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Limits to battery lifetime in photovoltaic applications
Solar Energy Vol. 58, No. 4-6, pp. 147-154.1996 Copyright 0 1996 Elsevier Science Ltd PII: SOO38-092X(96)00085-0 Printed in Great Britain. All rights reserved 0038-092X/96 $15.00 + 0.00
LIMITS TO BATTERY LIFETIME
IN PHOTOVOLTAIC
APPLICATIONS
DAVID J. SPIERS*+ and ASK0 A. RASINKOSKI** *Neste Advanced Power Systems UK, P.O. Box 83, Abingdon, Oxon OX14 2TB, U.K. and **NAPS Technology Laboratory, Neste Technology Centre, P.O. Box 310, FIN-06101, Porvoo, Finland (Communicated
by G. Wrixon)
Abstract-Battery lifetime in a photovoltaic
(PV) system is important in determining life-cycle costs and servicing requirements. Unfortunately, this is often not calculated with any certainty. We present a simple model for estimating PV battery lifetimes which are applicationand battery-specific, using data normally available (or easily estimated) at the time of system design. In a correctly designed and operated PV system, one of two properties will limit the ultimate lifetime of the battery: the cycle life or the battery’s resistance to internal corrosion. The cycle life is more or less independent of ambient temperature, but the resistance to internal corrosion falls rapidly at higher ambient temperatures. Whether the cycle life or the temperature-dependent corrosion is the limiting factor on battery life depends on the particular details of the photovoltaic system, especially the type of battery used, the daily depth of discharge and the average ambient temperature experienced. Illustrations are given of the particular circumstances for a variety of PV systems with open (vented) lead-acid batteries, ranging from rural lighting systems and vaccine refrigerators to large telecommunications systems. Where possible, the predicted lifetime is compared to actual field experience. In PV systems using tubular plate vented batteries, it is nearly always the temperaturedependent corrosion process that limits the battery lifetime, and not the cycle life. In larger PV systems in hot climates, active cooling of the battery enclosure (powered by photovoltaics) can sometimes increase battery lifetime, and a suitable battery-cooling system under development is described briefly. Copyright 0 1996 Elsevier Science Ltd.
1. INTRODUCTION
cantly reduced battery lifetimes or available capacities in PV use. Most of the batteries tested could recover under PV-type recharging from a prolonged stand in a deeply discharged condition. The capacities obtained for tubular plate vented (i.e. open, not “sealed”) batteries under PV-type conditions of charging and discharging were not significantly reduced from their nominal values. In this article, we present a simple model to predict the lifetime of vented lead-acid batteries in various types of PV system. This model is based on manufacturers’ reported cycle life and float service life data, which in most cases is readily available. An attempt is made to correlate this model with reported service lifetimes of PV batteries in real working systems, where no catastrophic factors have been encountered. However, in the real world of commercial photovoltaics, rather than demonstration projects, it is often difficult to obtain reliable information on the state of health of batteries installed many years ago at remote sites. In some cases, we have had to assume that if there has been no contact from the customer or user, then the batteries are still operating without problems. This article does not address the lifetime of valve-regulated (“sealed”) lead-acid batteries in PV systems. Although the same general principles hold for these types of batteries, there is
This article is aimed at helping design engineers and planners estimate the lifetime of a battery in a photovoltaic (PV) system, using information that is generally available about the specific PV application and the specific type of battery being considered. Most batteries used in PV systems will have a service lifetime which is less than that of the PV modules, so the battery lifetime is an important factor in the calculation of life-cycle costs and also when planning future maintenance requirements. In most practical uses of photovoltaics today, a solar module or array charges a battery. In nearly all of these cases, the battery used is of the lead-acid type. In a previous article (Spiers and Rasinkoski, 1995), we proposed that the lifetime of a lead-acid battery in a photovoltaic system was determined by three main circumstances: Primary factors: cycle life and high temperature resistance, which are common to all applications of batteries. Secondary factors: effects of sulfation and low overcharge, which are peculiar to PV use. Catastrophic factors: manufacturing faults, under-sizing, user abuse, freezing, etc, which are avoidable. In the same article, we showed that the effects of the secondary factors did not lead to signifi+ISES member. 147
D. J. Spiersand A.A. Rasinkoski
148
not yet sufficient field experience for them (i.e. over 5 years in the field, in many different climate types). Most, if not all, of the reported short service lives for such batteries in PV systems to date are either due to early models of these batteries having an internal design fault (now rectified) or to wrong specification of the charge controller. 2. CALCULATION METHOD 2.1. Cycle life In PV systems, the average currents are relatively low compared with the battery capacity (discharges are often between the 100 and 300 h rates). The daily cycling is often very shallow. However, in order to get the required data in a reasonable time, cycle lives are usually measured at relatively high rates (10 h rate or higher current) and at high depth of discharge (DOD), often 80%. The 80% DOD in published cycle life data usually refers to a percentage of either the capacity at the standard discharge rate (often the 10 h rate), or to the actual rate at which the cycling test was carried out. In PV use, the low discharge rates mean that available capacity can be much higher than the nominal capacity, especially for tubular plate vented batteries, which have a large reserve of free acid. In order to translate manufacturers’ cycle life data into meaningful numbers for estimating PV cycle life, we make some assumptions. (1) The total number of Ah discharged over the whole cycle life is a constant, independent of the DOD (Bode, 1977). Where cycle life data at different DOD is reported, it is often claimed that the product of cycle life and DOD is higher at low DOD. By using a constant value which is taken from high DOD data (e.g. 80%), we should obtain a conservative value. (2) The total number of Ah discharged over the whole cycle life is a constant, independent of the discharge rate. As far as we know, there is no experimental evidence for this at very low discharge rates. However, it is reasonable if we assume that the cycle life is dependent on the volume (i.e. density) changes in the battery plates. Note that the second assumption is not equivalent to the statement that the same number of cycles at a certain DOD are obtained at any discharge rate. To give a concrete example, a tubular plate battery may have a nominal capacity of 500 Ah at the 10 h discharge rate, and it
may give 1000 cycles of 80% DOD at this discharge rate. At the 120 h discharge rate, the available capacity may be 725 Ah. However, the battery will not give 1000 cycles at 80% of 725 Ah per cycle. Using our assumptions, at the 120 h rate it would either give 1000 cycles at 80% of 500 Ah (which is about 55% DOD referenced to the higher 120 h capacity of 725 Ah) or it would give approximately 690 cycles at 80% DOD based on a capacity of 725 Ah. We represent these assumptions by the following equation:
N;C;D,,-X,=L,
(1)
where N, is the number of reported cycles at depth of discharge Dadrelative to the standard (nameplate) capacity rating C, (often the 10 h capacity). L, is the total number of Ah for all cycles over the whole cycle life. X, is an arbitrary correction factor used to derate the manufacturers’data (which refers to continuous and regular cycling) for PV use (where the cycling is not continuous or regular). We have used X,=0.8 in the calculations in this article. The predicted cycle life (in years) is then simply given by: Y,=L,/(365D,)
(2)
where D, is the average daily cycling Ah that the battery experiences. If the electrical load is only switched on during the night (e.g. for lighting), then D, is equal to the average load Ah in a 24 h period, since the charging occurs during the day time, and all the discharging is at night. If the load is only switched on during the day, then D, will be very small and the predicted L, will be very large. If the load is continuous, D, will be reduced from the total daily load Ah by a factor (24-HJ24, where H, is the number of hours during the day when the PV array is charging the battery (i.e. when the array current is larger than the load). An approximation for this for any day is: K = &,(AhrlAh,)
(3)
where Hdlis the number of hours of daylight, Ah, is the total daily Ah load and Ah, is the total Ah of battery charging that the PV array could give. If there is no detailed data for the day length and available charging from the PV array, then a reasonable guess for H, is between 6 and 10 h for most systems.
