How to Size Solar Panels for Tiny Houses
aWhile anyone can draw solar power from an array, knowing how to size solar panels ensures that any house gets the solar power it needs without having too small and too few solar panels; knowing how to size also helps avoid “over-sizing”(as in having extra panels) as solar panels are expensive. Because tiny houses have a lower power consumption, its solar panel array(s) should be sized smaller(and cheaper) than most standard home solar arrays.
First, some ways to do solar array sizing con be done via online data and tools. Being able to use online solar insolation data and tools will at least provide a useful approximation(s) without resorting to any expensive methodologies. Afterwards, some factors that will need to be addressed in real-word applications will be covered to help improve upon the the calculations performed via data and tools from earlier.
I.Before Learning How to Size Solar Panels….
Here are some basic concepts to know about before doing actual solar panel sizing.
A.First, What is Solar Irradiance?
First to consider is the amount of solar irradiance. Solar irradiance(a.k.a. insolation) is power per unit area on the earth’s surface per unit time via solar energy; the common unit for daily insolation is kWh/m2/day. Daily insolation values are measured while taking into account the fact that the amount of solar irradiance(kWh/m2) at any time of the day varies depending on the day cycle(i.e. the insolation is stronger in the noon than near dawn and dusk).
B.Different Types of Insolation Data
When attempting to size solar panels for daily power needs, it’s important to know how much solar isolation is available daily and locally. Insolation data can be calculated by an individual(s), but would require expert knowledge and specialized equipment out of reach of many. Instead, there is publicly available insolation data collected by meteorologists and various organizations who use satellites. We will use publicly available insolation maps(available online) which show the local daily insolation over an area in grey/color-scale; there are also online tool which help similarly as well.
Before going into any maps, here are the basic components to total irradiation that needs to be known first as shown in this image below-left(this will make it easier to understand the insolation data types used in maps when I explain them):
Albeit self-explanatory, there are three main components to total radiation. There is the direct radiation which hits the surface at a perpendicular/normal angle; this is where most of the irradiance for the solar panel surface is. Then there is diffuse radiation, this is radiation that doesn’t hit the panel surface indirectly. Instead, it diffuses and scatters through the atmosphere’s particles until it hits the panel’s surface. Lastly, there is radiation that is reflected from a surface onto the panel; this surface can be from nearby land-formation.
Now that I have explained the total irradiance components, here are the 3 main types of insolation data that are commonly represented via insolation maps:
i.) DNI(Direct Normal Irradiance): This is the irradiation on a surface that is assumed to always be normal(or perpendicular) to coming solar rays at all times. A solar panel(s) being normal/perpendicular at all times is only possible if there are solar trackers that keep the panels facing perpendicularly to the sun’s rays at nearly all times; if solar trackers are indeed mounted, the solar panel array should theoretically get maximum power at all times. Know that this data set only takes into account direct radiation, not diffuse or reflected radiation; thus this data in complete to for sizing a panel array with solar trackers.
ii.) GHI(Global Horizonatal Irradiance): This is the total irradiation(or solar radiation) a horizontal surface receives(includes rays that hit the directly and perpendicularly) with respect to the horizontal panel surface. This includes rays that don’t hit the surface directly hit, but via scattering through the atmospheric particles. Additionally, there is some reflected irradiation but not much as the surface is flat on the ground. GHI data is mostly undesirable because solar panel will only get the most sun hours if it is tilted or mounted on solar trackers.
iii.) GTI(Global Tilted Irradiance): This is the total irradiance over a surface on the assumption that the solar panel surfaces are tilted to face the sun in degrees matching the Earth’s latitude at the location. Like GHI, GTI includes solar rays hitting both the surface perpendicularly and through diffusion through the atmosphere. Also, a tilted surface tends to absorb more reflected radiation than a flat horizontal surface. For solar panel installation, a titled setting is the best when there are no trackers to use. More on the science of tilting will be covered later in this post.
Although I covered three types of insolation data, I will focus mainly on GTI for panels that are(and should be) manually tilted or DNI for panels with solar trackers when we finally get to the examples. Now to cover the importance of tilting of solar panel and thus its importance in GTI and DNI data.
C.How Tilting Affects Daily Solar Insolation Absorption
Earlier, it was mentioned that the angle of a solar array’s tilt at each location/point is with respect to the location’s/point’s latitude. The latitude at the equator is 0o. At this point the panel is almost parallel to the ground. As the panel moves up the latitudes along with the curvature of the earth’s surface, less of the panel faces the sun which is why the panels have to be tilted to face the sun. The fact that needs to be done is proven via utilizing basic geometry on the Earth. The image below demonstrates that very well:
In the above diagram, because the earth is REALLY tiny compared to the sun and its surface, the solar rays are virtually parallel to each other with respect to the Earth’s curved surface. Theoretically, at 40.30 latitude, the solar panel(s) should be placed 40.30 with respect to the horizon to get maximum solar power year round. In the Northern hemisphere, the panel(s) have to face true South(not magnetic south) to gain maximum power whilst in the Southern hemisphere, the panels(s) would have to face true North. Another thing to consider is because there is a slight tilt on the Earth’s axis, the 40.30 panel tilt may not suffice year round. During the Northern hemisphere’s summer, the sun is a little higher in the sky and while in winter, the sun is a little lower; the reverse is true for the Southern hemisphere due to the seasons’ times being reverse of the north’s.
