# Radiation on a tilted surface

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Solar Expert Posts: 27
Hi!,

I want to calculate the irradiance that reaches on a Pv modules that have 90º of inclination from the horizontal. I already know the values for the global,direct and diffuse irradiance.

I am using different models to calculate this irradiance, like Liu-Jordan, Klucher, Reindl, Muneer, etc. But I have problems when is a sunny day (the theoretical results don't match with the real ones).

Anyone knows if there is any specific radiation model for this case (90º inclination and sunny day)??

Thank you!

• Banned Posts: 17,615 ✭✭✭
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Re: Radiation on a tilted surface

You might as well draw a number at random.

In the real world a lot of things get in the way of a solar panel's output matching the theoretical. Angle of the sun to the panel is certainly the biggest, and this changes not only with time of day but time of year as well. But atmospheric conditions will affect it, and they change daily too. Temperature is a big factor. So is elevation above sea level.

It sounds like you're trying to determine how much power a given size panel will put out if it is mounted vertical, such as on the wall of a building. For my money you can't beat taking some actual measurements. This could be done under controlled lab conditions where you can know the light intensity as well as angle/temp etc. The results then extrapolated to the real world, with allowances for variables.

Pardon my cynicism, but over many years I've had to fix a lot of things that failed because the design relied too much on theory. :roll:
• Solar Expert Posts: 3,009 ✭✭✭✭
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Re: Radiation on a tilted surface

Welcome to the forum.
The only time I adjust my panels to 90 degrees from horizontal is during Winter when the sun at my latitude is low on the horizon, and when so tilted, snow can't collect on them. This time of year with 90 degrees elevation, I get extremely little output were I am, as the sun is still high overhead, so unless I drop the panels back down from 90 degrees my batteries will go dead.
• Solar Expert Posts: 1,913 ✭✭
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Re: Radiation on a tilted surface

On vertical surface there is one more element - albedo, which is totally absent from horizontal.

Did you get the azimuth of your vertical surface correct? Did you get the Sun position correct?
• Solar Expert Posts: 27
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Re: Radiation on a tilted surface
You might as well draw a number at random.

In the real world a lot of things get in the way of a solar panel's output matching the theoretical. Angle of the sun to the panel is certainly the biggest, and this changes not only with time of day but time of year as well. But atmospheric conditions will affect it, and they change daily too. Temperature is a big factor. So is elevation above sea level.

It sounds like you're trying to determine how much power a given size panel will put out if it is mounted vertical, such as on the wall of a building. For my money you can't beat taking some actual measurements. This could be done under controlled lab conditions where you can know the light intensity as well as angle/temp etc. The results then extrapolated to the real world, with allowances for variables.

Pardon my cynicism, but over many years I've had to fix a lot of things that failed because the design relied too much on theory. :roll:

In fact I am working on a PV installed system in my University, and I need to check if the panel are giving the correct power. For that I am comparing my theorical output power with the real one, but in the case of the 90º panels the results are so different (it doesn't happen with the 25º panels). I am using pyranometers to measure the irradiance (global and diffuse) in horizontal, and temperature sensors to know the temperature of the modules. This differences are higher in summer, with higher temperatures...
• Solar Expert Posts: 27
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Re: Radiation on a tilted surface
NorthGuy wrote: »
On vertical surface there is one more element - albedo, which is totally absent from horizontal.

Did you get the azimuth of your vertical surface correct? Did you get the Sun position correct?

Well, I think I am doing every step correct, because in the case of 25º inclination the results are right...I am using:

CosOz=sin(Dec)*sin(Latitude)+cos(Dec)*cos(Latitude)*cos(W);
CosOi=sin(Dec)*sin(Latitude-90)+cos(Dec)*cos(Latitude-90)*cos(W);
W=(15*(TST-12))*pi/180;

where TST is the true solar time, Dec is the declination and the inclination factor is: Rb=CosOi/CosOz(b);

For the albedo, I am using the next formula (is for the reflected irradiance, but I think is the same right?): Greflect=Gtot*ro*(1-cos)/2;
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Re: Radiation on a tilted surface
JavierOL wrote: »
In fact I am working on a PV installed system in my University, and I need to check if the panel are giving the correct power. For that I am comparing my theorical output power with the real one, but in the case of the 90º panels the results are so different (it doesn't happen with the 25º panels). I am using pyranometers to measure the irradiance (global and diffuse) in horizontal, and temperature sensors to know the temperature of the modules. This differences are higher in summer, with higher temperatures...

You do realize that the rated Watts of a panel is devised under "ideal" lab conditions and that in the real world they tend to output about 80% of that on average? And that is with correct insolation (panel parallel to sun).