Limits to battery
2.2. Temperature-dependent
corrosion
Stationary batteries are often used in float service, where the voltage is held constant by a mains charger, the small float current keeping the battery completely charged for any emergency situation. Cycling is effectively zero in this application. In the limit of very shallow PV cycling, we might expect the conditions to be rather similar. The lifetime of a battery in float service is quoted by manufacturers as the expected service life at a particular float voltage and, very importantly, at a particular ambient temperature. The battery lifetime limitation in this case is corrosion of the positive grid material, which is dependent both on the applied voltage and the temperature. It is generally accepted in the battery industry that an increase in temperature of 10°C will lead to a halving of the expected life in float service. The lifetime based on this temperaturedependent corrosion process is given as: r, = JLX,IC2”((T,” - T,W)l
(4)
where x is the predicted lifetime in years, L, is the stated lifetime for float service, at the standard ambient temperature T,, and T,, is the average temperature of the battery environment. X, is another arbitrary correction factor to compensate for the fact that the battery voltage is not truly constant, and, as with the other correction factor X,, we have used a value of 0.8 in these calculations. If T’, is less than T,, a higher battery lifetime than the quoted standard lifetime L, would be predicted. To be conservative, we only use equation (4) for T,,> = T,. At lower temperatures, we assume the lifetime is the same as at x. The value of T,, depends on the type of battery installation. For unheated buildings or for battery boxes mounted in the shade of a PV array, the average temperature can normally be approximated by the average outside air temperature, provided that the battery itself generates negligible heat. At the low rates common in PV systems this is certainly justifiable for vented batteries, but for valve-regulated batteries the heat produced on overcharge can be significant if the battery enclosure cannot reject heat to the surroundings easily. If the batteries are mounted in an equipment shelter, where the electrical load itself is a heat source, then the battery temperature can be expected to be above the outside air temperature. Just how much this is
lifetime
149
depends on the shelter design and actual equipment details. In the special case of a battery mounted in the same room as a PV-powered vaccine refrigerator, the refrigerator itself will cause some heating of the room, and again the average battery temperature can be considered to be a few degrees higher than the outside air. In this article we have assumed the room to be 5°C higher than the outside air, when averaged over the whole year. This may be a little pessimistic, but should lead to conservative battery life predictions. 2.3. Overall battery life The actual lifetime predicted will be whichever of Y, or x calculated above is lower. F will be dependent on the ambient temperature, but independent of the daily depth of cycling. In contrast, Y, will be independent of temperature (within reasonable limits) and should depend only on the daily depth of cycling. For regular loads, it is more convenient to talk in terms of days of autonomy rather than daily depth of cycling, as this is less dependent on systemspecific details. The larger the number of days of autonomy, the lower the daily depth of cycling. Note that the battery manufacturers’ data for both cycle life and float life refer to an end of life when 80% of the original battery capacity remains. In actual PV service, this point may be passed without notice in systems with relatively high autonomy. The lack of capacity may only become apparent if the full autonomy reserve is called upon. Therefore, it would not be surprising to find reported cases of batteries still operating in the field after their predicted end of life. In this article we have presented the predicted battery lifetimes as a plot against ambient temperature of the battery (see Figs 1-3). The temperature-dependent corrosion limit is a curve which shows the halving of predicted life for every 10°C increase. The limits caused by cycle life are shown as a series of horizontal lines for different numbers of days of autonomy. These figures have been calculated on the basis of one annual average temperature and one typical value of daily cycling depth being sufficient to characterise the system. The figures quoted as predicted lifetimes in Tables 1 and 2 are calculated much more accurately by computer, using typical values for each month of the year, and particular site information. In general, the agreement between the two calcula-
D. J. Spiers and A. A. Rasinkoski
150 Years 14,
6
0 20
I
II
Ih
II
II
4 I
22
24
26
28
30
32
34
,
II
36
38
40
annual average temperature, deg C Fig. 1. Lifetime limits for open tubular plate batteries in PV systems with a continuous load. Corrosion limit, i); cycle life limit for autonomy periods of 3 days, +; 4 days, Q; 5 days, - + -; 6 days, - x -.
Years 16
20
22
24
26
28
30
32
34
36
38
annual average temperature, deg C Fig. 2. Lifetime limits for open tubular plate batteries in CFS49IS PV vaccine refrigerator systems. Corrosion limit, U; cycle life limit with daily icepack freezing, -&; without daily icepack freezing, Q.