If one want’s to see an in-depth comparison of variable(this means solar trackers) and fixed tilting along with how to find suitable angles for tilting a solar array to during summer and winter, check out this great link on finding the optimum tilt of solar panels.
D.What are Peak Hours?
Peak hours are essential to knowing how to calculate daily obtained solar power with respect to solar array sizing if mounted trackers are not used to follow sunlight. Over the day, the solar power is at minimum near the dawn and dusk hours and solar power is maximum at hours around noon at nearly every location. The daily insolation is distributed over a bell curve with a maximum of 1 kW/m2 as shown in the diagram below:
From the above diagram, the reason that 1 kW/m2 was used is because most solar panels are rated using a solar insolation input of 1 kWh/m2. In fact, the most common rating, called STC(Standard Testing Conditions), requires that the panels are rated while under 1 kW/m2 of artificial light; more on STC will be covered late in this post.
If the area underneath the bell-curve from the left is converted to the rectangular block to the right, the number of peak hours can be determined from the block width on the time axis. If 7 kWh/m2 was measured over a surface and over solar panels rated for 1 kW/m2 solar insolation input: (7 kWh/m2 )/(1 kW/m2 ) = 7 hours or 7 peak sun hours. So, basically, the location has 7 peak sun hours.
II.How to Size Solar Panels Examples
Now to go on to the examples that will show how peak hours are used in solar panel sizing. There are 3 examples each based on using a different online tool to approximate the daily sun hours:
- 1st Example covers sizing using only an isolation map(which uses color to determine how much insolation an area has avg. over the year). This only accounts for solar panels tilted at latitude.
- 2nd Example uses a virtual isolation map that covers the local insolation values of America, Europe, and other parts of the world. With the virtual database, one can utilize various toggles to view a location’s insolation based on DNI, GHI, and Tilt to Latitude. Additionally, if one clicks on a location, one can view the average insolation for each month of the year(which is important as you’ll later understand).
- 3rd Example uses a tool similar to the one in the 2nd example. This tool uses a database to create and show an insolation map using radio buttons based on data type(avg., min. , or max insolation), month of insolation, and instrument orientation(i.e. tilt at latitude or solar trackers). This example mainly illustrates a way to size a solar array that uses solar trackers.
A.Example #1 : Sizing a Solar Array with an Insolation Map
Here is a relatively recent GTI color scale map from the NREL (National Renewable Energy Laboratory). Although this map was printed in 2008, it is recent enough to use for a rough solar array estimation.
The above GTI map shows the average daily solar insolation(kWh/m2/day) over the “surface”. Each point in the above color-coded area represents a point where the surface is tilted towards the south. The angle of the tilt at each point is with respect to the latitude at the location. The solar panels are tilted to the south at each location’s respective latitude angle because more solar energy can be captured better than with panels parallel to earth.
Here are the conditions for this example:
- The calculated daily power capacity need is about 225 Amp-hr(which isn’t uncommon).
- The used solar panel array is 17.5 volts and initially consists of five 150 Watt panels to charge a 12 volt battery bank; this array can and will be expanded as needed.
- The location where the array is to be placed is around Richmond, VA and the array is properly tilted to get maximum power.
Looking at the GTI map and “eye-balling” the color of the area around Richmond,VA to the color scale below, the area is colored in the insolation range of 4.93 -5.06 kW-hr/m2(or W-hr/m2 ); we’ll go with 5.00 kW-hr/m2(or 5000 W-hr/m2 ) as middle value.
Note: I “eye-balled” the color by using a much bigger version of the U.S. Insolation Map for Flat Plates Tilted at Latitude than the one posted above. If one wants to use a different insolation map, it can be found on the NREL website’s map search as this site is where this map originated from.
First divide 5000 W-hr/m2 by 1000 W/m2 (as most panels are rated at STC) to get peak hours.
The calculated peak hours is 5 peak hours; note that there are some DNI and GTI maps that will show peak hours instead of W-hr/m2 or kW-hr/m2 .
The solar array are initially made up of five 150 watt panel which total to a 750 Watt array.
5 hr * 750 Watt = 3750 Watt-hr
Finally, 3750 Watt-hr is divided by 17.5 volts(from the array voltage) to get amp-hr
3750 Watt-hr / 17.5 volts ≈ 214.29 amp-hr.
As can be seen, the array is a little small; let’s try to add one more panel to the array. Six 150 Watt panels together makes 900 watts.
