A Study of Lead-Acid Battery Efficiency Near
Top-of-Charge ( Impact on PV System
Design )
ABSTRACT
Knowledge of the charge efficiency of lead-acid
batteries near top-of-charge is
important to the design of small photovoltaic
systems. In order to know how much energy is
required from the photovoltaic array in order to accomplish
the task of meeting load, including periodic full
battery charge, a detailed knowledge of the battery charging
efficiency as a function of state of charge is required,
particularly in the high state-of-charge regime, as
photovoltaic systems are typically designed to operate in
the upper 20 to 30% of battery state-of-charge. This paper
presents the results of a process for determining battery
charging efficiency near top-of-charge and discusses
the impact of these findings on the design of small
PV systems.
BACKGROUND
Batteries are often necessary in photovoltaic (PV) systems to store energy generated while the
sun is shining. Therefore, it is
important to understand the specific
requirements of batteries when designing a PV system.
This includes an understanding of the amount of energy
that will be lost in battery charging. Overestimating
these battery charging losses results in a larger
PV array than required, whereas underestimating them
results in unanticipated loss of load as well as the possibility
of damaging batteries because of lack of providing
a periodic high state-of-charge. It
is generally understood that battery charge efficiency
is high (above 95%) at low states of charge and that
this efficiency drops off near full charge. However, actual
battery charge efficiencies are often stated as though
efficiency is linear across all states of charge, with general
guidance that it drops off at higher states of charge.
Details concerning actual charge efficiency as a function
of state-of-charge (SOC) would be very useful to PV
system designers to allow informed trade-off decisions
involving battery size, battery daily depth of discharge
and PV array size. Hence, a procedure has been
developed, and is described herein, to acquire these efficiency
versus SOC measurements. Preliminary results
agree with existing general knowledge, and provide
the details of charge efficiency versus state of charge
for the specific battery under test. Specific
charge versus state of charge information is particularly
important for systems where a very large battery
(that is, one designed to normally operate in the upper
10% or less of state of charge in order to achieve high
load availability) is used. For example, a PV system for
an area light may be designed to allow the light to not function
for a couple of nights per year, but a communication
repeater may be only allowed a couple of hours
per year of outage time (often less). One common method
for increasing the availability of PV systems is to increase
the size of the battery. Increasing battery size in a
system implies that the battery will be operating at a higher
average state-of-charge. If a 100 amp-hour (Ah) battery
is used in a system with a 30Ah daily load, then one
would expect the battery to be operating in the 70% to
100% SOC regime on the average. If this same load was
operated with a 300Ah battery, then the battery would
be expected to operate in the 90% to 100% SOC regime
on the average. Because charge efficiency decreases
with increasing battery state-of-charge, the system
with the larger battery may also need a larger PV array
to account for the higher losses associated with operating
at a higher average SOC. Battery charge efficiency
is also a function of charge rate, with lower rates
resulting in higher efficiencies. The larger battery will
be operating with a lower charge rate, which will result
in higher charge efficiency. A decision on increased
array size must be made with full knowledge of charge
efficiency at the actual charge rate being employed.
The testing reported on here examined a single
sample
of the Trojan 30XHS battery. This is a 12-volt, flooded,
lead-antimony battery rated 130Ah at the 20 hour
rate by the manufacturer. Testing in PV applications,
where charging is rarely in accordance with manufacturer’s
recommendations, indicates that this battery
has a “PV capacity” of about 100Ah, and that is the
value that will be used as this battery’s capacity in this
paper.
CHARGE RATE SELECTION
For this initial test sequence, a single charge and discharge rate was selected. The rate was
chosen as one of many that is
typically seen in PV systems. For the 100Ah
Trojan 30XHS battery, a charge and discharge rate
of 3.3 amps, or C/30, was selected. PV system batteries
will normally have charge rates that vary from about
1/10th the battery capacity to about 1/50th the battery
capacity, or C/10 to C/50, with discharge rates varying
from about C/10 to C/150. A moderate rate of C/30
was selected from these ranges, resulting in 3.3 amps.
It is important to select a charge and discharge rate
that is similar to that used in PV systems because these
rates will have a significant effect on battery charge efficiency,
An example demonstrates the origin of these ranges.