40
Limits to battery
lifetime
151
Years
20
22
24
26
28
30
32
34
36
38
40
annual average temperature, deg C Fig. 3. Lifetime limits for flat plate “SolarPower” batteries in PV rural lighting systems. -C-; cycle life limit for autonomy periods of 2 days, h; 3 days, Q; 4 days, -+-; Table 1. Battery
Location Argentina Saudi Arabia Djibouti Jordan Oman Oman Venezuela Kenya Guinea Chad Vietnam
Location
telecom telecom ac system telecom telecom telecom telecom demo telecom telecom telecom
‘High altitude
1984 1984 1985 1987 1987 1987 1988 1990 1992 1993 1993
5 10 ?4 20 10 5 10 8 5 3 5
plate batteries
Battery replacement
Autonomy
_
days days days days days days days days days days days
Table 2. PV-powered
vaccine
Installed
Capacity Ah
1 1 2 1 2 2 location,
with tubular
_ 1994 _ 1’ 994 _ _ _ _ _
so ambient temperatures are relatively low. shelter, so at a higher average temperature than outside
Fridge tvve
Ghana Maldives Bolivia Tanzania Ethiopia Ethiopia
PV systems
Installed
Type
‘High altitude location, ‘Batteries in equipment
charging
so ambient
1986 1987 1989 1991 1992 1992 temperatures
refrigerators
are relatively
tion methods is within approximately 0.5 year. The spread of predicted lifetime values in the tables reflects that the calculations were done
Service life years >ll >ll 9 18 7 >8 >I >5 >3 >2 >2
1993 _ _ _ _
loads Predicted years
Notes
10-12 8 6 8-10 7-8 7-8 10-11 11 7-8 4-6 6-8
1
2 2
Predicted vears
Note
1
ambient.
with fixed battery
Battery renlacement
360 360 200 300 200 200
and regular
Corrosion limit, 5 days, - x ~
size
Service life Years I 18 16 >4 >3 >3
5-6 5 12 6-8 9-11 5-l
1 1
low.
for several different sites (with different air temperatures) and do not represent calculation uncertainties.
D. J. Spiers and A. A. Rasinkoski
152
3. CALCULATED COMPARISON
RESULTS
WITH FIELD
AND DATA
3.1. Systems with tubular plate batteries constant loads
and
Figure 1 shows a graph of the cycle life limits for systems with continuous constant loads and 3, 4, 5 and 6 days of autonomy, as well as the temperature-dependent corrosion limit lifetime. Cycle life predictions for autonomy periods of more than 6 days lead to predicted lifetimes that are always higher than the temperaturedependent limit. The graph was calculated for a tubular plate vented battery with a stated cycle life of 1000 cycles at 80% DOD (10 h rate) and a float service lifetime of 1.5 years at 20°C. Correction (safety) factors of 0.8 were applied to both values. It can be seen that the temperature-dependent corrosion limit determines the predicted lifetime in the following cases: (i) for 3 days autonomy and annual average ambients above 27°C; (ii) for 4 days autonomy and annual average ambients above 24°C; (iii) for 5 days autonomy and annual average ambients above 21°C; (iv) for 6 days autonomy and above, at any ambient temperature. This means that the temperature controls the battery lifetime in most professional PV systems (e.g. telecommunications systems) in most sunny parts of the world. Table 1 shows a selection of actual site details (Selhagen and Sandell, 1995; Duval and Lacroix, 1995; Fanning, 1995) which go back as far as 1984 (installation date). Also shown are the predicted battery lifetimes according to our model. In only two of these systems are there reports of actual battery changes so far for what can be described as “normal old age” of the battery. For the system in Oman, this occurred more or less at the predicted time. For the system in Djibouti, the battery was reportedly used for 9 years against a predicted lifetime of 6 years, although it is quite possible that this battery had significantly less than 80% of its capacity remaining when replaced. The system in Saudi Arabia has a battery still operating after 11 years, when the predicted lifetime is 8 years. Of the other systems, those in Argentina, Jordan and Oman would appear to be getting close to their predicted lifetime, and it would be interesting to carry out a capacity check on these batteries. Note that the combination of a hot climate and siting the batteries inside the equipment shelter for the system in Chad means that the
predicted battery lifetime is particularly reduced. It is in cases like this that a battery cooling system could pay for itself by increasing the battery lifetime. 3.2. Vaccine refrigerator
systems
PV-powered vaccine refrigerators present an interesting case, because the electrical consumption of the refrigerator is also a function of the average ambient temperature. Figure 2 shows predicted lifetimes calculated for tubular plate vented batteries (200 Ah/l0 h) with a NAPS CFS49IS vaccine refrigerator system. The same battery lifetimes and factors were used as in the previous section. The lowest curve is the lifetime resulting from temperature effects. The curve above it represents the cycle life limitation for heavy duty use (freezing 2.4 kg icepacks every day) and the segment of the upper curve represents the cycle life for light duty (no regular icepack freezing). It can be seen that, with this temperaturecombination, the particular dependent corrosion is always the life-limiting factor for the batteries. The cycle life limitation only becomes apparent at lower ambient temperatures if (a) a refrigerator with higher consumption is used, or (b) a smaller battery is used (leading to deeper daily cycling) or (c) a battery with lower cycle life (e.g. flat plate type) is used. Table 2 shows details of some vaccine refrigerator projects (Vegel, 1995; Fanning, 1995), together with the predicted lifetimes. Often these are projects involving several health centres in different locations, so again the predicted lifetime figures reflect the spread of actual location ambient temperatures. Only in Ghana have the batteries so far needed replacement, and the actual service lifetime of 7 years was a little more than the predicted lifetime of 5-6 years, based on the estimated temperature inside the battery room. Of the other systems, only that in the Maldives seems to have passed its predicted lifetime, and it would be interesting to check the condition of this battery. There are some years to go before the other systems in this table will reach their predicted battery lifetimes, and it will be interesting to check on these in future years. 3.3. Rural lighting systems for houses, usingflatplate batteries In contrast with telecommunications, vaccine refrigerator, etc. systems, where the user is usually able to afford a tubular plate battery which
Limits to battery
will give a reasonable lifetime, individual home owners who install a small PV system for lighting, etc. demand a low cost battery. In most cases the tubular plate battery is not affordable in such systems, and a flat plate battery has to be used. The most common type of flat plate lead-acid battery is the car or truck battery used for starting, lighting and ignition (SLI). Other types of flat plate batteries are produced for special uses such as on boats and caravans, for powering invalid carriages or golf carts, and for PV use. Such batteries have somewhat thicker plates and other internal differences to the normal SLI design. In the Nordic countries, a large application for PV is for lighting, etc. in summer holiday homes. Here, flat plate batteries modified for PV use (“SolarPower”) are used. The positive plates are somewhat thicker (2-2.5 mm) than in car batteries, and there are various other internal modifications. We have measured a cycle life of around 200 cycles at 80% DOD for such batteries in the laboratory. The usage pattern in such summer holiday homes is very variable, but typically the battery will receive between 10 and 20 deep (80%) discharges in a year. Using our calculation method above, the cycle life limit should then be between 8 and 16 years (allowing an 80% safety factor). Although float life data do not exist for such batteries, an informed guess would be around 5 years at 20°C based on the thickness of the positive plates and also the typical service life of a heavyduty SLI battery with the same plate thickness. The year-round average temperature in such summer cottages in Finland, Norway and Sweden is less than 10°C so the temperaturedependent corrosion process is slowed down significantly, and the lifetime limit caused by corrosion might be estimated at around 8-10 years or more. Although it is very difficult to know the exact service lifetime of the “SolarPower” batteries in such domestic systems, our best information (Pylvalainen, 1995; Vegel, 1995) is that it is somewhere between 7 and 10 years. In one particular holiday cottage system (Vegel, 1995), the two batteries are 10 years old and still have more than 75% of their initial capacity. Therefore, the above model predicts battery lifetimes for flat plate batteries in Nordic countries reasonably well. If there are more than 20 deep discharges per year, we would expect the cycle life to become more of a limitation than the positive plate corrosion. Figure 3 shows the predicted lifetime of the