5 hr * 900 Watt = 4500 Watt-hr
4500 Watt-hr / 17.5 volts = 257.143 amp-hr.
In the later case, enough amp-hrs is produced to meet the daily 225 amp-hr needs. While this is a rough method that demonstrates how to size a solar array, the next example will be a little more elaborate.
B.Example #2 : Sizing a Fixed Tilted Solar Array with an Online Tool
This time, the solar panel sizing will be done using an online tool while all the conditions(like required daily amp-hr and site location) used in the previous example will stay the same.
The first tool that will be used is called the Solar Prosector which was created by the NREL(National Renewable Energy Laboratory). This is a tool that provides geo-spatial data on the amount of solar insolation at any locale in the United States. It is made using aggregated solar insolation data all the way to 2009.
Here are the instructions on how to use this tool:
First, open a link to the Solar Prospector by NREL in a new browser tab.
When one first opens this site, there is a “solar prospectus tool description” pop-up that shows up first. After reading the pop-up, click the “do not show this message again” checkbox and then close the pop-up window.
The site’s default should look like this after closing the tool description pop-up:
On the left is the “layers” tab. Under “solar resources”, there are 3 main types of solar insolation data sets depending on the solar panel orientation. A closeup is shown below:
The three check boxes that I checked are the three types of solar irradiance data that overlays the U.S. map on the basis of local conditions(like average metrics of various weather conditions) and solar panel tilt orientation.
The description of the different types of solar irradiance data can be found by right-clicking the click-box description and selecting “Metadata”; a description of the data will be shown. However, the three check boxed data types shown in the above image matches what has already been explained earlier. If using the Solar Prospectus, only check the Avg. Annual Tilt at Lat.(for mixed manual tilt) as this one is the most useful.
After I check off the Avg. Annual Tilt at Lat.(same as GTI), I’ll zoom to Richmond, VA which I used earlier.
Note: zooming is done with the zoom arrows(on top left of map) and scrolling is done by holding the left-click of mouse and moving in desired direction. When on desired location, double click on spot to get check-boxed data
First, here are the results of the Avg. Annual Tilt at Lat.(or GTI) for Richmond, VA:
Here, however, the average daily peak sun hours is about 5.00; which just about matches what was found from the irradiance map from Example #1.
What is new, however, is that the above data shows the avg. monthly irradiance at tilt lat. for a year. They avg. irradiance for each month often vary quite significantly form the average of 5.00. This is due to the amount of irradiance available during the warmer and colder seasons; which in turn are caused by the Earth’s tilted axis.
Going back to the data, the months from March to September have solar peak hours above 5.00 whilst the months from October to January have solar peak hours under 5.00. In fact, the month with the lowest irradiance is December which only has 3.82 peak hours. If one wanted to size a solar panel system to 5.00 peak hours, this would likely work only from March to September while the other months would provide insufficient solar power.
There are some options as to how to approach the disparity in solar insolation between the warmer and colder months:
i.) Option #1.One option is to size for the month with the lowest irradiance, which is December here. That is to increase the solar array size to the point where 3.82 kW-hr/m2 worth of irradiance daily is enough to avoid shortages at anytime.
In order to get 225 amp-hr under 3.82 instead of 5.00 peak sun hours, more than six 150 Watt solar panels will be needed unlike in Example #1. We will try seven panels first.
7 * 150 Watt = 1050 Watts
3.82 (kW-hr/m2 )/ 1 (kW/m2) = 3.82 hours; divide irradiance with 1 (kW/m2) to get peak sun hours.
3.82 hr * 1050 Watts = 4011 W-hr
4011 W-hr/ 17.5 volts = 229.2 amp-hrs
As it can been calculated, seven 150 Watt panels are enough to ensure that the devices gets it daily required 225 amp-hrs.
ii.) Option #2.The second option is to leave the array sized for 5 peak sun-hours. In that case, only solar power will be used from March to September for the full daily 225 amp-hrs needed. For the other months, total device usage should be decreased to less than 225 amp-hrs daily.
For example, if six 150 Watt solar panels are used on December, where the avg. daily peak sun hours is about 3.82 hours, the daily amp-hrs used will have to be reduced to:
(3.82 hrs * 900 Watts) / (17.5 volts) = 196.46 amp-hrs
This means that for a fixed array of 900 Watts and under 3.82 sun hours, amp-hrs usage has to be reduced from 225 to 196.5 amp-hrs to avoid over draining of battery.
To be able to reduce consumption as needed, one has to be aware of how much solar insolation is available throughout the year, whether it’s from publicly available data or from solar irradiance measuring devices, and adjust accordingly. Consumption reduction can be combined with the previous and next option if desired.
iii.) Option #3.In the case that one neither wants to increase the solar array size from 900 Watts or reduce the 225 amp-hrs daily usage, the last option is to supplement the amount of power generated during the cold months to make up for smaller peak sun hours.