Consider a load, including losses, that
requires 15Ah per day from the PV
array. In an area of a good solar resource
of 5 kWh/m²/day, also referred to as 5 sunhours per
day, this energy will be acquired from the array over
the daylight hours, with peak current of 3 amps (15 Amp-hours/5
sun-hours) occurring in the hour around noon.
A typical design might require “5 days storage” for the
batteries. That is, the batteries would be required to provide
75Ah to the load with no additional solar energy input.
PV systems are typically designed with a “lowvoltage- disconnect”
(LVD) to keep the battery from experiencing
100% discharges. A typical LVD might be designed
to allow 75% discharge. This then implies that the
75Ah energy storage is 75% of the battery capacity, so
we will be considering a 100Ah battery. Therefore, the peak
charge rate will be 100/3=33, or a charge rate of C/33
(that is, the charge rate is equal to the battery capacity
divided by 33). A 3 sun-hour per day locale would
require a larger array with a 5 amp peak, resulting in
a peak charge rate of C/20. If the load is a light that is on
all night, the discharge rate will be 15Ah/12hours = 1.25
amp or C/80. If the load remains 15Ah per day, but is
spread over 24 hours per day, the discharge rate will be
C/160.
TEST PROCEDURE
All tests were performed on a Digitron/Firing Circuits BTS 600 charge/discharge test unit, which
charges with pure dc (as observed on
an oscilloscope.) This test unit allows
programming several test sequences, then performs
the tests while monitoring and logging the test data.
The test equipment and battery are in an air conditioned
room with the room temperature maintained near
72°F. The battery temperature was monitored and recorded.
Because of the low charge/discharge rate of the
testing (C/30), the battery and room temperatures remained
essentially the same. All discharges
were to 10.5 volts to ensure consistency
in counting amp-hours. The battery was first charged
and discharged through 10 complete cycles in order
to “form” the battery and ensure consistent results. Full
recharge (as opposed to the partial charges used to charge
the battery with a specific number of Amp-hours) was
performed by bringing the battery voltage to 14.8 volts
and then maintaining regulation voltage (14.8 volts) by
tapering the current for 10 hours. A
test procedure was developed to charge the battery in
steps beginning with approximately 65% capacity, then increasing
the input in 8Ah increments until about 100Ah output
is obtained on discharge. The Digitron tester calculates
both amp-hours and watt-hours for each data point,
so both Ah and energy efficiency can be easily obtained
with the same set of test data.
Two types of efficiency are calculated using the test
data. These will be referred to as overall
average efficiency (the efficiency
from zero SOC to that SOC under test)
and incremental efficiency (the efficiency between
two non-zero states of charge, for example, between
80 and 85% SOC). After the initial regime of 10 full
charge/discharge cycles, the battery was charged with 68Ah
which was estimated to result in about 65% SOC, or
that would provide about 65Ah on discharge. The 68Ah
charge actually resulted in an average discharge of 65.9Ah.
After the battery was charged with 68Ah, it was then
discharged to determine the amp-hours available, and
charge efficiency was calculated. This procedure was
repeated several times for each SOC level in the testing.
The amp-hours input was then increased and the next
level of SOC was examined in a similar manner.
RESULTS
The results of this testing are displayed graphically in Figure 1. Each data point in Figure 1
represents at least four tests. Some
represent more than this, as some tests were
repeated at random to verify repeatable results. The greatest
variance in test results for each step was 5.8%, with
several of the steps resulting in variance in results of less
than 2%. The data is represented as a minimum value
of amp-hours extracted for each charge level, a maximum
value and the average. This graph shows that the
scatter among data is relatively small. Figure
2 shows the conversion of the amp-hours out versus
amp-hours in to efficiencies. Notice that there are two
curves, one displaying overall efficiency from zero state
of charge to the particular state of charge under test,
and the other showing incremental efficiency between
states of charge. Notice also that the overall efficiency
shows high values, with full charge represented by
approximately 85% efficiency, a commonly used value for
battery charge efficiency. More importantly, notice the dramatically
lower efficiencies for the increments above about
80% state of charge, where most values are below 60%
efficiency, and full charge is represented by less than
50% efficiency. (Actually, full charge, resulting in 100Ah
output has not been reached in the testing to date. The
greatest output was 96.5Ah, which resulted from 116Ah
input. An attempt to achieve 100Ah output will be made
as part of the conclusion of this testing.)
