How to size a small solar-electric system by Ross Signal
CONTENTS: Introduction
1) Electrical Concepts
2) Calculating Electricity Demand
3) Sizing the Solar Panels
4) Sizing the Batteries
5) Charge Controllers, Etc. Conclusion
This article gives some simple “cocktail napkin” calculations for sizing a smallish solar-electric system. By getting a rough idea of the costs and the potential output, you can decide early on whether solar power is feasable for your specific remote-power needs.
I was introduced to solar power through helping an anthropologist friend prepare for 15 months of field-work. He needed to power equipment such as a laptop computer, lights, tape recorders and a video camera, all in a remote hamlet in the Solomon Islands. In the course of researching product literature, developing an energy budget, and testing his equipment, I came to grasp what factors most influence the sizing of the different components. As most discussions of solar energy are focused on house-size systems, I hope that this step-by-step account may be useful for other people who are basically interested in a small or a transportable system.
For further information, representative equipment and prices, I recommend the SUNELCO catalog. The cover price is $5.00. (P.O. Box 1499, Hamilton MT 59840-1449, Phone: 800-338-6844)
I assume that if you are reading this, you must have a hunch that there is enough sun at your planned location to make solar energy practical. (In general you must get decent sun at least once a week; battery storage over longer periods becomes unwieldy.) What we will try to do here is calculate the panel and battery sizes needed for your intended use, and from that some round numbers for prices.
If you’re wondering, a tiny 5-watt system (just enough to run a light for a couple hours a night) starts at about $100; prices go up from there.
1) Electrical Concepts
The calculations involved in sizing a solar-energy system are not too forbidding; they do not involve anything more than a little addition and multiplication. However before you begin, you do need to become familiar with the units used in electricity and to get a bit of an intuitive feel for the quantities represented by these units.
The units relevant to this discussion are VOLTS, amperes or AMPS, WATTS, AMP-HOURS and WATT-HOURS.
Briefly, electric power involves harnessing the stong desire of electrons to move along a wire, in response to the electric field created by a battery, etc. VOLTS reflect the force or strain with which each single electron pushes; AMPS reflect the numbers of electrons per second which flow past some point in a wire. WATTS express the rate of useful work these busy electrons actually accomplish by pushing through some load circuit.
The watt is the unit which relates most directly to our own experience: e.g. how bright a light shines or how strong a motor is. In fact it is simply the metric equivalent to the English unit Horsepower (though it might sound a bit goofy to rate lightbulbs by horsepower).
As you might imagine, to achieve a useful wattage X, you could either harness a small number of electrons each pushing very strongly, or else a huge number of electrons each pushing somewhat weakly. This is the insight behind the useful formula:
VOLTS X AMPS = WATTS
For exmple a 60-watt spotlight in your kitchen, which is connected to 120-volt house wiring, would draw a current of 0.5 amps. But consider a 60-watt car headlight: even though it has the same wattage as the household lamp (and is the same brightness), it is powered by the lower voltage of a 12-volt car battery. So to achieve the same wattage the current which flows must be 10 time greater, or 5.0 amps.
Amps and watts are rates, i.e. they involve TIME–e.g. how many electrons flow or how much work is done per second. When you want to talk about TOTAL power consumed, it’s useful to use the unit watt-hours, which is simply the product of watts times hours. (For example, [kilo]watt-hours are the units measured on your electric bill.) When we start to look at batteries, it’s typical to talk about their capacity in amp-hours. We’ll go into that one a little later, but again, this is just amps X hours.
There are many good general discussions of electricity available, so I won’t go into any more detail here.
2) Calculating Electricity Demand
To size a solar-powered system you need to begin by quantifying the demand for electricity .
As a starting point, write down every piece of electrical equipment which you hope to use. By looking at the owners manual, specification sheet, or manufacturer’s nameplate, try to find the voltage and the wattage or amp rating for each device. Once you know the voltage, amps can be converted to watts and vice-versa using the formula above.
If this information is not available, you may need to MEASURE the amps of current drawn by a device. A multimeter able to read currents up to 5 or 10 amps can be purchased for $40 or so, or borrowed for the purpose. (Making this measurement requires temporarily rewiring things so that power also flows through the meter; this can involve some messy cabling gymnastics I won’t try to go into here.)