One of the first options is to add another type of renewable power to the system. The options are wind or hydro power. Wind tends to work well during colder seasons which produce more wind; however, the site still has to be cleared for “wind breakers”. Hydro can work as long as there is a suitable site; however, watch out for frozen water.
Another option is to use an electric generator that runs on fuel like propane, bio-diesel, and etc. This is more suitable for a temporary use than as a long term supplement because using fuel repeatedly over weeks or months can be expensive. However, one has to take into account how much of the generator’s power can act as supplemental power. Also, how much fuel will be needed has to be calculated to determine whether the fuel generator option is viable.
iv.) Option #4.The last option is to utilize net-metering. Net-metering is a program where any excess electricity generated by the provider’s renewable energy generator can be sent towards the public power grid, and the utility company provides a renewable energy credit(s)(REC). This REC(s) can later be cashed in with the utility company later on to “purchase” the electricity.
During the summer months, a solar array can likely generate excess power that the owner does not need. He/she can then utilize his/her local utility company’s net-metering program to send excess electricity into the power grid and get a REC(s) from said company. When winter comes and the solar radiation is down, the solar array owner can turn in the REC(s) into the company for “free” electricity and use it supplement the small amount of solar power generated during the winter. In a sense, the solar array owner “carried over” the excess electricity from summer/spring to fall/winter.
Taking all this into the context of this example #2, we will(still) assume that our tilted at latitude solar array generates 5 sun-hours/day on average. If you look at the months from March to September on the NREL Prospector map for Virginia, you will notice that these months generate more than than 5 kWh/day. The months of October to February, on the other hand, generate less than 5 kWh/day on average. If this array is connected to the grid via meter, the array owner can covert the excess solar power into REC(s) to use during the winter. Looking at the kWh/day spread for the months, the excess solar power from March to September seems greater than the solar power deficiencies from October to February; theoretically, the REC(s) for the spring/summer solar excesses should pay off the fall/winter deficiencies.
Net-metering is quite a popular option because one can avoid costly additions like additional solar panels or a wind turbine/tower. However, it’s important that the connection to the power grid is available and is not fragile in the face of possible severe winter weather.
Now to look at a sizing example where the solar array(s) is installed with trackers.
C.Example #3 : Sizing an Array with Solar Trackers
It is possible to extrapolate the DNI data from the Solar Prospectus to take into account the possible diffuse and reflected irradiance for use; and then attempt to use the data. However, using extrapolated data seems too uncertain to use in solar array sizing. Instead, a different online tool will be used.
This tool doesn’t seem to have a clear name to me, so I will call this the solar radiation map generator. This tool uses a database that aggregates solar radiation data from 1961-1990 on a monthly basis. This tool presents irradiance data for an annual or month-specific daily average on a color-coded map. Also, the data is tailored to what type of solar array orientation is selected on site whether the array is tilted, has single or dual-axis tracking, or etc.
You can right-click the following link to open the U.S. Solar Radiation Map Generator tool on a separate browser tab.
This tool’s page should look like this screenshot:
If one sees and reads the above page, it should be self explanatory how to use this tool. If one wants to look at the data used to generate the map for accuracy reasons, the “here” link near the header shows the data used.
For this sizing example, the first selected input under “1. Select data type” will be Average. Minimum and Maximum usually reflect outlier/extreme values that don’t occur often enough to justify sizing an array(s) to those values.
The next selected input is under “2. Select a Month”. In this sizing example, I will generate a map for March, July, December, and Annual each. The three month maps under 2-axis trackers will be used to compare to the values under latitude tilt from the Solar Prospectus. The Annual map will be used to highlight the overall gain in solar harnessing via dual-axis trackers over tilt at latitude.
The last input variable is the solar panel orientation under “3. Select and instrument orientation”. The choice here will be the Two Axis: Tracking Flat Plate option because this harnesses the most watts and flat plates are more common than solar concentrators. If one’s system has a different panel orientation, the choice can be changed later. If you want to know more about the different orientation types, there is a link to describe the orientations.
After selecting the inputs , the “View the Map” button at the bottom will generate the map(s).
Before starting, here is the color-coded map key for local insolation:
i.) Insolation Maps for March, July, December, and Annual
Now to insert the input values to get the generated maps.
Now here is Insolation map for March for a Flat Plate Array with Dual-Axis trackers:
Around the area that seems to be Richmond, VA, the area is orange while close to the border with the yellow area up North. Looking at the key, the area is probably around 6.0 kW-hr/m2. The GTI value from the Solar Prospectus was around 5.26 kW-hr/m2. Comparing this to the GTI value to the dual-axis value, this is about a 14% increase in solar power. Lets now check the solar power increase for March.