.
Clearly, the use of assumed charge efficiencies in the range of 80% will not result in a fully
charged battery when this battery is
expected to operate in the upper 20% of
it’s state of charge. It is expected that these results will hold
up well for other deep-cycle flooded lead-antimony batteries
as well.
INTERMEDIATE FULL CHARGE CYCLES
An observation early in the testing required a change in the test procedure. The original intent
had been to perform several partial
charge/discharge cycles in sequence.
For example, charge to 68Ah input, discharge, then
charge to 68Ah input and so on until the four complete
cycles at 68Ah input were complete. Then fully charge
and discharge the battery before proceeding with the
next level. It was seen early in the testing that this was
not going to work, as the capacity resulting from 68Ah
input dropped with each succeeding cycle when no full
charge cycles were performed between partial charge cycles.
Therefore a full charge and discharge cycle was added
between each partial charge/discharge cycle. This
result has important implications to operational PV
systems. That is, if a battery is partially charged for several
consecutive cycles (for example, the array is marginally
sized and there is a series of less than full sun days
in the winter) the useable battery capacity decreases each
cycle, even though the same amount of energy has been
presented to the battery each day. This is the result of
battery inefficiencies, electrolyte stratification, and sulfate
buildup during these partial charges. An associated
full charge, with its attendant gassing, is needed
to destratify the electrolyte and remove the residual
sulfate. This sulfate buildup can become a problem
if this pattern continues for several months. In the
short term it can be reversed by a full “equalizing” type
charge, which, in most cases is not possible in small PV
systems. Battery equalization requires a PV charge controller
that has been specifically designed to include this
function. At low charge rates (for example, less than C/40)
equalization may not be possible because of charging
time limitations. In any case, this reduction in useable
capacity will impact system availability and should
be understood.
FURTHER TESTING
The current set of tests will be completed by decreasing the input to the battery progressively until
a point is found at which the
incremental charge efficiency stabilizes, implying
that this value will prevail throughout the lower states
of charge. During this testing, earlier tests will be repeated
as a check and to investigate the continued health
of the battery (that is, looking for changes in results
that would indicate changing battery health.) Finally,
these testing procedures will be applied to other batteries
to see how common the results are and to examine
variations that may be found.
CONCLUSIONS
A test procedure has been developed to allow the examination
of battery charge efficiency as a function of battery
state of charge. Preliminary results agree well with
established general understanding that the charge efficiency
of flooded lead-antimony batteries declines with increasing
state-of-charge, and that charge efficiency is a non-linear
function of battery state-of-charge. These tests
indicate that from zero SOC to 84% SOC the average
overall battery charging efficiency is 91%, and that
the incremental battery charging efficiency from 79% to
84% is only 55%. This is particularly significant in PV systems
where the designer expects the batteries to normally
operate at SOC above 80%, with deeper discharge
only occurring during periods of extended bad weather.
In such systems, the low charge efficiency at high
SOC may result in a substantial reduction in actual available
stored energy because nearly half the available energy
is serving losses rather than charging the battery. Low
charging efficiency can then result in the battery operating
at an average SOC significantly lower than the system
designer would anticipate without a detailed understanding
of charge efficiency as a function of SOC. During
normal weather, capacity degradation will not be evident,
but it will manifest itself when the battery is called
on to provide the full purchased capacity, which will
be found to be unavailable. Extended operation in a low
SOC environment can also result in permanent loss of
capacity from sulfation if the battery is operated for long
periods of time without a sufficient recovery or equalizing
charge.
The impact of low charge efficiency at high states of
charge has the greatest potential impact on
systems where high energy
availability is needed. Such systems usually
utilize large batteries to ensure energy availability during
the longest stretches of bad weather. This may not
provide the energy required if the PV array is insufficient
to provide a recovery charge for batteries at 90%
SOC and above, where charge efficiency is very low. Charge
efficiencies at 90% SOC and greater were measured
at less than 50% for the battery tested here, requiring
a PV array that supplies more than twice the energy
that the load consumes for a full recovery charge. Many
batteries in PV systems never reach a full state of charge,
resulting in a slow battery capacity loss from stratification
and sulfation over the life of the battery.