BTW, the type of panel will make a difference too. Amorphous panels have their 'collectors' aimed sort of randomly and will produce a better average power in all conditions (albeit lower per area over all). On the other end monocrystaline are the most 'angle specific' for harvesting Watts. So you have a case where the amount of power falling on a given area is not necessarily collected by the panel due to the way it hits the face of the cells.

Try measuring the Isc of a small panel with a fixed light source: change the angle of the panel in respect to the light and watch the difference in available current. Compare this with your pyranometer under the same condition.
• Solar Expert Posts: 27
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Re: Radiation on a tilted surface
You do realize that the rated Watts of a panel is devised under "ideal" lab conditions and that in the real world they tend to output about 80% of that on average? And that is with correct insolation (panel parallel to sun).

BTW, the type of panel will make a difference too. Amorphous panels have their 'collectors' aimed sort of randomly and will produce a better average power in all conditions (albeit lower per area over all). On the other end monocrystaline are the most 'angle specific' for harvesting Watts. So you have a case where the amount of power falling on a given area is not necessarily collected by the panel due to the way it hits the face of the cells.

Try measuring the Isc of a small panel with a fixed light source: change the angle of the panel in respect to the light and watch the difference in available current. Compare this with your pyranometer under the same condition.

The issue is that the system is already working, and the panels are fixed so I can't change their inclination to make some testings. I am comparing the real power that is coming into the inverters, with the theorical power that they should give (I am using the formula Pout=Pnominal*(Gtot/1000)*(1+Y(Tmodule-25)), where Y is the coefficient of the variation of the power with the temperature ).

So, I only have problems in the case of 90º and sunny day... that means that maybe I have a mistake in my calculations, or maybe the panels are not working right under this conditions...

That's why I am trying to use another radiation model for this specific situation...
• Solar Expert Posts: 1,913 ✭✭
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Re: Radiation on a tilted surface
JavierOL wrote: »
Well, I think I am doing every step correct, because in the case of 25º inclination the results are right...I am using:

CosOz=sin(Dec)*sin(Latitude)+cos(Dec)*cos(Latitude)*cos(W);
CosOi=sin(Dec)*sin(Latitude-90)+cos(Dec)*cos(Latitude-90)*cos(W);
W=(15*(TST-12))*pi/180;

where TST is the true solar time, Dec is the declination and the inclination factor is: Rb=CosOi/CosOz(b);

You probably got formulae right, unless you derived them by yourself

If I were you, I would check my calculations against solar position calculator, such as this one.
JavierOL wrote: »
For the albedo, I am using the next formula (is for the reflected irradiance, but I think is the same right?): Greflect=Gtot*ro*(1-cos)/2;

It depends on what the reflective surface is. In right conditions I was getting 30% of total light on the panels reflected from the snow! If you get grass, you will receive very little. It's hard to get the reflective coefficient (ro?) right.

Do you just want to measure these things, or the model is your goal?
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Re: Radiation on a tilted surface

As Marc suggests, you can get any convenient size solar panel and throw a low value resistor on it and measure the output voltage.

For silicon panels, your panel should agree with the actual solar irradiation within about 10%--And you are using a real panel, so that is going to be a better "sensor" for your needs (responds the same as your larger panels)... You can test your formula against a "real panel" that you can pan and tilt as needed. You could also try "shadowing" or using tubing to map the amount of direct and indirect power you are seeing.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 27
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Re: Radiation on a tilted surface
NorthGuy wrote: »
You probably got formulae right, unless you derived them by yourself

If I were you, I would check my calculations against solar position calculator, such as this one.

It depends on what the reflective surface is. In right conditions I was getting 30% of total light on the panels reflected from the snow! If you get grass, you will receive very little. It's hard to get the reflective coefficient (ro?) right.

Do you just want to measure these things, or the model is your goal?

Well my goal is to use a model which simulates as well as possible the behavior of the modules.

In the solar position calculator I realized that the cosinus of the zenith angle doesn't match with mine...Do you know if the formula for the solar hour angle is wrong?
W=15(TST-12) [º]; * TST is right calculated!
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Re: Radiation on a tilted surface

Basically you're looking to see if the installed vertical panels are outputting their maximum or if one or more are defective. Not being able to remove a panel and test it under controlled circumstances is a limitation. Therefor the suggestion of taking a "known good" panel and measuring its output at vertical in the same location and comparing that to its test standards.

You probably will not determine anything is wrong. A defective panel tends to put out zero, not low Watts. You could measure the current of each with a DC clamp-on Ammeter to see if there is any discrepancy between them.

But it really comes down to "what you get, you get" because other than changing out an actually dead panel there's nothing you can do to boost the results caused by low insolation. If the power isn't there, it isn't there.
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Re: Radiation on a tilted surface
JavierOL wrote: »
Do you know if the formula for the solar hour angle is wrong?
W=15(TST-12) [º]; * TST is right calculated!