Remember, running heaters, cooking, or powering beefy motors are NOT attractive applications for solar electricity–the size of the system would need to be impractically large. If you plan to provide any general lighting using your setup, light fixtures using compact fluorescent lamps are the only ones worth considering (sometimes referred to as “PL” lamps –“U” shaped tubes 3 or 4 inches long). Their efficiency is substantially higher than any other type, and the color of the light is quite decent.
At this point you should have written down the voltage of every device, and have arrived at a wattage figure for each. Next, make a guess at how many hours you will use each device in a week; think about both typical and “worst case” weeks. Multiply the hours for each item by its wattage to get an estimate of the watt-hours used per week.
This number is your index of how big a dent each item will put in your energy budget. You will now begin to get a feeling for which items are the real energy hogs: It’s not at all uncommon for one or two items to completely dwarf the energy consumption of all the others. This new perspective may even make you re-evaluate what you want to attempt.
Examples ***********
Compact fluorescent light: 12 volts X 0.65 amps = 7.8 watts X 18 hours/week = 140 watt-hours/week
VHF radio: Transmitting: 12 volts X 4.5 amps = 54 watts X 1.5 hrs/week = 81 watt-hrs/week Receiving: 12 volts X 1.2 amps = 14.4 watts X 2.5 hrs/week = 36 watt-hrs/week
(And so on for the rest of the equipment. . . )
This is also the time to think about the voltages of the devices you plan to use. The main thing to consider is that you will save yourself from some serious headaches if you are able to standardize everything at one voltage–most commonly 12 volts.
When you use household power, there is no difficulty having a 6-volt radio here and a 9-volt phone answering machine there, since inexpensive and efficient AC adapters are available to make the required voltage conversion. THERE IS NO EQUIVALENT WAY OF DOING THIS WITH DC BATTERY POWER! If you have a 12-volt battery system and need to run a 6-volt device from it, all the ways of doing this are more or less ugly, inefficient, or expensive.
It’s also preferable to avoid running devices from their own internal rechargable batteries. Recharging any battery is an electrochemical reaction which can waste more than 1/3 of the power applied. So you don’t want to recharge little batteries from bigger ones: You then go through that wasteful process twice.
Likewise, it is possible to run 120-volt AC (house current) devices from battery power, using a device called an INVERTER. But once again this is a fairly clumsy and expensive option; and not all equipment runs well on the “dirty” AC power an inverter provides.
Any of these conversions wastes power, and means that your solar equipment will have to be that much larger, costlier and heavier to lug around–you want to avoid all these inefficiencies if possible. But at a minimum, you want to be sure that at least the biggest energy-users on your list are run directly from the main batteries.
If some indispensable, energy-hogging device requires 6, 24, or 48 volts you CAN create a whole solar system which runs at this voltage–but the widest choice of lamps, radios, and other general equipment is available for 12 volts. If you are still in the shopping stage, this is a very good reason to seek out 12-volt versions of all the equipment you require. I’ll assume a 12-volt system for the rest of this discussion.
If you MUST use a device which will not run directly from a 12-volt battery, take the watt-hours per week you calculated for it above and DOUBLE that number to allow for conversion inefficiencies.
3) Sizing the Solar Panels
Add up the watt-hours for each piece of equipment to arrive at your TOTAL DEMAND for a typical week. Now that you have a ballpark number for this, you can begin to think about the size of the solar panels and batteries.
The panels themselves are the most expensive component of the system, several times the cost of batteries, so let’s start with them. If the number of panels required looks excessive, you can go back to the demand side and think about what to cut.
Start by making an estimate of how many hours of sun will be available per week at your location. This is an area which is fraught with uncertainty and wishful thinking, but do your best.
If there are seasonal variations, consider the worst-case scenario. Keep in mind that you get very little power when the sun is low in the sky; count only hours when the sun is well above the horizon. At many locations there are tall obstructions which can cut into the hours of sunlight which fall on any particular spot. Unfortunately sunlight “filtered” through branches and leaves is also useless–any patch of shade on a panel tends to block the flow of current. A trickle of power can sometimes be produced in cloudy weather; but ignore that for now and estimate only how many sunny hours you expect in a typical week.
One way or another come up with your WEEKLY SUN HOURS guesstimate. Take your demand figure from above (the watt-hours per week) and divide it by the sun hours. This gives you the average OUTPUT WATTS that your system would need to produce every hour the sun is shining.