lifetime
153
same SolarPower battery if it is used in a rural home lighting etc. system which is used every night. Normally, such systems are specified to have 3-5 days autonomy, and Fig. 3 shows that at ambient temperatures below about 30°C the cycle life will limit the predicted nominal service life to a little less than 2-3 years. However, that figure applies to the battery reaching 80% of its initial capacity (in practice, the battery will be used beyond this limit, if possible) and it also assumes that the full available Ah provided by the PV is used (in practice, this is not often the case). We might therefore expect a service life of 3-4 years in practice. Note that if a smaller battery is used (e.g. one giving only 2 days of autonomy), the deeper daily cycling will restrict the predicted service lifetime to around 1 year, and in practice the real service lifetime will probably be less than 2 years. If a normal car (SLI) battery is used in such rural home systems, it will have thinner plates than the SolarPower battery, which will result in a cycle life of less than 200 cycles at 80% DOD (often significantly less), and it will also probably have a predicted float life of less than 5 years at 20°C. Whilst we have not drawn a lifetime graph for such SLI batteries in rural home PV systems, we can estimate that the service lifetime will be even more dependent on the cycle life, and will be lower, probably by a factor of 2 or more, than the above figures for the thicker plate battery. A large rural home PV electrification project in any country should consider very carefully whether local unmodified SLI batteries (which will probably need replacement every 2 years or so) are the best option, or whether suitably modified batteries for PV use are more desirable (which will probably give at least double the service life of the SLI battery, but at less than double the cost). The long life and low maintenance requirements of PV rural electrification systems could be outweighed by battery replacement logistical and environmental problems if sufficient attention is not paid to the battery specification. 4. A POSSIBLE BATTERY-COOLING SYSTEM FOR LARGE INDUSTRIAL PV SYSTEMS When the cycle life of the battery is sufficiently large (e.g. for a tubular plate design) and where the autonomy provided by the battery is sufficiently large (as it is in most non-domestic PV systems), then the ultimate battery lifetime
D. J. Spiers and A. A. Rasinkoski
154
depends on the ambient temperature. For systems with autonomy of 5 days or more and a continuous load, the service lifetimes predicted by Fig. 1 for batteries in differing annual average ambient temperatures are approximately 12 years at 20°C 8.5 years at 25°C 6 years at 30°C 4.2 years at 35°C and 3 years at 40°C. If a battery is operating at over 30°C average temperature, then providing cooling to reduce this average temperature to 25°C or below would have a significant effect on the battery life. We have been developing over the past few years a small dc air conditioning unit of the compressor type. Its electrical consumption is approximately 70 W,, and its cooling effect is approximately 200 Wth. Preliminary tests and calculations indicate that a separate small PV system of around 200-250 peak Watts could provide this small air conditioner with sufficient cooling power to reduce the ambient temperature of a small, well-insulated, battery room sufficiently to prolong the life of batteries in hot climates. The additional cost of the PV-powered cooling system could be justified for larger professional PV systems of sufficient battery size and in areas of sufficiently high ambient temperature. So far, the small air conditioner has only been tested under laboratory and domestic conditions. However, we hope to test it soon in professional PV application. a suitable Unfortunately, the device is too large to be applicable to battery cooling alone in smaller PV installations such as vaccine refrigerators with PV array sizes below about 1 peak kW. 5. CONCLUSIONS A simple model is proposed to determine the ultimate service lifetime of a vented lead-acid battery in photovoltaic applications. This model requires only data that is normally readily available, i.e. the cycle life and float service life from the battery manufacturer, plus the site ambient temperature, electrical load and expected PV array output. Although it is often difficult to obtain actual battery service lifetimes from PV systems in remote areas that were installed several years ago, we have checked what field information we have against our model, and found that the results are in broad agreement.
The same general principles apply to other types of battery, for example valve-regulated lead-acid batteries, and we hope in the future to compare predicted values with actual field data for these. In PV systems which use tubular plate vented batteries, and have autonomy periods of 5 days or more, the battery lifetime is almost always controlled by its resistance to high ambient temperatures and not by the cycle life. Examples of such systems are telecommunications sites and vaccine refrigerators. In these, attention should be paid to keeping the battery ambient temperature as low as possible (without, of course, running into the risk of freezing the battery acid at low states of charge). In larger systems in hot climates, a small PV-powered air conditioner can reduce the battery working temperature sufficiently to increase the expected battery service life significantly. In small domestic PV systems which use flat plate lead-acid batteries for reasons of low cost, the battery lifetime is more likely to be controlled by the cycle life, especially in cases where the load (e.g. lighting) is used every day and the autonomy period is generally low (5 days or less). Use of standard car batteries in rural PV lighting systems may result in battery lifetimes that are probably unacceptably short because of their limited cycling capability, unless a large autonomy period (i.e. high ratio of battery capacity to daily load) is used. The use of a thicker plate battery, specially designed for use in PV applications, with a cycle life equivalent to 200 or more discharges at 80% of the nominal capacity would result in a more acceptable battery life for rural PV home systems, and should give a lower overall life cycle cost for the battery. REFERENCES Bode H. (1977) Lead-Acid Batteries, Wiley Interscience, New York, p. 333. Duval J. and Lacroix B. (1995) NAPS France, internal communication. Fanning J. (1995) NAPS Kenya, internal communication. Pylvllainen H. (1995) NAPS Finland, internal communication. Selhagen L. and Sandell P. (1995) NAPS Sweden, internal communication. Spiers D. J. and Rasinkoski A. A. (1995) Predicting the service lifetime of lead/acid batteries in photovoltaic systems. J. Power Sources, 53, 245-253. Vegel M. (1995) NAPS Norway, internal communication.
