Solar energy is something that can be used worldwide to generate inexpensive electricity, and is viable for everyone to consider from a generous to small budget. What is particularly important is to plan your system properly. With all the diy information now available, you should be able to plan the right system for you at the right budget.
If you have available funds but limited time, you can hire someone to design your plan for you. But choose carefully and research prudently, so that you can decide the best people to design your system as well as the right company to buy from and to handle the installation. The more you know the better you will be able to operate the system & maintain it. If your situation is one of more time and a smaller budget, you can still do a good job on a diy project. And with the time to research and learn, you will be better equipped than some to manage as well as maintain the system better after installation, which will save you even more money in the long run.
How Solar Energy is converted to Electricity
Solar panels are comprised of a set number of photovoltaic cells each joined together in order to increase the voltage & current of the solar panel when exposed to sunlight. Each of these cells is made up of silicon semiconductor materials. When the sun’s rays hit the semi-conductor, some of the energy is absorbed by the cell in the form of electron excitement in semiconductor atoms (eg. silicon). When this energy is sufficient (ie. visible light radiation), the electron is freed from its normal attachment to its original atom, and is free to move. A large number of these interactions creates excess charge on the solar cell and an electric current and voltage results. The effect of the solar panel itself is then just the combined effect of all the solar cell currents & voltages.
Factors affecting Available Solar Energy
The factors that affect the amount of solar energy available from the Sun are listed as follows;
The distance of the earth from the Sun. This is a factor because the earth’s orbit although being nearly circular, it is slightly eliptical. The amount of solar power available at any distnace from the Sun varies according to distance as follows: P œ 1/r^2 (where œ = proprtional to, ie. solar power (P) decreases with the square of the distance(r)). Solar power usually denotes electrical power produced by a solar system, but here it is synonymus with solar energy, & simply means solar energy per unit time (ie. P = E/t)
Reduction in power of solar radiation due to atmospheric absorption, scattering & reflection.
Change in the spectral content of the solar radiation due to greater absorption & scattering at some wavelengths.
Diffuse or indirect component into solar radiation.
Local variations in the atmosphere, including water vapour, clouds & pollution.
The angle of incidence of sunlight, which is affected by time of day, season & latitude. The angle of incidence is very important because it determines the effective thickness of atmosphere that the sunlight must travel through.
Distance
The distance of the earth from the Sun implies the solar power available at the earth’s outer atmosphere to be 1366 – 1412 w/m² corresponding with the maximum earth-sun distance to minimum earth-sun distance respectively. The thickness of atmosphere significantly reduces the amount of sunlight reaching the surface. As illustrated by the source, the component of incident sunlight reaching the surface directly (ie. without interference) = 70%, where a further 7% reaches the surface indirectly (ie. diffuse & scattered light). This implies that for an angle of incidence of 90 degrees to the surface. The solar power reaching the surface as direct sunlight & indirect forms to be as follows, assuming a clear day without significant other factors interfering (eg. water vapour etc.);
direct incident sunlight Pd = 0.7* (1366 _ 1412) = 952 _ 988 W/m²
indrect sunlight Pi = 0.07*(1366 _ 1412) = 95 _ 99 W/m²
Total sunlight Pt = 0.77*(1366 _ 1412) = 1052 _ 1087 W/m²
However the assumption that the angle of incidence is 90 degrees to the surface rarely occurs.
The Angle of Incidence
The angle of incidence, where less then 90 degrees (ie. not normal), has the effect of increasing the effective thickness of atmosphere that the direct sunlight must travel through. The amounts of absorbed, scattered & indirect sunlight increases proportionally to the atmosphere traversed by the light. The effective atmosphere thickness traversed by sunlight can be expressed by;
Ti = Tn / sin i
where Ti = thickness of atmosphere traversed @ angle of incidence i, &Tn = atmospheric depth (normal to surface).