Insolation map for July for a Flat Plate Array with Dual-Axis trackers:
The area of Richmond,VA seems to be in a pinkish orange. The collected solar radiation via dual-axis trackers is possible around 7.9 kW-hr/m2. The GTI value from the Solar Prospectus was around 5.53 kW-hr/m2. Comparing this to the GTI value to the dual-axis value, this is about a 43% increase in solar power. This is clear a much greater increase than for March.
Here is the Insolation map for December for a Flat Plate Array with Dual-Axis trackers:
The area of Richmond,VA seems to have a summer green color and the area just borders the mint green area. The collected solar radiation via dual-axis trackers is most likely around 4.0 kW-hr/m2. The GTI value from the Solar Prospectus was around 3.82 kW-hr/m2. Comparing this to the GTI value to the dual-axis value, this is about a 5% increase in solar power on average. On”sunnier” winters, the increase could reach 10%+.
Here is the Yearly Insolation map for a Flat Plate Array with Dual-Axis trackers:
Near the Richmond, VA area, the yellow and orange areas border each other. According to the color code, this area gets 6.0 kW-hr/m2 as the daily average yearly. The Solar Prospectus showed 5.0 kW-hr/m2 as a yearly daily average for a fixed tilt. If the solar orientation is flat array with dual-axis tracking, the increase in solar radiation absorption is 1 peak-hour or 20% greater for the daily yearly average.
ii.) Maps Analysis
If one look closely at the insolation values from these three maps and compares with the insolation values from the solar prospectus, one would have noticed that there are greater increases in insolation values(or peak hours) during the warmer as opposed to the colder months.
Because of the Earth’s axis is tilted, there is an uneven delivery of solar radiation to the Earth’s surface. When the Northern hemisphere is tilted towards the sun, it summer in the North and winter in the South. When the Northern hemisphere is tilted away from the sun, it winter in the North and summer in the South. Because of the somewhat steep axis tilt, which ever north-south hemisphere tilts towards the sun will get most of the irradiance whilst the other hemisphere gets less irradiance due to being partly “shielded” from the sun. The hemisphere which gets less irradiance gets colder which causes water to condense in the atmosphere creating cloud cover which in turn further hampers solar radiation from reaching the earth’s surface.
For solar arrays during the colder months, even if the arrays switch from being fixed tilted to having solar trackers, there is only a modest gain because the north-south hemisphere tilted away from the sun doesn’t get that much irradiance to begin with. In comparison, the north-south hemisphere that is tilted towards the sun gets much more irradiance which makes it easier for arrays solar trackers to capture more solar radiation. Hence, this is why solar trackers collect more solar radiation during the winter months over the summer months.
The last map simply illustrates that the annual daily average solar radiation absorption is 20% greater for a dual-axis solar tracker orientation over the tilt at latitude orientation.
iii.) Solar Trackers and Sizing
Like in Example #2, there are four ways on how to approach sizing. Here, the local and solar conditions used in Examples #1 & #2 will be used here as well.
a.) First is sizing according to the month with the lowest irradiance; which is December. Via dual-axis solar trackers, the insolation for December via Map Generator was found to be 4.0 kW-hr/m2 or about 4 peak sun hours. Let’s try to get the needed 225 amp-hrs.
6* 150 Watts = 900 Watts ; a six panel array
900 Watts * 4 hrs = 3600 W-hr
3600 W-hr / 17.5 volts = 205.7143 amp-hrs; this result implies that six 150 watt panels are not enough for sizing
(7 * 150 Watts * 4 hrs)/(17.5 volts) = 240 amp-hrs; seven panels for sizing still meets the needed 225 amp-hrs.
b.) Second is adjusting daily power consumption based on a fixed array size. Here the arrays can be sized for 6 peak sun hours since dual-axis solar trackers are used.
Here, we’ll try to used a five panel array as originally stated in the conditions.
(5* 150 watts * 6 hrs)/(17.5 volts) = 257.143 amp-hrs; this is more than enough for the 225 amp-hrs
Thanks to solar trackers, for the months(summer months) that have an average daily peak sun hours of six or more only require an array of five 150 watt panels as stated originally in the initial conditions; not a six panel array like in the Examples #1 & #2.
Going to a winter month, however, requires lower consumption. December will be used here.
(5* 150 watts * 4 hrs)/(17.5 volts) = 171.43 amp-hrs
While 5 panels with dual-axis solar trackers is good enough in the summer, it still is too low during the winter due to the fact that little additional irradiance is gained via dual-axis solar trackers during the winter. If one seriously intends to cut down on device usage, the drop will be a severe 53.6 amp-hrs. A five panel array may need to be reconsidered if it’s too difficult to cut back on.
c.) Third, there is the option of adding supplemental power to solar power. Like in the third option for Example #2, supplemental power options include micro hydro, small wind, and fuel-based generators as long the prerequisites are met for selected choice(s) of supplemental power.