LIMITS TO BATTERY LIFETIME
IN PHOTOVOLTAIC
APPLICATIONS
DAVID J. SPIERS*+ and ASK0 A. RASINKOSKI** *Neste Advanced Power Systems UK, P.O. Box 83, Abingdon, Oxon OX14 2TB, U.K. and **NAPS Technology Laboratory, Neste Technology Centre, P.O. Box 310, FIN-06101, Porvoo, Finland (Communicated
by G. Wrixon)
Abstract-Battery lifetime in a photovoltaic
(PV) system is important in determining life-cycle costs and servicing requirements. Unfortunately, this is often not calculated with any certainty. We present a simple model for estimating PV battery lifetimes which are applicationand battery-specific, using data normally available (or easily estimated) at the time of system design. In a correctly designed and operated PV system, one of two properties will limit the ultimate lifetime of the battery: the cycle life or the battery’s resistance to internal corrosion. The cycle life is more or less independent of ambient temperature, but the resistance to internal corrosion falls rapidly at higher ambient temperatures. Whether the cycle life or the temperature-dependent corrosion is the limiting factor on battery life depends on the particular details of the photovoltaic system, especially the type of battery used, the daily depth of discharge and the average ambient temperature experienced. Illustrations are given of the particular circumstances for a variety of PV systems with open (vented) lead-acid batteries, ranging from rural lighting systems and vaccine refrigerators to large telecommunications systems. Where possible, the predicted lifetime is compared to actual field experience. In PV systems using tubular plate vented batteries, it is nearly always the temperaturedependent corrosion process that limits the battery lifetime, and not the cycle life. In larger PV systems in hot climates, active cooling of the battery enclosure (powered by photovoltaics) can sometimes increase battery lifetime, and a suitable battery-cooling system under development is described briefly. Copyright 0 1996 Elsevier Science Ltd.
1. INTRODUCTION
cantly reduced battery lifetimes or available capacities in PV use. Most of the batteries tested could recover under PV-type recharging from a prolonged stand in a deeply discharged condition. The capacities obtained for tubular plate vented (i.e. open, not “sealed”) batteries under PV-type conditions of charging and discharging were not significantly reduced from their nominal values. In this article, we present a simple model to predict the lifetime of vented lead-acid batteries in various types of PV system. This model is based on manufacturers’ reported cycle life and float service life data, which in most cases is readily available. An attempt is made to correlate this model with reported service lifetimes of PV batteries in real working systems, where no catastrophic factors have been encountered. However, in the real world of commercial photovoltaics, rather than demonstration projects, it is often difficult to obtain reliable information on the state of health of batteries installed many years ago at remote sites. In some cases, we have had to assume that if there has been no contact from the customer or user, then the batteries are still operating without problems. This article does not address the lifetime of valve-regulated (“sealed”) lead-acid batteries in PV systems. Although the same general principles hold for these types of batteries, there is
This article is aimed at helping design engineers and planners estimate the lifetime of a battery in a photovoltaic (PV) system, using information that is generally available about the specific PV application and the specific type of battery being considered. Most batteries used in PV systems will have a service lifetime which is less than that of the PV modules, so the battery lifetime is an important factor in the calculation of life-cycle costs and also when planning future maintenance requirements. In most practical uses of photovoltaics today, a solar module or array charges a battery. In nearly all of these cases, the battery used is of the lead-acid type. In a previous article (Spiers and Rasinkoski, 1995), we proposed that the lifetime of a lead-acid battery in a photovoltaic system was determined by three main circumstances: Primary factors: cycle life and high temperature resistance, which are common to all applications of batteries. Secondary factors: effects of sulfation and low overcharge, which are peculiar to PV use. Catastrophic factors: manufacturing faults, under-sizing, user abuse, freezing, etc, which are avoidable. In the same article, we showed that the effects of the secondary factors did not lead to signifi+ISES member. 147
D. J. Spiersand A.A. Rasinkoski
148
not yet sufficient field experience for them (i.e. over 5 years in the field, in many different climate types). Most, if not all, of the reported short service lives for such batteries in PV systems to date are either due to early models of these batteries having an internal design fault (now rectified) or to wrong specification of the charge controller. 2. CALCULATION METHOD 2.1. Cycle life In PV systems, the average currents are relatively low compared with the battery capacity (discharges are often between the 100 and 300 h rates). The daily cycling is often very shallow. However, in order to get the required data in a reasonable time, cycle lives are usually measured at relatively high rates (10 h rate or higher current) and at high depth of discharge (DOD), often 80%. The 80% DOD in published cycle life data usually refers to a percentage of either the capacity at the standard discharge rate (often the 10 h rate), or to the actual rate at which the cycling test was carried out. In PV use, the low discharge rates mean that available capacity can be much higher than the nominal capacity, especially for tubular plate vented batteries, which have a large reserve of free acid. In order to translate manufacturers’ cycle life data into meaningful numbers for estimating PV cycle life, we make some assumptions. (1) The total number of Ah discharged over the whole cycle life is a constant, independent of the DOD (Bode, 1977). Where cycle life data at different DOD is reported, it is often claimed that the product of cycle life and DOD is higher at low DOD. By using a constant value which is taken from high DOD data (e.g. 80%), we should obtain a conservative value. (2) The total number of Ah discharged over the whole cycle life is a constant, independent of the discharge rate. As far as we know, there is no experimental evidence for this at very low discharge rates. However, it is reasonable if we assume that the cycle life is dependent on the volume (i.e. density) changes in the battery plates. Note that the second assumption is not equivalent to the statement that the same number of cycles at a certain DOD are obtained at any discharge rate. To give a concrete example, a tubular plate battery may have a nominal capacity of 500 Ah at the 10 h discharge rate, and it
may give 1000 cycles of 80% DOD at this discharge rate. At the 120 h discharge rate, the available capacity may be 725 Ah. However, the battery will not give 1000 cycles at 80% of 725 Ah per cycle. Using our assumptions, at the 120 h rate it would either give 1000 cycles at 80% of 500 Ah (which is about 55% DOD referenced to the higher 120 h capacity of 725 Ah) or it would give approximately 690 cycles at 80% DOD based on a capacity of 725 Ah. We represent these assumptions by the following equation:
N;C;D,,-X,=L,
(1)
where N, is the number of reported cycles at depth of discharge Dadrelative to the standard (nameplate) capacity rating C, (often the 10 h capacity). L, is the total number of Ah for all cycles over the whole cycle life. X, is an arbitrary correction factor used to derate the manufacturers’data (which refers to continuous and regular cycling) for PV use (where the cycling is not continuous or regular). We have used X,=0.8 in the calculations in this article. The predicted cycle life (in years) is then simply given by: Y,=L,/(365D,)
(2)
where D, is the average daily cycling Ah that the battery experiences. If the electrical load is only switched on during the night (e.g. for lighting), then D, is equal to the average load Ah in a 24 h period, since the charging occurs during the day time, and all the discharging is at night. If the load is only switched on during the day, then D, will be very small and the predicted L, will be very large. If the load is continuous, D, will be reduced from the total daily load Ah by a factor (24-HJ24, where H, is the number of hours during the day when the PV array is charging the battery (i.e. when the array current is larger than the load). An approximation for this for any day is: K = &,(AhrlAh,)
(3)
where Hdlis the number of hours of daylight, Ah, is the total daily Ah load and Ah, is the total Ah of battery charging that the PV array could give. If there is no detailed data for the day length and available charging from the PV array, then a reasonable guess for H, is between 6 and 10 h for most systems.
