
response to a negative current step is generally the mirror image of the 
voltage response to a positive step as shown in FIG. 12. 
The transient voltage changes induced by a current step depend on the 
charging status of the battery. More particularly, the charging status of 
the battery determines how fast the charging voltage rises (or falls) in 
response to a positive (or negative) current step. For a substantially 
discharged battery, the voltage may rise rapidly to the plateau voltage, 
while for a battery that is nearly fully charged the voltage may rise at a 
slower rate. 
Analogous to the techniques using voltage steps as probes, a ratio may be 
derived from the voltage changes in response to a current step and used as 
an indicator of the charge efficiency. In a preferred embodiment, the base 
voltage 222, the plateau voltage 224, and a transient voltage 226 are 
measured. The transient voltage 226 is measured at a short period of time, 
such as 0.1 second, after the current step is applied to the battery. A 
transient-plateau voltage ratio, defined as the difference between the 
transient voltage and the base voltage divided by the difference between 
the plateau voltage and the base voltage, is then calculated. Analogous to 
the plateau-surge current ratio for a voltage step, this transient-plateau 
voltage ratio may be used in controlling the charging process. 
FIG. 13 shows a simple current-controlled charging technique using current 
steps as probes. This technique is analogous to Technique One described 
above. As illustrated in FIG. 13, at the beginning of the charging 
process, the initial parameters, including the initial charging current 
and a fixed reference level, are set (step 228). The initial charging 
current set by the current controller may be at a relatively high level, 
which may be the current limit of the charger. 
As the charging continues, the charging voltage and current as well the 
charging time are detected and may optionally be displayed on a monitoring 
device (step 230). The charging voltage is checked to see whether it 
exceeds a preset upper voltage limit (MAX.sub.-- V) (step 232). If so, the 
charging current is decreased (step 234). If not, the current is checked 
to see whether it exceeds a preset upper current limit (MAX.sub.-- I) 
(step 236). If so, the current is decreased (step 234). If it is 
determined that the charging current is negative (step 238), then the 
charging current is increased to provide a positive current to the battery 
(step 240). 
If the charging voltage and current do not exceed the preset limits and the 
charging current is not negative, it is then determined whether the 
battery has been fully charged (step 242). This determination may be made, 
for instance, by checking the magnitude of the charging current. If the 
charging current has dropped below a small fraction (such as 10%) of the 
input capacity of the battery or a small value (such as 2 Amperes), the 
battery may be deemed fully charged. If the battery is found to be fully 
charged, the charging is either stopped or switched into a conditioning 
mode (step 244). In the conditioning mode, the current is kept at a small 
constant value and the charging voltage is monitored to equalize the cells 
and destratify the electrolyte of the battery. 
When it is determined that the time to measure the transient-plateau 
voltage ratio has arrived (step 246), the current controller causes the 
power supply to change the charging current by a small step (step 248), 
which can be either positive or negative. Negative current steps may be 
used until a negative charging current is reached. 
Because the charging current may vary significantly over the charging 
process, it is preferred to dynamically adjust the magnitude of the 
current step to more effectively probe the charging state. In the 
preferred embodiment, the current step magnitude 250 (FIG. 12) is set to 
be a small fraction (such as 10%) of the charging current plus a constant 
small addition (such as 0.5 Amp). The small constant addition is added to 
ensure that the current step magnitude is sufficient to allow accurate 
measurements even when the charging current is low. 
The voltage detector senses the voltage changes caused by the current step 
(step 252). The measured voltage values are then used by the analyzer to 
calculate a transient-plateau voltage ratio (step 254). The calculated 
ratio is then compared to the fixed reference level (step 256). If the 
ratio is higher than the reference value, the charging current is 
increased (step 240). On the other hand, if the measured ratio is below 
the reference level, then the charging current is decreased (step 234). 
Because the magnitude of the charging current may vary significantly, 
preferably the amount of current increase or decrease is adjusted 
according to the magnitude of the charging current. The above described 
steps are then periodically repeated as the charging continues. 
This charging technique with a single fixed reference level is relatively 
simple to implement. It will be appreciated by those skilled in the art 
that more complex techniques, such as one analogous to Technique Two 
described above which uses a dynamically adjusted reference level, may be 
implemented according to the teaching of the invention. 
EXAMPLE 5 
Again by way of example, FIGS. 14 and 15 show data of a charging process in 
which a Group 24 automotive battery is charged with Technique Three 
described above. The fixed reference level for this charging process is 
set at 0.4. The charging current is limited to 75 Amperes, and the 
charging voltage is limited to 16 volts. 
During the charging process, a probe current step is applied every 10 
seconds. The magnitude of the probe current step is set to be 10% of the 
charging current plus 0.5 Amp. For each probe current step, a transient 
voltage is measured at 0.1 second after the current step, and a plateau 
current is measured at 0.25 second after the current step. 
When the transient-plateau current ratio falls below the fixed reference 
level, the charging current is reduced by 0.5 times the magnitude of the 
probe current step. When the transient-plateau current ratio is above the 
reference level, the charging current is increased by an amount equal to 
the difference between the ratio and the reference level times the 
magnitude of the probe current step. 
FIG. 14 shows the charging current curve 260, charging voltage curve 262, 
and the cumulative charging capacity curve 264 in ampere-hour (Ah). The 
charging current stays high at the beginning of the charging process then 
drops continuously as the charging continues. After the current falls to 2 
amperes, it is kept at that level to condition the battery. FIG. 15 shows 
the variations of the measured transient-plateau voltage ratio over the 
charging process. 
In view of the foregoing detailed description, those skilled in the art 
will appreciate that the disclosed invention may be used to charge many 
different types of batteries, including, but not limited to, sealed and 
recombinant lead acid batteries, without departing from the scope of the 
invention. Although the invention is not limited to use with a particular 
battery type, those skilled in the art will appreciate that the invention 
is particularly useful for charging recombinant batteries since when so 
charged, those batteries will not experience thermal run-away due to high 
charging voltages or currents. 
Moreover, those skilled in the art will appreciate that, although certain 
values for voltages and currents have been disclosed herein, all of those 
values were presented in the context of charging a 12-volt lead-acid 
battery. The voltage and current values will of necessity differ in 
proportion to the capacity of the battery being charged. Thus, it will be 
appreciated that the values of current and voltage given herein are by way 
of illustration, not limitation.