The diect (Pd) and indirect solar power(Pi) reaching the surface at an angle of incidence(i) of sunlight is then;
Pd = 0.7 * sin i * (1366 _ 1412) = (952 _ 988) * sin i (nb. 1366 _ 1412 = Poa = outer atmosphere power range)
where the 1366 = winter solstice & 1412 = summer solstice in the southern hemisphere (reverse for northern)
Pi = 7/30 * (Poa-Pd) : NB an approximation for indirect since the 7/30 factor may vary with atmospheric thickness.
Pt = Pd + Pi
The angle of incidence varies according to latitude, the latitude of the sun perpendicular with respect to the season (ie. 23.5“ North to 23.5“ South) & the time of the day. Now for the case of solar noon, the angle of incidence is simply the latitude of the sun perpendicular according to the seasons (ie. 23.5 degrees south to 23.5 degrees north) subtracted from (90-latitude {degrees south} of the location concerned).
Solar Noon Diurnal Maximum
Therefore just considering latitude & seasonal effects on the angle of incidence, by keeping the time of day @ solar noon: The seasonal effect, which is the latittude of the Sun’s normal radiation(Is), in terms of the Julian day (J, ie. numbered day of year 1-365) in the southern hemisphere as follows;
is = 90 - 23.5 * sin((J-80)/91.3) nb. in the northern hemisphere +23.5“ instead of -23.5“
The lattitude effect on the angle of incidence is simply;
iL = 90 – L ; where L = “ lattitude south
The combined effect of season & lattitude is then;
i = is - L = 90 – 23.5 * sin((J-80)/91.3) – L
The above equation for i applied into the solar power equations (of the previous section) then allows the available solar noon power maximum to be calculated for every day troughout the year.
Example
For Adelaide (35“ south) at solar noon on a clear day, solar power could be estimated for the following times of the year below;
Seasonal Variation
Autumn or Spring Equinox i = 90-35 = 55° Pd = (988+952)/2 * sin 55 = 970 * 0.819 = 794 W/m²
Julian day = 80 / 242 Pi = (Poa-Pd)*7/30 = (1366-794) * 7/30 = 572*0.233 = 133 W/m²
Pt = 794 + 133 = 927 W/m²
Summer Solstace i = 55 + 23.5 = 78.5° Pd = 988 * sin 78.5 = 966 * 0.980 = 968 W/m²
Julian day = 344 Pi = (1412-988) * 7/30 = 422 * 0.233 = 98 W/m²
Pt = 968 + 98 = 1066 W/m²
Winter Solstice i = 55 – 23.5 = 21.5° Pd = 952 * sin 21.5 = 952 * 0.366 = 348 W/m²
Julian day = 164 Pi = (1366-348) * 7/30 = 1018 * 0.233) = 238 W/m²
Pt = 348 + 238 = 586 W/m²
Day of Year
Now solar power @ solar noon is about the maximum recorded for any day & varies according to time of season (23.5“ north to 23.5“ south). Using the Julian day in the angle of incidence enables the solar noon power to be calculated for any day throughout the year.
solar noon power maximum
Pd = 0.7 * sin i * (1366 _ 1412) = (952 _ 988) * sin i where i = 90 – Is - L = 90 – 23.5 * sin((J-80)/91.3) – L
where angle of Incidence seasonal affect Is = 23.5*sin[(J-80)/91.3] & L= ° lattitude south
Pi = 7/30 * (Poa-Pd)
Pt = Pd + Pi
Time of Day
A similar set of equations then apply to the solar power at the surface for the time of day.
However the time of day is more complex. This is because the diurnal curve of solar power or solar angle with time is only symmetrical at the solstices. At the equinoxes, this curve displays the maximum assymmetry. This is due to the earth’s axial tilt of 23.5°. It implies that the spring equinox has an early dawn & early dusk, with warmer mornings & cooler solar energy afternoons, as the autumn equinox has late dawns & late dusks with cooler mornings & warmer afternoons. All other times during the year are inbetween the solstice symetrical & equinox assymetrical case..
The simplest case is that of the equinoxes at the equator, where the sun starts & finishes at 0“ lattitude, so that the angle of incidence (it, time of day effect), can be expressed solely as a function of time of the day as follows;
itw = (h-6)/6*90 where h=hour of the day & (h-6) hours past solar 6am
This also defines the east – west component of the angle of incidence, which is constant throughout the year.