Limits to battery
2.2. Temperature-dependent
corrosion
Stationary batteries are often used in float service, where the voltage is held constant by a mains charger, the small float current keeping the battery completely charged for any emergency situation. Cycling is effectively zero in this application. In the limit of very shallow PV cycling, we might expect the conditions to be rather similar. The lifetime of a battery in float service is quoted by manufacturers as the expected service life at a particular float voltage and, very importantly, at a particular ambient temperature. The battery lifetime limitation in this case is corrosion of the positive grid material, which is dependent both on the applied voltage and the temperature. It is generally accepted in the battery industry that an increase in temperature of 10°C will lead to a halving of the expected life in float service. The lifetime based on this temperaturedependent corrosion process is given as: r, = JLX,IC2”((T,” - T,W)l
(4)
where x is the predicted lifetime in years, L, is the stated lifetime for float service, at the standard ambient temperature T,, and T,, is the average temperature of the battery environment. X, is another arbitrary correction factor to compensate for the fact that the battery voltage is not truly constant, and, as with the other correction factor X,, we have used a value of 0.8 in these calculations. If T’, is less than T,, a higher battery lifetime than the quoted standard lifetime L, would be predicted. To be conservative, we only use equation (4) for T,,> = T,. At lower temperatures, we assume the lifetime is the same as at x. The value of T,, depends on the type of battery installation. For unheated buildings or for battery boxes mounted in the shade of a PV array, the average temperature can normally be approximated by the average outside air temperature, provided that the battery itself generates negligible heat. At the low rates common in PV systems this is certainly justifiable for vented batteries, but for valve-regulated batteries the heat produced on overcharge can be significant if the battery enclosure cannot reject heat to the surroundings easily. If the batteries are mounted in an equipment shelter, where the electrical load itself is a heat source, then the battery temperature can be expected to be above the outside air temperature. Just how much this is
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149
depends on the shelter design and actual equipment details. In the special case of a battery mounted in the same room as a PV-powered vaccine refrigerator, the refrigerator itself will cause some heating of the room, and again the average battery temperature can be considered to be a few degrees higher than the outside air. In this article we have assumed the room to be 5°C higher than the outside air, when averaged over the whole year. This may be a little pessimistic, but should lead to conservative battery life predictions. 2.3. Overall battery life The actual lifetime predicted will be whichever of Y, or x calculated above is lower. F will be dependent on the ambient temperature, but independent of the daily depth of cycling. In contrast, Y, will be independent of temperature (within reasonable limits) and should depend only on the daily depth of cycling. For regular loads, it is more convenient to talk in terms of days of autonomy rather than daily depth of cycling, as this is less dependent on systemspecific details. The larger the number of days of autonomy, the lower the daily depth of cycling. Note that the battery manufacturers’ data for both cycle life and float life refer to an end of life when 80% of the original battery capacity remains. In actual PV service, this point may be passed without notice in systems with relatively high autonomy. The lack of capacity may only become apparent if the full autonomy reserve is called upon. Therefore, it would not be surprising to find reported cases of batteries still operating in the field after their predicted end of life. In this article we have presented the predicted battery lifetimes as a plot against ambient temperature of the battery (see Figs 1-3). The temperature-dependent corrosion limit is a curve which shows the halving of predicted life for every 10°C increase. The limits caused by cycle life are shown as a series of horizontal lines for different numbers of days of autonomy. These figures have been calculated on the basis of one annual average temperature and one typical value of daily cycling depth being sufficient to characterise the system. The figures quoted as predicted lifetimes in Tables 1 and 2 are calculated much more accurately by computer, using typical values for each month of the year, and particular site information. In general, the agreement between the two calcula-
D. J. Spiers and A. A. Rasinkoski
150 Years 14,
6
0 20
I
II
Ih
II
II
4 I
22
24
26
28
30
32
34
,
II
36
38
40
annual average temperature, deg C Fig. 1. Lifetime limits for open tubular plate batteries in PV systems with a continuous load. Corrosion limit, i); cycle life limit for autonomy periods of 3 days, +; 4 days, Q; 5 days, - + -; 6 days, - x -.
Years 16
20
22
24
26
28
30
32
34
36
38
annual average temperature, deg C Fig. 2. Lifetime limits for open tubular plate batteries in CFS49IS PV vaccine refrigerator systems. Corrosion limit, U; cycle life limit with daily icepack freezing, -&; without daily icepack freezing, Q.