However, in the previous option, there was a deficit of 53.6 amp-hrs for using a 5 panel array with dual-axis solar trackers. Compared to the third option for Example #2 which used a six panel array tilted at solar, the required amp-deficit is higher and thus the supplemental power option(s) would have to create more power to make up for the deficit. It may be better to increase the array size in this case.
d.) Fourth and lastly, there is the net-metering option(as explained earlier) if a local utility company offers this program. The monthly solar insolation values provided by solar tracker maps should at least be marginally greater than the values provided by the NREL Prospecter map(for arrays tilted at latitude) shown earlier for the same Richmond, VA area. The REC(s) provided by the local utility should theoretically be enough to “pay” for the electricity during the fall/winter months.
III.Solar Panels Sizing in the Real World
A.Local Conditions and Considerations
To determine how real world conditions affect solar panels and its sizing, it’s important to determine what the conditions are there first. Here are some real world conditions(including one already covered) that affect actual solar panel sizing:
When it comes to solar panels, the surrounding temperature affects a solar panel’s efficiency.
Normally, electrons at rest (low energy) are excited by the sun (high energy), and the difference between their excited and rest energies creates a potential difference (voltage) within the solar panel(s).
When the surrounding heat is absorbed into the panel(s), the electrons at rest state gain some energy. When the sun finally hits the panel(s), the difference between the “rest” state and the excited state is lower; thus resulting in less power produced. However, if the surrounding temperature is colder than usual, the rest energies is will lower then usual. When the sun finally hits the cooled panel(s), the different between the rest and excited state will be greater than in warmer temperatures resulting in a higher voltage and thus more power.
When the temperature increases or decreases for the solar panel(s), the power efficiency changes roughly by a certain fraction of a percentage for every 1°C increase/decrease within the solar panels’ operating temperature range. This means that the changes in power efficiency can be calculated or explained in a linear relationship.
Here is an example:
There is an installed solar panel rated to produce 150 Watts under STC. Under STC, the panel outputted 150 Watts when the surrounding temperature was around 25°C. Hypothetically, for every 1°C change, about 0.48% of the power output changes. The value of 0.48% isn’t uncommon for solar panels, but the actual drop can vary a little depending on the panel; so it’s best to check the panel’s specification or with the manufacturer for the actual percentage change. On the spec. sheet, the % change per °C is the temperature coefficient ‘Pmax‘. Here is are two examples to apply this:
If the surrounding temperature is 32°C(common on summer days) while all other STCs are constant, then there is an efficiency drop.
(7°C increase)* 0.48 = 3.36% drop in power
Under 32°C with all other STC values constant, the output of a 150 Watt panel becomes
150 watts * ((100-3.36)/100) = 144.96 watts.
Although high temperatures can reduce efficiency, most days and places with high temperatures tend to be quite sunny with little cloud cover thus providing several peak sun hours. Slight drops in efficiency may become negligent. Now consider if the surrounding temperature was at 15°C(on a chilly day) while all other STCs are constant, then there is an efficiency increase for reason as explained earlier.
(10°C drop)* 0.48 = 4.8% increase in power
Under 15°C with all other STC values constant, the output of a 150 Watt panel becomes
150 watts * ((100+4.8)/100) = 157.20 watts.
While the efficiency and power would increase under colder temperatures, colder days are like to have more cloud cover and don’t tend to be sunny. This means fewer peak sun hours. The best times to get max. efficiency solar power during colder days is when the clouds clear up after a rain shower or snow day.
The first and main thing to consider regarding local wind conditions is to gauge how strong is it. Solar panels have to be mounted securely so a strong wind doesn’t rattle the solar panels on the mount or blow them off. Also, make sure debris won’t blow onto the panel(s).
Even with secure mounting and low winds, the wind still has an effect on solar efficiency. Earlier said, low temperatures make panels more efficient. On chilly windy days with little cloud cover, the a blowing wind can actually cool/ventilate a solar panel(s).
iii.) Atmospheric Pressure:
While this may seem irrelevant, atmospheric pressure does affect solar power. Because of atmospheric particles, much solar radiation is diffused leaving a portion of the solar radiation to hit a solar array or surface.
For example, an array on the ground could have been measured to produce 1000 Watts. However, if this solar panel was taken into space, that array may produce 1400 Watts as the wattage produced on the ground isn’t necessarily the upper limit in power production. This is because solar radiation traveling through space is not long hindered by anything, it can all fall on the solar array. Also, the fact that the temperature gets cooler as the solar array moves up and leaves the atmosphere, and as long as it doesn’t leave the operating temperature range, the production also improves.