The size of solar panels is often given in watts, which sounds quite convenient since we just came up with a number for the wattage we need. But unfortunately the RATED watts of a solar panel are under IDEAL conditions only; furthermore they does not take into account the power wasted in the battery-recharging process.
Here is a list of some factors which reduce the power to less than the “ideal” wattage: Partial clouds; panels pointed more than 30 degrees away from sun; dirt; weak, low-angle sunlight; high panel temperatures; shading from branches or leaves; aging of panels; manufacturing variations; voltage drop from long wiring runs; etc., etc.
ITo compensate for all these “real-world” factors, as well as the inefficencies of battery recharging, one rule of thumb is to buy enough panels to give you a rated wattage TWICE the output wattage you calculated. Of course you are free to be even more conservative, especially if you know for certain that one of the factors above will be a serious problem at your location.
Panels are available in sizes ranging from under 5 to more than 80 watts; for even higher wattages you generally buy a set of several panels of matching size. Some typical prices from the 1995 Sunelco catalog are $6.50-$10.50 per rated watt for rigid panels, and $11.00-$14.50 per rated watt for flexible roll-up panels. (Larger wattage panels have lower costs per watt.)
Panel SIZE can be a consideration too: Estimate about 1 sq. foot for every 10 rated watts for the rigid panels; or about 2.5 sq. feet per 10 watts for the flexible ones. Note that all the larger-wattage panels use a GLASS cover, which may not be acceptable for more rugged uses. The limit for plastic-laminated panels is about 30 watts (though several of these can be connected together in parallel).
Do you end up with numbers which are totally unacceptable? If so, it may be time to skip back up to the demand figures and re-evaluate your priorities.
Example ************
360 watt-hours/week demand; divided by 24 sun hours/week = 15 output watts required. Min. panel size 30 watts (rated power); price about $260, size about 3 square feet.
4) Sizing the Batteries
Solar panels themselves are basically simple and trouble-free. The real headaches in a solar electric system involve BATTERIES.
Nickel Cadmium (NiCad) cells are the most familiar type of rechargable battery in smaller sizes; but when larger and larger capacities are needed, the price of these quickly becomes exorbitant. Until there is some major new breakthrough, we are stuck with the truly archaic technology of LEAD-ACID batteries. Sad to say, these puppies are heavy and generally cranky to deal with. Your solar panels and charge controller exist to try to keep these high-strung electrochemical devices in a good mood over the longest possible service life.
One variant of the lead-acid battery is the “gel-cell,” in which the acid electrolyte is immobilized as a jelly. This type is much easier to cope with than the wet-cell type (no topping-off of water is required, etc.) but they are more expensive and are not available in the largest capacities. However this type is the only practical option for air transport or more rugged uses.
The battery capacity you choose is limited by two things: the longest sunless period you must endure; and the maximum acceptable battery weight. As you might expect there can be a trade-off between the two.
Battery capacity is measured in the somewhat odd-looking unit of AMP-HOURS or “Ah”. Why not watt-hours, the “correct” unit for total energy stored? Well, once you have set up a system where everything runs on 12 volts (or whatever) you tend to stop thinking about voltage (since it’s always about the same). To calculate how much juice each device uses, it’s most convenient to work directly in amps (for one thing, that’s what your multimeter shows). So say you have a lightbulb that draws one amp: How soon will it run down the battery? It’s easiest to answer questions like that if batteries are rated in terms of “amp-hours”: e.g., a 30 amp-hour battery is one that will run your one-amp light for 30 hours.
The only thing confusing about this is that a 30 Ah, 12v battery is NOT the same as a 30 Ah, 6v battery. The 12v battery is twice as large and heavy, and stores twice as many watt-hours of total power. Use amp-hour ratings only to compare batteries OF THE SAME VOLTAGE.
If you really only get sun one day out of every seven, you are going to have a problem. First, you will need a zillion solar panels, so that on the one day the sun shines you can make up for the whole week’s energy use. You will also need a ton of battery storage to keep you going for the 6 other cloudy days.
Worse still, Lead-acid batteries really don’t like total discharges, and will fail quite early if you regularly run them down all the way. The battery should really be sized so that it rarely goes below about 2/3rds full. (Yes, this is the OPPOSITE of what you may be used to from your NiCad AA cells.)
You might be feeling smug now if you expect to get sun every single day–after all, you will only need storage capacity to carry you through a few hours of each evening. But while you are in much better shape in this case, you still can’t make your battery TOO small. The reason is that when a battery is undersized, it cannot absorb all the charging current the panels put out–it just gets hot (which shows energy is being wasted) and the stress on the plates can also lead to early failure.