40
Limits to battery
lifetime
151
Years
20
22
24
26
28
30
32
34
36
38
40
annual average temperature, deg C Fig. 3. Lifetime limits for flat plate “SolarPower” batteries in PV rural lighting systems. -C-; cycle life limit for autonomy periods of 2 days, h; 3 days, Q; 4 days, -+-; Table 1. Battery
Location Argentina Saudi Arabia Djibouti Jordan Oman Oman Venezuela Kenya Guinea Chad Vietnam
Location
telecom telecom ac system telecom telecom telecom telecom demo telecom telecom telecom
‘High altitude
1984 1984 1985 1987 1987 1987 1988 1990 1992 1993 1993
5 10 ?4 20 10 5 10 8 5 3 5
plate batteries
Battery replacement
Autonomy
_
days days days days days days days days days days days
Table 2. PV-powered
vaccine
Installed
Capacity Ah
1 1 2 1 2 2 location,
with tubular
_ 1994 _ 1’ 994 _ _ _ _ _
so ambient temperatures are relatively low. shelter, so at a higher average temperature than outside
Fridge tvve
Ghana Maldives Bolivia Tanzania Ethiopia Ethiopia
PV systems
Installed
Type
‘High altitude location, ‘Batteries in equipment
charging
so ambient
1986 1987 1989 1991 1992 1992 temperatures
refrigerators
are relatively
tion methods is within approximately 0.5 year. The spread of predicted lifetime values in the tables reflects that the calculations were done
Service life years >ll >ll 9 18 7 >8 >I >5 >3 >2 >2
1993 _ _ _ _
loads Predicted years
Notes
10-12 8 6 8-10 7-8 7-8 10-11 11 7-8 4-6 6-8
1
2 2
Predicted vears
Note
1
ambient.
with fixed battery
Battery renlacement
360 360 200 300 200 200
and regular
Corrosion limit, 5 days, - x ~
size
Service life Years I 18 16 >4 >3 >3
5-6 5 12 6-8 9-11 5-l
1 1
low.
for several different sites (with different air temperatures) and do not represent calculation uncertainties.
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3. CALCULATED COMPARISON
RESULTS
WITH FIELD
AND DATA
3.1. Systems with tubular plate batteries constant loads
and
Figure 1 shows a graph of the cycle life limits for systems with continuous constant loads and 3, 4, 5 and 6 days of autonomy, as well as the temperature-dependent corrosion limit lifetime. Cycle life predictions for autonomy periods of more than 6 days lead to predicted lifetimes that are always higher than the temperaturedependent limit. The graph was calculated for a tubular plate vented battery with a stated cycle life of 1000 cycles at 80% DOD (10 h rate) and a float service lifetime of 1.5 years at 20°C. Correction (safety) factors of 0.8 were applied to both values. It can be seen that the temperature-dependent corrosion limit determines the predicted lifetime in the following cases: (i) for 3 days autonomy and annual average ambients above 27°C; (ii) for 4 days autonomy and annual average ambients above 24°C; (iii) for 5 days autonomy and annual average ambients above 21°C; (iv) for 6 days autonomy and above, at any ambient temperature. This means that the temperature controls the battery lifetime in most professional PV systems (e.g. telecommunications systems) in most sunny parts of the world. Table 1 shows a selection of actual site details (Selhagen and Sandell, 1995; Duval and Lacroix, 1995; Fanning, 1995) which go back as far as 1984 (installation date). Also shown are the predicted battery lifetimes according to our model. In only two of these systems are there reports of actual battery changes so far for what can be described as “normal old age” of the battery. For the system in Oman, this occurred more or less at the predicted time. For the system in Djibouti, the battery was reportedly used for 9 years against a predicted lifetime of 6 years, although it is quite possible that this battery had significantly less than 80% of its capacity remaining when replaced. The system in Saudi Arabia has a battery still operating after 11 years, when the predicted lifetime is 8 years. Of the other systems, those in Argentina, Jordan and Oman would appear to be getting close to their predicted lifetime, and it would be interesting to carry out a capacity check on these batteries. Note that the combination of a hot climate and siting the batteries inside the equipment shelter for the system in Chad means that the
predicted battery lifetime is particularly reduced. It is in cases like this that a battery cooling system could pay for itself by increasing the battery lifetime. 3.2. Vaccine refrigerator
systems
PV-powered vaccine refrigerators present an interesting case, because the electrical consumption of the refrigerator is also a function of the average ambient temperature. Figure 2 shows predicted lifetimes calculated for tubular plate vented batteries (200 Ah/l0 h) with a NAPS CFS49IS vaccine refrigerator system. The same battery lifetimes and factors were used as in the previous section. The lowest curve is the lifetime resulting from temperature effects. The curve above it represents the cycle life limitation for heavy duty use (freezing 2.4 kg icepacks every day) and the segment of the upper curve represents the cycle life for light duty (no regular icepack freezing). It can be seen that, with this temperaturecombination, the particular dependent corrosion is always the life-limiting factor for the batteries. The cycle life limitation only becomes apparent at lower ambient temperatures if (a) a refrigerator with higher consumption is used, or (b) a smaller battery is used (leading to deeper daily cycling) or (c) a battery with lower cycle life (e.g. flat plate type) is used. Table 2 shows details of some vaccine refrigerator projects (Vegel, 1995; Fanning, 1995), together with the predicted lifetimes. Often these are projects involving several health centres in different locations, so again the predicted lifetime figures reflect the spread of actual location ambient temperatures. Only in Ghana have the batteries so far needed replacement, and the actual service lifetime of 7 years was a little more than the predicted lifetime of 5-6 years, based on the estimated temperature inside the battery room. Of the other systems, only that in the Maldives seems to have passed its predicted lifetime, and it would be interesting to check the condition of this battery. There are some years to go before the other systems in this table will reach their predicted battery lifetimes, and it will be interesting to check on these in future years. 3.3. Rural lighting systems for houses, usingflatplate batteries In contrast with telecommunications, vaccine refrigerator, etc. systems, where the user is usually able to afford a tubular plate battery which
Limits to battery
will give a reasonable lifetime, individual home owners who install a small PV system for lighting, etc. demand a low cost battery. In most cases the tubular plate battery is not affordable in such systems, and a flat plate battery has to be used. The most common type of flat plate lead-acid battery is the car or truck battery used for starting, lighting and ignition (SLI). Other types of flat plate batteries are produced for special uses such as on boats and caravans, for powering invalid carriages or golf carts, and for PV use. Such batteries have somewhat thicker plates and other internal differences to the normal SLI design. In the Nordic countries, a large application for PV is for lighting, etc. in summer holiday homes. Here, flat plate batteries modified for PV use (“SolarPower”) are used. The positive plates are somewhat thicker (2-2.5 mm) than in car batteries, and there are various other internal modifications. We have measured a cycle life of around 200 cycles at 80% DOD for such batteries in the laboratory. The usage pattern in such summer holiday homes is very variable, but typically the battery will receive between 10 and 20 deep (80%) discharges in a year. Using our calculation method above, the cycle life limit should then be between 8 and 16 years (allowing an 80% safety factor). Although float life data do not exist for such batteries, an informed guess would be around 5 years at 20°C based on the thickness of the positive plates and also the typical service life of a heavyduty SLI battery with the same plate thickness. The year-round average temperature in such summer cottages in Finland, Norway and Sweden is less than 10°C so the temperaturedependent corrosion process is slowed down significantly, and the lifetime limit caused by corrosion might be estimated at around 8-10 years or more. Although it is very difficult to know the exact service lifetime of the “SolarPower” batteries in such domestic systems, our best information (Pylvalainen, 1995; Vegel, 1995) is that it is somewhere between 7 and 10 years. In one particular holiday cottage system (Vegel, 1995), the two batteries are 10 years old and still have more than 75% of their initial capacity. Therefore, the above model predicts battery lifetimes for flat plate batteries in Nordic countries reasonably well. If there are more than 20 deep discharges per year, we would expect the cycle life to become more of a limitation than the positive plate corrosion. Figure 3 shows the predicted lifetime of the