The north-south component of the angle of incidence varies according to time of the day & seasonally (ie. Julian day). This component can be expressed as follows;
itn = 23.5*cos{90*[(J-80)/91.3 + (h-6)/6] + L
The relative diurnal solar power curve through any day through the year can then be expressed as;
sin(itw) * sin(itn)
and the angle of incidence it = asin(sin(itw)*sin(itn)
This angle can then be used with previous equations to compute actual solar power values throughout the day, using the Poa value corresponding to season (1366 sh winter solstace _ 1412 sh summer solstace). The Julian day can be used to interpolate between the two values & then compute Pd & Pi = solar power at the surface.
A simplified approximation of how the time of day affects solar power for direct sunlight is the equinox @ the equator case as a % of the solar noon maximum;
Ph = Pd*sin(90*h/6) where 0 < h < 12 (ie. solar noon h=6)
then sin 60 = sin(90*4/6) = sin(90*8/6) = 0.866 (ie, 87% of solar maximum @ 10am & 2pm)
sin 45 = sin(90*3/6) = sin(90*9/6) = 0.707 (ie. 71% solar maximum @ 9am & 3pm)
sin 30 = sin(90*2/6)=sin(90*10/6) = 0.5 (ie. 50% solar maximimum @ 8am & 4pm)
Note:
Solar noon, & other times listed will likely vary slightly from your time zone times according to the longitude upon which your time zone is placed compared with your locations longitude.
Equaions refer to net power available from the Sun, which approximate power available to a 2D tracking solar panel device. Otherwise, where the solar panel is fixed or a one demensional tracker, the angle of the solar panel becomes less than perpendicular to sunlight, & decreases the available solar power accordingly. Of course solar panels are not 100% efficient either, so a percentage according to the rating of the solar panel or solar cells would approximate the proportion of available power effectively producing electricity in the system.
Once the system is working, measurements from the panel can be used to determine (a) power being received from the Sun at any one time, or (b) cumulative power over a day, week, month, season, year etc.. Measured values can be compared with those from these equations. Note also variation can occur on a clear day due to other factors (eg. humidity & pollution).
Application
Simple equations such as these can be used to create a spreadsheet of potential solar power at your latitude, & indicate seasonal effects easily to the level of daily solar noon maximum solar power. This is useful in the initial feasibility plans for a solar system, in that it indicates the solar power available throughout the year to consider in design, (eg. the number & type of solar panel & batteries etc. needed for your electrical requirements of voltage & amperage). The usefulness of such data includes estimation of the number of consecuitve clear days to recharge a battery (or set of them). Also whether clear days are sufficient to power your needs at various times of the year using different systems. Other references that are useful include:
Solar power average maps for your area, which also take into account average sunlight hours
Diurnal solar power curves for various times of the year @ your latitude.
Where solar is shown to be more marginal, wind power may be a more satisfactory solution, or a solar system assisted by a wind turbine. Information is very important in deciding on how to go about a solar electrcity project at your budget, but everything you’ll need to know can be found on the internet if you’re persistent.
Solar water & air heaters are other aspects affected by the angle of incidence of the Sun & cloud cover, but these are less sensitive generally than solar electrcity to these issues. Solar requirements though for water or air heating should still be investigated before venturing into a project. Solar is a better way of heating due to the higher efficiency of solar heating (90 & 70 % respectively for water & air) than electricity (30%). It is therefore worthwhile having a solar water heater at least in addition to any solar electrcity system, due to its high efficiency & because it significantly reduces the potential load on the system. Solar water & air heaters are fairly cheap projects compared to solar electricity, & will repay the investment over a few years. Even so, the initial investment is still significant for contractor installation (ie. several 00), so that when time is available, the diy solar water heater & diy solar air heater options can be just as good at a fraction of the cost, while providing design options to best suit the situation & the knowledge to enable system monitoring & maitenance.
Solar energy is free energy & we should all use it as much as we can, so all the best in your quest to harness this free for all energy.