Take the rated wattage of panels you calculated above and divide it by the system voltage (ordinarily 12 volts) to get the PEAK PANEL AMPS. Probably the MINIMUM acceptable battery size (in amp-hours) would then be your panels’ peak amp output times 10. A preferable capacity (for best efficiency and battery lifespan) would be the panel amps times 15 or 20.
Cold temperatures seriously reduce the capacity of lead-acid batteries; if you expect cold weather, err on the side of a larger battery.
If you need enormous cloudy-day storage capacity, you might go even bigger. Take your estimate of the total watt-hours of demand per week, and divide by the system voltage (ordinarily 12 volts) to get amp-hours per week. The MAXIMUM useful battery size would be roughly 4 times this figure.
But any more than this is pointless, especially after weight and cost are considered. To stay healthy, a battery needs to be brought back to 100% charge from time to time. If the battery is too oversized relative to the panels, it can take forever to get there. Older batteries tend to self-discharge to some extent, and for really large ones this can amount to a significant “phantom” drain. The combination can mean the battery never quite gets charged all up the way, which again leads to a shorter lifespan.
For 12-volt gel-cell batteries, you can figure prices (very roughly) at about $2.50 an amp-hour. Perhaps more importantly, figure a WEIGHT of about 3/4 lbs. per amp-hour too–thus shipping can add significantly to the final cost.
For some remote uses, the weight of the battery can be the limiting factor that determines how large a system is possible. For example, if one person must carry the battery on foot, you are limited to about 60 lbs. This implies a battery of no more than 80 amp-hours, and thus a panel array rated at about 50 watts–100 watts at the most. Depending on the number of sun hours per week, this might prove to be a significant constraint. (Of course you may be able to pack in several batteries, one by one, and then connect them in parallel.)
Example: **********
Panel rated at 30 watts; divided by 12 volts = 2.5 peak amps Minimum battery size: 2.5 X 10 = 25 amp-hours. (Roughly $63.00 and 19 lbs.) Preferred battery size: 2.5 X 20 = 50 amp-hours. (Roughly $125.00 and 38 lbs.)
Maximum battery size: 360 watt-hrs weekly demand; divided by 12 volts = 30 amp-hours; 30 X 4 = 120 amp-hours. (Roughly $300 and 90 lbs.)
5) Charge Controllers, Etc.
The last element of the system is a charge controller; this can include various readouts which help you monitor loads and the condition of the system. Inexpensive controllers start at about $60, while a heftier unit with an LED charge meter might be $150. In any case the primary function of this device is to cut off the flow of charging current once the battery is full. When batteries reach 100% charge, they cannot absorb any more energy; forcing further current through them simply begins to cook the battery. It doesn’t take very much of this before the electrolyte starts to fizz away or there is permanent damage to the plates. Charge controllers also “taper off” the charging current somewhat as the battery approaches full charge. (For very small panels the charge controller is sometimes omitted.)
You will also need some kind of panel mounting supports suitable for your site’s winds, mounting location, available materials, etc. The costs of cabling and connectors can also be significant. It sounds paradoxical, but a 12-volt system requires fatter copper conductors than 120-volt household wiring. (This has to do with the greater amps needed to provide equivalent watts, as discussed in the electricity section above.) Unfortunately, the longer the wiring runs required, the MORE important it become to use very heavy-gauge cabling, or else the power lost to cable resistance becomes excessive. To avoid spending a hundred dollars on an armload of copper, it’s simplest to locate your battery and loads as close to the panels as possible.
Example **********
Typical system costs to provide 360 watt-hours per week: 30 watt panel, $260 50 amp-hour battery, $125 Basic charge controller, $60 Misc. mounting hardware and cables, $40
TOTAL: $485 (excludes shipping charges)
Conclusion
This should not be taken as a complete design manual for a solar electric system, as there are many details and possible complications which are not covered here. But I hope this has given you enough information to either rule out solar electricity for your puposes, or else to suggest a ballpark price for what you have in mind.
For my anthropologist friend, solar replaced trudging up mountain trails with drums of kerosene and cartons of disposable batteries–for him, the costs were completely justified. For a few hundred dollars, it’s possible to take a reliable power source just about anywhere; I hope this article has encouraged you to consider it.