Looks good to me. The Earth rotates 15 degrees per hour (360 degrees divided by 24 hours) and astronomical noon is when the Sun is exactly on the South. That's what this formula describes.

If you're after a model, I will suggest again that you look at PVWatts algorithms.

If you're troubleshooting panels, there are better approaches.
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Re: Radiation on a tilted surface

Report nr. 6/2011 Potential and Challenges for Building
(PDF)

This was a report (written mostly in English) about solar for Norway... It does have some solar related math/models in it...

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 27
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Re: Radiation on a tilted surface
Basically you're looking to see if the installed vertical panels are outputting their maximum or if one or more are defective. Not being able to remove a panel and test it under controlled circumstances is a limitation. Therefor the suggestion of taking a "known good" panel and measuring its output at vertical in the same location and comparing that to its test standards.

You probably will not determine anything is wrong. A defective panel tends to put out zero, not low Watts. You could measure the current of each with a DC clamp-on Ammeter to see if there is any discrepancy between them.

But it really comes down to "what you get, you get" because other than changing out an actually dead panel there's nothing you can do to boost the results caused by low insolation. If the power isn't there, it isn't there.

Well in fact my work is only to check if the panels are working right or not... but I need to justify why it happens.I know that the response of the panel is lower than what the manufacturer says, but not so different... The panels are working for three years, I don't think they are defected, so the problem has to be in other point...
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Re: Radiation on a tilted surface

Oh... Panels can go bad... My 3.5 kW array went bad after about 6 years... Over the period of about one week, it went from "everything looks OK" to "huh, this seems to be producing about 1/2 the power I would have expected on this nice sunny day) GT system.

Most of the panels had a very light brown haze (looked like coffee stain) right above each panel's junction box (apparently overheated).

A "cheap" DC Current Clamp DMM can make it real easy to compare strings--Very frequently, one string will have a "problem" while the others are OK--For quick check, you are looking for "differences".

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 1,913 ✭✭
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Re: Radiation on a tilted surface
JavierOL wrote: »
Well in fact my work is only to check if the panels are working right or not... but I need to justify why it happens.I know that the response of the panel is lower than what the manufacturer says, but not so different... The panels are working for three years, I don't think they are defected, so the problem has to be in other point...

If you want to measure irradiance, you can use a tool called Luxmeter. Just hold the sensor flat on the panel, so it looks the same direction the panel is looking.

However, even before doing this it is good to look at the current to see if strings are different between themselves using the tool that Bill suggested.
• Solar Expert Posts: 27
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Re: Radiation on a tilted surface
NorthGuy wrote: »
Looks good to me. The Earth rotates 15 degrees per hour (360 degrees divided by 24 hours) and astronomical noon is when the Sun is exactly on the South. That's what this formula describes.

If you're after a model, I will suggest again that you look at PVWatts algorithms.

If you're troubleshooting panels, there are better approaches.

Well the issue is that the radiation models differ in how the diffuse irradiance is calculated, and the direct always is calculated in the same way (using an inclination factor).

So, If I have problems in sunny days, it means that the direct irradiance is much higher than the diffuse, so the difference between the models is minimal...
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Re: Radiation on a tilted surface

Guessing that diffuse radiation is less than 10% of the average solar output--So if you are getting wildly different numbers (i.e., 50% less than expected output), you have some solar problems (or other math issues).

However--If you have low sun elevation and lots of shiny surface out front (water, sand, ice, snow), then diffuse radiation (reflections from field in front of array) could be on the order of direct solar radiation. No generic set of static models is going to address your specific needs.

But--Again, just a "small" solar panel plugged into a mAmp or Amp meter set next to the solar array will give you the "effective" irradiation within ~5% of your actual solar array. More than close enough to confirm if the array is functioning correctly or not.

Except for cell temperature correction... Vmp is reduced as temperature rises--So MPPT type controllers (GT Inverters, MPPT charge controllers, etc.) will have to be corrected for temperatures +/- 25C/77F standard test conditions.

Solar cells outputting current into a dead short--Current rises as cell temperature increases--But it is probably around 1/10th the change vs Vmp--So, current change due to temperature can usually be ignored in most applications.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 27
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Re: Radiation on a tilted surface
BB. wrote: »
Guessing that diffuse radiation is less than 10% of the average solar output--So if you are getting wildly different numbers (i.e., 50% less than expected output), you have some solar problems (or other math issues).

However--If you have low sun elevation and lots of shiny surface out front (water, sand, ice, snow), then diffuse radiation (reflections from field in front of array) could be on the order of direct solar radiation. No generic set of static models is going to address your specific needs.

But--Again, just a "small" solar panel plugged into a mAmp or Amp meter set next to the solar array will give you the "effective" irradiation within ~5% of your actual solar array. More than close enough to confirm if the array is functioning correctly or not.