If by any chance, one installs a tiny house with a solar array on a high mountain(like the ones from the Appalachian or Rock Mountains) where the atmosphere is thin, colder, and have little cloud cover, there is likely to be a small increase in output power from the array compared to the rated output from the ground.
iv.) Varying Peak Hours at Different Months:
Earlier in Example #1, The solar irradiance map showed only the average daily solar insolation over the entire year. It can give the mistaken impression that the average daily solar insolation at a specific location/latitude is same throughout the year when it in fact varies.
For the Examples #2 and #3, for Richmond VA, the local daily average insolation for the year is 5.0 kW-hr/m2 for a fixed tilt at latitude, and 6.0 kW-hr/m2 for a dual-axis solar tracking array. Because these are average values, the summer months will have daily avg. irradiance greater than the avg. while the winter months will have less than the average due to Earth’s tilt. Thus, relying on the average daily insolation for the year to do array sizing will lead to improper sizing for the months that produce less insolation than daily yearly averages.
As used in Examples #2 & #3, the Solar Prospectus and the Map Generator Tool can be used to find the average daily solar insolation per month; the latter can be used for arrays with a solar tracking orientations. Look back to Examples #2 & #3 if you have not already done so to see how to use these tools.
Lastly covered in Examples #2 & #3 is how to pursue array sizing in three ways:
- Size the array in accordance with the Month that produces the least daily avg. insolation; which is often December.
- Adjust devices’ usage during month to avoid using more power than can be harnessed.
- Add supplemental power(if you don’t want to increase array size) during less sunnier months via various means like small wind, micro hydro, and/or fuel-based generators.
B.Solar Panel and System Considerations
Various aspects in a renewable power system also affect solar array sizing. Plate tilting won’t be covered because that has already been covered earlier.
i.) Power Losses in System Components:
Besides inefficiencies in solar power absorption caused by local insolation and weather conditions, any inefficiencies in the entire renewable power system will affect how much solar power will actually reach outside the sockets for daily power needs.
In such systems, the first main sources of inefficiency are from the charge controller and the inverter. When sizing the charge controller and inverter, taking into account the efficiency values of these devices is standard. Read these two previous posts which have sections about how to take into account solar charge controller and inverter inefficiencies:
- Battery bank sizing with a section on inverter sizing
- Charge controller basics to understand how much electricity passes though a charge controller
Taking these two into account will have some effect on the final sizing.
ii.) Solar Panel Quality:
Tied to the previous section, the solar panels’ efficiency is tied to its grading. The grading ranges from “A” to “D” with “A” being the best while “D” is the worst.
Panels graded “A” should have no defects what so ever; this means no micro-cracks, no doping fade, no thickness deviation, smears or marks, and etc. They’re essentially like new and will last the longest. Also, there are no “A+” or “A++” for this and other grades as these are labels mainly for advertising hype.
Grade “B” are still functional but can have “minor” defects; this includes doping fade, cells with marks in the wafers, thickness deviation, color deviation, and etc. This grade tends to be found on panels that were not made to the meet grade A standards or the panel got its defects from having been used.
The lower grades of “C” and “D” include damages ranging from noticeable breaks to unusable. These should be avoided for any solar power system.
Going with grade “A” panels is the safest bet as there is little way to determine the implications of the defects of any panels graded “B” to lower. Finally, when taking solar cell types into consideration, the best solar panels for home-based power are Mono-Crystalline Grade “A” panels.
iii.) More Details on Solar Trackers:
Earlier in Example #3, I talked about solar trackers. I only talked about how solar trackers increased solar power collection and nothing else. There are two types of solar trackers which are passive and active solar trackers.
Passive solar tracking works by utilizing fluid(i.e. freon) filled canisters. These canisters utilize the uneven heating of the solar array by the sun the gasify the freon to force it into a cooler area thus causing the solar array rack to move. This link here provides more details on how passive solar trackers work. The main point is that passive solar trackers don’t use additional electrical power.
Active solar tracking, on the other hand, utilizes servo motors to move the array to follow the sun. The solar trackers utilize chronology or solar sensors to keep the array(s) facing the sun. Because electrical components are used, it’s important to know how much power is being used daily by the trackers so the solar array and battery bank sizing can all be adjusted accordingly. Normally, solar arrays with a greater surface area will require solar tracker systems that consume more power than arrays with a smaller surface area.
Here is an example of how active solar trackers’ power consumption plays into array and battery bank sizing:
To get an idea of how much power active solar trackers consume, take a look at the dual-axis solar trackers products from haosolar.com. For the solar array sizing examples #1-3, about six-to-seven 150 watt panels were used for an array. This array likely doesn’t go over 25 m2. Using the haosolar website as a reference, the daily power consumption of about ≤0.02 kw-hr/day seems feasible. In Examples #1-3, the panels are 17.5 volts in parallel.