lifetime
153
same SolarPower battery if it is used in a rural home lighting etc. system which is used every night. Normally, such systems are specified to have 3-5 days autonomy, and Fig. 3 shows that at ambient temperatures below about 30°C the cycle life will limit the predicted nominal service life to a little less than 2-3 years. However, that figure applies to the battery reaching 80% of its initial capacity (in practice, the battery will be used beyond this limit, if possible) and it also assumes that the full available Ah provided by the PV is used (in practice, this is not often the case). We might therefore expect a service life of 3-4 years in practice. Note that if a smaller battery is used (e.g. one giving only 2 days of autonomy), the deeper daily cycling will restrict the predicted service lifetime to around 1 year, and in practice the real service lifetime will probably be less than 2 years. If a normal car (SLI) battery is used in such rural home systems, it will have thinner plates than the SolarPower battery, which will result in a cycle life of less than 200 cycles at 80% DOD (often significantly less), and it will also probably have a predicted float life of less than 5 years at 20°C. Whilst we have not drawn a lifetime graph for such SLI batteries in rural home PV systems, we can estimate that the service lifetime will be even more dependent on the cycle life, and will be lower, probably by a factor of 2 or more, than the above figures for the thicker plate battery. A large rural home PV electrification project in any country should consider very carefully whether local unmodified SLI batteries (which will probably need replacement every 2 years or so) are the best option, or whether suitably modified batteries for PV use are more desirable (which will probably give at least double the service life of the SLI battery, but at less than double the cost). The long life and low maintenance requirements of PV rural electrification systems could be outweighed by battery replacement logistical and environmental problems if sufficient attention is not paid to the battery specification. 4. A POSSIBLE BATTERY-COOLING SYSTEM FOR LARGE INDUSTRIAL PV SYSTEMS When the cycle life of the battery is sufficiently large (e.g. for a tubular plate design) and where the autonomy provided by the battery is sufficiently large (as it is in most non-domestic PV systems), then the ultimate battery lifetime
D. J. Spiers and A. A. Rasinkoski
154
depends on the ambient temperature. For systems with autonomy of 5 days or more and a continuous load, the service lifetimes predicted by Fig. 1 for batteries in differing annual average ambient temperatures are approximately 12 years at 20°C 8.5 years at 25°C 6 years at 30°C 4.2 years at 35°C and 3 years at 40°C. If a battery is operating at over 30°C average temperature, then providing cooling to reduce this average temperature to 25°C or below would have a significant effect on the battery life. We have been developing over the past few years a small dc air conditioning unit of the compressor type. Its electrical consumption is approximately 70 W,, and its cooling effect is approximately 200 Wth. Preliminary tests and calculations indicate that a separate small PV system of around 200-250 peak Watts could provide this small air conditioner with sufficient cooling power to reduce the ambient temperature of a small, well-insulated, battery room sufficiently to prolong the life of batteries in hot climates. The additional cost of the PV-powered cooling system could be justified for larger professional PV systems of sufficient battery size and in areas of sufficiently high ambient temperature. So far, the small air conditioner has only been tested under laboratory and domestic conditions. However, we hope to test it soon in professional PV application. a suitable Unfortunately, the device is too large to be applicable to battery cooling alone in smaller PV installations such as vaccine refrigerators with PV array sizes below about 1 peak kW. 5. CONCLUSIONS A simple model is proposed to determine the ultimate service lifetime of a vented lead-acid battery in photovoltaic applications. This model requires only data that is normally readily available, i.e. the cycle life and float service life from the battery manufacturer, plus the site ambient temperature, electrical load and expected PV array output. Although it is often difficult to obtain actual battery service lifetimes from PV systems in remote areas that were installed several years ago, we have checked what field information we have against our model, and found that the results are in broad agreement.
The same general principles apply to other types of battery, for example valve-regulated lead-acid batteries, and we hope in the future to compare predicted values with actual field data for these. In PV systems which use tubular plate vented batteries, and have autonomy periods of 5 days or more, the battery lifetime is almost always controlled by its resistance to high ambient temperatures and not by the cycle life. Examples of such systems are telecommunications sites and vaccine refrigerators. In these, attention should be paid to keeping the battery ambient temperature as low as possible (without, of course, running into the risk of freezing the battery acid at low states of charge). In larger systems in hot climates, a small PV-powered air conditioner can reduce the battery working temperature sufficiently to increase the expected battery service life significantly. In small domestic PV systems which use flat plate lead-acid batteries for reasons of low cost, the battery lifetime is more likely to be controlled by the cycle life, especially in cases where the load (e.g. lighting) is used every day and the autonomy period is generally low (5 days or less). Use of standard car batteries in rural PV lighting systems may result in battery lifetimes that are probably unacceptably short because of their limited cycling capability, unless a large autonomy period (i.e. high ratio of battery capacity to daily load) is used. The use of a thicker plate battery, specially designed for use in PV applications, with a cycle life equivalent to 200 or more discharges at 80% of the nominal capacity would result in a more acceptable battery life for rural PV home systems, and should give a lower overall life cycle cost for the battery. REFERENCES Bode H. (1977) Lead-Acid Batteries, Wiley Interscience, New York, p. 333. Duval J. and Lacroix B. (1995) NAPS France, internal communication. Fanning J. (1995) NAPS Kenya, internal communication. Pylvllainen H. (1995) NAPS Finland, internal communication. Selhagen L. and Sandell P. (1995) NAPS Sweden, internal communication. Spiers D. J. and Rasinkoski A. A. (1995) Predicting the service lifetime of lead/acid batteries in photovoltaic systems. J. Power Sources, 53, 245-253. Vegel M. (1995) NAPS Norway, internal communication.