Except for cell temperature correction... Vmp is reduced as temperature rises--So MPPT type controllers (GT Inverters, MPPT charge controllers, etc.) will have to be corrected for temperatures +/- 25C/77F standard test conditions.

Solar cells outputting current into a dead short--Current rises as cell temperature increases--But it is probably around 1/10th the change vs Vmp--So, current change due to temperature can usually be ignored in most applications.

-Bill

Ok thank you I will try to make some tests...anyway, do you know any inclination factor calculator?? maybe the problem is there and I don't know how to check it...
• Solar Expert Posts: 27
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Re: Radiation on a tilted surface
You do realize that the rated Watts of a panel is devised under "ideal" lab conditions and that in the real world they tend to output about 80% of that on average? And that is with correct insolation (panel parallel to sun).

BTW, the type of panel will make a difference too. Amorphous panels have their 'collectors' aimed sort of randomly and will produce a better average power in all conditions (albeit lower per area over all). On the other end monocrystaline are the most 'angle specific' for harvesting Watts. So you have a case where the amount of power falling on a given area is not necessarily collected by the panel due to the way it hits the face of the cells.

Try measuring the Isc of a small panel with a fixed light source: change the angle of the panel in respect to the light and watch the difference in available current. Compare this with your pyranometer under the same condition.

Sorry but when you say that he rated Watts of a panel in the real world tend to output about 80% of that on average menans that if I use the STC parameters for my power output formula and I want to compare with the real power I should multiply my results per 0.8?? Im not sure because my formula is as follows:

Pout=Pnom*(Gtot/Gstc)*(1+Y(Tc-25);

and the factor Gtot/Gstc will consider this decrease, or not??
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Re: Radiation on a tilted surface

Here is the reference page that NREL.gov uses for PV Watts:

http://www.nrel.gov/rredc/solar_resource.html

What values do you use for "Y" and "Tc"?
BB. wrote: »
So, looking at the Data Sheet:

Temperature Coefficient CS6P-235/240/245/250/255P Electrical Data
• Pmax -0.43 %/℃
• Voc -0.34 %/℃
• Isc 0.065 %/℃
• NOCT 45±2℃ (Normal Operating Cell Temperature

So, if you your air temperature is 30C and you have a 15C rise for a cell temperature of 45C, and you are using an MPPT charge controller, the calculation should look something like this:
• Power = 245 watts [1 + (-0.43 %/℃ power derate) * (Tcell - Tstd)]
• Power = 245 watts [1+ (-0.0043 /℃ power derate) * (45C - 25C)] = 222.95 watts (note % shifted decimal point removed)

And assume 95% efficient controller:
• 222.95 watts * 0.95 = 212 Watt output to battery (ignoring wiring losses)

Our standard rule of thumb for relatively warm locations with typically dirty/aging panels, wiring losses, and less than clear blue sky would be:
• 245 watts * 0.77 panel+controller derating = 189 Watts typical maximum power from array+controller

-Bill

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 27
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Re: Radiation on a tilted surface
BB. wrote: »
Here is the reference page that NREL.gov uses for PV Watts:

http://www.nrel.gov/rredc/solar_resource.html

What values do you use for "Y" and "Tc"?

-Bill
The Data Sheet of the modules gives me the next values:

Pmax -0.48 %/K
Voc -0.37 %/K
Isc 0.01 %/K
NOCT 45±2℃

The Tc I get from temperature sensors installed on the panels.

But my formula is slightly diffetent: Power = Pnominal * (Gtotal/Gstc)*(1+Y(Tc-Tc_stc)); where Gtot y the global irradiance that reaches the panels, and Gstc is 1000 W/m2. I think that this "factor" is like the efficiency of the panels... PVWatts use the same formula (http://energy.sandia.gov/wp/wp-content/gallery/uploads/Marion_NREL_PVWatts.pdf)
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Re: Radiation on a tilted surface

Since you have Pmax, you should use that for "Y" on a MTTP charge controller (or GT Inverter).

What are you measuring for TempCell? Do you have an IR thermometer you can measure the glass face temperature (sometimes, you have to put a piece of masking tape (or similar) to get an accurate measurement of glass (and other shiny surface temperatures) with an IR thermometer. Always wonder if glass=cell temperature or if there is a significant difference (due to relatively poor thermal transfer of glass). It may be one of those "differences" that is too small to care about.

I have wondered how hard that is to measure "accurate" cell temperature--Do you use a temperature probe on the rear of the panel and cover it with a bit of insulation (so you get a better estimate of the true cell temperature vs the (guessing) poor thermal conduction properties of the rear backing)?

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 27
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Re: Radiation on a tilted surface
BB. wrote: »