200 watt-hrs / 17.5 volts ≈ 11.43 amp-hrs
If the tilted at latitude array from Example#2 was fitted with dual-axis solar tracking, over 200 watt-hrs would have be gained from tracking to make a net gain after power consumption and the battery bank has to be sized up with an additional 11.43 amp-hrs. Ultimately, one must see the manufacturer’s specifications with any solar trackers to determine power consumption.
The last things with regards to solar tracking are tracking angle accuracy and costs.
Tracking angle accuracy refers to how many degrees the array’s face deviates from facing the sun completely. A tracking system should have angle accuracy within 5o. In actuality, there should be as little deviation as possible as there are tracking systems with accuracy with <1o. If the solar tracking array deviates outside 50, the power drop is significant.
Finally, anyone choosing to install solar trackers must account for the costs of installation and maintenance. Installing a solar tracking system can be quite expensive. If the array already produces sufficient power while only being tilted at latitude, solar tracking wouldn’t be worth the investment. In other cases, it may be better to simply add 1-2 additional panels instead of buying a tracking system. Costs that come with solar tracking include concrete foundation, rotational bearings, motors or Freon canisters, other moving parts, and etc. Another major cost of solar tracking systems is that because its harder to set up personally, people will like have to be hired both for installation and for maintenance. Installing and maintaining an array tilted at latitude is much easier for an individual by comparison and thus cost effective.
Ultimately, I believe people should use solar trackers only when one can afford the costs of installation and maintenance while not being able to utilize more panels. Otherwise, more solar panels would be better.
iv.) Solar Panels not rated in STC:
Despite the fact that STC don’t match real world condition most of the time, solar arrays are still sized according to the STC(that is the light intensity of 1000 Watts/meter2) because the nearly all panels are rated to STC. In recent times, places with a progressive history on solar power(like California and New Mexico) have unveiled new testing standards besides STC that attempt to better mimic real world conditions. Here is a table showing some of them:
Besides the STC standard, here are probably a few others you didn’t know about. Right-click to open a new window to see the commentary for these different testing conditions standards as this is where the table originated from.
Note from the table that not all standards use 1000 W/m2 testing radiation like STC does. For example, NOCT uses 800 W/m2 as testing radiation. What this means in sizing is that the local daily insolation will be divided by 800 instead of 1000 to get peak sun hours; then do sizing calculations accordingly.
Lastly, for example, Mr.A is trying to compare two solar panels with one rated under NOCT and the other rated at STC. It may seem wiser to use the NOCT rated panel over the STC one as the former follows more real world conditions and thus easier gauging of output power. However, the comparison should not be done this way because that is akin to comparing an apple to an orange. Only compare an apple to an apple and move from there.
C.Some Final Considerations
Although many real-world factors have been covered, it’s important to know that even when trying to size an array as accurately as possible, there can always the possibility of sizing being thrown of due to possible changes in local insolation or some system error being missed. In short, make sure that the system allows room to add additional panels to the array or add a supplemental power source(s) in case the harnessed power comes up short.
Earlier, when discussing about power losses due to inefficiencies due to system/mechanical and natural conditions, there are often too many to account for even if one takes into account for some of the more obvious ones like lowered irradiance from shading/cloud-cover, solar panels, charge controller, and inverter inefficiencies. One approach is to follow a rule of thumb and assume about 70-75%(initially) of the assumed theoretical power produced is real power that can be used. This means that if 4.5 kW-hrs were theoretically collected daily from the solar array, devices’ usage should initially aim to be around 3.2 kW-hrs. Later on, the usage can be adjusted depending on actual power produced. If actual available power was around 3.8 kW-hrs, the devices’ power consumption can be increased. If at less, consumption can adjusted down.
The final thing to cover about is the wiring of solar arrays. As solar panels are made of individual panels with (+) and (-) terminals; knowing how panels are wired together enables one pick the best wiring configuration and wire in additional panels or remove them when sizing. The wiring three configurations are series, parallel, and series-parallel hybrid; each has its benefits. If you wan’t to know more about how to wire solar arrays, this link will show how to connect multiple solar panels into an array.
By now, you should be able to size a solar array with decent accuracy in a low cost manner by using the necessary math, online tools, and taking into account as many real-world factors as possible.
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Image Attributions(You may skip this):
- Header Image: “Photovolts” (CC BY-SA 2.0) by /\ \/\/ /\ via Flickr
- Image showing Three Parts of Solar Radiation: Modified the Diagram from this webpage explaining solar radiation components.
- Solar Rays on Tilted Globe Diagram: Diagram originally from blog.civitasenergy.com
- Solar Insolation Bell-Curve Diagram: Graphs from pveducation.org
- Solar Irradiation Map: 2008 Solar Map of USA By NREL [Public domain], via Wikimedia Commons
- Online Tools’ Screenshots(everything after the Solar Map by NREL): Screen shots from using the Solar Prospectus and Online Map Generator Tool. You may use these if you give proper attribution as explained in this site’s “Content Reuse & Attribution Policy” from the bottom.
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